Sounds
Casey O’Callaghan
A dissertation
presented to the faculty of
Princeton University
in candidacy for the degree of
Doctor of Philosophy
Recommended for acceptance
by the Department of Philosophy
November 2002
c Copyright by C. O’Callaghan, 2002. All rights reserved.
Abstract
This dissertation is about sounds and auditory perception. It is motivated
in the spirit of work on the metaphysics and perception of color. In Chapter
1, I motivate and develop an account according to which sounds are events.
In particular, a sound is the event of an object or interacting bodies disturbing a surrounding medium in a wave-like manner. The sound just is
the disturbance event itself. I develop this ‘Event View ’ of sounds to account for several pervasive sound-related phenomena, including sound wave
transmission through barriers and constructive and destructive interference.
The subject of Chapter 2 is echoes. I argue that echo experiences are
illusory experiences of ordinary primary sounds. Just as there is no new
object that we see at the surface of a mirror, there is no new sound that
we hear at a reflecting surface. Rather, the sound we hear as an echo just
is the original sound, though its perception involves illusions of place, time,
and qualities. The case of echoes need not force us to adopt a conception
according to which sounds are persisting object-like particulars that travel
through space.
A theory of sounds must address the audible qualities: pitch, loudness,
and timbre. In Chapter 3 I argue that despite the failures of simple forms
of physicalism about the audible qualities to account for psychophysical
evidence, a promising form of physicalism can be developed on the basis of
recent accounts of pitch experience. According to this alternative view, pitch
is a physical property that sounds possess independently of their relations
to perceivers, and is not the “subjective correlate of frequency.” Pitch,
however, is interesting only from an anthropocentric perspective.
In Appendix A, I begin to develop the alternative (physicalist) view
proposed in Chapter 3. Recent work on critical bands provides the basis for
the account of pitch I advocate. Finally, I argue that the account in terms
of critical bands can be extended to provide candidates for the properties of
timbre and loudness.
iii
By listening, one will learn truths.
By hearing, one will only learn half truths.
Lucky Numbers 6, 14, 19, 27, 30, 34.
From a fortune cookie.
iv
Contents
Abstract
iii
List of Figures
vii
List of Tables
viii
Acknowledgements
ix
1 Sounds and Events
1.1 What is a Sound? . . . . . . . . . . . . . .
1.2 Three Theories of Sound . . . . . . . . . .
1.3 Locatedness and the Wave View . . . . .
1.4 The Argument from Vacuums . . . . . . .
1.5 The Event View . . . . . . . . . . . . . .
1.6 Transmission . . . . . . . . . . . . . . . .
1.7 Destructive and Constructive Interference
1.8 Concluding Remarks . . . . . . . . . . . .
.
.
.
.
.
.
.
.
1
1
1
3
7
10
13
17
19
.
.
.
.
.
.
.
.
.
.
.
21
21
22
24
25
27
30
30
31
34
37
40
2 Echoes
2.1 Introduction . . . . . . . . . . . . . . .
2.2 The Event View of Sounds . . . . . . .
2.3 The Problem of Echoes . . . . . . . .
2.4 The Solution . . . . . . . . . . . . . .
2.5 Are Echoes Distinct Sounds? . . . . .
2.6 Do Echoes Show That Sounds Are Not
2.6.1 The Argument from Echoes . .
2.6.2 Sounds Do Not Travel . . . . .
2.6.3 Re-encounters . . . . . . . . . .
2.6.4 Some Unsavory Consequences .
2.6.5 Conclusion . . . . . . . . . . .
v
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
Events?
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
2.7
2.8
Is the Illusion Tolerable? . . . . . . . . . . . . . . . . . . . . .
Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . .
3 Audible Qualities
3.1 Introduction . . . . . . . . . . . . . . . .
3.2 Simple Views of Pitch . . . . . . . . . .
3.2.1 The Very Simple View . . . . . .
3.2.2 The Simple View . . . . . . . . .
3.3 Problems with the Simple View . . . . .
3.4 The Standard (Subjectivist) View . . .
3.5 The Alternative (Physicalist) View . . .
3.6 Audible Qualities and the Event View of
3.7 The Doppler Effect . . . . . . . . . . . .
3.8 Concluding Remarks . . . . . . . . . . .
A The Alternative View
A.1 Pitch and Critical Bands . . . . . . .
A.1.1 The Pitch of Complex Tones
A.2 The Musical Relations . . . . . . . .
A.3 Spectrum Shift . . . . . . . . . . . .
A.4 Timbre and Loudness . . . . . . . .
Bibliography
.
.
.
.
.
.
.
.
.
.
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
. . . . .
Sounds
. . . . .
. . . . .
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
40
42
.
.
.
.
.
.
.
.
.
.
43
43
44
44
45
47
48
52
54
56
59
.
.
.
.
.
66
66
72
76
80
83
87
vi
List of Figures
3.1
3.2
3.3
3.4
3.5
Sinusoidal Motion . . .
Fourier Composition . .
The Mel Scale of Pitch .
The Bark Scale of Pitch
Vibration Transmission
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
60
61
62
63
65
A.1 Critical Bandwidth as a Function of Frequency . . . . . . . .
A.2 Equal Loudness Contours . . . . . . . . . . . . . . . . . . . .
85
86
vii
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
.
List of Tables
3.1
Selected Critical Bands
. . . . . . . . . . . . . . . . . . . . .
viii
64
Acknowledgements
I thank the students and faculty of Princeton University, who have been
so generous with their time while discussing these ideas. Particular thanks
in this respect are due to Paul Benacerraf, John Burgess, Gilbert Harman,
Scott Jenkins, Simon Keller, Sean Kelly, Michael Nelson and Jeffrey Speaks.
In addition, Mark Johnston bought me a very important beer, Brian Loar’s
guidance has been invaluable, and Ann Getson’s wit has been a presence.
Special thanks are due to my advisor, Gideon Rosen, who has provided a
paradigm of how philosophy should be done; to Peg Kelly and Frank Kelly;
and to Emily Koehn, the most devout Event theorist.
ix
Chapter 1
Sounds and Events
1.1
What is a Sound?
Sounds are the public objects of auditory perception. When a car starts it
makes a sound; when hands clap the result is a sound. Sounds are what
we hear during episodes of genuine hearing. Sounds have properties such as
pitch, timbre and loudness. But this tells us little about what sort of thing
a sound is—which metaphysical category it belongs to. This is the question
I wish to answer.
1.2
Three Theories of Sound
Locke held that sounds are properties of bodies. More specifically, he held
that sounds were secondary qualities: sensible qualities possessed by bodies in virtue of the “size, figure, number, and motion” of their parts, but
nonetheless distinct from these primary attributes. 1 Robert Pasnau has
recently proposed an account according to which sounds are physical properties of ordinary external objects. 2 On what I shall call the Property View
an object “has” or “possesses” a sound when it vibrates at a particular frequency and amplitude. Pasnau follows Locke in claiming that sound is a
property of objects, though he reduces sound to the primary quality that is
the categorical base of Locke’s power, i.e., that of vibration or motion of a
particular sort.
The received view of auditory scientists and physicists is quite different.
It holds that a sound is a disturbance that moves through a medium such as
1
2
Locke, Essay II.viii (1975), p. 138.
Pasnau (1999) and (2000).
1
CHAPTER 1. SOUNDS AND EVENTS
2
air or water as a longitudinal compression wave. Vibrating objects produce
sounds, but sounds themselves are waves. When we hear sounds we do
not hear bodies or properties of bodies; we hear the pattern of pressure
differences that constitutes a wave disturbance in the surrounding medium.
The common interpretation of Aristotle is that he held a very similar
view. De Anima II.8 says that “sound is a particular movement of air,” 3
which seems to indicate that Aristotle held a version of the received view, or
as I shall call it, the Wave View. We can, however, take our interpretative
cues from other passages in the same chapter and arrive at a view that has
certain advantages over the other two theories and will be at the core of
the alternative I will develop. At 420b13, Aristotle says that “everything
which makes a sound does so because something strikes something else in
something else again, and this last is air.” 4 So, a striking causes or makes
a sound when it happens in air. The sound itself is a movement. But the
sound need not be the motion of the air itself. Instead it may be the event
of that medium’s being disturbed or moved. The idea is to treat ‘movement’
as the nominalization of a transitive verb and focus on constructions like ‘x
moves y’ instead of ‘y is moving’. “For sound is the movement of that which
can be moved in the way in which things rebound from smooth surfaces when
someone strikes them,”5 then means that sound is the air’s being disturbed
by the motion of an object. A sound is not motion, but the act of one
thing moving another. This is not the Wave View that most attribute to
Aristotle,6 but the beginnings of the Event View of sound.
According to the Event View, sounds are particular events of a certain
kind. They are events in which a moving object disturbs a surrounding
medium and sets it moving. The strikings and crashings are not the sounds
themselves, but the causes of sounds. The waves in the medium are not the
sounds themselves, but rather the effects of sounds. Sounds so conceived
possess the properties we hear sounds as possessing: pitch, timbre, loudness,
duration, and as we shall see, spatial location. When all goes well in ordinary
auditory perception, we hear sounds as they are.
3
Aristotle, De Anima 420b10 (1987), p. 179.
Aristotle, De Anima 420b13 (1987), p. 179.
5
Aristotle, De Anima 420a20 (1987), p. 178. My italics.
6
See Pasnau (2000).
4
CHAPTER 1. SOUNDS AND EVENTS
1.3
3
Locatedness and the Wave View
According to the Wave View, sounds are waves: a particular sound is a
train of waves that is generated by a disturbance and moves through the
surrounding medium. But this is not how things seem. When we hear a
sound, we hear it to be located at some distance in a particular direction.
In ordinary cases sounds themselves, not merely their sources, seem to be
located distally. Auditory scientists call this phenomenon ‘externalization’. 7
Sounds are not perceived to travel through the air as waves do. They are
heard to be roughly where the events that cause them take place. If auditory experience is not systematically illusory with respect to the perceived
locations of sounds, then sounds are not waves, since they are not perceived
to be where the waves are.
The argument depends on a phenomenological claim. Sounds are perceived to have more or less determinate locations. When we hear a clock
ticking, the sound seems to be “over there” by the clock; voices are heard
to be in the neighborhood of speakers’ heads and torsos; when a door slams
in another part of the house, we know at least roughly where the accompanying racket takes place. I mean that we experience sounds, in a wide
range of cases, to be located at a distance from us in a particular direction.
When we do not, as when a sound seems to “fill a room” or “engulf” us, the
sound is perceived to be “all around,” or at least in a larger portion of the
surrounding space. Hearing a sound located “in the head” when listening to
earphones is another sort of sound location perception, albeit a touch odd. 8
Given the phenomenological facts, the degree to which auditory location
perception is illusory or misleading should follow from a theory of sound.
No theory should make the fact of location perception a wholesale illusion,
though individual instances of location perception might mislead about the
actual locations of sounds. Thus, I might correctly hear a stereo speaker’s
sound as located at the speaker itself; but I might undergo an illusion as of
hearing the sound to be located five feet to the right of that speaker. In both
cases, I correctly perceive the sound to have a location, but the experience is
inaccurate in the second instance. Occasionally, sound location perception
is to some degree anomalous, as when sound seems to be all around in
a reverberant room, when it seems to be in the head during headphone
7
Gelfand (1998) refers to this phenomenon as ‘extracranial localization’: “Sounds heard
in a sound field seem to be localized in the environment,” p. 374.
8
Gelfand (1998) refers to this phenomenon as ‘intracranial lateralization’: “Sounds
presented through a pair of earphones are perceived to come from within the head, and
their source appears to be lateralized along a plane between the two ears,” p. 374.
CHAPTER 1. SOUNDS AND EVENTS
4
listening, or when the sound seems to be “behind” a jet plane overhead.
Whether and when a sound can literally fill a reverberant room, be inside
the head of a subject, or be behind an airplane will depend upon one’s theory.
The phenomenon of locatedness spells prima facie trouble for the Wave
View. Sound waves pervade a medium and move through it at speeds determined by the density and elasticity of the medium. Yet we neither hear
sounds as air sloshing around the room nor as moving roughly 340 meters
through the air each second. Imagine a scenario in which engineers have
rigged a surround-sound speaker system to produce a sound that seems to
be generated by a bell across the room. This sound subsequently seems
to speed through the air toward you and enter your head like an auditory missile. This would indeed be a strange experience, one unlike our
ordinary experiences of sounds generated by relatively stable objects and
events. Sounds are perceived to be relatively stationary with respect to
their sources. The sound of a moving train seems to move only insofar as
the train itself moves. When the train stops moving, so does its sound.
The trouble for the Wave View is serious. Since sounds are heard as
having stable distal locations, either the sound is not identical with the
sound waves, or we misperceive one important aspect of sounds. If the sound
is identical with the sound waves, the situation is not that we sometimes
misperceive sounds, as when a sound ahead is heard to be behind; rather,
we systematically misperceive the locations of sounds. That is, we hear the
locations of all sounds incorrectly since we never hear a sound to move just
as wavefronts do. Since sounds are among the things we hear, we should
take the phenomenology of auditory experience seriously when theorizing
about what sounds are. If the phenomenon of locatedness is not systematic
misperception, then sounds are not sound waves.
The Wave theorist might reply,
The immediate objects of auditory perception—what we hear—
are waves. Sounds just are waves. Waves and their properties
are the causes of perceptions of pitch, loudness, and duration;
however, we hear these qualities to be located at the place where
the waves originate, i.e., at their source. Sounds seem to be
where their sources are, and to this extent, auditory perception
is illusory. But this illusion is a beneficial one, given our interest
in sound sources as constituents of the environment. It is no
surprise that we hear sounds to be located where distal objects
and events are.
CHAPTER 1. SOUNDS AND EVENTS
5
The Wave theorist’s response avoids the conclusion that sounds are not
identical with waves by accepting that we are subject to wholesale illusion
in one salient aspect of auditory experience. The strategy is to assuage
concern about the location illusion by providing another candidate for bearer
of the spatial properties and by highlighting the illusion’s potential benefits.
Notice the tactic: by invoking the location of the source, the Wave theorist
avoids assigning potentially problematic locations to sounds.
But sounds have pitch, timbre, and loudness. An account that entails
that sounds are located where instances of pitch, timbre, and loudness are
heard to be is preferable to one that convicts auditory perception of systematic illusion about the locations of its objects. Can we eliminate illusion from
the Wave theorist’s account entirely? One promising approach rejects the
phenomenological claim as it stands. Instead, it says that we hear sounds to
have pitch, timbre, loudness, and duration, though not as having locations.
Rather, we hear ordinary events and objects as located and as the generators
or sources of audible qualities that lack spatial properties entirely. We do
not mistakenly perceive the locations of sounds, we simply fail to perceive
their locations.
This is the Wave theorist’s best way to avoid the dilemma. She says
sounds are not heard to have locations, they are heard to have located
sources. The picture is this: sounds are waves; waves have sources; sounds
are heard to come from their sources, but not themselves to have locations;
only sources are perceived to have locations. This description provides a
compelling account of the phenomenology that is consistent with the Wave
View. Unfortunately for the Wave theorist, it fails. To see why it fails we
need to consider just how a sound can seem to come from a location.
The problem is that sounds themselves must be heard to have particular
locations for sound sources to be heard as located. For the Wave theorist,
the basic audible qualities are qualities of sounds, and sounds are waves.
Thus, waves have the audible qualities. The response we are considering
is that we hear objects and events as located by way of the sounds they
generate. But we cannot hear just non-located audible qualities and located
objects, full stop. This would amount to a precarious perceptual situation.
How could non-located qualities provide locational information about their
sources in perception?
One way is for locational information to be encoded temporally, for example, by time delays between waves reaching the ears. This information
must be conveyed somehow in conscious perception. In audition this is accomplished by awareness of the audible qualities of pitch and timbre, and
their loudness and duration. If these are the aspects of sounds we experi-
CHAPTER 1. SOUNDS AND EVENTS
6
ence, and if they are to convey information about the locations of material
objects and events, then sounds themselves, and their qualities, must be
heard as located. If the Wave View is correct, the location illusion remains.
A distinction can be drawn between hearing sounds themselves as located
and perceiving information about the locations of material objects, stuffs,
and events in the environment by means of audition. The question is whether
the latter would be possible without the former. If hearing sounds and their
qualities as located is required in order to perceive or form judgements about
the locations of material objects and events in audition, then the Wave
View is forced to say that auditory perception is in one central respect
illusory. Ordinary introspection of one’s auditory experience supports the
claim that we indeed hear sounds as located. Imagine an experiment in
which the engineers mentioned above generated a pure 1000 Hz tone of
moderate loudness that seemed to be about ten feet directly ahead of you in
the middle of the air. You are allowed to open your eyes and walk around,
but you can neither see nor feel nor smell anything in the sound’s vicinity.
Your experience would be of just a sound and its qualities, and not of any
other objects, stuffs, or events located where it seems to be. The sound is
heard as an independent existent located in space. Though most ordinary
auditory experiences are of sounds generated by events and things, these
sounds are heard as being entities distinct from their sources. Sounds are
heard to have locations, by way of which they provide perceptual information
about the locations of their sources. 9
If the phenomenological claim is an accurate description of the experience of sounds, and if it is true that in order to perceive the locations of
sound sources, audible qualities and sounds themselves must be perceived as
located, then either the Wave View attributes widespread illusion to auditory perception or the Wave View is false and sounds are not simply waves
in a medium. Short of accepting and explaining the illusion, the Wave theo9
Another way we might imagine the situation is as follows. We hear sounds, but not
as located in any way. We learn the locations of sound sources by an unconscious process
something like what is referred to as ‘blindsight’ by perceptual theorists (see, e.g., Block
(1995)). So, the locational information is represented through a course of subconscious
perception. Our perceptual awareness of the connection between sounds and sources must
then be explained. If this can be done and the description we are considering is correct,
my claim that audible qualities are consciously heard as having locations must be false or
due to widespread illusion. I think it is manifestly correct that audible qualities are heard
as having locations, and that this is demonstrable by various behavioral and introspective
tasks. Widespread illusion is precisely what the Wave theorist is trying to avoid. It is
preferable to explore alternative conceptions of what sound is than to go to such lengths
to make the theory fit with the phenomenology.
CHAPTER 1. SOUNDS AND EVENTS
7
rist’s best strategy is to impugn my description of the phenomenology. She
should say that sources, not sounds themselves, are heard as located. This
requires rejecting the argument that in order to hear sound sources as located, sounds must be heard as located. The blindsight analogy raised in
footnote 9 is one route around the dilemma for the Wave theorist shy about
claiming that we fail to perceive, or systematically misperceive, the locations
of sounds.
I am convinced that the phenomenological claim is correct as it stands
and that sources are heard as located only if sounds are. So I need a way to
avoid this difficulty. My theory must not imply that sounds move through
the air. The Property View is tailor-made to capture the phenomenology of
locatedness. It, however, falls to a separate objection.
1.4
The Argument from Vacuums
The Property View says that sounds are properties of things like bells, tuning
forks, and whistles; more specifically, sounds are the vibrations of material
objects. The view entails that sounds are roughly where we perceive them
to be. Unfortunately, the Property View also entails that sounds can exist in
the absence of a transmitting medium. That is, sounds can exist in a vacuum
(just as things can have colors in the dark), since all that’s required for an
object to have a sound is that it vibrate in the right way. Nevertheless, we
have good reasons to believe that the existence of a sound requires a medium.
If there can be no sounds in vacuums, the Property View is false. 10
In Berkeley’s first dialogue between Hylas and Philonous, Hylas argues
against the Property View in favor of the Wave View by deploying the
Argument from Vacuums. It begins with the premise that a bell struck in
water or air makes a sound, but in a vacuum it does not. Hylas concludes
that sound must be in the medium.
PHILONOUS. Then as to sounds, what must we think of them:
are they accidents really inherent in external bodies, or not?
HYLAS. That they inhere not in the sonorous bodies, is plain
from hence; because a bell struck in the exhausted receiver of
an air-pump, sends forth no sound. The air therefore must be
10
This argument is independent of my causal argument against the Property View (see
“What Sound Is Not: Pasnau on Sound” (ms)). According to the causal argument, the
Property View cannot accommodate the fact that sounds are generated by their sources—
that is, that there exists a causal relation between a sound and its source. See “What
Sound Is Not” for further discussion of why the Property View fails.
CHAPTER 1. SOUNDS AND EVENTS
8
thought the subject of sound. [The sound which exists without
us] is merely a vibrative or undulatory motion in the air. 11
The argument is:
1. A bell struck in a vacuum makes no sound.
2. So, sound does not exist in the absence of air.
3. So, air is the subject of sound (i.e., the Wave View is true).
4. The Property View is false.
Notice a few things. If a bell struck in a vacuum makes no sound, then
sound does not exist in the absence of air and the Property View is false. 12
But it does not follow that the Wave View is true. Air might be required
for the existence of sound without itself being the subject of sound. Even if
its first premise is true, the Argument from Vacuums does not establish the
truth of the Wave View. Room exists for an alternative theory of sounds
according to which no sounds occur in vacuums.
Furthermore, the first premise must be established if it can be used
against the Property View. Why say there are no sounds in vacuums?
Hylas baldly assumes there are not. We would like to have some reason,
preferably independent of an explicit theoretical commitment, for denying
(or affirming) that sounds exist in vacuums.
A first pass: “When the bell is struck in a vacuum we know there is no
sound because none can be heard by any ordinary creatures; if a medium is
added, we can hear it, so the sound must require the medium.” Problem:
The fact that no sounds are ever heard in the absence of a medium shows
only that a medium is required for there to be veridical perception of sounds.
It does not show that a medium is necessary for there to be a sound. 13 This
is the Property theorist’s wedge in the Argument from Vacuums.
Suppose one strikes a bell in a vacuum chamber containing a (hypothetical) perceiver. The perceiver can hear nothing. Our problem is that without
a theory of what sounds are we are unable to confirm whether or not there
is a sound. Barring a declared theoretical commitment, how do we decide if
the bell makes a sound?
11
Berkeley (1975), pp. 171–2. Also quoted in Pasnau (1999), p. 321.
Air is meant to be representative of any medium in which sound waves travel.
13
Berkeley, of course, had reason enough to conclude that there are no sounds in vacuums, since he accepted that nothing exists unperceived.
12
CHAPTER 1. SOUNDS AND EVENTS
9
Perhaps because the bell struck in a vacuum is not a possible object of
auditory experience, it does not make a sound. Though I see no good reason
to deny that there are sounds beyond the ken of perception, this argument
gets us closer to what we are looking for. A sound, if anything, is the bearer
of the properties of pitch, timbre, and loudness. Suppose we could establish
that there is neither pitch, nor timbre, nor loudness when the bell is struck
in the vacuum. We could then reasonably conclude that there is no sound.
The bell struck in a vacuum has no sound because it has none of the qualities
necessary for the existence of a sound.
