Definitions of Timbre (compiled by G. Sandell)

Helmholtz (1885)

"When we hear notes of the same force and same pitch sounded successively on a piano-forte, a violin, clarinet, oboe, or trumpet, or by the human voice, the character of the musical tone of each of these instruments, notwithstanding the identify of force and pitch, is so different that by means of it we recognize with the greatest of ease which of these instruments was used." (p. 19) "...the amplitude of the vibration determines the force or loudness, and the period of vibration the pitch. Quality of tone can therefore depend upon neither of these. The only possible hypothesis, therefore; is that the quality of tone should depend upon the manner in which the motion is performed within the period of each single vibration." (p. 19) " what extent can the differences of musical quality be reduced to the combination of different partial tones with different intensities in different musical tones?" (p. 65) "There has been a general inclination to credit quality with all possible peculiarities of musical tones that were not evidently due to force and pitch. This was correct to the extent that quality of tone was merely a negative conception: But very slight consideration will suffice to show that many of these peculiarities of musical tones depend upon the way in which they begin and end: . . . differences in the quality of tone of struck strings...partly depends on the rapidity with which the tone dies away." (p: 66) "When we speak in what follows of musical quality of tone, we shall disregard these peculiarities of beginning and ending, and confine our attention to the peculiarities of the musical tone which continues uniformly. But even when a musical tone continues with uniform or variable intensity, it is mixed up, in the general methods of excitement; with certain noises, which express greater or less irregularities in the motion of the air." (p. 67) "Such accompanying noises and little inequalities in the motion of the air, furnish much that is characteristic in the tones of musical instruments... Notwithstanding the absence of these noises, it is generally possible to discriminate the-different musical instruments; although it must be acknowledged that under such circumstances the tone of a French horn may be occasionally mistaken for that of the singing voice; or a violoncello may be confused with an harmonium: . . . In the present chapter we shall at first disregard all irregular portions of the motion of the air; and the mode in which sounds commence or terminate, directing our attention solely to the musical part of the tone, properly so called, which corresponds to a uniformly sustained and regularly period motion of the air..." (p: 68) "...differences in musical quality of tone depend solely on the presence and strength of partial tomes; and in -no respect on the differences in phase under which these partial tones enter into composition. It must be here observed that we are speaking only of musical quality as previously defined." (p: 127)

Fletcher (1934)

Textbooks customarily believe that loudness, pitch and timbre correlate directly with sound intensity, fundamental frequency and overtone structure... "but these experiments show that a simple one-to-one relationship does not exist." (p. 59) One might define timbre as "that characteristic of sensation which enables the listeners to recognize the kind of musical instrument producing the tone, that is, whether it is a cornet, a flute or a violin." (p. 67) "...changes in loudness or pitch; without in any way changing the overtone structures, will also produce changes in timbre." (p. 68) "...timbre depends principally upon the overtone structure; but large changes in the intensity and the frequency also produce changes in the timbre." (p. 68)

Seashore (1938)

"Tone quality has two fundamental aspects, namely, (1) timbre; which is the simultaneous presence or fusion of the fundamental and its overtones at a given moment, and (2) sonance, the successive presence or fusion of changing timbre; pitch, and intensity in a tone as a whole. The first may be called simultaneous fusion; the second; successive: Each of these may be reduced to the constituent factors which are recordable and measurable and, from the physical point of view, represent the structure of the tone." (p: 95) "In general, we may say that, aside from accessory noises and inharmonic elements, the timbre of atone depends upon (1) the number of harmonic partials present, (2) the relative location or locations of these partials in the range from the lowest to- the highest, and (3) the relative strength or dominance of each partial." (pp. 96-97) ". . . we obtain a definition of timbre as follows: Timbre is that characteristic of a tone which depends upon its harmonic structure as modified by absolute pitch and total intensity. . . .we must also take phase relations into account. Physically the timbre of the tone is a cross section of the tone quality for the moment represented by the duration of one vibration in the sound." (p. 97) Definition of sonance: he first observes that when viewing a movie of any moving object; although we are being presented a series of discrete snapshots of the object appearing stationary, our experience is of actual motion of the object, because the successive snapshots fuse. "The same principle of fusion appears in hearing. In tonal hearing, successive waves come so fast that they cannot be heard as individual waves; that is, we cannot separate the timbre or the pitch or the intensity in one wave from that in the next wave by hearing. The result is that they fuse and for a given period of time, the mean period of clear perception, we hear a resultant pitch; intensity; or timbre which tends to be an average for what is represented in the series of waves that can be grasped in one -moment of perception: The timbre of atone corresponds to the single instantaneous picture; sonance corresponds to the picture progression." (pp.103-104).

