Center for Computer Research in Music and Acoustics August 1982
Department of Music Report No. STAN-M-11
INSTRUMENTAL TIMBRE AND RELATED ACOUSTICAL PHENOMENA IN THE PERCEPTION OF MUSIC
John M. Chowning, John M. Grey, James A. Moorer, Loren Rush
Research sponsored by National Science Foundation
CCRMA DEPARTMENT OF MUSIC
Stanford University Stanford, California 94305
Ongoing research at the Stanford Center for Computer Research in Music and Acoustics has been aimed at the investigation of the perception of musical timbre, using advanced developments in the field of digital signal processing for the preparation and presentation of auditory materials. Various Interwoven phases of research have been undertaken; they are oriented towards uncovering the distinctive features and dimensions In musical timbre perception. More recently, we have been looking at the perception of timbre In temporal contexts, attempting to more directly relate laboratory findings to the normal activity of musical perception. In the same vein, we have also initiated the cross-cultural study of musical perception, examining the effects of timbre on the way in which musical sounds are combined with one another; we are looking for common underlying perceptual principles that can explain widely varying musical traditions that exist in different cultures. Finally, we are also able to relate timbre with our acoustical phenomena in music perception, such as dynamic loudness, apparent duration and apparent onset time of time-varying, naturalistic tones.
This research was supported by the National Science Foundation under Contract NSF BNS 77-22305-Al,2. The views and conclusions contained in this document are those of the authors and should not be Interpreted as necessarily representing the official policies, either expressed or Implied, of Stanford University, any agency of the U. S. Government, or of sponsoring foundations.
The primary perceptual attributes of sound most studied in the field of psychoacoustics have bee pitch, loudness and localization. Although there has been much speculation about the perception c timbre, there has been far less substantive work on this vastly complex topic of audition. Since timbre is multidimensional, corresponding to diverse and interactive attributes of tone, it has been particular] difficult to study. Furthermore, there exists no generally accepted definition of timbre in terms of ii constituent elements. Timbre has been most often negatively defined as the differences serving t distinguish two signals that are equal in pitch and loudness. This does not delineate the possible physical bases for the phenomenal differences, nor does it discuss the various phenomenal aspects c timbre. Throughout the history of timbre research, different operational definitions have bee employed, each suggesting a particular list of physical properties for generating stimuli and a particular subjective measurement of timbre. Unfortunately, little work has utilized stimuli that match sound perceived in normal, every-day settings; most signals used in psycho acoustical research have failed t achieve the dimensional richness found in naturalistic sounds.
In much of the classical research on timbre, the definition of timbre has been operationally over limited to consist only of a steady-state spectrum; at that, this spectrum has almost always been limited to components having harmonic frequency ratios. Certainly, this provides a way of formulating manageable research topic, and yet, today we still possess far too little knowledge about the perception of timbres more characteristic of music; naturalistic sounds are time-varying in nature and not stead) state. Furthermore, we have almost no knowledge about the perception of timbre in such naturalistic listening conditions as musical contexts; a majority of research has been limited to isolated sound outside of any temporal context. Another notable limitation of past research is that most studies have been exclusively oriented towards musical timbres of the non-percussive and periodic variety. We have no basis for extending research findings to include the different kinds of percussive and inharmonic sounds that occur in our own musical practice, and which in fact serve as the basic tribal foundation in certain other musical cultures of the world, such as Indonesian music
Limitations in past research have been due, in part, to the possibilities of signal generation in the laboratory. Until recently, it has been impossible to generate artificial stimuli which could duplicate the complexities inherent in natural sounds. The equipment available up until the last decade was no capable of producing signals with a high degree of control or reliability. This was a factor in forcing the more limited definitions of timbre employed for research purposes. However, with advances ii digital signal processing techniques, many of the former limits of equipment and techniques to contra the production of signals have been overcome. In principle, a digital computer can generate any sign and a loudspeaker can transducer; it also can analyze any signal that a microphone can transmit into it memory. Much of our work has been oriented towards perfecting the techniques for these two complementary processes, analysis and synthesis, and applying them to more complex musical timbre: both harmonic and inharmonic, and to musical contexts. Our aim in this process has been to come t model the essential acoustical elements of musical timbre, those significant aspects of a signal that are salient in the perception of timbre and closely related musical dimensions.