The sound of a bell seems to have different qualities when the bell is
struck in air and water, and different ones yet in helium and liquid mercury.
When the very same striking event occurs in a vacuum, it is inaudible. If
a sound exists in a vacuum, it must have some definite pitch, timbre, and
loudness. What loudness, for example, does it have? The loudness it would
have been heard to have if it had been surrounded by water? The loudness it
would have been heard to have if it had been surrounded by air? A decision
here will be to a significant extent arbitrary and will not reflect the relevant
ways in which the loudness of a sound depends upon the medium in which
it is generated.14 The Property theorist might hope that ideal or standard
conditions for perceiving the “true sounds” of things can be formulated as
they can for colors.15 But the way in which daylight or white light might
be counted as ideal for revealing the true colors of things finds no analog
in sound. Neither air nor water nor helium does a substantially better job
divulging the subtle vibrations of an object in the way that full-spectrum
light reveals the reflective properties of a surface. If there is no ideal medium
in which to hear the true sound of an object, that is, if the qualities of a
sound depend upon the medium in which it is generated, then it is doubtful
whether the object vibrating in a vacuum has a pitch, timbre, or loudness.
It is therefore doubtful whether there is any sound.
The medium-dependence of audible qualities shows that we are justified
in drawing a stronger conclusion than that some necessary condition for
sound perception is missing in a vacuum. A necessary condition for there to
be a sound is missing.16 If sounds do not occur in vacuums, the Property
14
See §A.4 for further discussion of this dependence.
Pasnau (1999) appeals to just such a hope, p. 322.
16
Might we say that sounds are properties that objects have only when in the presence
of a medium, and thereby save the Property View? The sound property assigned to
the object must, however, depend on the specific properties of the particular medium
surrounding it in order to avoid the objection raised in the text. The sound differs only
when the medium differs. This is no longer the Property View. It is a relational view
15
CHAPTER 1. SOUNDS AND EVENTS
10
View is false. Moreover, we showed in §1.3 that the Wave View entails
systematic illusion about where sounds are. The Event View, however, is
a natural alternative that attributes the right locations to sounds and does
not entail that sounds exist in vacuums. The Event View is that particular
sounds are events in which a medium is disturbed or set into wave-like
motion by the movement of a body or interacting bodies. These disturbance
events take place where we perceive sounds to be, and, because no medium
is present to be affected, a vacuum contains no sounds.
1.5
The Event View
Particular sounds are events.17 Sounds take time and involve change—at
a minimum they begin, and usually they end. A number of qualitatively
different stages or a single tone of uniform loudness may compose a sound.
The sounds are the events in which a medium is disturbed or changed or
set into motion in a wave-like way by the motions of bodies. Events such
as collisions and vibrations of objects cause the sound events. Among their
effects may be sound waves propagating through a medium and the auditory
experiences of perceivers. Medium-disturbing events are what we hear to
have particular pitch, timbre, loudness, and location. A body counts as
in a state of sounding—making a noise—just in case it is in the midst of
generating or causing a particular sound. Whenever there is a sound there
is a sounding.
The tuning fork struck in air is a simple case. The striking is an event
that “makes” a sound in virtue of the process by which the arms of the fork
oscillate and create regular compressions and rarefactions in the surrounding
air. Its creating the disturbance constitutes the tuning fork’s sounding. The
event of the tuning fork’s disturbing the medium is the sound. We perceive
this sound event to have a constant pitch and timbre, a duration, a location,
and diminishing loudness. In contrast, the sound of an owl’s call is a more
complex event characterized by a temporally extended pattern of changing
pitch, timbre, and volume. Each call sounded is an event consisting of the
involving object and medium which is closer to the truth about sound, not the view that
sound is an intrinsic property of objects.
17
My theory of sounds as events should be relatively insensitive to what particular
theory of events is the correct one (e.g., Lewis (1986), Davidson (1970), Kim (1973)).
Within reason, whatever events turn out to be, sounds should be events. Accordingly, I
wish to work with the intuitive notion of events as particulars which take time, occur over
an interval, and may or may not essentially involve change.
CHAPTER 1. SOUNDS AND EVENTS
11
owl’s lungs and syrinx disturbing the surrounding air in a given pattern. The
tuning fork and the owl alike are recognizable by the sounds they create.
Auditory perception also makes us aware of events in our environment.
We learn by audition how the furniture is arranged and when it is being
moved. How is this possible if sounds themselves are the events that we
hear? The Event View says that a sound is an event whose cause is the
event heard to “have” or “make” the sound, and implies that the sound
and its cause are in close spatio-temporal proximity. When we hear the
sound of a glass breaking, that sound is an audible event constituted by
the fracturing glass affecting the air. The breaking of the glass causes the
medium-affecting event that is the sound event. This latter event has the
audible qualities of pitch and loudness. The medium-affecting event is near
the breaking event, but the two do not occur in just the same space-time
region. That the two sorts of events occur close to each other, however,
does not sufficiently explain why we are aware of sound generating events in
auditory perception. A sound also carries qualitative information that can
be used to identify its generating event after perceivers learn to associate
the sound with the cause. The sound’s pattern of pitch, timbre, loudness,
and duration indicates that a glass has broken; the location of the sound
points us in the direction of the mess.
So, there is the event of an object or substance setting a medium into
periodic motion. This is a sound. The kind of motion depends on the form
and makeup of the object or substance, what it does to disturb the medium,
and the physical characteristics of the medium itself. The sound event has
a location and a pattern of pitch, timbre, loudness, and duration. There are
also the generating events that cause sounds and the objects that are said
to make a sound in virtue of instances of their sounding.
Sounds are individuated along three primary dimensions: causal source,
spatio-temporal continuity, and qualitative change. Intuition is sometimes
silent, but we do have implicit in our practices principles for saying when
sounds are the same or different. The Event View captures these principles.
To count as the numerically same sound particular, a candidate must have
the very same token causal source and be spatially and temporally continuous throughout its entire history. If either the causal source changes or there
is a spatial or temporal discontinuity, we say that there are different relevant
sound particulars—a temporally seamless transition from a trumpet playing B-flat to another trumpet playing the same note counts as involving two
different sound tokens. The sense in which the sound from a single trumpet
is different when it seamlessly goes from playing a B-flat to an A is that
CHAPTER 1. SOUNDS AND EVENTS
12
the trumpet’s state of sounding is different. Perhaps different sound events
correspond to these different states of sounding at the two times. Still, there
is one sound event of which each note instance is a part, and in this sense
both are parts of a single continuous sound. Such a sound might extend
over considerable time and space and change greatly in its qualitative characteristics. At times it may be loud and high-pitched and at others it may
be faint and low, but as long as it has the same causal source in terms of its
generating event or object, and is spatio-temporally continuous, it counts as
the very same sound particular.
It follows that numerically distinct instances of sounds that fall under
the same qualitative characterization are not the very same sound in any
sense stronger than qualitative identity. Temporally discrete sounds from
the same causal source and spatially separated sounds generated by different sources can at best be different instances of the same qualitative sound
type. Philosophers sometimes do, however, speak of performances of songs
and symphonies as events that are tokens of sound types, despite the fact
that they need be neither temporally nor spatially continuous—they may
incorporate periods of silence and multiple sources. We can say the same of
bird calls. But these are complex events that involve patterns of individual
sound events when they occur. Distinct sound particulars are arranged to
comprise a whole that may require or allow for discontinuities of various
kinds. The ontology of music and complex sound universals enjoys its own
vast literature. What I want to point out is that the Event View is capable
of capturing the ways in which we take sounds to be individuated. The principles I have mentioned may be disputed; but there is often obscurity about
how events are to be individuated. The Event View, in that case, predicts—
correctly—that there is a certain amount of obscurity and arbitrariness in
our verdicts concerning how many sounds we have heard. 18
The Event View is a natural way to avoid the objections posed in §1.3
and §1.4. Particular soundings have audible locations determined by where
the medium-disturbing process occurs. Sounds, then, move through space
in just those ways we expect them to, for example, when a train passes in
the distance. The subject-directed missile-like sound does not ordinarily
arise. The Event View also accounts for what we learn about sound from
the Argument from Vacuums: we are justified in claiming that a medium is
necessary for there to be a sound. Since a medium is required for there to be
a medium disturbance, there is no sound in a vacuum. The Event theorist
18
Thanks to Gideon Rosen for disputing several of my sound individuation principles
and helping me to see this last point.
CHAPTER 1. SOUNDS AND EVENTS
13
maintains that sounds are neither entirely in the surrounding medium nor
simply properties of objects. If the arguments against the prevailing views
are compelling, the Event View is a theoretically cogent solution.
Several lines of objection force elaboration of the Event View. The Event
View provides for natural accounts of several phenomena that pose difficulties for any theory of sound.
1.6
Transmission
So far, I have said that a sound is an event of a medium’s being disturbed
or set into motion in a particular way by the activities of an object, body or
mass. But this seems too lenient, to allow too many sounds. Consider the
following two forms of objection.
First Form
Suppose you are underwater and hear the sound of something
that happens in the air above, say, the striking of a bell. The
Event View seems to imply that there is a sound at the interface
of the air and water since indeed there is a medium-affecting
event there. The air, a mass or body, sets the water, a medium,
into motion. This is phenomenologically inaccurate. We do not
hear the sound to be at the surface of the water; we hear it to
be above in the air.19
Second Form
The preacher outside Marx Hall is loud. When I shut the window I do not hear him as well. The window muffles the sound.
Nevertheless, the window also sets the medium inside the room
into motion. According to the Event View, is the sound located
at the windowpane? We do not hear it as being there—the sound
still seems outside.
In both forms, sound waves generated in one medium pass into another kind
of medium. The first describes travel across a single interface; the second
involves travel through a solid barrier. In each, at the relevant interface—
the air-water interface in the first case and the window-room interface in
the second—the motion of a body disturbs the medium it adjoins. Yet since
we do not ordinarily take ourselves to hear sounds at such places, intuition
19
Here, and in the discussion that follows, I will ignore misperception of the sound’s
location that results from refraction. This does not affect the arguments and conclusion.
CHAPTER 1. SOUNDS AND EVENTS
14
has it that no sound occurs at either the interface or the barrier. Must the
Event theorist count these events as sounds? 20
The problem of transmission is not unique to the Event View. Each of
the views canvassed faces a version of the objection. The Property View is in
roughly the same straits as the Event View. The Property View implies that
the sound is a property of the air mass in the first case and the windowpane
in the second, since each vibrates at a particular frequency and amplitude.
Even the Wave View, on which sounds are waves, faces a dilemma. What
is the source of the sound? Is it the bell or the air-water interface? The
preacher or the window? Each is in a sense the cause of the waves “in the
medium” in which the sound is heard. An acceptable version of the Wave
View must acknowledge that we perceive locations in auditory perception,
even if these are the locations of sound sources. Just as the Event theorist
needs to say which events are the sounds, the Wave theorist must say which
things count as sources of sounds. Though the problem is not unique to the
Event View, the Event theorist owes an account of sounds and transmission.
The Event theorist’s options are: (a) deny there is a sound where transmission occurs and explain why the Event View does not entail that there
is; (b) accept that sounds accompany transmission events and reconcile this
with the intuitive description of the experience. Contrary to first appearances, option (b) is somewhat attractive. 21 Ultimately, however, this re20
In fact, there is a slightly more troubling extension of this objection. Sound waves
are transmitted by means of collisions among the particles of a medium. If each one of
these collisions is an event in which an object (a particle) disturbs a medium, then the
Event View seems to imply that each of these events is a sound. We might respond that
these molecules do not count as objects in the ordinary sense enlisted in the conception
of a sound. This is unsatisfactory. We are discussing ontology, and must not artificially
limit the scope of what counts as an object in order to suit the purposes of our favorite
theory. At any rate, this extension illustrates the potential extent of the difficulty that
sound wave transmission poses for the Event theorist.
21
Suppose we accept that what occurs at a transmitting surface or barrier is a sound—
that the medium disturbance is a genuinely audible event. Granted, this event is caused
in very different way from the primary sound produced by an event such as striking a
bell or shutting the door. It comes about because sound waves reach a medium with a
considerably different density and elasticity and transfer a portion of their energy to that
medium (the sound transmission coefficient of a medium is a constant that depends on
the density, mass, and elasticity of the material. The portion of wave energy transmitted
from one medium to another is a direct function of the degree of similarity between the
sound transmission coefficients of the two materials). But what occurs at the transmitting
surface or barrier is still notable from the point of view of the Event theorist. The surface’s
activity is the proximal cause of motion in the surrounding medium that culminates in
auditory experiences. Two puzzling facts about auditory perception in such cases remain.
First, transmitted sounds seem to come from where the original, or primary, sound event
CHAPTER 1. SOUNDS AND EVENTS
15
sponse and the burgeoning world of sounds it proposes are unsatisfactory.
It strains the imagination to suppose that a multiplying of sounds occurs
each time sound waves travel across an interface or through a barrier. Our
accounting should be more sober.
Suppose we deny that a sound occurs when a “new” medium is disturbed
by a pre-existing sound wave. Option (a) suggests a different way to conceive
of the perceptual situation. We say that the interface or barrier distorts
our perception of the primary sound’s location and qualities, not that we
perceive a secondary sound with its own location and set of qualities caused
by the primary sound. A single sound exists above the water or outside
the window, but one may not have an ideal experience of that sound if
impediments to perception intervene.
This picture is more accurate from a phenomenological standpoint. The
indications are that we have a perceptual bias toward the locations of sound
generating events, that is, cases in which sounds are caused to exist by
events of the everyday material sort. Auditory perception makes us aware
of sounds produced by events such as doors shutting and waves breaking—
sound generating events. We hear the sound created by the striking of the
bell above water, and the sound of the preacher proselytizing outside the
takes place. The sound of the preacher does not ordinarily seem to be at the window; it
seems to be outside. If there is in fact a sound at the window, it must preserve cues about
the location of the initial sound. We perceive sounds as localized thanks to information
contained in sound waves. When the waves from a source arrive at a surface or barrier,
most of the information they carry about the direction and distance to that source remains
intact when the abutting medium is set into motion. The result is a sound perceived to
be located at the primary source, not at the transmitting barrier. If sounds occur where
transmission does, the secondary sound preserves the primary sound’s location information. This accounts for the misperceived locations of transmitted sounds. Second, we
classify sounds according to the types of events that we perceive to produce them. Yet
sounds do not ordinarily appear to be produced by collisions between sound waves and
surfaces or barriers. The primary sound, however, determines the purported secondary
sound’s qualities. Though less loud, the supposed secondary sound’s qualitative and temporal profile would be roughly that of the primary sound. The secondary sound, which
is caused by waves from the preacher’s voice reaching a window, would thus resemble the
primary sound. Given the preservation of location cues and the qualitative similarity of
primary and secondary sounds, secondary sounds would be carriers of information about
occluded primary sounds and would not be perceived to arise from events that occur at
the window. This view attributes a great deal of illusion to auditory perception. The
previously mentioned attraction is that it makes being a sound an intrinsic property of
events. If being a sound is being a medium-disturbing event, then what makes something a
sound is just that it has the physical makeup required of such a disturbing. There are not
further extrinsic requirements stemming from the event’s causal or temporal relations. If
a window interacts with a medium to produce a disturbance, that window makes a sound
no matter how its activities arose.
CHAPTER 1. SOUNDS AND EVENTS
16
window. Events of transmission occur when the waves from one sound event
cause motion in an object or body that is passed on to another medium.
We do not hear events of transmission or indeed anything at their locations
when we hear a sound beyond an interface or through a barrier.
The language of this distinction suggests a theoretical solution consistent
with the Event View. To speak of a sound as generated by a source implies
that the sound is caused by and distinct from the event that brought it about;
we also speak of sound waves being generated by sound producing events.
The idiom suggests that neither the sound nor the sound waves exist in any
form prior to the event of generation. In contrast, the idiom of transmission
applies to an event that is involved in passing along a wave disturbance that
already exists. When a transmission event causes a medium disturbance of
the sort that poses trouble for the Event theorist, both events depend for
their existence upon a prior sound event. The distinction between medium
disturbing events that introduce sound waves into an environment and those
that transmit them is natural and based on the events’ roles in a regular
causal network.
The medium disturbing events that are the sounds are the events in
which a wave disturbance is introduced into the environment by the activities
of some material object, body, or mass. Disturbance events in which a prior
sound’s waves are passed on or transmitted into a different medium are not
in any ordinary sense sounds. An event of transmission must have a sound
in its causal history, and a (generated) sound need not. Being a sound is
a matter partly of occupying a particular causal-functional role. A central
feature of the causal role distinguished by how we speak is that sounds are
events caused by generating events such as collisions, but are not caused by
waves simply passing through barriers and interfaces.
Sound generating events such as cymbal collisions cause or generate
sounds. Sounds are events in which a disturbance is introduced into a
surrounding medium, that is, they are events in which an object actively
disturbs a medium. The sound waves that result from the sound event,
which are also in a sense generated, are transmitted through the surrounding medium and the materials and objects it contains. Events in which the
motion of sound waves causes barriers and intervening matter to set adjacent media into motion are not events in which a disturbance is introduced
into the environment. Such transmission events are among the ordinary
inaudible activities of sound waves that carry information about the initial
CHAPTER 1. SOUNDS AND EVENTS
17
sound and propagate through various materials. Transmission events do not
ordinarily give rise to sounds.22
This account appeases intuition. The problem of deciding which of multiple sounds we listen to when sound waves pass through an interface or
barrier does not get off the ground. But the “innocent” picture according to
which being a sound is entirely a matter of what happens near the surfaces
of objects whose activities affect a medium is threatened. We must adopt a
broader perspective that acknowledges the causal relations of several distinct
kinds of events. This is not cause for alarm, nor is it a surprise given the
organization of sound-related experience. Sounds furnish us with awareness
of sound generating events, which are of paramount interest for what they
tell us about the world. They tell us such things as how the furniture is
arranged and when it is being moved. Transmission events, however, enjoy
little utility beyond what we learn through their effects on how we perceive
the primary sounds they occlude: when we perceive a sound as muffled,
we learn that a barrier may intervene. Given, first, our interest in ordinary
events that take place among material bodies, and, second, how these events
are related to sounds, it is no wonder that the primary disturbances should
be distinguished by audible qualities.
1.7
Destructive and Constructive Interference
As commonly demonstrated in high school physics classrooms, sound waves
interfere with each other. Suppose you are in an anechoic room in which
two tuning forks tuned to E above middle C are simultaneously struck. As
you move around the room, there are places from which you hear the sound
to be soft and places from which you hear the sound to be loud; there are
places from which you hear neither sound.
This phenomenon occurs because at any time the total pressure at a
point in the room equals the algebraic sum of the pressures of all the sound
waves at that point. It is therefore possible, when sound waves are out of
phase with each other, for the total pressure at some point or in some area to
remain constant while separate sound waves pass through that point or area
simultaneously. A listener positioned at such a point hears nothing. When
22
I say “ordinarily” in light of the following sort of case. Suppose sound waves reach
a barrier and induce vibrations in that object. The barrier might then itself generate a
sound in addition to the sound whose waves induced the barrier’s vibrations. This is not
an ordinary case of sound wave transmission, however, and should be subsumed instead
under resonance. Resonating is sounding since the resonating object actively disturbs the
medium, and does not merely passively transmit existing sound waves.
CHAPTER 1. SOUNDS AND EVENTS
18
sound waves cancel, the interference is destructive. Likewise, when the waves
are completely in phase at a point, the total pressure varies with the sum
of the components’ amplitudes. The sound seems twice as loud as either
tuning fork at these points thanks to constructive interference. Altering the
phase or vibration characteristics of one of the tuning forks may result in
beating, a periodic variation in perceived amplitude from a particular point.
Here is the problem. Take the example of complete destructive interference described above. The Wave theorist can explain that you hear no
sound from where you stand because the pressure is constant at that point
and hence there is no sound.23 By contrast, the Event View implies that
each tuning fork makes a sound even though you hear neither one from the
point of interest. If sounds are not sound waves and the Event View is correct, then you hear no sound at all when there are two. Is the gap a fault
line in the Event View?
Interference phenomena do not undermine the Event View. The interference arguments do show that waves carry information about sounds. The
Event theorist should not deny this when he says that the sound is not
identical with the waves. Waves can be involved in the process by means of
which a sound is heard without the sound’s just being the waves. The Event
View provides an intuitive and compelling alternative to the standard account of destructive interference. The Event View says there are two sounds,
two events of a disturbance being introduced into a medium. These disturbances travel as compression waves and may reach a perceiver, where they
cause perceptions of the original sound event. Waves obey the principles
of interference, and if no variations in pressure exist, no sounds are heard.
Ordinarily, a lack of pressure variations indicates the absence of sounds and
sound sources. Complete destructive interference resembles the absence of
sounds because factors conspire to create nodes where the pressure does not
vary. These factors include the spatial arrangement of the two sources, the
frequency and amplitude at which the sources oscillate, and the temporal
relations among the activities of the sources, i.e., the phase difference of the
sources. A perceiver located at a node will hear neither sound, and may
believe that no sounds occur. This does not entail that the room contains
no sounds. The observer is simply unable to perceive the sounds because of
her particular point of view.
23
Of course, there are still in a sense two waves passing through that area, but their
summed amplitude is zero. So, in a sense, there are two sounds at that point even though
none is heard. The Wave theorist does not escape entirely. If, however, by ‘the wave’
we mean something that depends only on the total pressure at various points, there is no
wave and no sound at the point of interest.
CHAPTER 1. SOUNDS AND EVENTS
19
That there are indeed two sounds can be confirmed in several ways. One
can move to a point where one or the other sound is audible, move one or
both of the sources so that the nodes are shifted, alter the phase difference
in the vibrations of the two objects to remove nodes completely, or simply
remove one of the sources to eliminate interference entirely. These exercises
show that each tuning fork makes a sound that can be heard independently of
the other in the right circumstances. Sometimes, however, another sound’s
presence can interfere with perceiving a given sound. Experience need not
reveal from a particular vantage point all the surrounding environment’s
sounds. What we perceive from a very limited vantage point need not be
the entire story about sounds.
The case of constructive interference is very similar. Due to the spatial
and temporal relations among events of sounding, a perceiver in the right
location may experience multiple sources to have greater loudness than any
single source present. This is again the result of the additive properties
of sound waves. It is less surprising that the subject’s loudness experience
should increase in the presence of two sources than that it should decrease,
as in destructive interference. Beating is perhaps less intuitively comprehensible, but is also an explicable result of how the source events are arranged
in time and space, and of the subject’s vantage point on these events. 24
1.8
Concluding Remarks
The Event View replaces the picture according to which sounds fill the air
and travel as waves. Instead, sounds are events that occur where objects and
bodies interact with the surrounding medium. Sounds are events that take
place near their sources, not in the intervening space. Sound waves travel
through the air carrying information about these distal events, and are the
proximal causes of sound experiences in subjects; however, sound waves
are not sounds. The revision more accurately captures how we experience
sounds to be.