Wood (19??)

"Musical 'Quality'.--If a note of a given pitch is played successively on two different musical instruments, and played with exactly the same loudness, we can distinguish between the two sounds and refer each to its appropriate instrument: The basis of this judgment is the 'quality' of the sound. The piano, the violin, the voice, the flute &c., each has its own characteristic 'quality'. The German word for it is 'klängfarbe; the French word (frequently borrowed in English) is 'timbre'. But quality not only enables us to distinguish between two notes produced on different kinds of instruments, it also enables us to distinguish between two notes produced on two different instruments of the same kind. What distinguishes the voice of one singer from that of another and is characteristic of an individual voice is its quality." (p. 61)

Licklider (1951)

"The timbre of a complex sound has usually been defined as the subjective quality that depends upon the complexity or overtone structure of the physical sound. We have seen; however, that both the loudness and the pitch of a complex tone are influenced to some extent by its overtone structure. We must, therefore, not fall back upon the ill-defined notion that timbre has to do with the distribution or pattern of pitch and loudness in the total sensation Until careful scientific work has been done on the subject, it cam hardly be possible to say more about timbre than that it is a 'multidimensional' dimension." (p. 1019)

Ellis (1885)

Alexander Ellis, translator of Helmholtz's On the Sensations of Tone; struggled with the decision of translating Helmholtz's word Klängfarbe: "I can find no valid reason for supplanting the time-honoured expression quality of tone. Prof. Tyndall quotes Dr. Young to the effect that 'this quality of sound is sometimes called its register, colour, or timbre:' Register has a distinct meaning in vocal music which must not be disturbed. Timbre, properly a kettledrum, then a helmet, then the coat of arms surmounted with a helmet; then the official stamp bearing that coat of arms (now used in France for a postage label), and then the mark which declared a thing to be what it pretends to be. Brun's 'Guinea's stamp', is a foreign word, often odiously mispronounced; and not worth preserving. Colour I have never met with as applied to music, except at most as a passing metaphorical expression: But the difference of tones in quality is familiar to our language." (p. 24, footnote)

ANSI (1960)

" 12.9 Timbre. Timbre is that attribute of auditory sensation in terms of which a listener can judge that two sounds similarly presented and having the same loudness and pitch are dissimilar. NOTE: Timbre depends primarily upon the spectrum of the stimulus, but it also depends upon the waveform, the sound pressure, the frequency location of the spectrum, and the temporal characteristics of the stimulus." (ANSI 1960, p: 45; also in ANSI, 1973)

Levarie and Levy (1968)

"When a violin and oboe; of instance, play the same pitch with the loudness, we can yet distinguish the two tones by their timbre. This property is often ailed the 'tone quality' or the 'tone color.' I advocate ignoring these names, because they tend to create confusion. Tone 'quality' is too general, for logically pitch and loudness are also qualities. Tone 'color' is an optical term which is out of place in acoustics." (p: 63) "...the indirect bearing of loudness on timbre. For as the loudness of atone increases, overtones are aroused that may have been negligible  before; and as it wanes; some overtones are dampened and lost before others. The result is a change of timbre concomitant with a change in loudness." (pp: 63-64) "The point need not be belabored that the smallest change in any agent participating in the creation of a tone...evokes a change in the actually sounding overtone series and hence a corresponding modification of the total timbre. . . . Any change of pressure or position necessarily brings about a fresh overtone constellation; and if a new pitch or a new degree of loudness is the primary purpose of such a change, timbre can justifiably be thought of as an attribute that perpetually characterizes the other properties of a tone. The singer Luisa Tetrazzini claimed that every pitch has its appropriate 'natural' timbre, and many wind players would agree:" (p: 13?)