Ongoing research at Stanford University's Center for Computer Research in Music and Acoustics h been to investigate the perception of timbre, making use of the most recent developments in the file· of digital signal processing and multidimensional perceptual scaling. Various interwoven phases research has been explored.
A. Analysis by synthesis
A major line of our research program has been in the area of analysis by synthesis research. Brief this type of work relates to the investigation of timbre perception through the digitization (recorder into the computer) of natural instrumental tones, their analysis (using digital signal procession techniques) and subsequent synthesis based upon the acoustical information obtained from the anal: (this may be altered for the resynthesis). Of central interest in this work is the perceptual salience any alteration of the acoustical information used for resynthesizing a natural timbre. Discriminate then, is the primary perceptual measurement in most studies. The intent of this area of research twofold: 1) to uncover the perceptually significant features which are discriminable when eliminate and 2) to reduce the complexity of the acoustical representation of timbre to its most perceptually salient attributes. The following specific projects have led to an increased understanding in both of the areas..
1. Higher-level data reduction.
The systematic exploration of simplifications of the acoustic information used for synthesis has yield· some of our most interesting findings in this area. Visiting scientist C. Charbonneau and Cr performed a study that led to very promising findings. The aim of the work was to further simplify the mode! for timbre that was based on the earlier work of Grey (1975), testing the simplifications I their discriminability with the already successfully simplified tones of an earlier study (Grey and Moorer, 1977; Appendix IX). The degree of further new simplifications which remained virtual indiscriminable was impressive.
a) Our first successful simplification involved the reduction of the number of independent amplitude functions necessary for the resynthesis of a tone. An average temporal amplitude function was constructed on the basis of the amplitude functions of all the harmonics (scaled in time such that all would begin and end together). This single time function then was substituted for each of the may independent harmonic amplitude functions by scaling its peak amplitude to that of the particular harmonic (thus preserving overall spectral shape) and by scaling its time progression such that it beg; and ended at the same times as the original function for that harmonic (thus preserving the related' temporal pattern of the onsets and offsets of the harmonics of the tone). The method was found to I successful for a surprisingly large number of timbres, and the results indicate that the most important aspects of the temporal amplitude functions of the harmonics are their patterns of onset-offset are their spectral envelope, and not necessarily the fine details and differences of their individual shape The cases where this substitution was the least successful involved tones which had strongly shifter formant regions, the implication being that certain spectrally changing timbres will need more than οι single function to control the amplitudes of their harmonics through time.
significant simplification was made in the frequency domain. Here, it
was found that for large number of tones, a single frequency
function could also be successfully substituted for the man
independent temporal frequency functions
of the individual harmonics. Past research has shown the
substitution of constant frequency functions for
the time-varying functions was highly
discriminable, thus indicating that various factors of the temporal changes found in the acoustic:
analysis of the harmonics' frequency functions were indeed perceptually salient. In the present finding
a single time-varying frequency function was successfully substituted for the independent function
controlling the harmonics. Usually this function was that of the fundamental harmonic, scaled to the
various harmonic frequencies by multiplication.
A third area of simplification, given the
success of the above two simplifications in many cases, was
a simplified representation of the
timing pattern of onsets and offsets for the harmonics of a ton.
Smooth mathematical functions were
substituted for the actual pattern of entries and exits of the
harmonics. Success was found with
best-fitting third-order polynomial representations for the more
highly variant analyzed timing
relationships. The differences that were produced were generally on the
order of 5 milliseconds; hence the indiscriminability of the operation points out a temporal integration in hearing that would be expected on the basis of other psychoacoustic research (Dillon, 1979). The
perceptual cues important in the temporal structure of an instrumental timbre in the attack and decay, then, may often be represented in a more simplified manner than actually occurs acoustically. This has been recently supported by A. Benade (1981).
d) A final area of simplification in this
work involved simplification of the shape of the spectre
distribution. Here, we attempted to substitute formant-type representations for the actual distribution οf
spectral energy. It may be expected that this type of representation would remain indiscriminable for the original spectral shape because of masking and integration of energy within critical bandwidths in the ear. We found, however, that small changes in the actual levels of the harmonics were often easily
detected (similar to the findings of Dillon, 1979).