24
Experiences related to interference phenomena can, on the positive side, provide information about the sounds actually present that would be difficult to obtain otherwise
with unaided perception. Experience can tell us when two pitches are identical or if two
sounds are exactly in phase when such facts are beyond the scope of ordinary perceptual
discrimination. We tune a guitar by eliminating the beating between the open A string’s
note and the A of a pitch pipe. The two are in tune when the sound does not waver. Furthermore, one can tell that two sounds are exactly in phase when their combined loudness
peaks.
CHAPTER 1. SOUNDS AND EVENTS
20
The Event View is a natural account of what sounds are that avoids the
dilemma concerning where sounds are located. It implies that sounds are
distally located and stationary relative to their sources without making them
solely the properties of material things. We should not accept the view that
sounds are properties of objects because we have good reason independent of
the received view to think that sounds cannot exist in vacuums. The event
that the Event theorist identifies as the sound cannot occur in the absence
of a medium.
Taking sounds to be particular events of objects disturbing a surrounding
medium also furnishes a unified picture of what counts as a sound in cases
that pose problems for any such theory. Sounds do not occur at barriers
where transmission takes place. The phenomena accompanying constructive and destructive interference arise because of the spatial and temporal
relations among sound sources and because information about sounds is
transmitted by waves. In the next chapter, I develop an account according
to which hearing an echo is hearing with distortions of place and time. The
Event View entails no mysteries about sounds and sound experience. 25
25
Thanks to Gideon Rosen, Sean Kelly, Simon Keller, Jeffrey Speaks, David Lewis, and
Scott Jenkins for comments and discussion of these issues.
Chapter 2
Echoes
2.1
Introduction
Suppose you are at a fireworks display. You stand in an open field with a
single large brick building behind you. A colorful bomb’s recognizable boom
follows on the heels of its visual burst, but a moment later the boom’s echo
sounds at the brick wall behind the field. You have just heard a primary
sound followed by its echo.
I have argued that sounds are events. In particular, a sound is the
event of an object or interacting bodies disturbing a surrounding medium
in a wave-like manner. According to this Event View, the sound just is
the disturbance event. A theory of sound should provide an account of
echoes and echo perception. Echoes pose two potential problems for the
Event View. First, echoes appear to be distinct sounds located at reflecting
surfaces. But since the brick wall, for instance, merely reflects sound waves
and does not actively disturb the surrounding medium, the Event View
appears to have no sound to identify as the echo. Second, if the existence
of echoes shows that sounds themselves travel and can be re-encountered,
then sounds are not the events I have suggested.
I shall argue that echoes are not distinct from primary sounds, but also
that the case of echoes does not show that sounds travel. The account of
echoes and echo perception that I offer is that hearing an echo is hearing the
primary sound, but with distortion of place, time, and qualities—hearing an
echo is thus like seeing an object with a mirror. The experience of the echo
and of the primary sound seem to have distinct objects because we ordinarily
perceive events in their entirety only once. Sounds need not travel since that
by means of which we hear them does.
21
CHAPTER 2. ECHOES
2.2
22
The Event View of Sounds
Recall the motivations for the Event View. The received view of physicists and auditory scientists, which I have called the Wave View, is that
sounds are longitudinal pressure waves that propagate through a surrounding medium. My central argument against the Wave View also provides a
positive reason to recognize as the sound the particular event that I identify.
The argument rests on the phenomenological claim that sounds themselves,
and not just their sources, are perceived to be located. Ordinarily, they are
heard to be located at a distance and in a particular direction.
That sounds, not just sources, are heard to be located can be appreciated in several ways. First, sounds, if anything, are characterized by the
audible qualities of pitch, timbre, and loudness. Reflection upon experience
indicates that the bearers of audible qualities are themselves distally located. Second, we form perceptually-based beliefs concerning the locations
of material things and events on the basis of auditory experiences. Such
beliefs are made possible, in part, by impressions of the sounds things and
events produce. If information about the locations of things and events is
to be gleaned from hearing sounds, then either sounds must be heard to be
located roughly where those things and events are, or sounds must be heard
to come from such locations.
How are we to take talk of sounds’ being heard to “come from” a location? It might be that sounds are heard to come from a particular place
by being first heard at that place, and then being heard at intermediate
locations. This is not the case with ordinary hearing. Sounds are not heard
to travel through the air as scientists have taught us that waves do. Sounds
themselves are heard to be located. The sense in which sounds do “come
from” particular locations is that they have causal sources in those locations. If auditory experience is not systematically illusory with respect to
the perceived locations of sounds, and if auditorily-based beliefs about the
locations of things are possible, then the Wave View is false.
On the other hand, Robert Pasnau has recently defended what I have
called the Property View, according to which sounds are properties of the
objects ordinarily taken to be their sources. 1 Pasnau’s Property View fares
better with respect to the perceived locations of sounds, but fails to accommodate the fact that sounds are generated by their sources—that is, that
there exists a causal relation between a sound and its source.
1
Pasnau (1999) and (2000).
CHAPTER 2. ECHOES
23
It also entails that sounds can exist in a vacuum. I have argued that a
descendent of Berkeley’s Argument from Vacuums can be developed which
shows that a surrounding medium is a necessary condition on there being
a sound. The perceived sound of a tuning fork struck in air differs from
the perceived sound of the same tuning fork struck in water. In helium,
the sound seems different still. What is the sound of the tuning fork in a
vacuum? Since there is no analog for sound of white light’s or daylight’s
normative significance in revealing the surface properties of a thing—no
single medium is substantially better than a host of others at revealing the
way an object vibrates—there is no medium that has any claim to reveal
the “true sound” of the tuning fork. There is then no principled way to
decide what audible qualities the tuning fork has in the vacuum. Since the
qualities of the sound depend upon the medium in which it is made, and
since any decision about which audible qualities the tuning fork has in a
vacuum will be largely arbitrary, we are justified in concluding that the
tuning fork has no sound in the vacuum. The medium-relativity of audible
qualities indicates that a theory of sound should entail that sounds cannot
exist in a vacuum.
My Event View identifies the sound with the disturbing of the surrounding medium by the activities of an object or interacting bodies. Information
about sounds is transmitted by means of pressure waves, but the sound is
not the waves. The Event View captures the locatedness of sounds and
preserves the causal connection between sounds and their sources. It also
entails that a surrounding medium is necessary for there to be a sound.
I have provided accounts of wave transmission through barriers and of
constructive and destructive interference. 2 Now I will address echoes, a
special case of sound wave reflection.
2
When sound waves pass through barriers, no new sound occurs since only a preexisting wave disturbance is passed on. This is not a case of sound waves being created
by activities that do not amount to sound waves. During destructive interference, sounds
that are actually present in the environment are not heard because of the way information
about sounds is transmitted, i.e., by waves that undergo interference effects. Complete
destructive interference mimics the situation in which there is no sound at all (and therefore no sound waves). Constructive interference results in experience as of a sound that
is louder than any sound actually present. This, too, results from the properties of sound
waves. It is more intuitively palatable, however, that two sounds should present themselves
as a single sound of greater loudness.
CHAPTER 2. ECHOES
2.3
24
The Problem of Echoes
An account of echoes and echo perception should say what an echo is, explain
the distinctive phenomenology of echo experiences, and respect scientific
descriptions of the physical and perceptual processes involved.
When you hear the sound of the firework and its echo, certain features
of the experience are distinctive. First, you hear the echo after you hear
the primary sound.3 Next, you hear the primary sound to be located near
the explosion itself, but you hear the echo to be located near the reflective
brick wall. Though the echo appears to be a distinct sound, investigation
(perhaps mere visual awareness) reveals no sound source at the brick wall.
Nothing at the reflecting surface generates the sound. Finally, the echo and
primary sound ordinarily have similar qualities and duration. The degree
of distortion depends on the qualities of both the sound and the reflecting
surface.
Now, when the firework explodes, the surrounding air is disturbed, and
pressure waves travel outward toward you and toward the brick wall. When
the waves reach you, they contribute to your experience of the primary
sound. As waves reach the brick wall, an elastic collision takes place and
the wall re-directs the waves. These re-directed waves reach you and produce
the experience as of a second sound distinct from but somehow related to
the initial sound.
The trouble for the Event View is that a mere elastic collision occurs
at the brick wall. The brick wall does not introduce a disturbance into the
surrounding medium in virtue of its own activities. It simply gets in the
way of sound waves that are already present. The Event View appears to
have no disturbance event to identify as the echo.
If, however, sounds are particulars that persists and travel through the
medium, a simple resolution exists. Hearing an echo after a primary sound is
hearing the very same sound particular at two different stages of its continuous career. This, however, is incompatible with the Event View, according
to which sounds are events whose locations are stationary relative to their
3
This time gap is essential to enjoying the distinctive echo experience. When secondary
sound waves arrive at the ears less than about 50 ms after primary sound waves, the result
is an experience as of a single sound located between the two wave sources. Between
roughly 50 ms and two seconds, the result is experience as of a primary sound and an
echo. When the arrival delay is greater than about two seconds, experience is as of
two separate sounds that are entirely unrelated. I will focus on cases in which the echo
experience occurs and hope to generalize.
CHAPTER 2. ECHOES
25
sources. If the case of echoes shows that sounds themselves travel and can
be re-encountered, then sounds are not the events I have suggested.
2.4
The Solution
The echo just is the primary sound. According to the Event View, the echo
is the primary sound event perceived with distortion of place, time, and
qualities. The illusion is due to the behavior of sound waves and how sounds
are perceptually localized. Sound waves, which transmit information about
sounds, are the proximal causes of auditory experiences. Their direction
of onset determines the perceived location of a sound, and their rate of
travel results in the delayed echo experience. Filtering and dispersal at the
reflecting surface account for differences in the echo’s perceived qualitative
profile.
Hearing an echo, then, is hearing a primary sound. You hear the primary
sound, then after a short delay you hear the sound qua echo. What you hear
in each instance is the very same sound—the primary sound. The primary
sound is not an object-like particular that travels through space. It is an
event that occurs only once at the location of the sound generating event.
The traces of the primary sound—its sound waves—travel and encounter reflecting surfaces. When the waves return, an appropriately situated subject
will have an experience as of an echo, a seemingly distinct (though somehow
causally related) sound located in the direction of the reflecting surface. The
subject, however, hears only the original primary sound.
This account is analogous to a plausible treatment of seeing objects with
mirrors. Mirrors facilitate our seeing the very same objects and events that
occur in front of them, albeit with distortion of place (and perhaps qualities).
Likewise, reflecting surfaces allow us to hear the very sounds that occur in
front of them, albeit with distortion of place and time. But just as there
is no new object that you see when you look in a mirror, there is no new
sound that you hear at a reflective surface.
Hearing an echo after first hearing the primary sound is, on this account, an unobjectionable sort of re-encounter with the very same sound.
The sound event occurs once, say between t b and te . You experience it once
between t1 and t2 and again between t3 and t4 (both later than t2 ) because
the waves it creates return. The sound neither travels nor returns to you;
you experience the same distal event because of the way the event’s traces
travel. The situation is something like this. Suppose you hear the sound
of a firework. You then travel faster than the speed of the sound waves,
CHAPTER 2. ECHOES
26
overtake them, and halt. You then hear the sound again—it seems to be in
the same place it was before. We need not say that the sound travels, only
that the sound waves travel. Because information about sounds is transmitted through a medium via relatively slow waves, you are lucky enough to
experience the same sound event twice. The medium disturbance you hear
when you hear the sound for the second time is the very same disturbance
event you heard earlier. Echo perception is similar. A reflecting surface,
however, saves you the trouble of supersonic travel. You pay the price with
distortion of location.
Hearing an event that is past is thus like seeing an event that is past.
When you see a supernova from across the galaxy, you see that event as it
happened long ago. But you experience it to be present—to be taking place
now. So your experience includes a temporal illusion. Now, suppose there
were big mirrors in outer space. You could then see the very same earthly
event twice: once when it happens and once after its traces are reflected.
I could watch Game 7 of the 2001 World Series on November 4, 2001, and
then watch it again on November 4, 2002, in a mirror located one-half light
year away. If the mirror was big enough, I might even think there was a
game being played on a far-off planet that looked remarkably like Earth.
The case with echoes is a less exaggerated parallel.
Hearing an echo doesn’t involve such great distances. Still, the echo
experience and the primary sound experience seem not to have the same
object. If the echo is the same sound as the primary sound, why do we not
recognize them as such?4
The apparent distinctness is due to the nature of events and to how we
conceive of them in contrast to objects. If a primary sound and an echo
were the same object experienced at different times during one continuous
career, we would expect ordinary object recognition and re-identification to
occur, given their qualitative similarity. With objects we count on this sort
of recognition to ground the perceived continuity of the material world. 5
Events and time-taking particulars, however, are tied to a specific time and
place when they occur. Though Game 7 of the 2001 World Series might
4
Of course, we sometimes fail to recognize an object as one we have seen before, but
when the object is qualitatively similar on both occasions this requires special circumstances, such as great distances or the type of disorder mentioned in the footnote below.
Barring failures of recognitional capacities (including memory), we can usually be made
to recognize persisting objects.
5
Capgras syndrome is one form of delusional misidentification syndrome (DMS) in
which patients suddenly begin to believe that people and objects familiar to them have
been replaced by exact qualitative duplicates. This failure of perceived continuity is
notable and debilitating. See Breen, et al. (2000).
CHAPTER 2. ECHOES
27
have been located at any of various times and places, it it fact occurred
November 4, 2001, at Phoenix, Arizona. That very event cannot occur again
or elsewhere. And we implicitly recognize this: similar events experienced at
different times and places are taken to be distinct events. So, if we happen
to perceive the very same event over again, it should seem like a distinct
event.6 Since echo phenomenology arises when the very same event is heard
to be at a later time and different place, precisely what we should expect is
that the echo should seem distinct from the primary sound. The perceived
distinctness of echoes from primary sounds is predicted by the Event View.
So the Event View has the resources to count echoes as real sounds,
despite the absence of its characteristic disturbance event from the perceived
location of the echo. The account relies on securing the correct way to
conceive of echoes and echo perception. Upon doing so, we see that the
Event View has the right event on offer—the primary disturbance event.
2.5
Are Echoes Distinct Sounds?
Given that sounds are stationary relative to their sources, and that echoes
seem to be located at a distance from primary sounds, it is natural to say
that echoes are distinct from their primary sounds. The account I have
provided holds otherwise. What reasons have we to think that primary
sounds and echoes are not distinct sounds?
In a recent paper,7 Matthew Nudds has argued that if echoes are distinct
from primary sounds, then an echo cannot be distinguished from a qualitatively similar sound produced by a different source. We do distinguish
between the firework’s echo and a similar bang made by a firecracker tossed
out one of the brick building’s windows. This is supposed by Nudds not to
be possible if echoes are distinct from primary sounds.
This argument fails, so it cannot be used against the distinctness claim.
Suppose we accept that echoes are distinct sounds located at reflecting surfaces. Insofar as the primary sound, the echo, and the qualitatively similar
sound from a different source are all full-blown sounds, it is no objection
6
What about watching an instant replay? The same event (metaphorically) perceived
a second time does not seem distinct. But this is simply a matter of habituation—we are
used to seeing instant replays, which we know are representations of prior events. If you
have been asleep since the days of entirely live television, you might take a live picture
and its replay to be pictures of qualitatively similar events. Thus, we might become used
to thinking of echoes as primary sounds heard again with distortions of place, time, and
qualities.
7
Nudds (2001), p. 227.
CHAPTER 2. ECHOES
28
that we cannot distinguish the echo and the qualitatively similar sound simply on the basis of their intrinsic properties. Neither has intrinsic properties
that confer upon it a particular status—i.e., primary sound or echo—qua
sound and provide grounds for distinguishing it from the other. But we can
distinguish echoes from mere qualitatively similar sounds by their causal
relations. Echoes are sounds caused in part by sounds and sound generating
events that occur elsewhere. The firework’s echo is a sound at the brick wall
that has in its causal history the sound generating event and sound that
occur when the firework explodes. The mere qualitatively similar sound,
however, has as its cause a sound generating event closer to home, and lacks
the history of an echo. The sound of a firecracker that goes off near the
brick wall may be mistaken for the echo of the firework’s sound. But it lacks
the right sort of causal relation to the firework’s explosion and its sound. 8
8
What is “the right sort” of causal relation? Suppose the firecracker’s sound is causally
related to the firework’s sound, perhaps by a sound detector that activates a detonator.
Still arguing that the primary sound and the echo are distinct sounds, we say that the
echo is a sound that has in its causal history a sound generating event and sound located
elsewhere, where nothing intervenes but sound waves that propagate normally. Suppose
my striking a tuning fork causes, by no intervening means other than sound wave propagation, a second tuning fork to begin vibrating and sounding on its own. Does the condition
fail to distinguish between echoes and resonant sounds? In the case just described, the
second tuning fork’s sound is generated by the activities of that tuning fork, even though
those activities are caused by sound events that occur elsewhere. But an echo is arguably
not generated by the events that occur at its location. An echo is a sound that is entirely
generated elsewhere. The reflecting surface makes no contribution to the sound, where
this notion is fleshed out in terms of sound energy or a measure on the qualities of loudness
and pitch. The resonating object, however, contributes to the sound.
According to this proposal, when sound waves are reflected, a sound occurs. The sound
does not travel; the sound waves travel. The primary sound generating event causes the
echo, and only sound waves intervene. An echo is distinguishable from a qualitatively
similar sound since it is generated by events that occur elsewhere and has a sound in its
causal history. This is how to argue that primary sounds and echoes are distinct.
I do not find this satisfactory. It is a plausible principle that sound generating events
do not produce sounds at a distance. If the foregoing were correct, when sound waves
from a sound generating event encountered a reflecting surface, that sound generating
event would produce a new sound. Such “generation at a distance” might be explained in
terms of sound wave behavior, but suggests an ad hoc tailoring of the theory to meet the
phenomenology: why should the interaction between sound waves and a reflective surface
give rise to an entirely new sound?
Now, we should not take too seriously our pre-theoretical verdicts about the causal
structure of sound generating events and various types of sounds. It might be that a stable structure that acknowledges echoes as distinct sounds can be devised. The strategy,
as I indicate in the text, is not worth pursuing.
CHAPTER 2. ECHOES
29
Despite the phenomenological distinctness of primary sounds and echoes,
there are still four reasons that together suggest that echoes are not independent sounds that reside at reflecting surfaces.
First, awareness of an echo normally furnishes awareness of the event
that made the sound. Whether this awareness is direct or indirect derives
from whether sounds furnish direct or indirect awareness of such events, not
anything special about echoes. Both the sound of the firework’s blast and
its echo furnish awareness of the explosion, so if you only heard the echo
you would still be aware of the explosion. 9 Awareness of ordinary events by
means of echoes is not a deficient way to be auditorily aware of such events.
This suggests that the echo just is the explosion’s sound, not a qualitative
duplicate that furnishes, as it were, false or indirect awareness of earlier
events.
Second, we do not attribute dispositions to produce sounds with particular audible qualities to reflecting surfaces. Brick walls and canyons are
not disposed to make or have sounds when they reflect sound waves. Such
dispositions are attributed to the proper range of what we take to be sound
sources. But sounds normally seem to be caused, produced, or generated
roughly where they are perceived to be located. When a sound does not
seem to be located where there is a sound source, this is likely the result of
a physical-cum-perceptual process by which a sound is heard where there is
none.
Third, what occurs at the reflecting surface is not the introduction of a
wave disturbance into the surrounding medium. An elastic collision between
the surface and the medium occurs, causing the direction of wave propagation to change. The reflecting body passively re-directs the waves. Since
there is no new sound source—on either a Wave View, a Property View
or an Event View—it is reasonable to conclude that the echo is not a new
sound.
Finally, as mentioned in §2.4, an analogy with the visual case of seeing an
object with a mirror is compelling. Just as there is no distinct object located
at the mirror’s surface, there is no distinct sound located at the reflecting
surface. Illusion of place occurs when objects are seen with mirrors, and
9
Consider the following unusual phenomenon. A man is working on your house. When
you are in the right part of the house, and the wind is blowing in the right direction, you
cannot hear the sound of the hammering on the other side of the house. But, you can hear
the echo of the hammering as reflected off the exterior wall of a house down the street.
To hear this echo is still to be aware of the hammering. Thanks to Gideon Rosen for this
example.
CHAPTER 2. ECHOES
30
likewise, distortions of place and time occur when reflecting surfaces enable
us to hear the sounds that occur in front of them.
These four claims together suggest that echoes are not distinct sounds
that occur at reflecting surfaces. The account I have given explains the
apparent distinctness of primary sounds and echoes while maintaining that
primary sound and echo perception share a common external object.
2.6
Do Echoes Show That Sounds Are Not Events?
The observation that echoes are not distinct from primary sounds does not
lead immediately to the account of echoes and echo perception that I give in
§2.4. Suppose a sound is a particular that persists over time and travels like
an ordinary material object. An echo is then a sound that has existed for
some time and that has rebounded from a surface. Hearing a primary sound
and its echo would then be hearing the very same persisting particular at
different stages during its continuous career. 10 If the case of echoes forces
such a conception upon us, then sounds are not events and sounds are not
stationary relative to their sources, so the Event View is false.
2.6.1
The Argument from Echoes
Matthew Nudds has recently picked up this line of thought and offered the
following argument against the claim that sounds are events.
One of Newton’s minor triumphs in the Principia was a derivation of the velocity of sound. To test his derivation he measured
the time for an echo to return from the end of a colonnade in
Neville’s Court of Trinity College. Lacking anything resembling a
stop watch, he adjusted a pendulum to swing in rhythm with the
echoes of successively made sounds (Westfall (1980), pp. 455–
456). Newton used the pendulum to measure the time it took for
a sound to travel from its source down the colonnade to a wall
and then back again; he heard the particular sound that he had
produced a moment earlier reflected back to him. Here we have
a simple example of a sound existing even after the event which
produced it ceases (we can suppose) to exist, and which moves
independently of whatever produced it. It is also an example of a
10
Note that this conception fits nicely with the Wave View, though someone who endorses it need not be a Wave theorist. You might think that sounds travel through space
without identifying the sound with the waves.
CHAPTER 2. ECHOES
31
single sound being heard more than once: Newton re-encounters
a particular sound, as he must do if he is to time its journey
up and down the colonnade. Sounds, then, are particulars. Normally we think of events as things that, unlike objects, cannot be
re-encountered. The fact that we can re-encounter sounds suggests that they are perhaps best thought of as kinds of objects,
rather than as events; either way, not as properties. 11
What I shall call the Argument from Echoes is this:
1. Newton measured the speed of a sound by measuring the time it took
for the sound to travel down a colonnade and back.
