Perception of Musical Tension for Nontonal Orchestral Timbres and Its

Perception & Psychophysics 2000.62 (1), 66-80

Perception ofmusical tension for nontonal orchestral timbres and its relation to psychoacoustic roughness

DANIEL PRESSNITZER IRCAM-CNRS, Paris, France

STEPHENMcADAMS IRCAM-CNRS, Paris, France and Unicersite Rene Descartes, Paris, France and SUZANNE WINSBERG and JOSHUAFINEBERG IRCAM-CNRS, Paris, France

Can tension in nontonal music be expressed without dynamic or rhythmic cues? Perceptual theories of tonal harmony predict that psychoacoustic roughness plays an important role in the perception of this tension. We chose a set of orchestrated chords from a nontonal piece and investigated listeners' judgments of musical tension and roughness. Paired comparisons yielded psychophysical scales often sion and roughness. Two experiments established distinct levels ofthese two attributes across chords. A model simulation reproduced the experimental roughness measures. The results indicate that non tonal tension could be perceived consistently on the basis of timbral differences and that it was corre lated with roughness, the correlation being strongeras the perceptualsalience of otherattributes (such as high-pitched tones or tonal intervals) was reduced.

An impression of successive tension and release is a been proposed as a sensory basis for musical consonance common experience while listening to music. The study within the tonal system (Helmholtz, 1877/1954). ofthis intuitive notion is actually fundamental to West Comparing tension and roughness for a set of stimuli ern music theory and has been a matter ofdebate for both assumes that there is a parallel between a complex musical music analysts and cognitive psychologists. Whereas many concept and a basic sensory attribute. This requires a studies have helped us to understand tension perception preliminary specification ofthe two terms and ofthe rea in the tonal framework, the compositional practices of sons for taking a new perspective in considering them contemporary composers raise new questions. The use jointly. ofa musical material that does not draw on the implicitly shared tonal culture may disorient listeners and, hence, Musical Tension in a Tonal Context deprive them ofthe essential landmarks that schemas of The identification of tension-release schemas is the tension and release provide for the appreciation ofa mu starting point for most classical harmonic analyses of sical work. In this study, we propose to investigate the Western music. The method proposed by the music the perception oftension levels for nontonal orchestral tim orist Heinrich Schenker (1935/1979), for instance, de bres by musician and nonmusician listeners. We hypo fines hierarchical structural levels that are, in the end, re thesized that if tension could actually be perceived in ducible to a fundamental Ursatz, which is very similar to such a context, a basic psychoacoustic dimension known a basic pattern oftension and release. The generative the as roughness would account for an important part ofthat ory oftonal music (GTTM; Lerdahl & Jackendoff, 1983), perception. Roughness is an auditory attribute that has which attempts to account for music perception and un derstanding by principles derived from cognitive psy chology, holds the existence ofa network oftension and Part ofthis work was completed thanks to a Fyssen Foundation grant release to be a fundamental axiom. The links it creates to the first author. The authors thank two anonymous reviewers for ex between events over time help us to hear a piece in a co tremely useful comments on earlier versions ofthe manuscript. Corre herent way, rather than in the form ofa juxtaposition of spondence concerning this article should be addressed to either isolated sounds. These schemas have also been proposed D.Pressnitzer or S. McAdams, IRCAM, I place Igor Stravinsky,F-75004 Paris, France (e-mail: pressnitzer@ircam [email protected]). as a basis for arousal and emotion, underlining another aspect oftheir importance in music listening by trained -Accepted by previous editor, Myron L. Braunstein or untrained listeners (Langer, 1967; Meyer, 1956).