Schouten (1968)

"When describing a sound as it presents itself to us in auditory perception we are able to characterize it by various perceptual attributes. It may sound loud or weak, high or low, long or short. These attributes: loudness, pitch and duration are the easiest to ascertain in the overall impression of any sound. For all other qualities we have scarcely more at our disposal thin the one and all embracing term: timbre: A very vague way of brining all other unresolved attributes under one general heading. This is an extremely disappointing state of affairs. The tone of the violin, for instance; may sound [xerox copy disfigures one or two words here] and long. But these easily perceptible attributes are the very ones which are the least if invariant with respect to the particular sound of a violin. The vague heading "timbre", though, is precisely the one which covers those invariant acoustic properties which make us recognize the violin." (p. 35) "In most textbooks timbre is defined as the overtone structure or the envelope of the spectrum of the physical sound. This definition is hopelessly insufficient, as I hope to prove by demonstrating that timbre can be expressed in terms of at least five major parameters . . . " (p. 38) The five parameters are "l. The range between tonal and noiselike character, 2: The spectral envelope, 3. The time envelope in terms of rise, duration and decay, 4. The change both of spectral envelope (formant glide) or fundamental frequency micro­intonation), 5. The prefix, an onset of a sound quite dissimilar to the ensuing lasting vibration." (p. 42)

Risset and Mathews (1969)

They cite the generally accepted definition of timbre as "the attribute that enables the listener to identify the instrument producing the tone." (p. 23)

Plomp (1970)

He refines the ASA definition to "that attribute of sensation in terms of which a listener can judge that two steady complex tones having the same loudness, pitch and duration are dissimilar." (p. 398) Schouten's comments after Plomp: "We can play a violin at different loudnesses, different durations and different pitches, but it is always a violin: We say, well; that is its timbre. But this includes many aspects..." (p. 411) He lists harmonic sounds, noiselike sounds, contributions of the time envelope, the way the onset differs from the rest of the tone, etc.. Plomp agrees that we need more carefully defined words, and using timbre to count for all of this is problematic.

Erickson {1975)

"Clearly timbre is a multidimensional stimulus: it cannot be correlated with any single physical dimension." (p. 4) "TIMBRE OR TONE COLOR? The word or phrase we use as a handy reference is much less important than the idea to which it refers. I generally use the term "timbre" but often use "tone color" in the same sense. Neither term is very satisfactory, nor is "tone quality" much of an improvement." (pp. 6-7) "Objections may be raise that musical timbre should be equated with the quality of the speaking voice rather than with the individual speech sounds; that it is the 'clarinet quality' rather than the individual sounds which is significant, and that the overall 'clarinet quality' corresponds to the quality of a speaker's voice. I do not mean to exclude this aspect of timbre: But overall 'clarinet quality' can be shown to have no clear-cut one-to-one relationship to the acoustical signal either! We can no more synthesize a clarinet from a single description of the signal than we can synthesize all the ah sounds we use in speech from a single acoustical recipe. Analysis of the gamut of clarinet tones might lead one the say that it is three instruments, rather than one!" (p. 3) In the section called "Timbre as Carrier": "The chief function of timbre in most Western concert music of the past has been that of carrier of melodic functions. The differences of timbre at different pitches and in different registers of instruments . . . have been treated as nuances." (p. 12) The contrast is the use of timbre as objects, where these differences are highlighted as much as possible (esp. by using disjunct melodic lines that prevent the listener from hearing timbre regularity).

Grey {1975)

"Timbre may refer to the features of tone which serve to identify that a musical sound originates from some particular instrument or family of instruments, for example, that it is an oboe, or perhaps some sort of double-reed instrument; or maybe just some woodwind instrument." {p. 1)

Hajda, Kendall and Carterette (1997)

"Based on research findings and [previous] definitions... it is clear that timbre has two principle constituents: (1) It 'conveys the identity of the instrument that produced it' (Butler, 1992, p. 238); and (2) It is representable by a palette or family of palettes {see Martens, 1985) in which tones from different sources can be related along perceptual dimensions. The first constituent is nominal or categorical in nature: the clarinet has a characteristic to its sound, regardless of the pitch, loudness, etc. The second constituent is a hybrid of categorical and ordinal organization: the clarinet is not nasal and is therefore differentiated from the oboe, which is nasal. On the other hand, the clarinet has attributes which make it unique:" (p: 302)

Roederer (1975)

"Timbre perception is, however, just a first stage of the operation of tone source recognition---in music, the identification of the instrument. From this point of view, tone quality perception is the mechanism by means of which information is extracted from the auditory signal in such a way as to make it suitable for: (1) storage in the memory with an adequate label of identification, and (2) comparison with previously stored and identified information. The first operation-involves learning or conditioning. A child who learns to recognize a given musical instrument is presented repeatedly with a melody played on that instrument and told: 'This is a clarinet.' Ibis brain extracts suitable information from the succession of auditory stimuli, labels this information with the qualification 'clarinet' and stores it in the memory. The second operation represents the conditioned response to a learned pattern: When the child hears a clarinet play after the learning experience, his brain compares the information extracted from the incoming signal (i.e. the timbre) with stored cues, and, if a successful- match is found; conveys the response: 'a clarinet.' On the other hand; if we listen to anew' sound, e.g., a series of tones concocted with an electronic synthesizer, our information-extracting system will feed the cures into the matching mechanism, which will then try desperately to compare the input with previously stored information: If this matching process is unsuccessful; a new storage 'file' will eventually be opened up for this new, now identified, sound quality. If the process is only partly successful; we react with such judgments as 'almost like a clarinet' or 'like a barking trombone."' (pp. 138-139)