2. Hearing an echo is re-encountering a particular sound.
3. Events, unlike objects, cannot be re-encountered.
4. Therefore, sounds are object-like particulars and not events.
2.6.2
Sounds Do Not Travel
The account just sketched is incompatible with my conception of sounds
and echoes. According to the Event View, sound waves, but not sounds,
travel independently of the objects and events that generate them. This
view is meant to capture the central phenomenological fact about locational
hearing—that sounds are located at a distance and in a particular direction.
Echoes, too, seem to be located distally near reflective surfaces.
Given that we do not hear sounds to move as sound waves do, we want
a non-question-begging reason to believe (1), according to which sounds
themselves travel. Consider the following two alternatives to (1).
1*. Newton measured the speed of sound waves by measuring the time it
took for him to hear an echo after hearing the primary sound.
1**. Newton measured the speed of sound waves, but not of a sound by
measuring the time it took for him to hear an echo after hearing the
primary sound.
Though (1**) is a strong replacement for (1), (1*) is uncontroversial. But (2)
does not follow from even (1*). Hearing an echo may not be re-encountering
the same sound at a later stage of its career, even if we owe the episodes
11
Nudds (2001), p. 221–222.
CHAPTER 2. ECHOES
32
of hearing to the same sound waves. The conclusion that sounds are not
events does not follow from the argument reconstructed with (1*).
It is certainly widely accepted that sounds travel. But why? In contrast
to (1*), (1) is not obvious. By now the following theme is well-rehearsed:
sounds are usually heard to travel only when their sources do. If sounds
seemed to you to emerge from their sources and to speed through the air
toward your head, we would send you to a specialist.
Maybe echoes are special. Perhaps the Argument from Echoes reflects
the fact that hearing a sound followed by its echo forms the basis of a strong
intuitive case for the belief that sounds travel. After all, the argument is
not meant to pre-judge the theoretical question of what a sound is. Rather,
it aims to enlist conceptions about sounds and echoes that are implicit in
ordinary beliefs to show that sounds are not events. Indeed, the perceptual
facts in the case of echoes ground a natural inference to the effect that sounds
travel. But the transition from experience to belief is not a matter of simply
lending credence to that which is already apparent in experience. Believing
that sounds travel requires more than just accepting the way things appear
to you. Take a sound, s. That s travels independently of its source is not
ordinarily part of the content of an auditory experience, and it does not
arise as part of the content of the experience when a sound is followed by
an echo.12 So the case of echoes must present further reasons that make the
belief that sounds travel intuitive.
One preliminary. We do assume that each sound is generated by some
event that is not a sound. It appears to be a working “assumption” of the
auditory perceptual system that each sound must be produced by some event
in the environment.13 Furthermore, it is an introspectible part of experience
when hearing a sound that the sound is a sound of something going on in
the surroundings. The belief is plausible since empirical evidence repeatedly
confirms that sounds are caused by “happenings” that take place among
12
One might think that this observation is all that is required to show that sounds do
not travel, if one thinks that a sound cannot have properties beyond those it is experienced
to have. This is too easy. I leave it open that sounds can have properties we are unable to
detect with our ears alone, and that there can be sounds we are entirely unable to hear.
Sounds may indeed move through space; whether or not they do will depend on what the
correct theory of sound is. This is not to say that our goal should not be a theory that
coheres with the contents of experience—sounds are, after all, among the things we hear.
We would like it if perception served as a reliable guide to reality, but whether it does
with respect to sounds is a matter to be decided by a variety of concerns.
13
See Blauert (1997), especially Chapter 2, “Spatial Hearing with One Sound Source”,
and Chapter 3, “Spatial Hearing with Multiple Sound Sources in Enclosed Spaces”.
CHAPTER 2. ECHOES
33
material things—we are hard-pressed to find sounds for which investigation
reveals no source events.
Now the fact that echoes strike us as causally related to events that occur
elsewhere—in fact, as generated by distal events—establishes a connection
to what we take to be the source of the primary sound. The echo of the
firework’s blast strikes us as being connected to the explosion that generates
the primary sound. Though the primary sound and the echo seem distinct,
they appear to share a common causal history.
But since no source appears to exist where the echo is heard to be, from
(i) the qualitative similarity of primary sound and echo; (ii) the time delay
between the experience of primary sound and of echo; and (iii) the shared
causal history of the primary sound and echo, it is natural to conclude that
what we think of as the primary sound and the echo are the very same sound.
Once we overcome the perceived distinctness and identify the primary sound
and the echo in thought, two facts—that the primary sound is heard to be
near the source at one time, and that the echo is heard to be at some distance
from the source slightly later—may encourage us to believe that the sound
has travelled.
Note that forming this belief requires us to ignore or implicitly reject the
possibility that two different sounds (with different locations) are generated
by the same event.14 This itself requires accepting either that a sound
cannot be generated at a distance from its source or that each sound has a
unique generating event. The latter is somewhat difficult to motivate, but
the former is quite plausible.
Even after accepting all of that, you are only entitled to believe that
the sound travelled from the perceived location of the primary sound to the
perceived location of the echo. Nothing about the naı̈ve perceptually-based
way of thinking about the situation allows you to go beyond this to the
belief that sounds travel as waves do, i.e., that the sound travelled from its
source to the reflecting surface and back to you. The case of echoes adds
little to the case for (1).
The force of (1) must come from one of two sources: an appeal to science
or an inference that fills the gap in the above line of thought. It is common
knowledge that information about sounds is transmitted by pressure waves
in a medium. To accept that sounds travel because sound waves travel,
however, is to complacently accept a caricature of scientific doctrine. 15 Part
14
I will assume that my account of §2.4, in which hearing an echo involves illusions of
place and time, does not strike us intuitively.
15
Disagreement about what a sound is exists even in the scientific community. Frequently researchers analyze and divide the terrain, and avoid commitment on the more
CHAPTER 2. ECHOES
34
of the business of science is to explain by way of discovering causal connections. Though sounds cause auditory experiences, and pressure waves cause
auditory experiences, the identification is unwarranted. To conclude, from
‘A causes C’ and ‘B causes C’, that ‘A = B’, is as fallacious as concluding,
from ‘guns kill people’ and ‘people kill people’, that ‘guns are people’. Given
that sounds and sound waves differ in significant causal and perceptible respects, it begs the question to conclude on the basis of science that sounds
travel.
Consider the following two inferences that attempt to bridge the gap
between sound sources and perceivers.
i. The sound was generated over there; I am here; since I heard the sound
it must have travelled to reach me.
ii. I heard the sound; then I travelled faster than the speed of sound
waves, stopped, and heard it again; so, the sound must have travelled.
But since the sound itself is perceived in every case to be stationary and
distant, these inferences are either question-begging or fallacious. It begs the
question to assume that the sound is identical with the waves, and therefore
travels. It is fallacious to conclude that since distance separates perceivers
from sound generating events, sounds must travel. Sounds need not travel
since that by means of which perceivers hear them—sound waves—can move
independently of sounds.
Premise (1) of the Argument from Echoes is seriously undermotivated.
2.6.3
Re-encounters
I have tried to undermine the claim that sounds travel independently of
their sources in part because the conception of sounds that it underwrites
is unattractive.
That hearing an echo after hearing its primary sound is re-encountering
the same persisting sound particular finds little support in perceptual experience. As I pointed out in §2.4, primary sounds and their echoes seem to be
distinct. A single object perceived at different times does not. Hearing an
echo is unlike re-encountering a person you have met before, and it is unlike
general question. To the extent that a commitment is made on the issue of identification,
physicists most frequently speak of sounds as waves. But there is a tendency among perceptual researchers to speak of distally located acoustic events and sounds in addition to
sound waves and auditory experiences. See Bregman (1990), Luce (1993), Carlile (1996),
Blauert (1997), and Gelfand (1998), for illustrations of this contrast.
CHAPTER 2. ECHOES
35
glimpsing someone carrying home the vase you saw earlier in a store window, even though the echo has an equally rich qualitative signature. Echo
perception does not bear the marks of object-recognition and identification
that characterize the experience of material objects and continuants with
relatively stable qualities. We find it reasonable to count echoes and primary sounds as distinct before doing philosophy. But to count earlier and
later states of persisting things as distinct objects is counterintuitive. 16
Matters get worse. Given a plausible thesis concerning sounds, accepting
an interpretation of (2) that makes the Argument from Echoes valid leads
to trouble.
First Thesis Sounds are extended in time.
Just as concrete objects occupy space, sounds occupy time. Each sound has
a duration: it begins at one time; it ends at another (if it ends at all); it
may involve a great deal of qualitative change. We arrive at the First Thesis
by way of two lemmas.
Lemma One Sounds are not, or certainly do not seem, wholly present at
each moment at which they exist.
Compare this with objects. It is plausible that all that is required to be a
particular object can be present at a moment, and thus, that a particular
object can be wholly present at each moment at which it exists. At any
particular moment, however, only a portion—a temporal part—of a sound
is present. That is, rather than a sound in its entirety, only a part corresponding to a property profile at a time is present at each moment during
which the sound exists.
Lemma Two Having a qualitative profile over time is central to the identity of a particular sound.
Consider a spoken word or a particular squawk from a raven. Each has
qualitatively different stages that constitute it, and sounds with different
profiles over time are different sounds.
The two lemmas and the First Thesis are independently plausible statements that express judgements grounded by our intuitive conception of
sounds.
16
In the debate about whether each material object is a series of suitably related temporal
parts or a single thing that undergoes changes in properties through time, that is, whether
things perdure or endure, it is the latter endurantist view that appears natural to common
sense and perceptual experience (see, e.g., Thompson (1983), who says of the metaphysic
of temporal parts: “It seems to me a crazy metaphysic—obviously false,” p. 210). The
perdurantist must motivate the view with philosophical considerations.
CHAPTER 2. ECHOES
36
Now the Argument from Echoes relies on the claim that events are not
the sorts of things that we can re-encounter. We need a working conception
of what it is to encounter something in the relevant sense. I will continue to
assume that to encounter something is just to enjoy perceptual awareness of
it. So to the extent that we can speak meaningfully about encountering an
event, nothing more is required than to be in a suitable relation of perceptual
awareness to it. An alternate sense of ‘encounter’ means roughly the same
as ‘bump into’. This sense seems appropriate if sounds are the travelling
causes of auditory experiences, as the Argument from Echoes would have
it, but applies paradigmatically to objects and not to events. Since the
Argument from Echoes employs the fact that sounds can be re-encountered
to show that they are not events, this must not be the sense of ‘encounter’
in question. Otherwise, to show that we bump into sounds would suffice
to show that they are not events. But the argument seems to be: We can
certainly encounter events, we just cannot re-encounter them. So, if the
argument turns on something peculiar about echoes, ‘encounter’ must mean
something like ‘perceive’ or ‘enjoy perceptual acquaintance with’. 17 The
claim must be that while we can re-encounter sounds, we do not normally
think that we can re-encounter, that is, re-perceive, events.
Sharpening the sense of ‘re-encounter’ in this way is not enough to make
the Argument from Echoes valid. Consider the following thesis.
Second Thesis, Weak Version We sometimes re-encounter a particular
sound at a later stage during its completion.
Suppose I wake up to hear the loud, high-pitched beginning of the local
emergency siren’s wail. I then descend into the silent basement for two
minutes, after which I emerge to hear the nearly completed sound’s fading
low-pitched moan. Each time I experience a different part of the sound. So,
we can re-encounter a particular sound by encountering different parts of the
same temporally extended sound. Events, however, are often re-encountered
in this way, so the Weak Version of the Second Thesis is consistent with
sounds’ being events. What the Argument from Echoes needs in order to
show that sounds are not events is that we can re-encounter the very same
parts of a particular sound on separate occasions. From this it follows that if
we can encounter all of the parts of a sound on each of two different occasions,
we are capable of re-encountering the sound in its entirety. The import of
(2) must be the following strengthened version of the Second Thesis.
17
To make the notion line up with ordinary usage might require adding some proximity
requirement. Perceptual acquaintance suffices for the arguments that follow.
CHAPTER 2. ECHOES
37
Second Thesis, Strong Version We sometimes re-encounter a particular
sound in its entirety.
The Strong Second Thesis is the one intended to ground the argument
that sounds are not events. We do not ordinarily think of events such as
particular closings of doors and birthday parties as things that can be reencountered in their entirety since they occur at specific times and places.
Halloween is a different event each year that belongs to a class of like
events that each occur on some October 31. While we take for granted reencounters with persisting objects, to re-encounter a particular Halloween
would take a trick, such as time-travel.
In my account of echo perception, the reflection of sound waves from
a surface serves as the occasion for such a trick. You re-perceive the primary sound event because its traces rebound and return. So for the Argument from Echoes to be valid, the import of (2) must be that Newton
re-encountered, without any tricks and in its entirety, the very same sound
particular.
The trouble comes when we accept the First Thesis with its lemmas while
accepting (1) and a version of (2) that implies the Strong Second Thesis.
From the Strong Second Thesis, a particular sound can [without tricks]
be encountered in its entirety on two separate occasions. From the First
Thesis, each sound has duration—it begins and ends. Now consider hearing
a particular sound and its echo. It is an experiential fact that between t 1
and t2 , call this interval tp , we experience the primary sound. Likewise,
the echo is heard during some later interval te , which begins at t3 and ends
at t4 . By (2) and the Strong Second Thesis, the sound heard at t e is the
same (entire) particular sound heard at t p . Now, in light of (1), the sound
must travel and exist continuously between t p and te . It follows from this
that the re-encountered sound is perceived to begin and end multiple times
during which it continuously exists. Since something cannot continue to
exist after it has ceased to be, either sound duration perception—perceiving
that sounds begin and end—is illusory and the grounds for the First Thesis
are undermined, or the claim that sounds are persisting particulars that can
be re-encountered in their entirety is false.
2.6.4
Some Unsavory Consequences
Suppose (1), (2), and the Strong Second Thesis are correct. A proponent
might come to their defense as follows.
CHAPTER 2. ECHOES
38
When you perceive a sound to begin and end, you perceive the
sound’s spatial boundaries, its “front” and “back”, as it travels
past. We mistake the beginning of our experience of the sound
for the temporal beginning of the sound, and the end of our experience for the temporal end of the sound. The sound, properly
speaking, begins and ends only in the spatial sense. It has a
front and a rear, the experiences of which lead us to believe that
the sound begins to exist and then ceases. By experiencing the
spatial boundaries of a sound multiple times, the re-encountered
sound can seem to begin and end entirely on separate occasions.
The explanation of our perceptually-based confidence in the First Thesis
adverts to encounters with the spatial boundaries of sounds as they travel
past. These encounters correspond to perceived beginnings and endings of
sounds, while only our experience of the sound can properly be said to begin
and end.
From this conception, several unsavory consequences follow which together suggest that we are on the wrong track if our goal is to provide a
theory of the objects of auditory experience that is phenomenologically apt.
These consequences draw attention to desiderata that an alternative might
satisfy.
First, either it paradoxically implies that sound generating events, such
as firework explosions and door closings—events that cause sounds—are
not events, or it implies that we enjoy veridical perceptual awareness of
the durations of sound generating events by way of illusory awareness of
the durations of sounds. When we perceive sounds we are aware of the
events that bring them about. To hear the sound of the firework is to be
perceptually aware of the event that caused the sound—it is to be aware
that something has exploded; to hear the sound of a door closing is to
be aware that a door is closing. Since even on the conception of a sound in
question, the primary sound and the echo share a common sound generating
event, we perceive the very same sound generating event when we encounter
the sound and the echo. If to perceive an event is all that is required to
encounter that event, we re-encounter the sound generating event when we
hear an echo after hearing its primary sound. Since according to (4) we do
not re-encounter events in their entirety, the case of echoes shows that sound
generating events are not events!
That is absurd. Suppose we say that auditory perceptual awareness
of sound generating events is indirect and that we can re-encounter events
indirectly by directly perceiving something else, e.g., in this case a sound
CHAPTER 2. ECHOES
39
and an echo.18 When we perceive something to begin and end by means
of audition, our awareness is as of directly perceiving a sound to begin and
end. We are supposing, however, that this awareness is illusory—that we
only directly perceive the spatial boundaries of a sound that lacks duration
of the sort we attribute to it. How then are we indirectly aware of the
duration of the sound generating event?
Our indirect awareness of the duration of the sound generating event is
supposed to occur in virtue of our direct awareness of some aspect of the
sound itself.19 But it is strange to say that we indirectly perceive something
(the duration of a sound generating event) by way of directly perceiving
something else (the spatial boundaries of a sound) of which we have no
introspectible awareness. It is stranger yet to say that we indirectly but
veridically perceive something (the duration of a sound generating event)
by way of an illusion of direct perception (of the duration of a sound).
If veridical and introspectible awareness is required of that which is directly perceived in order for it to furnish veridical indirect awareness, then
the appeal to indirect perception (of the sound generating event and its
duration) does not avoid the absurd conclusion. The requirement may be
rejected if a more permissive attitude is taken toward the standards that
must be met for perceptual awareness, but even in that case a considerable
burden must be shouldered. The following must be accepted.
that sounds do not have the durations we think they have;
that it is possible to re-encounter, in the sense of ‘indirectly
perceive’, events; and
that it is possible to veridically perceive the durations of sound
generating events by way of the illusion of sound duration.
Suppose that the First Thesis must be rejected, and that perceiving
a sound involves perceiving a set of adjacent qualities that move through
space. When you hear a continuous scale played on an oboe, you experience
one note after another as they reach and move past you. What begins and
ceases is the stream of qualities that passes you and continues through the
medium. But then perceiving the qualities of sounds is also shot through
with illusion. Qualities which are at your ears, on this proposal, are heard to
be elsewhere. Each of the oboe’s notes is perceived as a stationary complex
18
So also we may watch the dousing of the fire, then perceive it again, indirectly, by
way of the resulting puff of smoke.
19
For it seems patently false—a violation of the transparency of auditory perception—
that we indirectly perceive the duration of a sound generating event by way of directly
perceiving the duration of our auditory experience.
CHAPTER 2. ECHOES
40
of audible qualities located in the vicinity of the oboe. If the sound moves
through the air, then this proposal is akin to the claim that colors travel
through space as light does though we see them to be located at surfaces.
Though sounds are not perceived as qualities of surfaces, they are perceived
as distally located. The forms of projective illusion attributed to perception
are similar.20 Thus, the second unsavory consequence of this view is that the
qualities of sounds are mistakenly perceived as located near their sources.
Third, it follows that the structure of our perceptual judgements and the
resulting conception of how sounds exist unperceived are faulty. We think
that sounds can exist unperceived in the following sense. When a car passes
me and goes out of range, I cannot hear its sound. The sound still exists,
but I cannot perceive it given my location and auditory capabilities. We
do not ordinarily think that a sound exists unperceived in the sense that it
exists after we have heard it and after the sounding has stopped. But on the
proposal being entertained, sounds exist long after the events that produce
them do, and, indeed, continue to exist well after we hear them. So, even
though you think the sound of a spoken word no longer exists after you hear
it, it goes on existing for as long as the corresponding waves travel through
the medium.
2.6.5
Conclusion
It is more difficult to motivate the claim that sounds travel than you would
expect from the way we sometimes talk. Echoes offer little to further the
case. The claim that sounds travel also underwrites a conception of sounds
and echoes that conflicts with central elements of the way we take sounds
to be. Since the Argument from Echoes assumes that sounds are persisting
particulars that travel and can be re-encountered, it fails to show that sounds
are not events.
2.7
Is the Illusion Tolerable?
The Event theorist’s account of echo perception posits spatial, temporal,
and qualitative illusions. Why, since I took the Wave View to task for its
systematic location illusion, is this not objectionable? One might even think
20
Note that this is not the same kind of projective illusion which is supposed to occur
when mental properties are experienced as properties of external objects, which some
theorists (e.g., Boghossian and Velleman (1989) and (1991)) believe occurs during color
perception.
CHAPTER 2. ECHOES
41
that the Wave View fares better in the case of echoes, since it only posits a
location illusion and an explicable duration illusion.
Illusions, per se, are not reasons for objection. But we are interested
in perception for what it can potentially reveal to us about the world. To
the extent that we take perception to be a reliable guide to certain aspects
of the world, we have an interest in reducing the amount of illusion we
attribute to perceptual experience. But illusions can inform us about the
mechanisms involved in perception and about aspects of the world which
we cannot directly observe. So we also have an interest in discovering the
illusions we actually fall prey to. If, however, an account proposes an illusion
whose spell we have independent reason to believe we are not under, all else
equal we should prefer an alternative which does not posit that illusion.
I have suggested that we have no reason to think that we are under the
illusions posited by the Wave View, and also that in the case of echoes there
are compelling reasons to believe that we do fall prey to the illusions posited
by the Event View. The Event View’s illusions have a signficantly different
status from the Wave View’s.
According to the account I have given of echoes and echo perception, the
illusions arise as a special case. While in ordinary sound experience we hear
sounds for the most part as they are, the experience of an echo occurs only
in quite special circumstances. The illusions posited by the Wave View are
systematic and pervasive.
The Event theorist’s illusions are explicable. Quality illusions occur because filtering and scattering that occur at reflecting surfaces distort information contained in sound waves. Illusions of place and time occur because
sound wave reflection mimics the situation in which a sound source exists at
the reflection site. So there are external states of affairs which explain why
experience attributes the properties it does when the illusion occurs. Because of this, the illusions in the case of echo perception are also predictable
once the mechanisms of ordinary sound perception are known.
Finally, the illusions that occur during echo perception are analogous to
illusions that occur in the visual case which we find interesting but unproblematic. Hearing the firework’s echo to be at the brick wall is like facing a
large mirror and thinking there is a piano in a room ahead of you. Hearing
the echo to occur after the primary sound is like seeing a supernova from
across the galaxy.21
21
You might worry that if the Event View is correct, the time-gap that occurs even in
ordinary sound perception—because sound waves travel relatively slowly—is problematic.
But it is simply an exaggeration of the time-gap that occurs in vision, and goes undetected
CHAPTER 2. ECHOES
2.8
42
Concluding Remarks
I have provided an account of echoes and echo perception that is consistent
with the Event View of sounds, according to which an echo just is a primary sound whose perception involves distortion of place, time, and perhaps
qualities. Echoes are not distinct from primary sounds. The impression of
distinctness occurs because when we immediately perceive happenings that
are past we perceive them as present, and because without special tricks we
perceive events in their entirety only once.
Once we recognize that echoes are not distinct from their primary sounds,
we need not be forced into the view that sounds are object-like particulars
which persist and travel. This view rests upon shaky foundations and has
consequences which force us to reject claims central to our perceptual beliefs
about sounds. Without that view the Argument from Echoes does not
establish the conclusion that sounds are not events. So we should prefer
the Event View, according to which a sound is the event of an object or
interacting bodies disturbing a surrounding medium in a wave-like manner. 22
unless somewhat large distances are involved. Note that Armstrong (1961) confusedly
thought sounds might not pose a time-gap problem.