Based upon the results of this work, a further study of the relationships among these simplification for the 16 different timbres used in earlier work (Grey & Moorer, 1977) was done. The analysis am interpretation of the data was recently published (Charbonneau, 1981). This work, as extendd both into inharmonic tones and musical contexts, is discussed below in the next two areas of research.
2. The analysis and perception of inharmonic timbres.
Several inharmonic timbres, both from Western music and also from the Indonesian musical tradition have been recorded into computer memory. We have digitized many of the percussive sounds used ii orchestral music of the Western tradition, including a wide variety of bell sounds. Additionally, w have digitized all of the sounds from two different orchestras of metallophones that represent two important sets of instruments in the Indonesian musical tradition: 1) several sets of Balinese gende wayang and 2) one complete Javanese gamelan.
Indonesian music is largely based upon timbres that produce inharmonic spectra, and we consider important musical material for perceptual research because it contains many of the most extreme differences from Western music in terms of timbral structure. These differences are important, because they have helped to distinguish learned and innate patterns of pitch perception (see Divenyi, 19 1980 and Houtsma, 19S0). We will discuss this more in section C, which looks into the perception relationships between timbre and intervals.
As a first step towards the analysis by synthesis process as applied to inharmonic timbres, we attempt to use the phase vocoder technique (Moorer, 1976) to analyze the acoustical properties of the timbre from Balinese gender wayang, an instrument typical of Indonesian music. After much testing, concluded that the phase vocoder presented problems with inharmonic spectra that were not ea< solved. The phase vocoder analyzes a signal with a set of evenly-spaced bandpass filters. This is id for harmonic tones, where the energy of the spectrum is evenly-spaced in frequency. However, where there is inharmonic energy, quite often it may be simultaneously analyzed by two adjacent filters. Τ recombination of outputs of two adjacent channels was found to be a non-trivial problem, due to n< linearities introduced into our system of analysis. Hence, we have temporarily abandoned the ph; vocoder in favor of developing alternative methods more appropriate for the analysis of inharmonic energy.
Working with J. Ο. Smith, a graduate student specializing in digital signal processing, we have b« developing a method of analysis based upon the output of individual tracking filters with compl output which can be transformed into amplitude and phase (or frequency) information. The filter c be set to any center frequency through time, and thus can track changing frequencies, always keeps the energy centered in its bandwidth, thereby overcoming the problem of energy being analyzed at t edge of a channel in the inharmonic case. The bandwidth of the filter can also be controlled, so that may be set to a value most appropriate for the particular spectral context; if there are several components that are close together, narrow bands can be used to analyze them. We expect that the technique will yield far more manageable acoustical data in the case of inharmonic tones than either our previous methods, which have been mainly appropriate to the harmonic case.
3. The analysis and perception of timbres in musical contexts.
We have taken first steps towards direct research into the effects of musical context on timbre perception. The study referred to above (Grey, 1978) shows that musical context has a strong effect the perception of timbre, and this effect is not easily predictable from studies of isolated tones. Strawn, a Ph.D. candidate at our center, is working on the analysis of musical contexts for his doctor dissertation.
For Strawn's thesis, a number of simple two and three note groups of notes have been record* examples of the most primitive musical contexts. Several different instruments have been digitizing including one brass, string and woodwind instrument. Different musical intervals were recorded, as w as different ways of playing the simple short musical phrases. We are looking at how one note change into the next, given the conditions of instrument, interval and articulation. Aspects of timbre in cont< will be the focus of this work. Mr. Strawn has succeeded in developing an algorithm for automatic modeling this data with line-segment approximations (Strawn, 1980).
Β. Multidimensional scaling
A second research area is the analysis of perceptual similarity data using multidimensional scalar techniques. Spatial representations of the perceptual relationships between stimuli are constructed : that distances between the stimulus points in the space correspond to their psychological "distances" measured by the similarity judgment. The similarity judgment is seen to be more neutral and general in nature than ratings of the stimuli upon more stimulus-specific verbal scales; in that the listeners a: not instructed to attend to specific attributes of tone, there is less inherent experimenter being introduced. The spatial representation, or solution, of the similarity data is then interpreted in terms < the physical properties of the stimuli underlying their relational arrangements.