There exists no simple, universally valid, and widely case, in the tonal framework, a set of established rules accepted definition of what tension and release actually implicitly shared by the audience is available to express are. To indicate the scope of the notion, let us take the tension and release. basic example ofthe authentic cadence in Western tonal harmony. In this succession oftwo musical events, a dom Musical Tension in a Nontonal Context inant seventh chord based on the fifth degree ofa major The problem is very different for a composer who does scale is considered unstable and dissonant, calling for a not wish to refer to tonality. Let us take, as an example, resolution to a tonic chord based on the first degree, which the genesis ofthe sequence chosen to be the basis for this is stable and consonant. It is generally accepted that this study (score shown in Figure 1). instability constitutes a tension, its resolution a release. Spectral analyses were performed on recorded notes The combination ofthese two is the well-known pattern played on a musical instrument-in this case, a double at the conclusion ofthe vast majority oftonal pieces writ bass with rapidly changing vibrato depth, speed, and ten in the 18th and 19th centuries. However archetypal, bow pressure. Sets offour to five partials, selected from this example embodies several aspects of the notion of among the strongest components of the analysis within musical tension. a fixed band of frequencies, were isolated to create a Tension is thought to be, in part, linked to the intrinsic reservoir of material. Eight chords from this reservoir consonant or dissonant aspect ofthe chords. The domi form the sequence used in this study. The chords were nant seventh chord contains a tritone interval, formerly arranged to create a tension pattern that was needed for known as diabolus in musica (considered to be dissonant, musical reasons. Since the chords resulted from a raw as one may guess), and induces tension. The tonic triad acoustic analysis, no classic tonal function could be as contains only a perfect fifth and a major third, two con cribed to them. Therefore, the composer chose to define sonant intervals, and therefore induces very little tension. an intrinsic tension value for each ofthem by means ofa Attempts were made to ground the idea ofintrinsic con computational algorithm. The greatest common divisor sonance in a feature of the acoustic world: the overtone of the constituent frequencies within a tolerance corre series. That is to say, a set offrequency components with sponding to a sixteenth ofa tone was held to be a quali an integer multiple ofa fundamental frequency has been tative indication of tension: the lower the divisor, the proposed as a physical basis for the phenomenon (Mer more inharmonic and, therefore, tense the chord was senne, 1636/1975; Rameau, 1722/1971). Theoriesempha considered to be. Figure 2 displays the output ofthe al sizing perception then introduced the concept ofroughness gorithm, each chord numbered along the abscissa hav that we will discuss below (von Helmholtz, 1877/1954). ing a computed value along the ordinate. The shape of Tension can also be thought ofin terms ofbeing an ex the curve was also used compositionally to reinforce this pectation, the fulfillment ofwhich brings a release. From tension contour with other musical parameters. this point of view, in the cadence example, the temporal This approach raises several questions. First, is the no succession of the two chords might playa role. The two tion oftension still relevant for material without any tonal notes of the tritone from the dominant chord are unsta function? Second, in the score, the movements are un ble and just one semitone apart from the tonic and the derlined by rhythmic and dynamic differences, whereas third of the tonic triad, which are stable. Therefore, the the tension algorithm used only average spectral domain tritone is said to resolve on the major third. This idea of data and did not take into account these supplementary resolution, or good continuation, has been proposed as a cues. To be coherent, steady-state timbral differences be musical parallel to the laws ofGestalt psychology (Meyer, tween the individual chords should be able to convey the 1956; Narrnour, 1990). tension movements alone. The first aim of this study Lastly, the arousal of the expectation could be linked was, therefore, to establish whether differences in ten to cultural habituation: The classic cadence pattern is rec sion that were not based on tonal, rhythmic, or dynamic ognized, and the resolution is expected. Neural nets have cues could actually be perceived by listeners for these or been able to reproduce the expectancies oflisteners con chestral timbres. In such an unfamiliar context, listeners cerning tonal music after a preliminary training phase would need to rely on universal psychoacoustic cues (Bharucha & Olney, 1989). The habituation consists in until style-specific cues could be learned. internalizing the organization oftonal pitch space (Krum hansl, 1990). In a study in which tension perception for Roughness both melodies and short chord sequences was investigated, Such a psychoacoustic cue may be found in auditory Bigand (1993) confirmed the existence ofexplicit or im roughness. Roughness is caused by the perception ofrapid plicit tonal acculturation. amplitude fluctuations in the range of20-200 Hz. Simul Within the tonal framework, several factors may, there taneous tones close in frequency can cause rough beats fore, have an influence on the perception ofschemas of (e.g., a minor second played in the medium register ofthe tension and release. These influences can be concurrent, piano). Experimental studies that have sought to quantify as in the case ofa perfect cadence, or contradictory, ifthe roughness perception have stressed its close relation to pe composer seeks some kind ofstructural ambiguity. In any ripheral auditory mechanisms. Beating tone pairs for 68 PRESSNITZER, McADAMS, WINSBERG, AND FINEBERG