In the case of a star, it may be questioned whether our immediate perception really involves any temporal illusion. It may be suggested that what
we immediately perceive is not the star, but a present happening, causally
connected with the extinction of the star many years ago. The star sends a
message to us, as it were, and we immediately perceive the message, not the
star. Now this suggestion may be correct in the case of a sound [fn. This
was pointed out to me by Dr. A.C. Jackson]. There seems to be some force
in thinking of sound as actually spreading out from its source, like a balloon
rapidly inflating. (And here I am not speaking of the sound-waves.) So when
two people ‘hear the same sound’ it may be argued with some plausibility
that they immediately hear two different things, because they are in different
positions (pp. 147–148).
Armstrong goes on to reject the analogy in the case of a star, since the only immediate
object of sight is “the star itself” and not light waves. He concludes that we sometimes
immediately perceive past happenings, though they seem present. I find it implausible
that a sound is like a rapidly inflating balloon, and that two people cannot hear the same
sound. So I reject Armstrong’s characterization of sound and accept that hearing past
sounds is like seeing past events. Both involve a time-gap and a temporal illusion.
22
Thanks to audiences at Princeton University, Florida State University, U.C. Santa
Barbara, and University of St. Andrews for helpful discussion.
Chapter 3
Audible Qualities
3.1
Introduction
Sounds are events in which objects or interacting bodies disturb a surrounding medium. Particular sounds have pitch, timbre, and loudness. A flute’s
notes are higher pitched than a tuba’s; middle C played on a piano has
a character different from middle C played on a trumpet; jet planes make
louder sounds than tractors. Given how audition works, physics has taught
us that frequency, wave shape, and intensity determine which pitch, timbre,
and loudness a sound auditorily appears to have.
A theory of sounds must address the audible qualities. What exactly
are pitch, timbre, and loudness, and how are they related to the physical
properties of frequency, wave shape, and intensity? Given psychophysical
evidence which indicates that there is neither a linear nor a logarithmic
function from the frequency of a sound to the pitch it is experienced to
have, auditory researchers have adopted the view that pitch is a subjective or
psychological property.1 That is, pitches strictly only belong to experiences.
They draw similar conclusions in the cases of loudness and timbre. I shall
suggest, however, that pitch, timbre, and loudness—though not identical
with frequency, spectral composition, and intensity—can be identified with
physical properties of sounds themselves. The Standard (Subjectivist) View
of the audible qualities does not follow from the failures of simple forms of
physicalism about pitch, timbre, and loudness; indeed, a promising physical
candidate for pitch can be extracted from recent work on pitch perception.
My focus primarily will be on pitch and problems that arise in saying what
pitch is, but I shall suggest that the account can be extended to timbre
1
See §3.3 and §3.4 for a full discussion.
43
CHAPTER 3. AUDIBLE QUALITIES
44
and loudness. According to this Alternative (Physicalist) View, the audible
qualities lack the independent scientific interest attached to those of the
Simple Views; they are, however, of interest from an anthropocentric point
of view.
The alternative holds that pitch, timbre, and loudness are properties that
sounds have in addition to frequency and intensity. Since pitch, timbre, and
loudness can be understood in terms of frequency and intensity, and since
frequency and intensity are properties ordinarily ascribed to waves, pitch,
timbre, and loudness appear to be properties of waves, not sound events as
I have construed them. I shall argue, however, that frequency and intensity
can be ascribed to sounds conceived as events. Thus, sound events as I have
characterized them have pitch, timbre, and loudness in addition to frequency
and intensity. The Event View of sounds is therefore capable of providing
an account of the audible qualities according to which they are objective,
physical properties of sounds.
3.2
3.2.1
Simple Views of Pitch
The Very Simple View
The Very Simple View of pitch can be extracted from the story we learned
about sounds in primary school. We were taught that the pitch of a sound is
the frequency of a pressure wave that travels through a medium such as air,
water, or helium.2 Whatever doubts we have about the natures of colors,
accepting the Very Simple View makes us happy to say that pitches reside
in the world beyond our minds. That is, that the quality we discern when
we hear pitch is just the property of having some frequency. When we tune
a trombone, one way to get its pitch right is by adjusting the frequency of
an F with an electronic tuner.
This Very Simple View accounts for salient aspects of the experience of
pitch. It explains the linear ordering of pitches: as frequency increases, so
does perceived pitch. A natural account of the musical relations also follows
from the Very Simple View of pitch. Small whole-number frequency ratios
form the bases of the octave (1:2), fifth (2:3), fourth (3:4), et al. One gets
the palpable sense that the natures of such audible relations are revealed by
this discovery.
2
Frequency is just the number of cycles per second, measured in Hertz (Hz).
CHAPTER 3. AUDIBLE QUALITIES
3.2.2
45
The Simple View
The Very Simple View is far too simple. The identification of pitch with
frequency approaches adequacy for pure or sinusoidal tones—sounds whose
accompanying waves are constituted by sinusoidal pressure variations. 3 (See
Figure 3.1: Sinusoidal Motion). For sinusoidal tones, increasing frequency
increases perceived pitch, and decreasing frequency decreases perceived pitch.
Pure sinusoidal tones are rarely encountered in nature, and many complex sounds that are not themselves sinusoids are perceived to have pitch.
Fourier showed that any complex sound which is not itself a sinusoid can be
analyzed in terms of sinusoids of various frequencies in differing proportions.
Fourier’s Theorem applies in virtue of the additive principles of wave-like
motion. So we can characterize any sound by citing the (maximum or rootmean-square4 ) amplitude or intensity of each of its sinusoidal constituents.
(See Figure 3.2: Fourier Composition of a Square Wave).
The constitutive role of individual sinusoids can be taken quite literally:
the phenomenon of sympathetic resonance demonstrates that complex tones
are made up of sinusoids of different frequencies. A pure sinusoidal tone from
one tuning fork causes a second tuning fork with the same characteristic frequency to begin sounding in virtue of its own induced sinusoidal motion.
A complex tone from a human voice, one of whose Fourier-predicted components shares a tuning fork’s characteristic frequency, induces that tuning
fork to resonate just as a sinusoidal tone of that frequency does. But a complex sound without a Fourier component at the tuning fork’s characteristic
frequency induces at best a weakened resonant sounding. The best explanation of sympathetic resonance is that a tuning fork’s resonant sounding is
caused by a sinusoidal constituent which is genuinely present in the complex
sound.
Pure sinusoidal tones are a variety of periodic sound. That is, they
repeat a certain motion regularly over any given interval. Some complex
sounds are also periodic. As a matter of empirical fact, just the periodic
sounds have pitch. Though periodic tones may occur within more “messy”
or “noisy” sources and thus cause pitch experiences, and sounds that are
not exactly periodic may appear to have pitch, pitched tones are generally
periodic sounds. If a complex signal is periodic and repeats at regular in3
I shall argue in §3.3, however, that the Very Simple View fails even for pure sinusoidal
tones.
4
The root-mean-square amplitude is a measure of the average magnitude of a varying
instantaneous amplitude. It is given by the square root of the mean of the squared
instantaneous amplitudes. For a sinusoid, the root-mean-square value is 0.707 times the
peak amplitude. Gelfand (1998), pp. 19–21.
CHAPTER 3. AUDIBLE QUALITIES
46
tervals, the frequency of each of its components (or partials) must have an
integer-multiple relationship to a fundamental frequency. The fundamental
frequency of a complex sound is the greatest common whole-number factor
of the sound’s constitutive frequencies. Thus, the fundamental frequency of
the complex (square) tone in Figure 3.2 is 1000 Hz.
Helmholtz demonstrated that the fundamental frequency of a complex
periodic tone determines its perceived pitch. 5 So the Simple View of pitch
is that the pitch of a sound is identical with its fundamental frequency; that
is, the pitch of a periodic sound is the greatest whole-number frequency by
which the frequency of each of its sinusoidal components is divisible without
remainder. According to this formulation a sinusoidal component at the
fundamental frequency may or may not actually be present in the complex
sound. The phenomenon of the “missing fundamental” demonstrates that
the fundamental frequency component need not be present for a sound to
have the same pitch as a sinusoid of that frequency. A tone with constituents
at 1200 Hz, 1300 Hz, and 1400 Hz has the same perceived pitch as a 100 Hz
sinusoid.6 Telephones, which filter low frequencies, illustrate the principle.
One hears a man’s voice to have the same pitch in person and over the
telephone, though the fundamental is absent from the telephone speaker’s
sound.7
The Simple View identifies pitch with fundamental frequency, which depends upon the frequencies of a sound’s sinusoidal constituents. It follows
that pure sinusoidal sounds and complex sounds such as those that exhibit
sawtooth or square wave patterns can share the same pitch in virtue of
sharing a fundamental frequency. The Simple View identifies pitches with
5
Helmholtz (1954).
See Helmholtz (1954) and Schouten (1940).
7
Terhardt, e.g., (1974) and (1979), has argued that this simple conception is inadequate
to account for all types of pitch phenomena. He has distinguished between spectral pitch,
which is pitch heard in virtue of constituent frequencies that are actually present in the
sound, and virtual pitch, which is heard despite the absence of a spectral constituent.
Terhardt has pointed out that a view analogous to the Simple View fails to account for
the fact that a single complex sound is often heard to have multiple pitches, determined
by both spectral and virtual pitches. He has also noted that both types of pitch may
be heard simultaneously, even at the same frequency! Terhardt’s conception depends,
however, upon individual pitches, spectral and virtual, being determined by constitutive
frequencies that are present in the sound. Indeed, individual spectral and virtual pitches
are identified with particular frequencies. So the Simple View that pitch is fundamental
frequency may not accommodate all salient pitch phenomena, but it is sufficient for my
purposes that once determined, pitches are identifiable with particular frequencies, and
that pitch determination is a matter that depends entirely upon which frequencies are
present in a complex sound.
6
CHAPTER 3. AUDIBLE QUALITIES
47
particular frequencies, and thus preserves the Very Simple View’s influential
account of the musical relations.
It has the further advantage of being supported by the physiology of auditory perception. The basilar membrane, located within the cochlea, is like
a long trapezoidal ribbon, different parts of which most actively resonate
in sympathy with a particular sinusoidal frequency. The basilar membrane
thus performs a sort of Fourier analysis, decomposing a complex signal into
its sinusoidal components. This spectral information is converted into electrical potentials by the hair cells, which activate auditory neurons. Given
frequencies activate portions of the auditory nerve that are “tuned” to those
frequencies, and this tuned or tonotopic organization continues up through
the auditory cortex where higher cognitive processes determine pitch or fundamental frequency from spectral information about the sound. 8 The significance of Fourier decomposition and tonotopic organization is that frequency
parameters appear to be preserved and represented through various stages
of the auditory physiology. In fact, electrodes can recover and reproduce
a sound presented to the ear from the subsequent auditory nerve signal. 9
It appears that pitch perception depends upon determining the frequencies
present in a complex signal. If pitch is fundamental frequency, the problem
of pitch perception is physiologically tractable.
3.3
Problems with the Simple View
The results of psychoacoustics give strong evidence of a subjective pitch
scale that correlates rather loosely with fundamental frequency. Though
pitch changes only if frequency changes, the magnitude of a pitch change is
neither identical with nor a constant function of the magnitude of its corresponding frequency change. Consider two types of psychoacoustic experiment.10 The first type consists of ‘Fractionalization’ experiments. Subjects
are presented with a given tone, and are then instructed to adjust a second (simultaneously presented) tone so that its pitch is one-half that of the
first tone.11 This process is repeated for many tones of different frequen8
A cat’s cortex is arranged in individual columns which are tuned to characteristic
frequencies. See Woolsey (1960) and Gelfand (1998), Chapter 6.
9
This is the so-called Wever-Bray effect. “Wever and Bray reported that if the electrical activity picked up from the cat’s auditory nerve is amplified and redirected to a
loudspeaker, then one can talk into the animal’s ear and simultaneously hear himself over
the speaker.” (Gelfand (1998), p. 136).
10
As described in Gelfand (1998), p. 354.
11
Stevens, Volkmann, and Newman (1937).
CHAPTER 3. AUDIBLE QUALITIES
48
cies. The second type are called ‘Equal Intervals’ experiments. In one such
experiment, subjects are instructed to adjust the frequencies of five tones
until they are separated by equal pitch intervals. 12 Fractionalization and
Equal Intervals experiments yield a remarkably consistent scaling of pitch
as a function of frequency, according to which equal pitch intervals do not
correspond to equal frequency intervals. 13 Doubling frequency does not uniformly double pitch: the frequency of a 1000 Hz tone must be tripled in order
to double its pitch; doubling the pitch of a 2000 Hz tone requires quadrupling its frequency. The accepted pitch scale extracted from psychoacoustic
data assigns to equal pitch intervals equal magnitudes in units of mels. The
mel scale is therefore an extensive or numerical pitch scale, in contrast to
the intensive frequency scale for pitch. 14 (See Figure 3.3: Pitch in Mels as
a Function of Frequency).15
Suppose we accept that the notion of pitch magnitude is well-founded,
and that Fractionalization and Equal Intervals experiments reliably determine the relationship between perceived pitch and frequency. If pitch perception is for the most part veridical, it follows that pitch is not identical
with frequency. It also follows, perhaps surprisingly, that the octave relation
is not a doubling of pitch. The octave relation is in some sense “the same
again (but higher/lower)”, but it is not “double in pitch”. Likewise, none
of the musical relations is a simple, small whole-number ratio between pitch
magnitudes. We require another characterization of the octave, fifth, et al.,
as relations between sounds with particular pitches.
The Simple View is inadequate if we wish to identify pitch with some
physical property of sounds that we veridically perceive. The relational
structure among pitches differs from the relational structure of frequencies.
In particular, changes in pitch magnitude do not correspond to uniform
changes in frequency magnitude.
3.4
The Standard (Subjectivist) View
The accepted view among auditory researchers is that pitch is a subjective
or psychological quality merely correlated with the frequency of a sound.
Gelfand (1998), for instance, states that “in formal terms, pitch is the psychological correlate of frequency, such that high frequency tones are heard
12
Stevens and Volkmann (1940).
Stevens, et al. (1937) and Stevens and Volkmann (1940).
14
Extensive scales preserve ratios between quantities, but intensive scales need not.
15
Another accepted pitch scale is slightly different. I shall discuss, in §3.5 and in Appendix A, the Bark scale introduced by Zwicker (1961) and Zwicker and Terhardt (1980).
13
CHAPTER 3. AUDIBLE QUALITIES
49
as being ‘high’ in pitch and low frequency tones are associated with ‘low’
pitches.”16 The Standard View among psychoacousticians is that pitch is a
mental quality in virtue of which we imperfectly perceive the frequencies of
sounds. Thus stated, the accepted view is that pitch is a quality of experiences much like a “quale” or “subjective feel” associated with frequency
perception. The Standard View is a form of philosophical subjectivism that
arises in response to the divergence between pitches and the external physical properties thought to be responsible for pitch experiences. Pitches are
thought to be internal, mental properties, and thus subjective in a natural
sense.
On the Standard View, sounds have frequency but not pitch. As such, it
is a form of error theory concerning auditory perceptual experience. Since we
take auditory experiences to furnish awareness of sounds and their pitches,
if the Standard View is correct then pitch is what Alex Byrne has aptly
described as “a perfectly monstrous illusion.” 17 Our ascriptions of pitch
properties to sounds are simply never true.
But it just does not follow from the fact that perceived pitch intervals
do not correspond to like frequency intervals that pitch is a property of
experiences that cannot be ascribed truly to sounds. I wish to propose
that an Alternative View of pitch according to which pitches are physical
properties of sounds is equally viable and captures more of the desiderata
that should be met by a philosophical theory of sounds. 18 If sounds have
a physical property whose variations correspond uniformly to variations in
perceived pitch and that is responsible for pitch experiences, then we can
avoid both eliminativism about pitch and error theories concerning pitch
perception.19
16
Gelfand (1998), p. 353. Similarly, Mestre, et al. (1998) say, “pitch is the subjective
quality associated with frequency.”
17
Byrne uses this phrase to refer to the status of colors according to error theorists.
Byrne (forthcoming), p. 9. Boghossian and Velleman (1989) and (1991), and Hardin
(1988) are contemporary proponents of color eliminativism.
18
In Appendix A, I attempt to develop such a physicalist alternative and to defend
it against objections that purport to demonstrate its inability to account for important
features of pitch and pitch experiences.
19
What about other options that neither attribute systematic error to pitch perception
nor eliminate pitches from the world of sounds? What we would like is a view that ascribes pitches to sounds and entails that most of the time, when things are going well with
hearing, we perceive sounds to have the pitches they actually have. One such view is that
pitches are dispositions, construed objectively, to cause subjects to have pitch experiences.
We must take care in formulating dispositionalism. If pitches are dispositions to produce
auditory experiences with a certain phenomenal character (compare, with respect to color,
CHAPTER 3. AUDIBLE QUALITIES
50
For now, we can summarize the respects in which the Standard View
falls short of a fully satisfactory account of the audible qualities, and thereby
illustrate the motivations for an alternative.
(1) If we accept that pitch is the property of sounds that is causally
responsible for our experiences as of sounds’ having pitch, and we accept that
sounds are external, objective (mind-independent) entities, we will prefer an
account according to which instances of the audible qualities are (1a) entirely
external to perceivers and (1b) objective qualities that are instantiated in the
world independently of perceivers and their responses. (1a) weighs against
the Standard View, and (1b) also counts against other forms of subjectivism
that assign distal locations to pitch instances. 20
Peacocke (1984)), we have no direct perceptual access to the pitches of sounds since we are
immediately aware only that we have an experience with certain phenomenal pitch properties. We can then infer or otherwise come to believe that sounds have dispositions to
cause in us particular phenomenal pitch properties, but we will never be auditorily aware
that some sound has a particular pitch. Byrne (ms) offers a more developed version of this
argument against what he calls ‘reductive dispositionalism’. This form of dispositionalism
does not leave us much better off than the Standard View.
Better to say that pitches are dispositions to produce experiences as of a sound’s having
a certain pitch. Byrne (ms) calls this view ‘nonreductive dispositionalism’. But the nonreductive dispositionalist must accept that auditory experiences present relational properties
of sounds—e.g., being disposed to sound high-pitched to perceivers of kind k—that we are
strongly inclined to think are monadic, or that auditory experiences do not present sounds
as having pitches, properly understood. Neither disjunct is attractive, but perhaps nonreductive dispositionalism, suitably motivated, is capable of capturing most of what we want
from a theory of pitch.
I do not hope to settle the question of whether pitches, and sensible qualities more generally, are dispositions. My aim is to present a view of pitch according to which pitches
are physical properties of sounds, and to defend it against objections that purport to
demonstrate its inability to account for important features of pitch and pitch experiences.
If sounds have a physical property that is responsible for pitch experiences, variations in
which correspond to variations in perceived pitch, then we can avoid eliminativism about
pitch and error theories of pitch perception. Given that the physical bases of dispositions
are central to understanding what dispositions are and when they are correctly ascribed
(cf. Martin (1994), Lewis (1997), and Fara (2001)), my project should be of interest to
the dispositionalist who aligns herself against the Standard View according to which pitch
is a psychological or subjective property.
20
Might sounds indeed bear pitch properties that are external to subjects though still in
some sense subjective or mind-dependent? If so, the extreme conclusions of the Standard
View might be avoided while maintaining the subjectivity of pitch. The most familiar
form of subjectivism about sensible qualities is formulated in terms of dispositions to produce characteristic kinds of perceptual responses (e.g., Locke (1975) and McGinn (1983)).
Pitch, then, is the subjective property sounds have in virtue of causing subjects to have
pitch experiences. But nothing about a sound’s being disposed to produce pitch experiences makes it the case that its pitch “depends” in some interesting sense upon subjects.
Rosen (1994) presents convincing arguments that to claim of certain properties that they
CHAPTER 3. AUDIBLE QUALITIES
51
(2) The Standard View entails that sounds themselves are not immediately characterizable in terms of pitch. If sounds can be correctly described
and classified by their pitches without reference to their frequencies or mention of perceivers’ responses, no widespread-error theory, eliminativism, or
projectivism is correct for pitch.
(3) Knowledge about at least some of the properties of sounds seems
to be possible solely on the basis of (perhaps suitably idealized) perceptual
experiences. If such knowledge is not acquired by inference, quasi-inference,
or some other indirect method, then the Standard View and other error
theories about the processes involved in perception and belief formation
about the audible qualities are false.
(4) Many philosophers maintain that the contents of perceptual experiences are exhausted by their representational or intentional contents—that
experiences can be fully characterized by how they present the world as being. Intrinsic qualities of experiences, in particular, need not be mentioned
in a full characterization of experiential contents. 21 The Standard View,
however, essentially makes reference to the psychological property of pitch
to account for the character of subjects’ auditory experiences. If intentionalism is the correct theory of perception, an explanation of the content of
auditory experience that adverts to a non-psychological pitch property must
be given.
(5) Perception seems to be a relatively reliable mode of access to information about the world. We think that beliefs formed on the basis of our
perceptual experiences are at least prima facie justified. To this extent we
have reason to resist the claim that auditory experiences are in some important respect illusory. A view that vindicates pitch experience is preferable
to one that attributes to hearing some substantial measure of error, either
in that we distort frequency relations or in that our pitch experiences fail to
discern any real property of sounds.
are “response dependent” is to mistake a distinction at the level of concepts or representations for a distinction at the level of properties or facts.
Perhaps pitches are basic, subject-dependent properties of sounds that cannot be identified with dispositions. But that makes pitches and their subjectivity, alike, mysterious
from the perspective of a moderately naturalistic understanding of the world. The Standard View thus appears to be the most viable view that is in some way subjectivist and
which meets the standards of explanation required by auditory science.
21
See, e.g., Harman (1990), Dretske (1995), Lycan (1996), Tye (1995) and (2000), and
Byrne (2001).
CHAPTER 3. AUDIBLE QUALITIES
3.5
52
The Alternative (Physicalist) View
Physicalism about pitch amounts to the claim that there are properties of
sounds themselves that can be described in the terminology of a physical
theory and which correlate well with the pitch experiences of normal human
hearers who are in circumstances that are favorable for hearing the pitches
of sounds.22 We need only look for an alternative to physicalism if such a
property is not in the offing or if further philosophical considerations prevent
us from identifying pitch with any property expressible in the language of
physics.23 The Standard Subjectivist View is motivated by the implicit
assumption that the psychophysical results discussed in §3.3 show that no
physical property of sounds can be identified with pitch since the most likely
candidate—frequency—cannot. I wish to challenge this implicit assumption.