We have explored the perception of temporal patterns for timbres as related to the similarity structu: for isolated tones. The formation of melodies based not upon pitch patterns, but rather upon pattern of timbre, was first proposed by the composer, Schoenberg. Recently, R. Erickson (1973) has revived interest in this topic with an experiment in timbre pattern perception, Grey collaborating in one phase of the experiment. We have looked at this topic more systematically in a pilot study, by producing simple temporal patterns of pitches and timbres, alternating at different rates. For example, the pitches continually alternating (A, B, C, A, B, C, ...) with four timbres continually alternating (trump< horn, bright cello, muted cello, trumpet,...). Whether the combined melody of pitches played by timbre is heard to perceptually segment into "threes", based on the pitch sequence, or "fours", based on the timbre sequence, depends upon the relationships of the timbres. In fact, we found that the similar structure for the tones as uncovered through multidimensional scaling was useful in predicting the strength segmentation based upon the timbral pattern perception versus the pitch pattern (Grey, 1977]
We have found in this preliminary research that a temporal context increases the perceptual importance of relationships along the spectral axis of the scaling solution, and decreases the strength ι relationships along the family-related, temporal axes. For instance, in the case above, the timbre pattern was dominant, and the segmentation of the sequence was not broken into "fours" but into "twos": the trumpet and bright cello formed one stream against the counter-stream of the horn and muted cell This was counter-intuitive in that it opposed instrument family membership (which would red υ "four" to "two" by joining trumpet-horn and cello-cello). However, it did correspond to links on the spectral axis of the similarity scaling. Systematic research has shown that the distances of timbres c the spectral axis predicts the strength of the timbral pattern versus pitch pattern, with tones mo separated in the spectral dimension forming more strongly independent timbre streams. This finding would seem to correspond with other results in the area of stream-segregation perception (McAdar and Bregman, 1979).
C. Harmonicity and the perception of intervals
Harmonicity refers to the frequency ratios of the energy within the spectral distribution of a timbre, the spectrum is harmonic, then it is composed of partials having integer frequency ratios with the frequency of the lowest energy (the fundamental). If it is inharmonic, then it has partials who frequencies are not in simple integer ratios to the lowest frequency of energy. The former type < timbre indeed serves as the foundation for Western music: vibrating strings, reeds, lips, vocal chord are typical means of excitation. The frequencies of vibration in the spectra of such sounds are near harmonic (there are small and perhaps insignificant departures from true harmonicity in most of the sounds). There are other musical traditions, such as Indonesian music, founded upon sound that an inharmonic in nature: vibrating bars free at both ends and gongs provide the sources of excitation. Additionally, many percussive instruments and bells within Western music comprise class inharmonic sounds.
In the research on musical timbre perception we found that most studies have been exclusive oriented towards Western musical timbres of the non-percussive and periodic variety. As a result research done at CCRMA, we have seen an increase in research on the perception of inharmonic timbres. Moreover, we have established contact with research groups in The People's Republic China who are currently working in this area (Ma, 1980 and Xiang-peng, 1978, 1980). Clearly, the feeling is international in scope that inharmonic spectra play an important part role in the perception of timbre and have heretofore been sorely neglected.
The relationship between spectral distribution (and timbral harmonicity) and the perception intervals has become an increasingly important topic. Some contemporary theories of pitch percept» consider pitch may be a learned attribute (Terhardt, 1974) and that it is possible that our music intervals are related directly to the harmonic overtone structure that we learn by association. If this the case, then the timbres that we hear from birth provide the materials for forming specific types associations. In our cultural experience, this material is harmonic in nature, hence, possibly, the intervals that we use in our music relates to those intervals found in the harmonic series, those have simple integer ratios, like the octave (2:1), fifth (3:2) and fourth (4:3) (see Divenyi 1979, 19S0 and Houtsma 19S0).
A contrasting point of view, which is the more classic view of Helmholtz extended by recent research (Plomp & Levelt, 1965; Kameoka & Kuriyagawa, 1969), is that the psychophysical roughness sinusoidal interactions predicts the composite consonance or dissonance of specific musical intervals, mathematical model for the dissonance of an interval exists, taking into account the specific frequency and amplitudes of all the partials of the simultaneous tones. Given harmonic spectra, the model predicts maximal consonance of those intervals used in Western music the set of intervals with simple integrations (the same ratios as found in the harmonic series). This theory goes on to show that tunings intervals close to integer ratios, but not exactly integral, will still be relatively high in consonance. The model accomodates the intervals actually used in modern, equal-temperament tuning. The model al seems to work to predict the relative consonance perceived for inharmonic tones (see Piszalski and Caller, 1979a,b).