T2 T4 T5 T6 ,-----, r--I " ~.-~'---' Flute ~ n

" III ~ .. Flute e> n

~~-f3---' tIl.~. fl--fl- l~;::-~---::;: " - ~ Violo e> n

r-3~ ru .. : Alto :~ fJ1J-<~PP-==P ~ 1 f ==- ==- pp

T7 1'8

0 0 -~ " 1"- 1"- Fl.l ~n P n--==ppp =:--n

~ 0 n 0 -f -i-!-!-~ 1\ 'I:: I:: 1= Fl.2 t) n P n--==ppp =:--n

" Cl. ~n P n--==ppp =:--n

1\ 1II_ Vln. ~n P n--==PPP =:--n .. AI. I r=- ~ =P ==-- n

Figure 1. Score of the excerpt from Streamlines (Fineberg, 1997), studied in our experiments. The chords indi cated at the top ofthe staff(T., etc.) were recorded individually, with the same durations and dynamic patterns, and constitute the eight orchestral timbres used as stimuli. which the frequency difference and mean frequency were used to measure the critical band, since the activation pat systematically varied (Plomp & Levelt, 1965) caused max terns on the basilar membrane oftwo elements ofa tone imum roughness to be perceived with a frequency differ pair necessarily have to overlap in order to interact and ence approximately equivalent to 25% ofthe auditory crit produce roughness (see Greenwood, 1991, for a review). ical bandwidth I (as measured by Zwicker, Flottorp, & Further studies refined the quantitative results according Stevens, 1957). As a matter of fact, roughness had been to roughness calculations for complex tones and led to MUSICAL TENSION AND ROUGHNESS 69

10 9 8

7 6 c .s 5 '"c «) E-< 4 3 2 1 0 2 3 4 5 6 7 8 Timbres

Figure 2. The tension measure originally computed by the composer. Timbres (T" etc.) are shown on the abscissa in an ordercorresponding to their appearance in the musical score. The scale along the abscissa is not continuous, but the lines between the points have been added to reveal the tension profile over time. The ten sion scale is arbitrary and was used by the composer as a ranking. computational models based on a sound's spectral com harmonic sounds was shown to correspond to their mu position (Hutchinson & Knopoff, 1978; Kameoka & sical consonance. An interval oftwo simultaneous tones Kuriyagawa, 1969a). The studies ofamplitude-modulated separated by a frequency ratio of 2: I (one octave) produces tones (Terhardt, 1974), of amplitude-modulated noise no roughness, as all the partials of the upper note will (Fastl, 1977), or of frequency-modulated tones (Kemp, correspond to partials ofthe lower note and will cause no 1982) underlined the link of roughness perception with beats. If the two tones are a just fifth apart (3:2 ratio), a the low-pass characteristic ofamplitude modulation cod few partials will be mistuned and will produce a little ing by the auditory system (Viemeister, 1977). Other com roughness. Ifthe frequency difference is a tritone (45:32), putational models have, therefore, been proposed that at a greater number of adjacent partials will cause beats tempt to predict roughness for natural sounds in the and roughness. It follows that the relationship between temporal domain, using signal-processing techniques frequency ratio and perceived consonance should be dif (Aures, 1985). Convergent approaches in the fields ofde ferent if the simultaneous tones do not have harmonic velopmental and comparative psychology have shown that spectra. This effect has been experimentally verified young infants (Schellenberg & Trainor, 1996) or members (Geary, 1980; Mathews & Pierce, 1980). Roughness has, of other species, such as birds (Hulse, Bernard, & Braaten, therefore, been proposed as a sensory basis on which tonal 1995), were more sensitive to differences in roughness of harmony was built, allowing the development of more simple intervals than to differences in interval size. The complex and style-specific rules. finding that different species perceive roughness may be However, most of the experimental results that sup related to the fact that amplitude modulation coding does port this proposition were obtained with simplified stim seem to be a basic feature shared by the auditory systems uli, and the experimental conditions (most often, direct ofboth mammals and birds (Langner, 1992). Physiologi judgments of consonance or pleasantness) used to ob cal correlates to roughness were also found in the dis tain them could be questionable in a real musical con charge patterns of auditory nerve units (Tramo, 1996). text. The contribution ofroughness to tension perception These results confirm the existence of a basic sound at in a musical context has, nevertheless, been addressed in tribute tightly linked to peripheral auditory mechanisms. a study concerning short chord sequences (Bigand, The musical repercussions ofroughness have been ad Parncutt, & Lerdahl, 1996). Roughness, as estimated by dressed as well in some of these studies (Hutchinson & model simulation, played a role in the tension judgments, Knopoff, 1978; Plomp & Levelt, 1965; von Helmholtz, together with other factors, such as implicit acculturation 1877/1954). The relative roughness oftonal intervals of to the tonal function ofthe chords. In addition to study- 70 PRESSNITZER, Me ADAMS, WINSBERG, AND FINEBERG ing directly the perception of tension in nontonal har ing-then-decreasing dynamic pattern (dal niente-mf-dal nientei. monies, a second aim ofthis study was to gather rough An example of the temporal and spectral characteristics ofone of ness estimates ofcomplex nontonal musical sounds and the stimuli is shown in Figure 3. For the sake ofconciseness, the 14 to investigate their contribution to tension perception. other figures corresponding to the other stimuli are not reproduced here but would be very similar. Thus, the stimuli differed mainly in their timbral characteristics. and we will refer to them henceforth as EXPERIMENT 1 orchestral timbres. Apparatus. The recording took place in IReAM's Espace de Method Projection concert hall. A pair of Schoeps microphones was placed Stimuli. A sequence of eight chords was chosen from Stream 5 m from the instrumentalists at an elevation of 3 m. The stereo sig lines (Fineberg, 1997). The score of this sequence, simplified by nals were transferred though a Neve V mixing table onto a Sony the composer for the needs of the experiment, is shown in Figure I. 7050 DAT recorder. They were subsequently digitally transferred The chords were played in an ensemble setting (two flutes, clarinet, and stored on a hard disk at a sampling rate of44.1 kHz with 16-bit violin, and viola) by professional musicians who were members of resolution through a Digidesign Protools interface. the ltineraire ensemble. These chords, sharing a homogeneous reg The experiment used a Soluna SI double-walled sound-insulated ister, were recorded separately with the same duration and increas- booth. The stimuli were played by a NeXT station through an ISPW