Plomp (1976)

"... harmonics manifest themselves in -the specific quality or timbre of the complex tone. . . . Timbre is multidimensional. ...we do not have a uni-dimensional scale for comparing the timbres of various sounds. The singular character of timbre become particularly apparent in the dictionary definition of timbre as 'the characteristic quality of sound that distinguishes one voice or musical instrument from another or one vowel sound from another' (Webster). In this broad sense, timbre depends upon several parameters of the sound including the spectral envelope and its change in time, periodic fluctuations of the amplitude or the fundamental frequency, and whether the sound is a tone or noise" (p. 85) Since we are dealing here exclusively with steady-state periodic sounds, timbre, too, will be considered in its most narrow sense as 'that attribute of auditory sensation in terms of which a listener can judge that two steady-state complex tones having the same loudness and pitch; are dissimilar'." (pp. 85-86) "The broad definition of the dictionary and the restricted one just given have one common characteristic: both are virtually negative descriptions. They stat that timbre is neither loudness nor pitch but say no more than that. This definitional vagueness is related to the multidimensionality of the attribute: The tone of a trumpet, containing many strong harmonics, sounds much brighter than a simple tone, but a bright-dull scale does not suffice for describing the diversity of auditory sensations of various complex tones. As early as 1890, Stumpf listed no less than 20 relevant semantic scales as wide-narrow, smooth-rough; round-sharp, etc:, concluding that this wealth of adjectives is comparable only with those used by wine merchants for extolling their products." (p. 86) "...the ear is not as 'phase deaf as had been suggested by earlier investigators." (p: &8) "...we may conclude that the effect on timbre of varying the phase spectrum of a complex tone is small compared with the effect of varying the amplitude spectrum." (p. 91) "...reverberation has...a substantial blurring effect on...timbres... Similarly, it can be shown that the spectral differences between the same vowel sounds produced by different speakers are not much larger than the differences introduced by reverberation." (p. 101) "...what is the effect on timbre if we vary the fundamental frequency, fb, of the stimulus? . . . [it] will depend upon whether timbre is determined by the spectral envelope relative to fb or by the absolute frequency position of the spectral envelope irrespective of f0.. ...a necessary condition for similarity of timbre for sounds with different fundamental frequencies is that they have similar spectral envelopes in terms of absolute frequency though this similarity will necessarily be less for greater differences of fundamental frequency." (p. 107) "clearly...timbre is determined by the absolute frequency position of the spectral envelope rather than by the position of the spectral envelope relative to the fundamental: . . . [Bismarck] found that sharpness as the major attribute of timbre is primarily related to the position of the loudness centre on an absolute frequency scale rather than to a particular shape of the spectral envelope. . . . The dependence of timbre upon frequency would imply that simple tones [sine waves] are also characterized by a specific timbre, to be distinguished from their pitch: Low frequency tones do indeed sound dull and high-frequency tones sharp... The observation that simple tones have some resemblance; depending upon their frequency, with particular vowels also supports this view. Subjects appear to be able to label simple tones rather well in terms of vowels... This resemblance is related to the frequency of the most characteristic formant or combination of formants." (p. 110) "The conclusion that sounds- with different pitch sound most similar if their spectral envelops correspond does not imply that no perceptual differences remain apart from pitch: The same vowel pronounced by a male and a female speaker will sounds quite different. . . . ...the spacing of the harmonics, determined by the fundamental frequency, is responsible for the timbre dissimilarity of sounds with different pitch but similar spectral envelopes." (p. 110)

Pratt and Dock (1976)

"Timbre-is that attribute of auditory sensation whereby a listener can judge that two sounds are dissimilar using any criteria other than pitch, loudness or duration."