Both theoretical viewpoints suggest that the specific set of intervals found in musical scales is related the timbral material out of which such scales are formed (albeit for different reasons). These theory are indistinguishable for harmonic tones, hence the increasing importance of understanding what happens with inharmonic spectra. We have begun to look at this issue in two ways. The first w; examines the perception of inharmonic spectra that are synthetically generated by stretching the frequency ratios of harmonic partials, and looks at various aspects of interval perception for such spectra. The second way examines the connection between the inharmonicity found in the natural timbres actually used in Indonesian music and the lack of simple-integer frequency ratios in the tuning of intervals; we seek, in this cross-cultural study of interval perception, to find underlies perceptual principles that can explain the widely varying tuning practices that exist in different musical cultures.
Our research in how harmonicity affects pitch perception and tuning has brought into the forefront the question of how harmonicity relates to fusion in timbre perception. A brief review of past resin in fusion, as well as current work being done in that area, will be discussed in section 3 below.
1. Stretched partial; and intervals
The basic materials used in this research were first suggested by J. R. Pierce. The spectrum of the inharmonic stimulus is synthetically generated by stretching the frequency ratios between the partials a harmonic tone by a similar stretch factor. Pierce (1966) was originally interested in a comparison the stretching of the partials with a similar stretching of the intervals used in musical contexts. He w; in essence, interested in assessing the influence of psychoacoustic consonance and dissonance on the sense of musical harmony. Traditional Western musical timbres have harmonic spectra, and the intervals used in tuning are simple-integer ratios. This has been hypothesized to relate to consonance and dissonance, where consonance relationships in intervals are maximal for harmonic series at simple integer ratios between fundamentals. An alternate hypothesis, however, is that the periodicity between fundamentals is the key factor in harmony, where simple-integer ratios are again the most period relationships. Since these two theories cannot be contrasted for normal Western practice, based c harmonic spectra, Pierce was interested in examining the effects under the conditions of stretched inharmonic spectra.
Working with M. V. Mathews, various experiments of stretched partials and stretched tunings we performed (Marcus, Mathews & Pierce, 1979). Findings indicate: 1) stretching does not destroy the key sensing ability of harmonic relationships; 2) stretching does destroy the perception of finality in harmonic cadence; 3) removal of selected dissonant overtones in a cadence using normal limber materials has little effect on the sense of finality, hence, dissonance relationships have little effect c the finality of normal musical cadences; however, 4) augmenting the dissonance relationships in cadence by using special timbres will have an effect on the sense of finality. The findings indicate that there are effects of the consonance relationships in the harmonic case that are preserved in the inharmonic cases, yet these effects do not necessarily relate to the perception of finality in cadences.
The use of these timbral materials in the study of interval perception was taken up by Dr. E. Cohen, research affiliate at our center. In her research (Cohen, 1979a,b,c,d), a number of experiments we done concerning the perception of intervals using these inharmonic spectra. She had listeners adjust the frequencies for one of two simultaneously sounding tones, both of which were composed of stretch* partials. The two intervals tuned were the octave and the fifth, normally having fundamental frequency ratios of 2:1 and 3:2, respectively, in the case of harmonic spectra. When there was more than a five percent stretch factor in the spectra, there were two distinctive styles of tuning that different individuals adopted. The first was tuning to match partials, hence preserving the relationships ι consonance found in the harmonic cases for perfect octaves and fifths. In the inharmonic, stretch* case, then, the octave and fifth were stretched by the same ratios as the partials. The alternate strategy found in other individuals was tuning the fundamental components only, to a 2:1 frequency ratio regardless of stretching and dissonance relationships. These individual differences turned up again the quite different research discussed immediately below, in part (b), of cross-cultural, naturalist perception.