Proponents of the Standard Subjectivist account of pitch classify sensory
response types according to the frequencies and intensities of the sounds that
give rise to those responses. In fact, Zwicker and Terhardt (1980) express
the subjective pitch of a sound as a function of its (fundamental) frequency,
and derive from this function a pitch scale in units called ‘Barks’ which, in
its relationship to frequency, closely resembles that of the mel scale. 24 (See
Figure 3.4: Pitch in Barks as a Function of Frequency). But frequency is, of
course, a physical property of sounds. The physicalist about pitch has as her
target precisely a property of sounds that varies with frequency just as the
subjectivist’s psychological pitch does. I argue in Appendix A that extant
accounts of pitch experience provide the materials to characterize just such a
property. Accepted subjectivist accounts, including Zwicker and Terhardt’s,
explain pitch experiences in terms of the activities of different portions of
the auditory system that respond to the presence of energy within ranges of
frequency (critical bands) which vary in magnitude throughout the audible
spectrum. (See Table 3.1: Selected Critical Bands). But such responsiveness on the part of the auditory perceptual system is responsiveness to the
presence of energy within certain perceptually salient frequency ranges since
the responses vary in proportion to critical band energies. The energy distribution across an ordering of those frequency ranges is thus a good candidate
22
Similar claims can be made for timbre and loudness.
One such consideration may arise out of cases of spectral shift or inversion of sensible
qualities with respect to external physical properties. See Appendix A, §A.4 for discussion.
24
The function from frequency to pitch in Barks (b) is:
23
b = 13 arctan(0.76f /1000Hz) + 3.5 arctan(f /7500Hz) 2 .
CHAPTER 3. AUDIBLE QUALITIES
53
upon which to base a realist account of pitches as properties of sounds. Characteristics of the distribution of energy across ordered frequency ranges are
perfectly objective properties that can be ascribed to sounds independently
of considerations about perceivers.
The physical property of sounds that serves as pitch candidate is thus
causally responsible for the activity of the auditory perceptual system that
subserves pitch experience. Energy within a particular range of frequency
causes activity proportional to that energy in a portion of the auditory
system which is tuned to that frequency range. Since that kind of activity is
the basis of pitch experience, pitch experiences are perceptual responses to
the physical pitch candidate. But since particular pitch experiences are not
simply responses to the frequencies of sounds, pitch perception is not just
frequency misperception. Pitch is therefore not the “psychological correlate”
of frequency.
If the physicalist proposal is correct, then certain sounds have pitch in
addition to frequency and intensity. Pitch is not identical to frequency, but
according to the current proposal, the pitch of a sound is intimately related
to its (fundamental) frequency, just as frequency is related to positions over
time. Pitch is thus a property that depends upon the frequencies of a sound’s
simple components—given a full characterization of the attributes of the
frequency ranges to which audition is sensitive, the pitch of a sound can be
determined from its frequency constituents. Pitch, that is, can be computed
as a complex function of frequency. Zwicker and Terhard’s function thus
specifies the relationship between the frequency and the objective pitch of
a sound.
Pitch, however, is anthropocentric. Humans and creatures like us are
sensitive to pitch in virtue of how our auditory systems are arranged, but
pitch is not terribly interesting from either a physicist’s point of view or from
the perspective of giving the simplest complete characterization of sounds.
It may be that pitch perception is more efficient from the standpoint of
designing the mechanisms for auditory perception, or is more useful for our
needs than frequency perception would be. Neither the fact that pitch is not
useful in scientific discussions of sound, nor the fact that only creatures with
a given type of sensory apparatus can detect pitch, however, implies that
pitches are not real properties of sounds that can be captured in physical
terms.
The account developed in Appendix A, in terms of weighted energies
within an ordering of frequency ranges, can be extended in several important directions. First, to give an account of the pitches of complex sounds;
second, to give an account of the musical relations that hold between sounds
CHAPTER 3. AUDIBLE QUALITIES
54
in virtue of pitch; third, to explain how timbre and loudness might be objective properties of sounds. The accounts given in Appendix A show that the
physical properties upon which the account of pitch is based play a prominent role in demonstrating that the audible qualities need not be considered
mere psychological correlates of the objective properties—frequency, spectral composition, intensity—in terms of which sounds are ordinarily characterized.
So, according to the alternative, pitch is an objective property of sounds
that is not identical with (fundamental) frequency. Pitch is the physical
property that disposes sounds to produce experiences as of pitch in suitably
equipped perceivers. This is the property in virtue of which sounds that
differ in timbre and loudness can be equivalent in “height”, and in virtue
of which periodic or musical sounds can be ordered according to the ratio
scale obtained by psychophysical methods. Particular sounds have pitch
in addition to frequency, though pitch is the more salient property from
the point of view of auditory perception. Pitch lacks the naturalness of
frequency, and is thus interesting only from an anthropocentric perspective.
3.6
Audible Qualities and the Event View of Sounds
I have been speaking as if the audible qualities should be understood in terms
of properties ordinarily ascribed to sound waves. Frequency and intensity,
in terms of which the critical bands account of Appendix A is developed,
are wave properties. The account is thus available to proponents of the
Wave View of sounds. But the Event View holds that sounds are events. In
particular, sounds are events in which objects or interacting bodies disturb a
surrounding medium in a wave-like manner. Since I have claimed that pitch,
timbre, and loudness, in addition to frequency and intensity, are properties
of sounds, they must be properties of the events I have identified as sounds.
There is, however, a clear sense in which frequency and intensity can be
ascribed to sound events.
First consider frequency as it is ascribed to waves. Frequency is a function of positions and times. The positions of particles in the medium at
different times characterize their vibratory motion, which in turn determines the pressure at a point in the medium. Frequency is the number of
cycles of motion per second that particles undergo, which we can track by
noting their points of maximum displacement. But particle displacements
are caused by the activities of the bodies that disturb them, and sounding
CHAPTER 3. AUDIBLE QUALITIES
55
bodies can themselves be ascribed a frequency. 25 Since the displacement of
a vibrating body immediately causes surrounding particles to be displaced,
the frequency with which a sounding body reaches one point of maximum
displacement corresponds directly to the frequency of the resulting wave in
the medium. (See Figure 3.5: Vibration Transmission).
Now, for simplicity we can treat the location of the disturbing event at
a time as the surface of interaction between the object and the medium. 26
When tracked through time, this surface itself vibrates with a frequency
that corresponds to the vibration frequency of particles that constitute the
surrounding medium. Let the frequency of the sound event be defined as the
vibration frequency of the disturbance surface. Since wavelength is inversely
proportional to wave frequency (frequency equals wavelength divided by
the speed of sound waves in the medium), the number of wave peaks that
pass through a point in a medium during a given time interval is just the
number that were created by the sounding body’s maximum displacement
during an earlier time interval of the same duration. 27 The frequency of
the sound event—that is, the frequency of the medium-disturbing event—is
therefore identical to the frequency of the subsequent wave. So the Event
View ascribes to sounds frequencies that match those of their waves in the
medium.
Pitch is a complex function of frequencies according to the Alternative
(Physicalist) View. Since the frequency of the sound event equals that of
the resulting wave, and since frequency is itself a function of locations and
times, pitch is a complex function of the location of the sound event over
time. Sounds then have the same Bark values as the waves they produce.
Sound events can therefore be characterized by pitches expressed in Barks.
Acoustical measurements of sound level are ordinarily expressed in decibels of intensity level (dB IL = 10 log(I/I 0 )).28 Intensity is defined as the
power (the rate at which energy is emitted (P = ∆E/∆t)) passing through a
25
Many sounding bodies have complex vibration patterns with different modes of sinusoidal vibration. In this case, a sounding can be ascribed a complex pattern of frequencies.
26
Cf. Bennett (1988):
“The ‘location’ of an event is its spatiotemporal location, i.e. where and
when it occurs. . . . A zone may be sizeless along one or more of its dimensions: . . . some fill spatial volumes and presumably others occupy only
planes, lines, even points,” p. 12.
27
Frequency is thus independent of the speed at which waves travel in a medium.
Where I0 is a reference intensity level. Also note that since intensity is proportional
to the square of pressure, converting from decibels of intensity level (dB IL) to decibels of
sound pressure level (dB SPL) requires squaring pressure values.
28
CHAPTER 3. AUDIBLE QUALITIES
56
surface per unit area (I = P/A). We can therefore express the intensity of a
sound event as the power transmitted per unit area on the surface that gives
the sound event’s location. This quantity is, in fact, often cited by physicists
interested in sound production. Because the power transmitted through this
surface depends upon the specific properties of the surrounding medium, the
intensity of the sound event varies with different media. Since the loudness
of a sound is a function of its energies or intensities within various critical
frequency bands, the loudness of a sound event is medium-dependent.
The Event View gives a more satisfactory account of a sound’s loudness
than does the Wave View because the Event View captures the phenomenon
of loudness constancy. That is, we do not perceive a sound itself to change
in loudness when we move away from it—a speaker’s voice does not itself
get louder just because I move to the front of the room. I may be in a better
position for optimal or comfortable hearing, but the qualities of the sound
do not differ with distance from its source. According to the Event View, a
sound’s intensity is a matter of the power through the surface that demarcates the disturbing-event’s location. And loudness is a complex function
of the sound’s intensity within various critical bands. But since intensity
diminishes as the inverse-square of distance from a sound source, the Wave
View, which attributes loudness (as a function of intensity) to sound waves,
does not capture loudness constancy. According to the Wave View, the
loudness of a sound itself changes as the sound moves away from its source.
3.7
The Doppler Effect
When a sound source and a subject move relative to each other, the pitch
of the sound appears to the subject different from the pitch of the sound
when the source and subject are stationary. An approaching train’s whistle
sounds higher in pitch than a stationary one, and a receding train’s whistle
sounds lower in pitch; a stationary train’s whistle sounds higher or lower
pitched when a subject approaches or recedes. The Event View apparently
implies that the sound of the whistle remains constant across all such cases—
the medium-disturbing event does not evidently change in light of source or
subject motion.
The Doppler effect comes in two forms. When a subject moves toward (or
away from) a stationary source (perceiver-motion Doppler ), he experiences
the sound as having a higher (or lower) pitch than when he is stationary.
More (or fewer) wavefronts reach the organs of hearing per unit of time and
therefore cause an experience as of a higher (or lower) pitch.
CHAPTER 3. AUDIBLE QUALITIES
57
The Wave View explains the perceiver-motion Doppler effect nicely. The
subject has an illusory or erroneous pitch experience because he moves relative to the stationary source. The Event View can offer a similar explanation. The subject undergoes an illusory pitch experience because information about sounds is transmitted through the medium by waves. The sound
of the stationary train’s whistle remains the same despite the subject’s motion.
Source-motion Doppler presents a unique problem for the Event View.
When a source moves toward (or away from) a stationary subject, the apparent pitch shift differs from that which occurs when the subject moves at
the same rate toward a stationary source. 29 According to the Wave View,
the sound itself changes in character with source motion since the waves
in the medium have a different frequency. Sound waves are actually more
tightly bunched as a result of the source’s motion through the medium. The
subject thus enjoys a veridical experience of a sound with different qualities.
The Event View, which identifies the sound with the disturbing event,
cannot readily explain the apparent change in sound quality in terms of
wave bunching. The pitch of the sound is determined by the vibratory
motion of the surface that defines the event’s location—but that vibratory
activity remains constant despite source motion. Event theorists have two
options. We can try to accommodate a difference in pitch in the sourcemotion Doppler, or we can deny that either type of Doppler effect amounts
to a genuine difference in the sound’s pitch. The latter subsumes both types
of Doppler to perceptual illusion.
29
Perceiver-motion Doppler: Suppose a subject moves toward a sound source which
emits 1000 waves per second (1000 Hz) at 100 meters per second. Since the speed of
sound waves (c) in air is 340 meters per second, the wavelength (λ) of 1000 Hz waves is
0.34 meters (λ = c/f ). So, in one second she will pass 1000 waves plus 100/0.34 waves, and
the apparent frequency is 1294 Hz. Source-motion Doppler: Suppose a source emitting
1000 waves per second moves toward a stationary subject at 100 meters per second. After
one second, 1000 waves will occupy a distance of 240 meters. This results in a wavelength
of 0.24 meters and frequency of 1417 Hz. (Physics-faq/acoustics: Acoustics FAQ).
CHAPTER 3. AUDIBLE QUALITIES
58
I opt for the latter.30 We should say that the sound event maintains
a stable qualitative character through changes in its position relative to
observers—whether due to its own motion or to the motion of observers.
The source-motion Doppler is thus an apparent shift in the pitch of a sound.
Is it independently plausible that both sorts of Doppler effect are cases
of perceptual illusion? Suppose that despite auditory appearances there is a
form of constancy judgement for pitch in both sorts of Doppler effect. Such
constancy judgements should be present in both the perceiver-motion and
the source-motion Doppler. That is, suppose that we withhold endorsement
of the claim that a sound shifts in pitch when either a subject or a sound
source is in motion with respect to the other, and instead judge that the
sound maintains a constant character despite our motion or the motion of the
source. It is plausible that such constancy judgements actually occur (and
can be elicited) when we hear sounds with moving sources—I don’t actually
think that a train’s sound changes when it speeds past the platform. Rather,
I’m inclined to think that I hear the train’s sound without distortion when
we both are stationary. If this is genuinely plausible, then we have good
reason to count both sorts of Doppler effect as perceptual illusions, just as
we do when visually-perceived qualities are Doppler “shifted”. Despite the
way things visually appear, once we take into account the motions of celestial
bodies, we do not judge that the colors of the stars are the ones they visually
seem to have. Thus, the Event View implies what is already reasonable, that
relative motion is not sufficient to change the audible qualities of a sound.
30
Why? Suppose that the pitch of a sound does change with source motion. We might
say that the disturbance event is different in this case because the interaction between
source and medium differs as a result of source motion. It is reasonable that the event
itself is different because its effects are different.
We should resist this for at least two reasons. First, though different causes and effects
are sufficient for there to be a different particular event, in this case they are not sufficient
to characterize the different qualitative character of the disturbing event. That is, pitch
is a quality of sounds, and different effects do not give reason to attribute a difference in
pitch to the disturbance event without sufficient intrinsic differences in the sound event
itself. Since the disturbance event, and in particular its vibratory motion, does not change
in relevant respects when it is in linear motion, we should not say that its pitch changes.
Second, even if we did say that the sound event changes with source motion, it would
follow that in cases of source-motion Doppler the sound has a different qualitative character
at different places on the surface that gives the event’s location. That is, the pitch of the
sound at the front of the whistle is different from the pitch of the sound at the rear of the
whistle. If motion suffices for pitch change in one direction, it suffices for pitch change
in the other. So the character of the medium disturbance varies with location along the
event surface. It is hard to see how linear motion alone could justify attributing different
pitch qualities to different spatial parts of a sound event.
CHAPTER 3. AUDIBLE QUALITIES
3.8
59
Concluding Remarks
I have argued that the failure of simple forms of physicalism about the audible qualities does not rule out the prospect of an account according to which
pitch is an objective, physical property of sounds. With attention to current
accounts of pitch experience, which are framed in terms of responsiveness to
sounds with certain physical attributes, we can extract a physical property
that both causes pitch experiences and varies with perceived pitch in the
right ways. The account also can be extended to capture timbre and loudness. Pitch is thus a property of sounds that is discerned during auditory
experiences, but which is not identical with fundamental frequency. Pitch
is also not simply the subjective or psychological correlate of frequency; it
is an objective property that sounds have in addition to frequency. Frequency may be a more natural property by which to classify sounds from
the perspective of the physical sciences, but pitch is an anthropocentrically
interesting property to which human hearers are sensitive.
Since pitch is a complex property that depends upon the frequency and
intensity of a sound, and frequency and intensity can be ascribed to medium
disturbance events without damage to those notions, the Event View has
available a full account of the audible qualities.
CHAPTER 3. AUDIBLE QUALITIES
60
Figure 3.1: Sinusoidal motion. [From Gelfand (1998), Hearing: An Introduction to Psychological and Physiological Acoustics, Third Edition, New
York: Marcel Dekker, Figure 1.5, p. 15, with permission.]
CHAPTER 3. AUDIBLE QUALITIES
61
Figure 3.2: Fourier composition of a square wave. [From Gelfand (1998),
Hearing: An Introduction to Psychological and Physiological Acoustics,
Third Edition, New York: Marcel Dekker, Figure 1.12, p. 24, with permission.]
CHAPTER 3. AUDIBLE QUALITIES
62
Figure 3.3: Pitch in mels as a function of frequency. [From Gelfand
(1998), Hearing: An Introduction to Psychological and Physiological Acoustics, Third Edition, New York: Marcel Dekker, Figure 12.1, p. 354, with
permission.]
CHAPTER 3. AUDIBLE QUALITIES
63
Figure 3.4: Pitch in Barks as a function of frequency. [From Gelfand
(1998), Hearing: An Introduction to Psychological and Physiological Acoustics, Third Edition, New York: Marcel Dekker, Figure 12.2, p. 355, with
permission.]
64
CHAPTER 3. AUDIBLE QUALITIES
b
Bark
0
fl ,fu
Hz
0
1
100
2
3
fc
Hz
b
Bark
∆fG
Hz
50
0.5
100
150
1.5
100
250
2.5
100
350
3.5
100
200
400
5
510
6
630
450
570
7
8
10
1270
5.5
2000
6.5
140
840
7.5
150
15
2700
16
3150
17
3700
18
4400
1000
8.5
160
19
9.5
10.5
210
1600
11.5
240
20
6400
21
7700
22
9500
1850
12.5
280
23
1480
1720
24
b
Bark
∆fG
Hz
1850
12.5
280
2150
13.5
320
2500
14.5
380
2900
15.5
450
3400
16.5
550
4000
17.5
700
4800
18.5
900
5800
19.5
1100
7000
20.5
1300
8500
21.5
1800
10500
22.5
2500
13500
23.5
3500
5300
190
1370
fc
Hz
2320
120
700
1170
12
13
110
920
1080
11
4.5
770
9
fl ,fu
Hz
1720
14
300
4
b
Bark
12
12000
15500
Table 3.1: Selected critical bands. Bark value b, lower (f l ) and upper (fu )
frequency limit of critical bandwidths, ∆f G , centered at fc . [Adapted from
Zwicker and Fastl (1999), Psychoacoustics: Facts and Models, Second Edition, New York: Springer-Verlag, Table 6.1, p. 159, with permission.]
CHAPTER 3. AUDIBLE QUALITIES
65
Figure 3.5: Vibration transmission. [From Gelfand (1998), Hearing: An
Introduction to Psychological and Physiological Acoustics, Third Edition,
New York: Marcel Dekker, Figure 1.4, p. 14, with permission.]
Appendix A
The Alternative View
A.1
Pitch and Critical Bands
What, then, is pitch? The Standard (Subjectivist) View supposes that pitch
is a subjective attribute of sensations or experiences because the relationship
between frequency and experienced pitch is neither linear nor logarithmic.
Consider pitch, expressed in mels, as a function of frequency (recall Figure
3.3). The standard account holds that this reflects the relationship between
frequency as an objective property of sounds and pitch as an attribute of
experiential states. But I shall claim that nothing about the case should keep
us from thinking that both pitch and frequency are objective properties
of sounds. The plausibility of this claim depends upon whether we can
provide a candidate property that varies as pitch does with frequency and
which explains why pitch is related to frequency as it is. The function from
frequency to pitch would thus inform us about the relationship between two
different properties of sounds, rather than about the relationship between
properties of sounds and sensations.
Recent accounts of pitch provide insight into both why the standard view
is a subjectivist view, and into how an objectivist theory of pitch should be
developed.1 Zwicker and Terhardt (1980) have developed an instructive account of the relationship between frequency and pitch. They have derived a
function from frequency to subjective pitch, expressed in units called ‘Barks’,
which strongly resembles that of the mel scale. 2 (See Figure 3.4: Pitch in
1
The scientific details of discussion to follow are drawn primarily from Zwicker and
Fastl (1999), especially Chapters 4 through 7, Gelfand (1998), and Zwicker and Terhardt
(1974).
2
The term ‘Bark’ is derived from the name of Barkhausen, an auditory scientist who
studied the relationship between loudness and intensity (Zwicker and Fastl (1999), p. 160).
66
APPENDIX A. THE ALTERNATIVE VIEW
67
Barks as a Function of Frequency). The function from frequency to pitch in
Barks (b) is:
b = 13 arctan(0.76f /1000Hz) + 3.5 arctan(f /7500Hz) 2 .
The resulting Bark scale, like the mel scale, preserves perceived ratios and
assigns the same magnitudes to pitch differences judged to be equivalent.
Now, the Bark scale is based on the notion of a critical frequency band.
Critical bands are supposed to be psychologically real entities which explain
the perceived pitch of a tone given its frequency and energy properties. A
critical band is characterized by a frequency range (its critical bandwidth)
around a given center frequency, to which that band is responsive. Evidence
for the existence of critical bands comes from experiments involving masking, where one tone is used to interfere with a subject’s ability to perceive
or detect the presence of another test tone. Masking experiments provide
significant evidence for critical bands because the capacity one tone has to
mask another is not independent of their respective frequencies. In particular, a masking tone whose frequency is near to that of a test tone more
effectively masks the test tone than does a masking tone whose frequency
is farther from that of the test tone. The effectiveness of masking decreases
as frequency separation increases. This gives evidence of a sort of frequency
selectivity within the auditory processing system. That is, as discussed in
§3.2.2, different portions of the auditory system deal with particular frequency ranges. When tones are near in frequency, masking occurs because
the sensation produced by one tone interferes with that of the other. As frequency separations increase, different portions of the auditory system carry
information about the sounds, so less interference results and masking is
less effective. Critical bands depend upon the tonotopic organization of the
auditory system.
Critical bands are ordinarily thought of as like filters with a roughly
triangular shape around a given center frequency. That is, they pass the
most energy at the center or characteristic frequency, and pass less energy
as a tone deviates from this center frequency. Beyond the critical bandwidth,
they pass no energy. According to this model, the auditory system is like a
bank of many overlapping filters that are responsive to different frequency
ranges and whose outputs determine the qualities a sound is heard to have.
Critical bands and their characteristic properties can be discerned by a
number of experimental procedures. 3 One such procedure discerns critical
bandwidth by determining the minimum bandwidth of noise required to
3
See Zwicker and Fastl (1999), Ch. 6, for a survey of such procedures.
APPENDIX A. THE ALTERNATIVE VIEW
68
maximally mask a simple tone at the center frequency. For a test tone at a
given center frequency, a narrow band of noise around the center frequency
begins to mask the test tone. As the noise band widens, it further masks the
test tone until a bandwidth is reached beyond which further noise does not
contribute to masking. This is said to be the critical bandwidth. Now, the
effectiveness with which noise or a masking tone interferes with the detection
of a centered test tone drops off with departure from the center frequency
until the critical bandwidth is exceeded and no further masking results. So,
the critical bandwidth is that bandwidth of noise that masks a simple tone
at a given frequency just as effectively as wideband white noise. Because
frequency components farther from the center frequency contribute less to
masking than those nearer to the center frequency, each frequency within
a critical band can be assigned a weighting with respect to the relative
importance to masking of energy at that frequency.