6000

lil 4000 :!:::: c: :::J "-

2 4 6 8 10 Time (s) o

-20 Viola Flute 1 Flute 2 ~. -. / iD ~ -40 . '. l/plarinet .. Q) "0 · Violin :::J lot :!::::: <, a. E -60 <

-80

~ .1 I -100}M I 500 1000 2000 5000 Frequency (log)

Figure 3. Waveform and long-term spectrum (obtained by Welch's method) oftheorchestral timbre 17. The pressure unit, as well as the origin ofthe decibel scale, is arbitrary. The spectral components corresponding to the fundamen tal frequencies of the notes played by the different instruments are indicated. MUSICAL TENSION AND ROUGHNESS 7 I

DSP card, Pro 10 digital-to-analog converters and power amplifier, three to five test trials, in which no feedback was given, this first and AKG K I000 open headphones. The measured sound level was stage lasted approximately 30 min. In the second part, listeners' at approximately 80 dBA, adjustable at the request of the subjects so tention was directed to one particular sound attribute, roughness. as to provide the most comfortable listening situation. The experi The concept of roughness was introduced through a typical sound ment was conducted in the PsiExp computer environment running example: a 1000-Hz sine wave that was amplitude modulated at on the NeXT workstation (Smith, 1995). 70 Hz, the modulation depth ofwhich could be varied at will. This Subjects. The experimental group was composed of30 listeners example was considered to produce no roughness if the modulation and did not include the authors. The subjects were 17-45 years old depth was zero, and the maximum roughness was obtainable with (M = 26). They came from widely different backgrounds, some a single amplitude-modulated tone when the modulation depth was working at IRCAM, others being recruited from a database ofvol one (Zwicker & Fastl, 1990). The subjects were instructed that the unteers. The group included 9 professional musicians (composers difference in the quality of the tone they heard when moving the or instrumentalists who had earned money making music over the modulation depth slider was caused by roughness. Special attention last year), 8 amateur musicians (amateur instrumentalists), and was paid to not associating roughness with the dissonant and un 13nonmusician listeners (with no musical training whatsoever). They comfortable aspects ofthe stimuli in the instructions. The 56 pairs were paid for their participation. One nonmusician listener did not were then presented again in random order, and the subjects had to finish the test and was subsequently removed from the results. make forced-choice comparisons concerning changes in roughness. Procedure. The experiment included two parts, one concerning The two parts were always presented in this order (tension judg tension, the other concerning roughness. In the first part, the eight ment, then roughness judgment) in order not to induce a bias in ten timbres were presented in all possible pairs in both orders without sion judgments because of prior knowledge concerning the notion repetition (56 combinations). The subjects had to make a forced of roughness. choice judgment for each pair. The question they had to answer was, Analysis methods. Using the forced-choice judgments as a basis, "Between the two sounds ofthis pair, do you hear an evolution from the eight timbres were ordered along a linear psychophysical scale, 'tension to release' or from 'release to tension' " (translated from to allow a comparison with the composer's predicted tension. A French tension and detente). They were allowed to define tension Bradley-Terry-Luce (BTL) analysis was performed (David, 1988). and release according to any criteria that seemed relevant. After This method makes the assumption that each timbre has a true value

3r-----,------r-----.----,-----r----,----.------,---,

'"Q) '"c "- ..c -, eo "- ;:l 0 "-~ ~ .... 0 0 C .S: -, / '"C "- Q) / Eo- / -1 / Y -2