2. Cross-cultural research on inharmonicity and interval perception
The timbres that predominate in most of Indonesian music are those having inharmonic spectra. It an important musical culture for perceptual research since it embodies many of the most extreme differences from Western music in several important musical dimensions. Among the most interest! of these differences are: 1) timbres with inharmonic spectra, as opposed to the harmonic spectra that ; the basis of Western music; 2) tuning systems that do not ordinarily contain simple-integer ratios _ intervals, as opposed to the many nearly simple-integer ratios found in the intervals of Western music (2:1, 3:2, etc.); and 3) the lack of standardization of intervals within scales between different sets instruments, as opposed to Western music, in which almost any instrument can play with any other d to standardization of tuning. We feel that there is a connection between timbre and tuning, specifics between the inharmonicity of the timbre and the non-integer, non-standard nature of the Indonesian tuning system for intervals.
The approach here is slightly different from the above approach to the topic, because we are looking at how an already developed musical system, acoustically based upon naturally inharmonic sound structures, constructs intervals in its tuning. In this way, we are examining the effect of actual inharmonic spectra on tuning in a fully developed, naturalistic setting. We are here specifically interested in the inharmonic timbres from Balinese gender wayang, a form of metallophone. We ha recorded and analyzed a number of such instruments that have been tuned by various Balinese tunc Here, we are attempting to uncover the significant effects of the inharmonic spectral structure on I choices of intervals in their tuning.
Perceptual research carried out in a cross-cultural context is attempting to uncover the relationships between timbre and tuning practices. We are interested here not only in the perceptual underpin of widely diverse tuning practices, Western versus Indonesian, but also in the possible differences perceptual styles for the two groups of people, based upon extremely different musical experience (Divenyi 1979, 1980 and Houtsma 19S0).
For our initial attack on the question, we have started research on the perception of the octave. Western musical practices, the perfect octave is considered to be a 2:1 ratio of fundamental frequency. This can also be expressed as 1200 cents (100 cents for each equal-tempered minor second, the distance between two immediately adjacent notes on the piano). In the Balinese instruments we measured, found that the octaves varied between 1130-1300 cents, and were not normally at 1200 cents. Τ tuning system in Bali actually insures that octaves on many instruments will either be too large or I small.
a) The ideal perceptual octave. Several recent psychoacoustic studies have concluded that the b perceptual octave for both simple and complex tones is generally slightly wider than a 2:1 ratio frequencies (Sundberg and Lindqvist, 1973; Ward and Martin, 1951; Hood, 1974; Risset, 1978). T: has also been put forth as a correlate and possible explanation of the stretched octaves found both piano tuning and in Indonesian tuning (Dowling, 1977). In order to get at this more directly, we are advisable to determine the frequency ratio for inharmonic tones that corresponded to the idea; perceptual octave with experienced Western musicians.
We noted, first, that all of the perceptual research on interval perception that came up with the finding that the perceptual octave was wider than 2:1 was done for sequential intervals. In music, the significance of the octave as a harmonic interval entails the simultaneous sounding of the two notes. Ν data existed for the best tuned perceptual octaves in the simultaneous condition, so we first set about I find whether the sequential condition had any bearing on the simultaneous case.
We used four spectral conditions in a tuning experiment. Listeners used a method of adjustment ι tune up the best perceptual octave. Many of the professional musicians used were experienced tuner One Balinese musician visiting America at the time were used. The four different spectra used were: pure tones (fundamental alone), 2) two-component tones (fundamental plus second harmonic), Balinese tones (fundamental plus inharmonic partials), and 4) modified Balinese tones (fundaments inharmonic partials and an added second harmonic). The frequencies of Balinese inharmonic ton» has been analyzed, and roughly correspond to the spectral ratios of an idealized vibrating bar free ; both ends: 1.0, 2.7, 5.4, 8.9, and so forth. It is most important to note that normally, there is an absent of energy near the frequency of a second harmonic. Most theoretical viewpoints on interval perception would predict that energy near the ratio of 2.0 (the second harmonic) is used in tuning the octave (the fundamental of the higher tone is in direct proximity with the second harmonic of the lower tone Hence, we created conditions (2) and (4) to test this.