From the perspective of understanding pitch, critical bands are very
significant for two reasons. First, critical bandwidth varies greatly with frequency. (See Figure A.1: Critical Bandwidth as a Function of Frequency).
Critical bandwidth is approximately 100 Hz for frequencies up to approximately 500 Hz, but above 500 Hz a rough estimate of critical bandwidth is
0.2 times the center frequency. Each critical band deals with a unique range
of frequencies, and that range increases substantially as center frequency
increases.
This leads to the second significant (and surprising!) result: critical
bandwidth correlates very well with pitch. Critical frequency bands simply correspond to nearly equivalent pitch distances (approximately 100 mels
per critical band or one Bark). Whether we take a critical band centered
at 1000 Hz (critical bandwidth 160 Hz) or one centered at 5000 Hz (critical bandwidth 1000 Hz), critical bandwidths amount to equivalent pitch
distances.4
4
In addition, each Bark corresponds to rough 27 units of the minimum detectable pitch
difference or just noticeable different between tones; a unit of just noticeable frequency
difference, however, grows substantially as frequency increases. Just noticeable frequency
differences range from ∼ 2 Hz at very low frequencies to nearly 200 Hz at high frequencies
(Zwicker and Fastl (1999), p. 161). Critical bands also correspond to roughly equal
distances along the basilar membrane or cochlear partition (1 Bark ≈ 1.3 mm), whereas
equal cochlear distances correspond to increasing frequency ranges from apex to base (0.2
mm ≈ 15–20 Hz at apex, 0.2 mm ≈ 500 Hz at base (Zwicker and Fastl (1999), p. 160)).
APPENDIX A. THE ALTERNATIVE VIEW
69
From these two facts, we can characterize the difference in pitch between
two frequencies, ∆p(f1 , f2 ), in terms of the function, G(f ), from center
frequency to critical bandwidth.5
Z f2
G(x) dx.
∆p(f1 , f2 ) =
f1
Pitch differences are a function of the critical bandwidths and center frequencies of the various experimentally determined critical bands.
But because the basilar membrane is thought to be an important part of
the basis for both critical bands and pitch perception, and because the basilar membrane is organized such that less physical space is assigned to a given
frequency range as frequency increases (see footnote 4), researchers posit
that there are only a finite number of critical bands whose center frequencies become more widely spaced as frequency increases. That is, each unit
of physical space along the basilar membrane subserves the same number
of critical bands, but increasing frequency ranges, so the center frequencies
of critical bands are separated by increasing frequency differences. Critical
band center frequencies decrease in density along the frequency scale. The
Bark scale thus assigns one unit to each critical bandwidth. Each unit of
Barks corresponds to the same number of centered critical bands. (See Table
3.1: Critical Bands).
What’s significant, again, is that the procedure does not begin by determining the different frequency ranges that correspond to equal pitch ranges.
Rather, it begins by discerning the masking relationships between tones of
different frequencies. These masking relationships show that critical bands
exist and make apparent the frequency selectivity of the auditory system.
But that critical bands discerned in this way should amount to equal pitch
intervals is anything but evident. It is nothing short of surprising that an
accurate pitch scale can be obtained simply by assigning one unit of criticalband rate to each experimentally discerned critical frequency band.
Zwicker and Terhardt’s Bark scale is thus an expression of pitch in intervals that correspond to the psychoacoustically determined critical bands,
and the result strongly resembles that of the mel scale of ratio pitch. The
Bark scale yields an expression of subjective pitch as a function of frequency,
but also explains this relationship in terms of the psychological and physiological mechanisms of sound perception.
Now, according to the “filters” conception of critical bands, the experienced attributes of a sound depend upon the output or critical band level
5
I owe thanks to Adam Elga for discussion of how to express this formulation.
APPENDIX A. THE ALTERNATIVE VIEW
70
(in terms of energy) of each of the critical bands in the filter bank. What is
distinctive about the critical band levels caused by sounds that are heard to
have pitch? How do they differ from those produced by sounds experienced
to be unpitched?
A wideband white noise whose energy is independent of frequency results
in a roughly equivalent critical band level for each of the overlapping critical
bands. If the critical band profile for a sound is a plot of the critical band
levels that sound produces for each critical band, the critical band profile of
white noise is a flat line at some energy level. 6 However, for a narrower band
of noise, critical bands within which some portion of that energy falls have
greater critical band levels than critical bands within which none of the noise
falls. The resulting critical band profile is that of a plateau. But noise has no
pitch. Sinusoids are the simplest pitched sounds, and are the constituents of
more complex pitched sounds. Sinusoids produce a distinctive critical band
profile. A sinusoidal tone at a particular frequency causes a substantially
greater critical band level for critical bands centered near that frequency
than for any other critical band. The critical band profile for a sinusoid is
that of a sharp peak at the critical bands centered closest to its frequency. If
the experienced attributes of a sound depend upon its critical band profile,
then the apparent pitch of a sinusoid depends upon its producing a maximum
critical band level in a very small subset of adjacent critical bands among
the many ordered critical bands.7
A proponent of the Standard View might identify pitches with critical
band maxima or with something that depends upon such activity. Either
way, the pitch that a sound appears to have depends upon the profile of
energies across many critical bands. Pitch is thus either identifiable with or
the immediate result of a certain type of critical band activation pattern.
Since critical bands are internal psychological entities, pitch is an internal
subjective property.
So the Standard View posits internal psychological entities—critical bands—
to explain, among other things,8 the dependence of masking on frequency
separation. A function from frequency to subjective pitch can be derived
just by taking into account the experimentally determined attributes of the
sequence of critical bands. The pitch of a sinusoidal tone depends upon the
pattern of critical band activations it produces. The critical band profile
associated with a sinusoidal tone is that of a peak critical band level in a
6
But see §A.4 for an amendment required in light of loudness phenomena.
Indeed, very narrow band noise is often heard to have a pitch, in particular for noise
bands at high frequency.
8
Critical bands also figure prominently in accounts of loudness. See §A.4.
7
APPENDIX A. THE ALTERNATIVE VIEW
71
single critical band or in a few adjacent critical bands. Thus, subjective
or psychological pitch depends upon a critical band’s having a significantly
greater level of activity than the others. This critical band’s location in the
ordering of critical bands determines the Bark value associated with the tone.
But something analogous to critical band levels or profiles can also be
ascribed to sounds themselves. If that is correct, then pitch can be seen as
an objective property that sounds possess. We begin with the straightforward recognition that critical bands are themselves characterized in terms
of a center frequency, a bandwidth, and a scaling factor for energy at each
frequency within the critical bandwidth. But frequency and energy or intensity are properties of sounds. So if we take a critical band to be a simple
frequency range around a given center frequency, then sounds themselves fall
within critical bands in virtue of their frequency characteristics. Given the
scaling factor associated with each frequency within a critical band, a critical band can be characterized as a class of pairs that consist of a frequency
and an energy weighting factor. The highest energy factor determines the
center frequency of the critical band, and energy weighting factors decrease
with distance from the center frequency. Now we can ascribe to every sound
a critical band profile in the following manner. Ascribe to the sound a critical band level for each critical band. The critical band level of a sound,
for a given critical band, is the sum of the products of the sound’s energy
at a frequency and the scaling factor for that frequency, for each frequency
within the critical band. The critical band profile for a sound is given by
ordering the critical band levels for all critical bands; it specifies the amount
of energy that the sound has within each of the fully characterized critical
bands.
Once we determine the critical band profile of a sound, we have a basis
from which to determine its various attributes, including its pitch, loudness,
and timbre. As before, for a sinusoidal tone to have a particular pitch is for
it to have a single critical band maximum within its critical band profile.
The critical band with the peak critical band level determines the sound’s
pitch in Barks.
Pitch is thus an objective though complex property of sounds. Having
a pitch is not a simple matter of having a particular frequency, though frequency determines pitch given a specification of critical bands. The account
depends upon rejecting the claim that pitches, and critical band profiles in
general, are just properties of the auditory perceptual systems of subjects.
Rather, the alternative holds that pitches and critical band levels are physical properties of sounds that our auditory apparatus is suited to detect.
APPENDIX A. THE ALTERNATIVE VIEW
72
Activity internal to our perceptual systems reflects the presence of energy
within various critical bands; that is, various parts of our auditory physiology, and the psychological mechanisms they ground, are tuned to energy
within different frequency ranges. So the property of having energy within
the specified critical bands is the property discerned in sound perception.
Having a critical band level sufficiently greater than other critical band levels
amounts to having a pitch.
An analogy with a device that determines the acceleration of an object
illustrates the essence of the contrast between the Standard View and the
alternative I have proposed. Acceleration is a property that an object has
which can be calculated as a function of its position over time—acceleration
depends upon positions and times, which look to be the simplest observable properties of an object that characterize its activity. Now, we are not
inclined to say that the acceleration detector measures a property whose
nature depends upon the construction of the device, in the sense that there
could be no such property if the device did not exist. Once we recognize
that some property of the object corresponds to the device’s output, there
is no temptation to say that the calculated acceleration is a property of
the detecting device or that acceleration metaphysically depends upon detecting devices. Acceleration is a property of the object which the device is
designed to detect. Similarly, once we recognize that critical band properties
of sounds correspond to pitch experiences, there is little temptation to identify pitch as the mere subjective correlate of frequency. Pitch experiences
track a property of sounds that varies with frequency. 9
Pitch is thus a complex property of sounds that depends upon their
patterns of critical band levels. It is given by a complex function of the
frequencies at which a sound has energy, and the function from frequency to
pitch in Barks expresses the pitch of a sound itself—not merely a sensation.
Since this function is derived from the attributes of the critical bands, and
because critical band properties can be ascribed naturally to sounds, pitch
is a property of sounds that is related to but not identical with frequency.
A.1.1
The Pitch of Complex Tones
The foregoing account of pitch in terms of critical band energies applies
straightforwardly to simple sinusoidal tones, for which a single critical band
has a maximum value. But complex sounds with many sinusoidal con9
Of course, critical band properties may not be of interest to physicists in the way that
acceleration is. They are, however, of interest to psychophysicists and to those who wish
to understand the distal physical causes of pitch experiences.
APPENDIX A. THE ALTERNATIVE VIEW
73
stituents also have pitch. The standard account of pitch perception for
complex tones has it that fundamental frequency is determined through
analysis of a tone’s Fourier frequency components. How can the alternative
account I have sketched explain pitch perception for complex tones without
adverting to fundamental frequency perception?
Recent accounts of pitch perception posit a complicated analysis of constituent frequencies to extract fundamental frequency. I shall consider one
such model of pitch perception—that of Terhardt, e.g., (1980), (1982a), and
(1982b)—and argue that it can be extended to the critical bands account
of pitch developed above. The result is that pitch perception for complex
sounds involves determining a critical band value in Barks; but the critical
band value itself corresponds roughly to fundamental frequency.
Complex sounds have more widely distributed critical band energy patterns than do simple sinusoids, but complex periodic tones still exhibit local
maxima at several critical bands. Pitches are therefore best conceived as
types of critical band profiles. A sound whose critical band profile has many
separate peaks corresponding to its sinusoidal constituents can be a member
of the same pitch as one whose critical band profile has a single peak. The
first problem is how to determine which complex sounds are members of
the same pitches as sounds that have single-peaked critical band profiles. A
simple answer is that they share a fundamental frequency, but we would like
an answer framed in terms of aspects of critical band profiles. The second
problem is how, if we are not perceiving fundamental frequency (because we
do not perceive frequency at all), we come to perceive simple and complex
sounds as having the same pitch. I shall suggest that Terhardt’s account
provides the materials to deal with both problems.
Call each local maximum a pitch determinant with a particular Bark
value. Each pitch determinant corresponds to a particular frequency; for
harmonic complex sounds—ones with pitch—these frequencies are integer
multiples of each other. No such simple relationship exists, however, between the corresponding Bark values of pitch determinants. For instance, a
complex harmonic sound with 200 Hz fundamental frequency and harmonics at 400 Hz, 600 Hz, and 800 Hz (or f, 2f, 3f, 4f) has pitch determinants
with Bark values of roughly 2 Barks, 4 Barks, 5.75 Barks, and 7.2 Barks.
Terhardt’s account of pitch perception relies on learned “templates” for particular harmonic sequences, which are formed on the basis of regular experience with harmonic complexes, in particular those which are predominant in
APPENDIX A. THE ALTERNATIVE VIEW
74
speech.10 We form the ability to recognize particular harmonic complexes,
such as (150 Hz, 300 Hz, 450 Hz, 600 Hz, . . . ), through their spectral constituents. We thereby acquire internal templates with such constituents as
components. But each component of a template has a corresponding value
in Barks, so the templates can themselves be considered as sequences of
pitches in Barks (e.g., (B1, B2, B3, B4, . . . , Bn)) as opposed to frequencies
(with the form (f, 2f, 3f, 4f, . . . , nf)). Templates construed in such terms
amount to sets of critical band maxima.
Each constituent of a complex tone is a member of various templates in
which it occurs as an upper harmonic. Terhardt’s claim is that an analysis
on the subharmonics of each constituent of a complex tone determines the
pitch that tone is perceived to have. 11 The analysis proceeds as follows. For
each of the n constituents of a complex tone, the first eight subharmonics
of fn are given by the fundamentals of the first eight harmonic sequences or
templates of which fn is an upper harmonic.12 Consider the complex sound
with constituents at 200 Hz, 400 Hz, 600 Hz, and 800 Hz. The subharmonics
for 200 Hz are first determined: 100 Hz is the second subharmonic (1:2) of
200 Hz since 200 Hz is the second upper harmonic in the sequence (100 Hz,
200 Hz, 300 Hz, . . . ); 66.7 Hz is the third subharmonic (1:3) since 200 Hz
is the third upper harmonic in the sequence (66.7 Hz, 133.3 Hz, 200 Hz,
266.7 Hz, . . . ). The final five subharmonics of 200 Hz are given by the ratios
1:4–1:8. Subharmonics are then determined for each of the complex tone’s
constituents.
A complex periodic sound’s constituents share various subharmonics.
Call a shared subharmonic a pitch candidate. Though several subharmonics
may coincide for two or more of the constituents, and therefore determine
several pitch candidates, the pitch candidate shared by the largest number of constituents determines the perceived pitch of a complex sound. A
comparison across subharmonics reveals that the fundamental frequency is
shared as a subharmonic by the most constituents. That is, 200 Hz, 400
Hz, 600 Hz, and 800 Hz all share only 200 Hz as a subharmonic. Thus, 200
Hz determines the perceived pitch of the complex sound. Sometimes other
pitch candidates are selected as “the pitch” of a complex sound, and often
10
Such learning is thought to take place very early in life, and probably begins in the
womb. See §A.2 for discussion of the basis of template formation—of why such templates
are acquired.
11
I will adopt, for simplicity, the non-standard convention of including a tone itself
among its subharmonics and upper harmonics.
12
So, for fn , the first eight subharmonics are given by gm where fn = 1g1 , fn = 2g2 , fn
= 3g3 , . . . , fn = 8g8 .
APPENDIX A. THE ALTERNATIVE VIEW
75
other pitch candidates are discernible within the complex sound. However,
a complex sound is most commonly pitch-matched with a sinusoid at its
fundamental frequency. This analysis explains both the “spectral” pitch of
complex sounds with a constituent at the fundamental frequency, and the
“virtual” pitch of sounds with a missing fundamental.
I claim that this analysis can be carried out with templates consisting not
of frequencies in whole-number multiple relationships, but of pitch values in
Barks which are derived from the critical bands model. Suppose we have a
complex tone consisting of constituents at 2 Barks, 4 Barks, 5.75 Barks, and
7.2 Barks. Each of these constituents appears in learned templates derived
from experience with complex harmonic sounds. Just as with the frequency
model, coincidence among the subharmonics of the pitch determinants gives
the pitch candidates and the pitch of the complex sound (which corresponds
roughly to the fundamental frequency). Since templates are just representations of sequences of simple pitches, the pitch of a complex sound can
be seen as settled by the pitches of its constituents and their subharmonics, which are given by simple harmonic sequences of critical band values.
Having a particular pitch, for a complex sound, is a matter of having critical band maxima that substantially coincide in their membership in other
salient (harmonic) sequences of simple pitches (alternatively, salient critical band profiles). Thus, though the pitch value of a complex sound has a
corresponding frequency value that roughly equals the sound’s fundamental
frequency, what we perceive is its pitch. The point of the subharmonics analysis is to determine which harmonic sequence each of the complex sound’s
constituents are most likely to be members of. Pitches, then, can be seen
as types of critical band profiles whose members exhibit a particular kind of
subharmonic sharing. The subharmonic shared determines the pitch value
in Barks. Though pitch perception for complex sounds may be a quite complicated affair, it need not rely on determining fundamental frequency.
The alternative account holds that pitch is an objective, physical property of sounds. The motivation for construing pitch as a subjective or psychological quality stemmed from the discrepancy between frequency and
perceived pitch. Given that sounds indeed have the properties I have identified as the pitch properties, and that these properties are causally responsible for what we take to be veridical pitch experiences, explanation of pitch
perception need not advert to mind-dependent properties. Pitches as the
alternative characterizes them are not, however, terribly interesting from
the point of view of the physical sciences. But they are salient from the
perspectives of auditory experience and the mechanisms by which we hear
APPENDIX A. THE ALTERNATIVE VIEW
76
sounds. Pitch is thus an anthropocentric property. 13 But the property of
having a pitch—that is, having or determining a maximal energy within
a given member of an ordering of frequency ranges—is neither mental nor
mind-dependent in any important respect.
A.2
The Musical Relations
The musical relations—octave, fifth, fourth, et al.—are commonly analyzed
as small whole-number frequency ratios between tones. But the octave,
fifth, et al., seem to be relations sounds bear to each other in virtue of
their pitch. If pitch is not just frequency, we need an account of the musical
relations that captures their distinctive features in terms of pitch. This need
is pressing. If we do not directly perceive frequency, but only pitch, as a
property of sounds, how do we perceive octave relations if not by perceiving
pitch relations?
Tones that stand in musical relations share certain affinities with each
other. The octave is the limit case of affinity, in that tones that stand in
the octave relation are “the same” in some sense while still different in pitch
height.14 Tones separated by a fifth share more affinity than tones in other
musical relations, but less affinity than octave-related tones. An account
of the musical relations should explain the relevant respects of affinity or
sameness.
So far I have been speaking of the pitch ordering as a simple linear ordering from lower to higher. This can be adapted to incorporate the musical
relations. Imagine twisting the line into a helix around a vertical axis so
that tones separated by an octave—tones that are “the same” in the relevant respect—have the same angle of rotation around the vertical axis. So,
for example, all of the C’s fall on a vertical line in ascending order of height.
According to this representation of pitch, the same notes at different pitch
heights have the same angular position, and each rotation of the helix corresponds to an octave. We want to know why certain sounds that differ in
pitch fall on a particular vertical line around the helix—that is, we want to
know the respect in which tones separated by an octave are the same. Since
pitch is explicated in terms of critical bands, we want to know how that re13
Just as colors are anthropocentric properties according to the view that colors are
types of surface spectral reflectances. See, e.g., most recently, Bradley and Tye (2001),
and Byrne and Hilbert (forthcoming in BBS ).
14
It bears restating that the octave is not a doubling in pitch, though those with musical
training sometimes apply the standard frequency analysis of the octave and mistakenly
take it to be a doubling of pitch.
APPENDIX A. THE ALTERNATIVE VIEW
77
spect of similarity can be gleaned from the critical bands explication of pitch.
Three empirical facts warrant mention. First, octave judgements on average diverge slightly from 2:1 frequency ratios. It follows that normal subjects either misperceive frequency ratios or perceive as the octave something
other than small whole-number frequency ratios. Second, subjects make far
fewer correct octave judgements for tones that are separated by more than
an octave or two. Finally, octave judgements concerning sinusoidal tones
are much more difficult to make than octave judgements for complex tones.
Complex sounds, recall, have multiple pitch determinants corresponding
to local maxima among critical band values. The pitch-determining analysis
for harmonic complex sounds yields multiple pitch candidates given by coinciding subharmonics of the pitch determinants, but the subharmonic shared
by the most pitch determinants is the pitch. The analysis into subharmonics
depends upon the notion of templates formed on the basis of experience
with harmonic sounds, primarily as they occur in speech. The question
arises, Why these particular templates? It may be that brute and simple
repetition is responsible for our acquiring templates with pitch values corresponding to frequency multiples (f, 2f, 3f, 4f, . . . ). A much more plausible
explanation is that the elements of such templates, when they occur simultaneously, have a high degree of what researchers have described as ‘sensory
consonance’.15 There are several factors that contribute to sensory consonance, including the phenomena described as “roughness”, “sharpness”, and
“tonalness”. Details aside, this is significant because roughness, sharpness,
and tonalness are each given an account in terms of critical band energies.
So, Zwicker and Fastl state with respect to roughness:
It is assumed that our hearing system is not able to detect frequency as such, and is only able to process changes in excitation
level or in specific loudness at all places along the critical-band
rate scale; thus the model for roughness should be based on the
differences in excitation level that are produced by the modulation [which results in roughness]. . . . Because masking level is
an effective measure for determining excitation, it can be used to
estimate the excitation-level differences produced by amplitude
modulation.16
Similarly, regarding sharpness:
15
16
See, e.g., Zwicker and Fastl (1999), Gelfand (1998), and Terhardt (1974).
Zwicker and Fastl (1999), p. 261.
APPENDIX A. THE ALTERNATIVE VIEW
78
It is helpful in developing a model of sharpness to treat sharpness
as being independent of the fine structure of the spectrum; the
overall spectral envelope is the main factor influencing sharpness. In Chaps. 6 and 8, it was shown that the spectral envelope is psychoacoustically represented in the excitation level
versus critical-band rate pattern, or in the specific loudness versus critical-band rate pattern. For narrow-band noises . . . sharpness increases with critical-band rate for center frequencies below
about 3 kHz (16 Bark). The increment . . . increases strongly for
higher critical-band rates.17
The point is that roughness and sharpness are fully explicable in terms of
energy within particular critical bands, so that sensory consonance depends
entirely on the amount and distribution of energy across various critical
bands. Particular harmonic templates can therefore be expressed as sequences of critical band values that have a high degree of consonance.