Rasch and Plomp (1982)

"Timbre is, after pitch and loudness, the third attribute of the subjective experience of musical tones. Subjectively, timbre is often coded as the function of the sound source or of the meaning of the sound: We talk about the timbre of certain musical instruments, of vowels, and of sounds that signify certain events in our environment (apparatus, sounds from nature; footsteps, the slapping of a door; etc.)." (p: 12) "In a restricted sense timbre may be considered the subjective counterpart of the spectral composition of tones. Especially important is the relative amplitude of the harmonics. . . . Recent research has shown that temporal characteristics of the tones may have a profound influence on timbre as well, which has led to a broadening of the concept of timbre... Both onset effects (rise time, presence of noise or inharmonic partials during onset, unequal rise of partials, characteristic shape of rise curve, etc.) and steady state effects (vibrato, amplitude modulation, gradual swelling, pitch instability; etc:) are important factors in the recognition and, therefore, in the timbre of tones." (pp. 13-14) "Sounds cannot be -ordered on a single scale with respect to timbre. Timbre is a multidimensional attribute of the perception of sounds." (p. 14)

Slawson (1985)

He chooses to dispense with the word timbre altogether; since the classical definition is inadequate, yet widely accepted (p. 19) A theory of sound color should be able "to specify how to preserve color under changes in the loudness or the duration of a sound. We would like to know how to change pitch without changing sound color: Moreover; if sound color itself is a complex phenomenon made up a several different aspects or dimensions, we must show how one aspect of color can be held invariant as other aspects are varies." (p. 17) "There is no agreement, however, about what constitutes an element of sound color. Is sound color to be associated with a specific musical instrument, say, a particular Stradivarius violin? . . . Or should the sound of all instruments of the same type be taken as the basic element of color? When the violin, any violin, is said to have a different 'instrumental color' from the oboe; we are using the term that way:" (p. 15)

Dowling & Harwood (1986)

"Timbre (or tone color) . . . refers to the differences of sound quality among various musical instruments, as well as among the various syllables of speech (hah vs. goo, for example). Sound vary in timbre along several dimensions; just as the syllables pah, poh, tah and toh differ on at least two dimensions. . . . timbre distinctions for speech sounds are fundamentally the same as those required for musical sounds:" (p: 5) "Timbre has always been the miscellaneous category for describing the psychological attributes of sound; gathering into one bundle whatever was left over alter pitch loudness, and duration had been accounted for. Unlike the psychophysical relationships involved in the latter categories, which are relatively straightforward, the relationship underlying timbre are complex and multidimensional . . . The psychological attributes clustered under the heading timbre fall along more than one psychological dimension; that is, sounds do not simply direr in how much timbre they have. And there are several physical dimensions whose variation causes changes in timbre that interact with each other in complex ways." (p. 63)

Houtsma (1989)

Interpretation of the ANSI (1960) definition: "According to this definition, timbre is the subjective correlate of all those sound properties that do not directly influence pitch or loudness. These properties include the sound's spectral power distribution; its temporal envelope . . . rate and depth of amplitude or frequency modulation, and the degree of inharmonicity of its partials. The timbre of a sound therefore depends on many physical variables." (p. 157)

Krumhansl (1989)

Problems in the definition of timbre:
. 1. "the complexity of acoustic measurements" (p. 43) which usually consists of "taking the form of spectral energy distributions and amplitude envelopes. These descriptions, however, are so complex that it is difficult to isolate characteristics that distinguish between timbres." (p. 44)
. 2. "the assumed independence of timbre from other dimensions of musical sound" (p. 43) "Can we really assume the differences in spectral energy distributions are completely uncoupled from pitch perception mechanisms in hearing?" (p. 44)
. 3: "generalizing the notion of timbre beyond the set of traditional orchestral instruments"
Different levels of timbral description:
. 1. "the expressive variations available to performing musicians" (45)
. 2. "commonalities shared by all oboe tones, all bowed violin tones, all timpani tones, and so on" (45)
. 3. Broader family t3istinctions or method-of-production distinctions: "percussive instruments, whose behavior is determined completely at the instant when they are set into motion; and instruments; such as blown and bowed instruments, whose behavior is controlled continuously." (45)
Alternative set of distinctions for describing sound (viz: Schaeffer; McAdams):
. 1. "varying degrees of temporal extent or musical complexity. . . . single, discrete sound events that are heard as being produced by a single source:" (45) . 2. "emergent properties, such as texture, density, streams, and musical gestures." (45)
. 3. "larger-scale musical forms or organizations that grow out of the sound material." (45)

Bregman (1990)