Findings, both for Western and Balinese listeners, was that the best perceptual octave indeed corresponded to a frequency ratio of exactly 2:1 in all four cases. This implies serious limitations in applying the findings of a stretched ideal octave, discovered from sequential tuning, to the simultaneous case most common in music. It also implies that if Balinese tuners wanted to tune in perfect octaves of 1200 cents, they would be able to do so. Hence we became interested in what aspect of the inharmonic sounds was important in establishing the octaves they actually use. This was done in study (b) below. (In research for her doctoral dissertation, Cohen found both stretched an compressed octaves in tuning simultaneous intervals with harmonic and inharmonic overtones, which contrasts with our findings. See (Cohen, 19S0a,b).)
b) Octaves in Balinese music. The next major step in our research project investigated the relationship between inharmonic timbres and the actual tunings of octaves in Balinese music. There were two possible hypotheses concerning the tuning practices in Bali. First, that the spectral components of the particular tones that were tuned determined the octave size for those tones. This would be based upon a dissonance interaction. The frequency ratios of 2.7 and 5.4 were considered possible determinants c a dissonance relationship that was close to 2:1 - in the actual sounds measured, the variance around 2 and 5.4 might have explained the variance found in the tuning of octaves. Contrasting with the hypothesis, our second hypothesis was that the absence of energy at the second harmonic eliminated a significant dissonance relationships with the fundamental of the upper tone, so that octave tuning became a process without the limiting interaction of dissonance. A third hypothesis, based upon the learning of spectral structures for particular sounds, leading to intervals in musical practice, ; mentioned above, was tested. However, we found no correspondence between the average ratios use for intervals and those between the partials of a normal tone. The perceptual learning theory was not pursued. Yet we are interested in more general aspects of perceptual learning, as in the contrast c Western and Balinese listeners, each trained in extremely different musical cultures.
This research involved the retuning of existing Balinese intervals to correspond more to perfect 2: octaves in the simultaneous condition. Actual musical examples were generated on the computer, using the real tones from the gender wayang instrument. Digital signal processing was used to retune the fundamental frequencies of the sounds. Also, processing was employed on the spectral structure of the sounds, retuning the upper partials and even adding in energy near the theoretical second harmonic Four experiments were performed, where the stimuli were: 1) Original sounds versus fundamentals π tuned to 2:1 octaves where the upper partials of the re-tuned fundamental were unchanged; 2) Origin: sounds versus fundamentals re-tuned to 2:1 octaves with the upper partials re-tuned at the same rati of shift with the shifted fundamental; 3) Original sounds with perfect second harmonics added versa fundamentals re-tuned to 2:1 octaves, upper partials unchanged and energy added in at a perfect second harmonic frequency, 2:1 from the fundamental; and 4) Original sounds with stretched second harmonics added versus fundamentals re-tuned to 2:1 octaves, upper partials unchanged and energy added in at a stretched second harmonic frequency, corresponding to the ratio found for the octave in the original tuning.
Tuning preferences among the paired alternatives for the four conditions were determined for Balinese musicians and instrument tuners. It was found that there were two individual styles of preference, that came out in conditions (3) and (4) above. With conditions (1) and (2), listeners preferred either the original tunings or the perfect octaves, consistently, showing that there were no strong determinants c octave size in a musical context with the original timbres of Balinese instruments. In conditions (3) an (4), certain listeners maintained a preference for one particular size octave, while other individual adjusted the preferred octave size to maximize the consonance relationship between the added partial; (near the second harmonic) and the fundamental of the upper tone, hence a perfect octave was preferred in the case of the 2:1 harmonic ratio and a stretched (original) octave was preferred for stretched ratio of the partial. These two styles of listening correspond to the individual difference found in Cohen's research in section (1) above.
We conclude from the findings that the inharmonic spectral structure of Indonesian sounds allows for non-standard tuning practices and non-integer frequency ratios because of the lack of energy near the second harmonic. This is in correspondence with a consonance and dissonance theory of interval; perception: there is no dissonance interaction with the fundamental of the upper tone in octave tuning so the process is not strictly limited to 2:1 frequency ratios to maximize consonance, as it is in Western music based upon harmonic series. The importance of consonance relationships between the upper partials of the original sounds, for instance the approximate 5.4 ratio of the lower tone to the 2.7 of the upper, was suggested not to play a major part in tuning preferences by the results of condition (2 Further experimentation may reveal this to be a possible factor, but for these sounds we found little evidence for a deterministic effect of spectral structure on octave tuning. Rather, Balinese music appears to be free to tune intervals as an active parameter of musical aesthetics, in contrast to Western music, precisely because there seems to be a lack of timbral determinism based on consonance a dissonance.