Again, complex harmonic sounds often have multiple pitch candidates
which result from coincidence of subharmonics. In some cases a pitch candidate other than one corresponding to the fundamental frequency is even
identified as the pitch of the sound. But subsequently-presented complex
tones that stand in the octave relation have several pitch candidates in common, and indeed have many subharmonics in common beyond those that
constitute pitch candidates.18 Given that alternate pitch candidates for a
single complex sound are actually perceptually discriminable (with proper
direction of attention), tones that stand in the octave relation have a substantial degree of perceptible commonality. Contrast the octave with the
fifth. Two tones related as fifths have fewer pitch candidates in common,
and also have fewer subharmonics in common beyond those pitch candidates.19 But the affinity between notes separated by a fifth can be seen to
17
Zwicker and Fastl (1999), pp. 241–242.
Take two complex tones with fundamental frequencies of 200 Hz and 400 Hz (with
corresponding pitch values of 2 and 4 Barks) and exactly four additional upper harmonics
each: 400 Hz, 600 Hz, 800 Hz, 1000 Hz; and 800 Hz, 1200 Hz, 1600 Hz, 2000 Hz, respectively. These two tones have in common pitch candidates at 100 Hz, 133 Hz, 200 Hz, and
400 Hz. In addition, they each have subharmonics at 57.1 Hz, 66.7 Hz, 80 Hz, 114.3 Hz,
150 Hz, 250 Hz, 266.7 Hz, 300 Hz, 333.3 Hz, and 500 Hz. (Each of these frequency values
in Hz can be converted to a pitch value in Barks).
19
Suppose we consider the previously-mentioned complex tone with 200 Hz fundamental
and a subsequent complex tone with 300 Hz fundamental frequency (each with their first
four additional upper harmonics: 400 Hz, 600 Hz, 800 Hz, 1000 Hz; and 600 Hz, 900 Hz,
1200 Hz, 1500 Hz, respectively). These two complex tones have in common, from among
their respective groups of subharmonics, pitch candidates only at 100 Hz and 200 Hz.
18
APPENDIX A. THE ALTERNATIVE VIEW
79
stem from their common pitch candidates and a fair number of common
subharmonics. This similarity, however, is less pronounced than that between octave-related tones. The respect in which octave-related tones are
the same is that they have a high degree of coincidence among their pitch
candidates and share a substantial number of subharmonics. 20
Two differently pitched tones therefore stand in the successive octave
relation just in case they share the maximum number of pitch candidates
possible given the pitch determinants each contains. This sharing results
from coincidence among the subharmonics of their respective constituents.
Tones stand in the relationship of fifths when their respective subharmonics
exhibit a given pattern of sharing with less coincidence. The account can
be extended to capture the relative similarity of tones standing in the other
musical relations. This avoids the need to posit a basic relation for each of
the musical relations.
Accounting for the musical relations in terms of shared pitch candidates
and subharmonics explains the empirical facts mentioned above. First, the
account depends upon positing templates that consist of critical band values,
which templates are already needed to explain pitch perception for complex
sounds. Template development most likely depends not simply upon frequency ratios, but upon more basic perceptible aspects of tones that are
themselves explained in terms of critical bands. Discrepancies between the
perceived octave and 2:1 frequency ratios occur because the critical band
values that constitute particular templates need not correspond exactly to
harmonic sequences. Next, multi-octave judgements are more difficult than
single-octave judgements because octave perception depends upon subharmonic coincidence. Complex tones separated by multiple octaves simply
have fewer of their first eight subharmonics in common as the number of
octaves increases. Octave judgements for sinusoidal tones are, for a similar
reason, more difficult to make than octave judgements for complex tones.
Simple tones have fewer subharmonics to compare and share no pitch candidates.
In sum, successive octave-related tones share pitch candidates in virtue
of having in common many of their constituents’ coinciding subharmonics.
This sharing is thus a matter of the two tones’ having in common memThey also have in common subharmonics at 50 Hz, 85.7 Hz, 120 Hz, 150 Hz, 300 Hz, and
400 Hz. There are simply fewer opportunities for coincidence than with octave-related
tones.
20
Simple sinusoidal tones are thought by researchers to stand in musical relations only
in a sense that is parasitic upon the musical relations of complex tones. See Gelfand
(1998), p. 356.
APPENDIX A. THE ALTERNATIVE VIEW
80
bership in salient harmonic templates. The templates are themselves determined by perceptible aspects of sounds, such as tonality, roughness, and
sharpness, that constitute sensory consonance. Each of these attributes is
explicable in terms of the critical band energies of various types of sounds.
The templates are acquired through experience with harmonic sounds—
speech, in particular—but reflect genuinely objective characteristics of sounds.
So, sharing subharmonics is a matter of belonging to the same simple pitch
sequences, which are characterized by the consonance of their elements. The
octave is the maximum degree of such sharing among sounds that differ in
pitch. Recall the pitch helix. When pitch height is expressed in terms of
Bark values, the octave relation—the relation that exists between successive
pitches with the same angular position—is determined by common membership in particular harmonic sequences. Such harmonic sequences are
determined by characteristics of critical band energy profiles and explain
the pitch of complex sounds. The critical bands account of pitch therefore
explains the affinities of tones that stand in musical relations.
A.3
Spectrum Shift
Spectrum inversion scenarios are familiar from discussions of color and color
perception.21 Audition presents an actual instance of a less drastic qualitative shift. Pitch discrimination depends upon activity at various places
along the basilar membrane which is transduced by hair cells into electrical impulses along the cochlea. Cochlear implants are designed to replace
damaged hair cells by stimulating cochlear nerves just as the basilar membrane would. A processor first analyzes the stimulus into various critical
band energies and then presents electrical impulses of appropriate strengths
to tuned nerves. But electrodes often are not placed with exact precision,
so the implant delivers impulses to nerves that are tuned to inappropriate
frequency bands. The result is that sounds seem higher or lower in pitch
than they do to normal perceivers.
Suppose Shifty has undergone cochlear implant surgery after losing his
hearing due to hair cell damage. Sounds at 10 Barks (1270 Hz) now seem
to him the same in respect of pitch as sounds at 12 Barks (1720 Hz) used to
seem when his hearing was normal. Suppose Norm has undamaged normal
hearing. Sounds at 10 Barks seem to Shifty the way sounds at 12 Barks
seem to Norm. Now imagine that Shifty was completely deaf from birth
before receiving cochlear implants.
21
See, e.g., Hardin (1988), Block (1990), and Byrne and Hilbert (1997).
APPENDIX A. THE ALTERNATIVE VIEW
81
Pitch shift due to cochlear implants presents a physicalist about pitch
with two challenges. I shall consider them in turn. First, the physicalist
must make it plausible that Shifty misperceives the pitches of sounds. For
suppose that Shifty and Norm are both presented with a sound at 10 Barks.
An intuitive description of the case is that (i) Shifty and Norm have different
pitch experiences in response to the very same sound. If (ii) neither of them
mistakenly perceives the pitch of the sound, then (iii) pitch must not be
the physical property I have suggested—since pitch and Barks come apart,
pitch is not what is given by Bark values.
Why accept (ii), that both Shifty and Norm have veridical pitch experiences when presented with a 10 Bark tone? Given that it is natural to say
that Shifty indeed misperceives the pitches of sounds, (ii) is only plausible
if we already hold a version of internalist subjectivism about pitch according to which pitch can vary independently of external physical stimulus,
or if sounds have multiple pitches capable of being discerned by different
perceivers. But if we accept that pitch is the property of sounds that is
responsible for the pitch experiences of ordinary hearers, then Shifty simply
misperceives pitch.
Couldn’t most of the population be fitted with cochlear implants, thereby
making the notion of a “normal hearer” useless? Not so. ‘Normal’ in this
context does not mean simply “common”. Rather, it refers to the usual
human means of sound perception. The cochlea is suited to detect the presence of energy within various portions of the audible spectrum, but cochlear
implants alter the ordinary causal processes involved in audition, and therefore contribute to abnormal pitch perception. Once we rule out skepticism
about whether those with auditory perceptual systems quite like our own
enjoy pitch experiences that are similar in character to ours, pitches are just
the properties of sounds responsible for those common experiences. Abnormal pitch perception is characterized by deviance from such common pitch
experiences. Since Shifty’s experiences exhibit such deviation, he misperceives the actual pitches of sounds.
This suggests a second argument. Despite the different way in which
Shifty’s experiences are caused, they are caused by sounds with particular
Bark values in a reliable way. In fact, since Shifty’s auditory experiences
are reliably caused by sounds with particular Bark values, and since he uses
the language of pitches just as we do, we might think that his thoughts and
experiences track just the same pitches that Norm’s do. If so, he does not
misperceive the pitches of sounds since his experiences purportedly represent
the very same property that Norm’s do. Sounds at, for example, 10 Barks
just produce in them experiences with different subjective characters. If so,
APPENDIX A. THE ALTERNATIVE VIEW
82
either (i) is false and Norm and Shifty enjoy the same pitch experiences,
or pitch experience is more than just a matter of representing an external
physical property.
Shifty does not, however, perform the same as Norm does in various
psychophysical experiments. Importantly, he performs systematically differently on masking experiments used to determine critical bandwidths. While
for Norm a band of noise 200 Hz wide maximally masks a tone of 10 Barks
(1270 Hz), Shifty requires a band 260 Hz wide to mask the same tone.
Likewise, Shifty’s just noticeable frequency differences differ from Norm’s
throughout the audible spectrum. Shifty and Norm even make different
judgements about the musical relations among tones. The upshot is that
since Norm’s critical band sensitivity differs from Shifty’s, their pitch experiences track different properties of sounds. When Shifty hears a sound at
10 Barks (1270 Hz), he perceptually responds to the presence of energy in a
larger frequency band than Norm does. Shifty’s pitch experience for a 1270
Hz tone reflects an energy maximum in a 260 Hz wide critical band. Since
the pitch a sound is heard to have depends upon its having a critical band
maximum within a particular ordering of bands, and since Shifty responds
to sound energies within differently centered critical bands, he and Norm
hear different pitch properties. But the properties Shifty detects are analogous in structure to those that ordinary perceivers detect. Shifty’s pitch
experiences in response to 1270 Hz tones and Norm’s pitch experiences in
response to 1720 Hz tones both reflect the presence of energy within a 260
Hz critical bandwidth. So Shifty misperceives pitches because, in light of his
miswiring, his 260 Hz wide critical band is miscentered. Shifty and Norm
indeed have different pitch experiences, and the difference in Shifty’s pitch
experience is captured by his representing a different property of sounds.
Why are the critical band properties discriminated by Shifty not equally
deserving of the name ‘pitch’ ? Creatures could have evolved, after all, with
auditory systems responsive to those properties of sounds. Would they not
then have counted as experiencing pitch?
Pitches are anthropocentric properties on the physicalist account I have
proposed. They are physical properties of sounds that interest us in light
of our perceptual capacities. It may be that other creatures could discern
properties of sounds quite similar to our pitches, but those would not be
our pitches. They would be remarkably similar, and ordered critical bands
would explain why their pitch-like properties exhibit a relational structure
quite like ours. But they would not be the same properties of sounds that
are responsible for our experiencing sounds to have pitch.
APPENDIX A. THE ALTERNATIVE VIEW
A.4
83
Timbre and Loudness
The critical bands account of pitch can be extended to timbre and loudness.
Since timbre depends upon the spectral constituents of a sound regardless of
phase, the specific timbric quality of a sound is determined by its distribution
of energy across all critical bands. Though two sounds may share a pitch,
their individual characters are constituted by the presence of energy within
different critical bands. Timbre is a matter of a sound’s critical band profile.
Loudness poses two unique complications for a theory of the audible
qualities. First, sound intensity (in dB) correlates only loosely with perceived loudness. For instance, the loudness of a 40 dB tone at 4.9 Barks
(500 Hz) is the same as that of a 60 dB tone at 0.5 Barks (50 Hz). (See
Figure A.2: Equal Loudness Contours).
Second, two tones of equal intensity that are separated by less than a
critical bandwidth have a combined loudness proportional to the sum of their
individual intensities. So two 60 dB tones at 8.5 Barks (1000 Hz) match the
loudness of a single 63 dB tone at 8.5 Barks (10 log(2I/I 0 ) = 3 dB increase).
This continues to be the case as the frequency difference between the two
test tones is increased up to the critical bandwidth (160 Hz). However, with
frequency separations greater than one critical bandwidth, the combined
loudness of the two tones increases gradually until, at a separation of 2000
Hz, their combined loudness matches a single tone of 70 dB—roughly double
the loudness of a 60 dB tone. With large frequency differences, the combined
loudness of two tones is given by the sum of their individual loudnesses.
Furthermore, the loudness of uniform noise is 3.5 times that of an 8.5 Bark
(1000 Hz) tone of the same intensity level.
Zwicker and Fastl conclude from this that
critical bandwidth plays an important role not only for the loudness of noises of different bandwidth, but also for the loudness
of two-tone complexes as a function of the frequency separation
of the tones.22
The critical bands account of pitch can thus be extended to provide
an account of the objective loudness of a sound. The weighting of energies
within particular critical bands must accommodate the relative contribution
to loudness made by sounds with energy in those critical bands. Indeed, the
specific loudness of a narrow-band tone, relative to other tones with the same
intensity, depends upon its weighted energy within an appropriate critical
22
Zwicker and Fastl (1999), p. 212.
APPENDIX A. THE ALTERNATIVE VIEW
84
band. The total loudness of a tone complex can then be understood as an
integration of specific loudness over all critical bands. 23 Two tones that fall
within a critical band have less energy over all critical bands, and therefore
less loudness, than equivalent tones separated by one or more critical bands.
The critical bands account thus provides an account of loudness that lends
intelligibility to empirical results which confound simpler views. 24
23
See Zwicker and Fastl (1999), Chapter 8, “Loudness,” for a full explication.
Thanks, in particular, to Adam Elga, Gilbert Harman, Gideon Rosen, and Jeffrey
Speaks for discussion and comments on the material in Chapter 3 and Appendix A.
24
APPENDIX A. THE ALTERNATIVE VIEW
85
Figure A.1: Critical bandwidth as a function of frequency. [From Zwicker
and Fastl (1999), Psychoacoustics: Facts and Models, Second Edition, New
York: Springer-Verlag, Figure 6.8, p. 158, with permission.]
APPENDIX A. THE ALTERNATIVE VIEW
86
Figure A.2: Equal loudness contours. [From Zwicker and Fastl (1999),
Psychoacoustics: Facts and Models, Second Edition, New York: SpringerVerlag, Figure 8.1, p. 204, with permission.]
Bibliography
[1] Aristotle. (1987). A New Aristotle Reader. J.L. Ackrill (ed.).
Princeton: Princeton University Press.
[2] Armstrong, David M. (1961). Perception and the Physical
World. London: Routledge and Kegan Paul.
[3] Bennett, Jonathan. (1988). Events and Their Names. Oxford:
Clarendon.
[4] Berkeley, George. (1975). Berkeley, Philosophical Works. M.
R. Ayers (ed.). London: Dent.
[5] Blauert, Jens. (1997). Spatial Hearing: The Psychophysics of
Human Sound Localization. Cambridge, MA: MIT Press.
[6] Block, Ned. (1990). “Inverted Earth.” In James Tomberlin (ed.), Philosophical Perspectives 4. Atascadero, CA:
Ridgeview.
[7] ——. (1995). “On a Confusion about a Function of Consciousness.” Behavioral and Brain Sciences 18: 227–247.
[8] Boghossian, Paul A. and Velleman, J. David. (1989). “Colour
as a Secondary Quality.” Mind 98: 81–103.
[9] ——. (1991).“Physicalist Theories of Color.” Philosophical
Review 100 (1991): 67–106.
[10] Bradley, Peter and Tye, Michael. (2001). “Of Colors, Kestrels,
Caterpillars, and Leaves.” Journal of Philosophy 98: 469–487.
[11] Breen, N., Caine, D., Coltheart, M., Hendy, J., and Roberts,
C. (2000). “Toward an Understanding of Delusions of Misidentification: Four Case Studies.” Mind and Language 15: 74–
110.
87
88
BIBLIOGRAPHY
[12] Bregman, Albert S. (1990). Auditory Scene Analysis: The
Perceptual Organization of Sound. Cambridge, MA: MIT
Press.
[13] Byrne, Alex. (2001). “Intentionalism Defended.” Philosophical Review 110: 199–240.
[14] ——. (forthcoming). “Color and Similarity.” Philosophy and
Phenomenological Research.
[15] ——. (ms).
manuscript.
“Colors
and
Dispositions.”
Unpublished
[16] Byrne, Alex, and Hilbert, David (eds.). (1997). Readings on
Color, Volume 1: The Philosophy of Color. Cambridge, MA:
MIT Press.
[17] ——. (forthcoming BBS). “Color Realism and Color Science.”
Behavioural and Brain Sceinces.
[18] Carlile, Simon. (1996). Virtual Auditory Space: Generation
and Applications. Austin, TX: R.G. Landes.
[19] Davidson, Donald. (1970). “Events as Particulars.” In Essays
on Actions and Events. Oxford: Clarendon Press, 1980.
[20] Dretske, Fred. (1995). Naturalizing the Mind. Cambridge,
MA: MIT Press.
[21] Fara, Michael. (2001). Dispositions and Their Ascriptions.
Princeton University Doctoral Thesis.
[22] Gelfand, Stanley A. (1998). Hearing: An Introduction to Psychological and Physiological Acoustics. 3rd ed. New York:
Marcel Dekker.
[23] Hardin, C.L. (1988). Color for Philosophers: Unweaving the
Rainbow. Indianapolis: Hackett.
[24] Harman, Gilbert. (1990). “The Intrinsic Quality of Experience.” In James Tomberlin (ed.), Philosophical Perspectives
4. Atascadero, CA: Ridgeview.
BIBLIOGRAPHY
89
[25] Helmholtz, Hermann. (1954). On the Sensations of Tone .
New York: Dover. (Translated conforming to the Fourth German Edition of 1877 by Alexander J. Ellis).
[26] Kim, Jaegwon. (1973). “Causation, Nomic Subsumption, and
the Concept of Event.” Journal of Philosophy 70: 217–236.
[27] Lewis, David. (1986). “Events.” In Philosophical Papers, Volume II. New York: Oxford University Press.
[28] ——. (1997). “Finkish Dispositions.” The Philosophical Quarterly 47: 143–58.
[29] Locke, John. (1975). An Essay Concerning Human Understanding. Peter Nidditch (ed.). Oxford: Clarendon Press.
[30] Lycan, William. (1996). Consciousness and Experience. Cambridge, MA: MIT Press.
[31] Martin, C.B. (1994). “Dispositions and Conditionals.” The
Philosophical Quarterly 44: 1–8.
[32] McGinn, Colin. (1983). The Subjective View: Secondary Qualities and Indexical Thoughts. Oxford: Clarendon.
[33] Mestre, J., Mullin, W.J., and Gerace, W.J. (1998).
“Course Notes for Physics 114, Theory of Sound
with Applications to Speech and Hearing Science.”
http://www-unix.oit.umass.edu/~phys114.
[34] Nudds, Matthew. (2001). “Experiencing the Production of
Sounds.” European Journal of Philosophy 9: 210–229.
[35] Pasnau, Robert. (1999). “What is Sound?”
Quarterly 49 (1999): 309–324.
Philosophical
[36] ——. (2000). “Sensible Qualities: The Case of Sound.” Journal of the History of Philosophy 38 (2000): 27–40.
[37] Peacocke, Christopher. (1984). “Colour Concepts and Colour
Experience.” Synthese 58: 365–382.
[38] Physics-faq/acoustics: Acoustics FAQ,
http://ear.berkeley.edu/acoustics.html.
BIBLIOGRAPHY
90
[39] Rosen, Gideon. (1994). “Objectivity and Modern Idealism:
What is the Question?” In Michaelis Michael and John
O’Leary-Hawthorne (eds.), Philosophy in Mind. Dordrecht:
Kluwer.
[40] Schouten, J.F. (1940). “The Residue, A New Concept in Subjective Sound Analysis.” Proceedings of the Koninklijke Nederlandse Akadademie 43: 356–365.
[41] Stevens, S.S. and Volkmann, J. (1940). “The Relation of Pitch
to Frequency: A Revised Scale.” American Journal of Psych.
53: 329–353.
[42] Stevens, S.S., Volkmann, J., and Newman, E.B. (1937). “A
Scale for the Measurement of the Psychological Magnitude
Pitch.” Journal of the Acoustical Society of America 8: 185–
190.
[43] Strawson, P.F. (1959). Individuals. London: Methuen.
[44] Terhardt, Ernst. (1974). “Pitch, Consonance and Harmony.”
Journal of the Acoustical Society of America 55: 1061–1069.
[45] ——. (1979). “Calculating Virtual Pitch.” Hearing Research
1: 155–182
[46] ——. (1980). “Toward an Understanding of Pitch Perception:
Problems, Concepts, and Solutions.” In G. van den Brink and
F.A. Bilsen (eds.), Psychophysical, Physiological, and Behavioral Studies in Hearing. Delft: University Press, 353–360.
[47] Terhardt, E., Stoll, G., and Seewann, M. (1982a). “Pitch of
Complex Signals According to Virtual Pitch Theory: Tests,
Examples, and Predictions.” Journal of the Acoustical Society
of America 71: 671–678.
[48] ——. (1982b). “Algorithm for Extraction of Pitch and Pitch
Salience from Complex Tonal Signals.” Journal of the Acoustical Society of America 71: 679–688.
[49] Thomson, Judith Jarvis. (1983). “Parthood and Identity
Across Time.” The Journal of Philosophy 80: 201–220.
BIBLIOGRAPHY
91
[50] Tye, Michael. (1995). Ten Problems of Consciousness. Cambridge, MA: MIT Press.
[51] ——. (2000). Consciousness, Color, and Content. Cambridge,
MA: MIT Press.
[52] Westfall, Richard S. (1980). Never at Rest: A Biography of
Isaac Newton. Cambridge: Cambridge University Press.
[53] Woolsey, C.N. (1960). “Organization of the Cortical Auditory System: A Review and Synthesis.” In G.L. Rasmussen
and W.F. Windle (eds.), Neural Mechanisms of the Auditory
Vestibular Systems. Illinois: Thomas, Springfield, 165–180.
[54] Yost, William A. and Watson, Charles S. (eds). (1987). Auditory Processing of Complex Sounds. New Jersey: Erlbaum.
[55] Zwicker, Eberhard. (1961). “Subdivision of the Audible Frequency Range into Critical Bands (Frequenzgruppen).” Journal of the Acoustical Society of America 33: 248.
[56] Zwicker, Eberhard and Fastl, Hugo. (1999) Psychoacoustics: Facts and Models, Second Updated Edition. New York:
Springer-Verlag.
[57] Zwicker, Eberhard and Terhardt, Ernst (eds.). (1974). Facts
and Models in Hearing. New York: Springer-Verlag.
[58] ——. (1980). “Analytical Expressions for Critical-band Rate
and Critical Bandwidth as a Function of Frequency.” Journal
of the Acoustical Society of America 68: 1523–1525.