-3 L----l --I... ..L-. L..-__~ _'_ .l.._____1_ __l 1 2 3 4 5 6 7 8 Timbres

Figure 4. Psychophysical scales for tension (solid lines) and roughness (dashed lines) for Experiment I. The timbres are labeled along the abscissa; the results of the BTL analysis and the standard deviations estimated by bootstrap are displayed along the ordinate. Empty circles represent the BTL values, and dots the means of bootstrap replications. The scales are not continuous, the lines between the points having been added for visual clarity. The scales are arbitrary and represent the contrast between items. 72 PRESSNITZER, McADAMS, WINSBERG, AND FINEBERG

according to tension or roughness. It is this value that we try to es overlap of the 90% confidence intervals between the timate. During any experimental comparison between two timbres, roughness and the tension values as the statistical infer listeners do not compare the true values but, rather, two associated ence criterion, differences are significant for T , 75, T6 , random variables whose distributions are centered on the true val 3 and T . Specifically, T and T are judged as being tense ues. In the BTL hypothesis, the distribution ofthe random variables 7 6 7 is approximated by a hyperbolic secant law with constant variance but not rough, whereas T3 and T5 are judged as being (this yields a cumulative distribution similar to the cumulative nor rough but less tense. mal, differing only at the tails). The proportions ofjudgments ob served are then used to estimate the true values. Additional Analyses The result of the BTL analysis is a single tension or roughness Influence of presentation order. The order of pre value for each timbre. To test whether the subjects judgedthat stim sentation is not considered in the BTL analysis: Each uli indeed differed with respect to tension or roughness, the differ ences along the psychophysical scales were compared with the pair oftimbres was presented in both sequential orders to standard deviation (SD; 68% ofthe central cases) ofthe results, as the listeners, on separate trials, and the judgments for the in an analysis ofvariance (ANOYA). However, an ANOYA assumes same pair were collapsed in a global proportion. The a normal error distribution, which is not necessarily the case here. general influence of presentation order was, therefore, A bootstrap analysis was therefore made, in which the SDs were es specifically tested to check whether it had an effect on timated by using an empirical distribution obtained by means ofre listeners' judgments. An order sensitivity coefficient (ose) sampling with replacement from the sample (Efron & Tibshirani, was defined as the percentage oftrials in which the first 1993). A bootstrap sample size of 100 was used, which is adequate for estimates ofSD. The SDs are displayed in Figure 4 around the timbre ofa pair was chosen as being more tense or rough. mean of the bootstrap values. The departure ofthe error from nor Ifpresentation order had no influence on judgments, the mality is noticeable by the asymmetry of the error bars about the first element ofa pair would be "chosen" as often as the BTL value. second one across trials, and the coefficient should be A test ofthe null hypothesis between two items at a given risk a equal to 50%. The statistical test for the ose was defined is usually achieved by examining the confidence intervals at 1 - 2a as follows: Ifthe 50% value is included in the confidence attached to each of them. If the confidence intervals overlap, the null hypothesis cannot be rejected. Therefore, the statistical crite interval at a given risk, order is considered as having no rion we will adopt for inferring a significant difference between val significant effect. ues at p < .05 is the comparison ofthe absolute difference between The ose is restricted to the interval [0, I], and the use the values with the 90% confidence intervals, defined as ±1.645 * ofits SD to estimate a confidence interval would require SD (Efron & Tibshirani, 1993). a transformation. To avoid that, the confidence interval was estimated by bootstrap and 90% percentiles. A boot Results strap sample size of 2,000 was chosen to estimate the The results are displayed in Figure 4. Let us consider confidence interval, defined as 90% ofthe results around first the tension measure (solid lines). The highest ten the central case (Efron & Tibshirani, 1993). Presentation sion value was obtained by timbre TI , whereas the lowest order was found to have a small but significant influence value was produced by T5• On the BTL psychophysical on tension judgments (ose = .44; ose E [.42 .47];p < .05). scale, the absolute difference between these two ex Order ofpresentation also slightly influenced roughness tremes is more than an order ofmagnitude (10 times) big judgments (ose = .47; ose E [.46.49]; p < .05). Despite ger than the SD attached to the judgments. Using the sig the marginal significance, the bias is small, and we in nificance criterion based on confidence intervals, the terpret this analysis as an indication that order had only differences between the extremes ofthe psychophysical minor importance for both tension and roughness judg scale are significant. Therefore, all the stimuli were not ments. From a practical perspective, the bias is small randomly judged as being equally tense. Closer exami enough to justify the BTL analysis that disregards pre nation ofthe psychophysical scale for tension indicates sentation order. that there were two broad groups: One, which included Listening and/or judgment strategies. The exami TI , T2, T4 , T7, was judged as being more tense, and the nation ofthe agreement between listeners is a means to other, which included T3 , T5 , T6 , T8 , as being less tense. estimate whether all the subjects responded in the same The differences within the groups are not significant, way or whether different strategies appeared among them. whereas the difference between any pair oftimbres across This examination is all the more important because our groups is significant. subject group included professional musicians as well as The psychophysical scale for roughness (dashed lines) amateur and nonmusician listeners, who were required can be examined in a similar fashion. The difference be to judge a complex notion such as tension. A relationship tween the most rough timbre, T2 , and the least rough tim between strategies and subgroups ofsubjects having dif bre, T6 , is an order of magnitude greater than the SDs. ferent musical education would indicate the influence of Significant differences in roughness were, therefore, musical training on the experimental task. perceived between our complex orchestral sounds. The A principal component analysis (PCA; Hotelling, detailed examination shows that the roughness values 1933) was performed to study the tension judgments were more regularly distributed along the psychophysi across subjects. Each listener was considered as a vari cal scale than were the tension values. able (as is the case in Q-factor analysis). The scores at A comparison between the two psychophysical scales tributed to each timbre, defined as the sum ofmore tense indicates that they differ for several timbres. With the non- judgments across the experimental trials for a given lis- MUSICAL TENSION AND ROUGHNESS 73