3. Spectral fusion
Recently, Mike McNabb, a composer and researcher at our center, discovered a perceptual phenomenon while experimenting with a vocal synthesis technique. He obtained the Fourier Transform of a soprano tone that was recorded and digitized at the center. He then synthesized tone, using additive synthesis, such that the spectral balance was the same as indicated by the Fourier Transform. At first, the frequency for each harmonic was kept constant; however, the tone did η sound vocal at all. In fact, it didn't even sound natural. When some vibrato was added, such that; harmonics were affected synchronously, the percept was strikingly realistic.
John Chowning explored this phenomenon even further. He synthesized a tone such that ea< harmonic (a sine tone) began one after another, but remaining sustained. Again, the spectral balance of the partials corresponded to the levels obtained from a Fourier Transform of a recorded soprano tone. With all harmonics playing, it was very easy to hear each harmonic separately, as if there we many sources, or voices (each source being a sine tone). But as soon as a common vibrato was add< to all the harmonics, the sound fused into a percept of a single source ~ that of a sung soprano tone.
These examples show that temporal aspects of a tone are important features of its timbre, even during its so-called steady-state portion. In other words, spectral balance alone cannot determine timbre because a constant spectrum may not fuse, and one can't really have timbre without fusion. Ti examples also raise this question: What are the characteristics of a sound that cause it to fuse into percept of a single source with a particular timbre?
Elizabeth Cohen has investigated the role of harmonicity (or the lack thereof) in the fusion of complex tones. She has found that fusion depends on temporal envelope, degree of inharmonicity, and spectral content (Cohen 1979a,b,d and 19S0a). Stephen McAdams, a graduate student at our center, is al investigating fusion and source identification for his doctoral research. Results of his preliminary work appeared in (McAdams and Bregman, 1979). The work of Cohen and McAdams will be valuable aid in determining the parameters for timbre.
D. Timbre and perceived onset
Finally, in this section we would like to cover some of the interests we have in looking at the relationships between timbre and other aspects of tone, such as perceived onset time, duration and loudness. We would expect rather direct and strong relationships between timbre and these other ton attributes because they are effects of similar acoustical dimensions. Spectral shape is a determinant ι timbre as well as of loudness. Similarly, the temporal envelope of a signal is a determinant of onset duration and timbre. Combining the two, a spectral shape that changes with time is a complex description of timbre, and also provides the material for making loudness, onset and duration judgments on naturalistic signals, such as actual musical timbres.
In past research, we have found, for example, that a model of loudness perception for steady-state spectral distributions (Zwicker & Scharf, 1965) was useful in modeling the timbral dimension relating perceived spectral brightness (Grey & Cordon, 1977). The recent derivation of a model for loudness perception for time-varying tones (Zwicker, 1977) presents encouraging possibilities for extending t\ model to include various other aspects of the perception of time-varying tones. Already, this model hi been useful in analyzing various aspects of the perception of timbre.
12 I. Perceived onset time
We have long been interested in formal models for the temporal properties of tone. One possible ι related to the above, concerns modeling the relationships actually found along temporally-related dimensions of timbre perception uncovered in our multidimensional scaling studies. Various subject correlates to these temporal dimensions have been noted, one being the "hardness" or "explosiveness" the attack (found with D. L. Wessel, 1977). In the hopes that this attribute may have something to with perceived onset time for tones, Cordon and Crey have run an experiment to equalize the on times for the timbres used in the original studies.
The procedure (like that of J. Vos and R. Rasch, 19S0) involved the setting of two tones (e.g. A and to be locked into rhythmic phase such that their alternating series (i.e. Α Β Α Β Α Β „.) made perceptually isochronous rhythm and the perceived onset of the Β tones perfectly bisected the duration between the A tones. By adjustment, the listener set the temporal delay between A and B, where I physical delay between all A's and all B's was equal. In looking at the relative delays for the differ stimulus tones, all of which were taken from the set used in the multidimensional scaling studies, independent measure of onset time has been achieved.
Regardless of the success of the experiment in terms of modeling our temporal axes from the scale research, we still have data for the onset relationships among a set of timbres. We hope to be able mode! These onset relationships taking advantage of the temporal features of the new model; loudness perception mentioned above (Cordon, 191).
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