On the ASA definition: "This is, of course; no definition at all. For example; it implies that there are some sounds for which we cannot decide whether they possess the quality of timbre or not. In order for the definition to apply; two sounds need to be able to be presented at the same pitch, but there are some sounds, such as the scarping of a shovel in a pile of gravel, that have no pitch at all: We obviously have a problem: Either we must assert that only sounds with pitch can have timbre, meaning that we cannot discuss the timbre of-a tambourine or of the musical sounds of many African cultures, or there is something terribly wrong with the definition." (p. 92) He points out that part of the problem may stem from-the fact that pitch and loudness are controlled in musical instruments in straightforward, consistent ways, but timbre is not. The methods of varying timbre ''vary from instrument to instrument: . . . When we do find a characteristic of sound that can be obtained on different instruments, such as vibrato, the characteristic tends to be given a label and no longer falls into the nameless wastebasket of 'timbre'." (p. 93) His requirements for a vocabulary for timbre include having labels for salient dimensions that should (1) "act in psychologically simple ways" and should "have straightforward physical definitions." (pp. 93-94) However; he also says: "Until such time as the dimensions of timbre are clarified perhaps it is better to drop the term timbre" (p. 94)

Rossing (1990)

His table 5.1, "Dependence of subjective qualities of sound on physical parameters" lists timbre as being weakly dependent on pressure and duration, moderately dependent on frequency and envelope, and strongly dependent on spectrum: (p: 80) Comment on the ANSI (1960) definition: "This definition suggests that judgment of timbre must take place under conditions of equal loudness and pitch (and probably equal duration as well)." (p. 125) "Timbre or tone quality depends on the frequency of atone, its time envelope, its duration, and the sound level at which it is heard. Under most conditions, the timbre of a complex sound is insensitive to the phase of its components:" (p: 137) . Cho, Hall and Pastore (1993 ) "Normalization is a type of perceptual constancy that can be loosely defined as the process by which the perceptual system adjusts for differences between sources in order to preserve an intended perceptual message." (p. 3) "Timbre is the subjective attribute of source (instrument) that is based on invariant properties that uniquely characterize the tones produced by the source: Unfortunately, the pursuit of an adequate definition of timbre is both related to and dependent upon establishing which characteristics (or combination of characteristics) are important for perceptually determining an instrument's distinctive sound quality." (pp. 6-7)

Handel (1995)

"We will use the term timbre to refer to the perceptual qualities of objects and events; that is, 'what it sounds like.' Traditionally, timbre has been thought of as related to one acoustically measurable property such as that each note of an instrument or each spoken sound of one voice would be characterized by a single value of that property. . . . due to the interactive nature of sound production, there are many stable and time­ varying acoustical properties. It is unlikely that any one property or combination of properties uniquely determines timbre. The sense of timbre comes from the emergent, interactive properties of the vibration pattern. . . . One possibility is that timbre is perceived in terms of the actions required to generate the event. . . . The perception of the production invariances would allow us to hear the same object in spite of large changes in the acoustical signal: Another possibility is that timbre is perceived simply in terms of the acoustic properties and that the connection between the acoustic properties and the object is learned by experience. In this view, the acoustic properties are used to figure out what event was most likely to have produced that sound." (p. 426)


REFERENCES (incomplete)

. American National Standards Institute (H960). USA Standard Acoustical Terminology (Including Mechanical Shock and Vibration) Sl.1-1960 (R1976). New York: American National Standards Institute.

. American National Standards Institute (1973). Psychoacoustic terminology S3:20. New York: American National Standards Institute.

. ANSI { 1960). See American National Standards Institute (1960).

. ANSI (1973). See American National Standards Institute (1973).

. Bregman, A. (1990). Auditory Scene Analysis. Cambridge, MA: MIT Press.

. Cho, J.L., Hall, M.D. and Pastore, R.E. (1993). Normalization of musical instrument timbre. Unpublished manuscript.

. Rowling, V. and Harwood, D: (1986). Music Cognition: New York: Academic Press.

. Ellis, A. (1885). Translator's note. In Helmholtz (1885).

. Erickson, R. (1975). Sound Structure in Music: Berkeley: University of California Press.

. Fletcher, H. (1934). Loudness, pitch and the timbre of musical tones and their relation to the intensity, the frequency and the overtone structure. Journal of the Acoustical Society of America 6, 59-69.

. Grey, J.M. (1975). An Exploration of Musical Timbre. PhD dissertation, Stanford University. Issued through the Department of Music, Center for Computer Research in Music and Acoustics,