Listeners and all the subjects have comparable coefficients for this dimension (see Figure 5). In addition, the examination .6 ofthe component scores shows that the order ofthe tim bres from left to right corresponds to the ordering by in creasing tension given by the BTL analysis (Figure 4). .4 Thus, there is a consensus among the listeners as to the ordering of the timbres along the first dimension, since .2 all the listeners have essentially the same coefficients with C'l.... respect to this dimension. =Q) The coefficients of the individual listeners are regu =0 0 larly spread along the second component, indicating dif S-o ferences among the subjects. However, the distribution U -.2 ofsubjects according to their degree ofmusical training (P, professional; A, amateur; and N, nonmusician; see the procedure details) shows no particular cluster ofone -.4 category. Therefore, this dimension cannot be explained in terms ofdifferences in explicit musical education (as measured by our criterion). Concerning the timbre -.6 scores, the component opposes Ts' T6 , and T7 to T3 and -.6 -.4 -.2 0 .2 .4 .6 T4 . An interpretation for this component will be pro Component 1 posed in the General Discussion section.?

Timbres EXPERIMENT 2

2 Fusion and Specificities Let us consider again the way the timbres were com 1.5 posed. Because ofthe use ofspectral analyses ofnatural +T8 sounds, the score contains many notes that have quasi 1 +T6 harmonic relationships. For instance, for T7 (see Figure 3), the viola and the flute are almost one octave apart. The C'l .... 0.5 +T7 harmonics ofthe different instruments overlap to a great =Q) extent. The feeling that derives from this technique, which =0 0 +T1 +T2 is central to the composer's aesthetic, is that offusion be S- +T5 tween the instruments. It would be difficult for us to de 8-0.5 fine acoustically what is meant by the word fusion. Let -1 +T4 us just point out qualitatively that a systematic interroga +T3 tion ofthe subjects after Experiment 1 showed that none -1.5 ofthem was able to name the five instruments used. Lack of segregation has been shown to be related, for exam -2 ple, to difficulty in identifying simultaneously presented vowels (de Cheveigne, McAdams, Laroche, & Rosen -2 -1 0 2 berg, 1995). Component 1 However, careful listening to the timbres reveals the presence ofsalient features in some ofthem. Timbres T , Figure 5. Results of the principal component analysis for the 6 T , and T contain a high flute note that was to be played tension judgments of Experiment I. Top panel: Listener coeffi 7 s cients for the two first principal components. Professional musi at a moderate dynamic (see the score in Figure 1). In the cians are denoted as P, amateurs as A, and nonmusicians as N. recorded performance, these notes emerge from the tim Bottom panel: the component scores for each of the timbres are bres (see, for instance, the amplitude ofthe Flute 2 com displayed. Timbres are denoted as T. to Ts, as in Figure 4. ponent in Figure 3) and give rise to what we call a sur face specificity. For T3 and T4 , intervals with a harmonic function can be discovered in the score (for instance, in tener, were considered to be the observations. The cor T3 , a perfect fifth between the flutes and an almost major relation matrix between listeners could essentially be de third between the clarinet and the second flute). These scribed by two principal components, accounting together intervals evoke a strong syntactic function in the tonal for 75% ofthe variance. The other components, explain system. In the composer's original intention, they should ing less variance than did the original variables, are not have been blended into the global timbre, but the rela considered any further. tive balance between the instruments made them salient The first component is, by definition, the main dimen in our recordings. This constitutes what we call a har sion ofthe data. It accounts here for 56% ofthe variance, monic specificity. 74 PRESSNITZER, McADAMS, WINSBERG, AND FINEBERG

6000

Ul 4000 :!: C ...::J 10 Q) 2000 .£ e- 10 :!:... 0 .0... ~ ~-2000 ::Jen en Q)... a. -4000

-6000 0 2 4 6 8 10 Time (s) 0

Viola Flute 1 Flute 2 -20 ~. / m -. Clarinet ~ -40 Q) "0 ::l :t=a. Violin E -60 « ."" ..

-80

500 1000 2000 5000 Frequency (log)

Figure 6. Waveform and long-term spectrum ofthe remixed timbre T7• The pressure unit, as well as the origin of the decibel scale, is arbitrary. The spec tral components corresponding to the fundamental frequencies of the notes played by the different instruments are indicated.

A new experiment was designed in which modifica This removes a potential cue for auditory segregation tions of the acoustic stimuli were done under the com (Bregman, 1990). After the remixing ofthe eight timbres, poser's supervision to obtain better fusion, according to a procedure similar to that in Experiment I was used to his vocabulary. A multitrack recording was used to make establish psychophysical scales for tension and roughness. a new version ofthe timbres in which the relative level ofeach instrument, as well as the evolution ofthe levels Method over time, was modified. Again, no systematic acoustic Stimuli. New versions ofthe timbres employed in Experiment I criterion for fusion can be proposed. Nevertheless, the were used. The same performances were selected, but the relative balance between the instruments' volumes, as well as their tempo acoustic analyses ofthe new version of T7 are shown as an example in Figure 6. In this case, the remixing had ral evolution, was modified by remixing. An artificial room effect the effect ofcorrecting the balance between the instru was added with a Lexicon processor, to reproduce the natural room color present in the stimuli ofExperiment I. ments, most notably between Flute I, Clarinet, and Flute 2. Apparatus. The multitrack recording on a 33.24A Sony multi The waveform also displays a more regular envelope, the track recorder was made with five Neuman KM 140 cardioid mi attacks ofthe different instruments having been smoothed. crophones, placed 50 ern from each performer's instrument. The MUSICAL TENSION AND ROUGHNESS 75

3.----r----,---.,-----.-----,-----r----,.-----r---,

-2

-3 L----l. -L- L-__-.l- .L-__---I... -l.-__---I_---l I 2 3 4 5 6 7 8 Timbres Figure 7. Psychophysical scales for tension (solid lines) and roughness (dashed lines) for Experiment 2. The timbres are labeled along the abscissa; the results of the BTL analysis and the standard deviations estimated by bootstrap are displayed along the ordinate. Empty circles represent the BTL values, and dots the means of bootstrap replications. The scales are not continuous, the lines between the points having been added for visual clarity. The scales are arbitrary and represent the contrast between items.

remixing was done through a Neve V mixing table to a Sony DAT others. Therefore, the subjects could now establish more 7050 player. The apparatus to play back the stimuli and to collect than two tension levels. Within the groups, the rank order results remained identical to the one used in Experiment I. ing of T7 and T8 decreased, whereas that of T3 increased. Subjects. A group of 10 subjects, from 18 to 45 years of age However, the psychophysical scale for tension still dif (M = 27), participated in the experiment. The subjects had not par ticipated in Experiment I and were recruited in the same manner. fers from the one predicted by the composer's algorithm, The experimental group included 2 professional musicians, 4 ama especially for timbres T6 , T7 , and T8• teur musicians, and 4 nonmusician listeners. They were paid for On the psychophysical scale for roughness, T1 becomes their participation. the most rough timbre, and T8 the least rough. The dif Procedure. The experimental procedure remained strictly iden ference in their BTL values is larger than in Experiment I, tical between the two experiments. although the SDs are also larger. However, the difference is still significant. The general pattern remains similar,

Results but the rank ordering of T6 and T7 increased. The methods ofanalysis defined in Experiment I were The consequence of these changes in both psycho used, and the results are shown in Figure 7. For tension physical scales is that they now overlap to a much greater judgments, the differences ofthe stimuli giving extreme extent, in comparison with the results obtained from Ex values (now TI and T8 ) are more accentuated than in Ex periment I. Only one timbre, Ts' displays a significant periment I, and the difference (according to the criterion difference between tension and roughness values. A cor defined in Experiment I) is still significant (p < .05). relation coefficient was computed to describe the re The general response pattern remains similar: A distrib semblance between tension and roughness judgments. ution into two broad groups is obtained, with the excep The confidence interval ofthe correlation coefficient (re tion that TI is now significantly more tense than all the stricted to [- I, I]) was estimated by bootstrap and 90% 76 PRES SNITZER, McADAMS, WINSBERG, AND FINEBERG

percentiles. The result in this second experiment was r = to give the global roughness that constitutes the model .94; r E [.84.96], whereas the first experiment gave r = output. The corresponding analytic formula developed .53; r E [.32 .73]. With the exception ofthe significant by Parncutt can be found in Bigand et al. (1996). difference for Ts (for which we find no plausible interpre This model has theoretical weaknesses. The calcula tation), these results suggest that roughness could now tion ofroughness between two frequency components is be sufficient to explain tension perception ofthe remixed actually derived from experimental results (Plomp & timbres. Levelt, 1965), but the influence ofdifferences in ampli tudes between interacting components, as well as the Replication ofthe Additional Analyses simple addition between partial roughnesses, is not. This The additional analyses performed on the results of extrapolation of data concerning equal amplitude tone Experiment 1 were repeated for the new experimental pairs to tone complexes is likely to be incorrect (Kame data. Order ofpresentation was found to have significant oka & Kuriyagawa, 1969a; Vos, 1986). This model was influence neither on tensionjudgments nor on roughness nevertheless tested, because its input is in a form similar judgments. to that of the composer's original algorithm. More gen The peA analysis revealed a quasi-unidimensional erally, it is well adapted to musical notation, where solution, with a first consensus component that reflected chords can be represented by a list of component notes the BTL psychophysical scale explaining 73% ofthe vari (frequencies). ance. The second component, accounting for only 15% To simulate our empirical findings, the data fed into of the variance, explains not much more variance than the model should be the notes written in the score, with do any of the original variables. This indicates that, in all the amplitudes equal. However, a spectrum also has to this second experiment, the tension judgments could al be associated with each note, because beats between par most exclusively be explained in terms ofthe consensus tials are an essential source of roughness (Kameoka & dimension. Kuriyagawa, 1969b). Therefore, hypothetical spectra with four partials and a 12dB/oct rolloffwere chosen. This rep MODEL SIMULATION resents a schematization ofthe stimuli but remains plau sible, considering the register and instrumentation used A computational model of roughness (Hutchinson & (see Figures 3 and 6). Knopoff, 1978) was tested to try to reproduce the exper The computed roughness values are shown in Fig imental results. The model considers a set offrequencies ure 8. The correlation between the BTL analysis of ex and amplitudes U;, aj) intended to represent the spectral perimental roughness judgments of Experiment 1 and composition ofa given sound. For each possible pair (i,j) computed roughness is (r = .83; r E [.73 .90],90% con of components, a partial roughness rij is computed ac fidence interval estimated by bootstrap percentiles). For cording to their frequency difference. All the partial rough the roughness psychophysical scale obtained in Experi nesses, normalized by the amplitudes, are then summed ment 2, the correlation is (r = .88; r E [.81 .94]). The ex-

.25,-,------,------,--,-----,-----,--,-----,--,

'"g ..Q be .15 ::l ....0 "C s::l .1 S-o U

.05

O'----'----'----.L..---'----'__-L-_--L__--'-----' 1 2 3 4 5 6 7 8 Timbres Figure 8. Model calculation of roughness for the eight timbres. The roughness scale is arbitrary. MUSICAL TENSION AND ROUGHNESS 77 perimental roughness judgments are, therefore, generally estimations were then obtained in two distinct ways (an concordant with the model simulation. experimental evaluation and a model simulation) that With respect to using the model as a compositional gave converging results. Lastly, the significant differences tool, it is also possible to qualitatively compare its output observed in Experiment I between tension and roughness with the composer's original tension predictions, shown show that the subjects were indeed able to differentiate in Figure 2. Considering roughness as a tension indica tension and roughness. tor, the model is globally better at predicting the experi mental judgments; timbre T7 , for instance, was predicted Comparison Between the Two Experiments as bearing a low tension value but was experimentally Experiment I displayed significant differences be judged as being both tense and rough. The model repli tween psychophysical scales for tension and roughness, cates this finding. differences that generally disappeared in Experiment 2. Our interpretation of this is based on the specificities GENERAL DISCUSSION mentioned earlier. Although the status of these speci ficities is hypothetical, this hypothesis allows us to ac Tension and Roughness count for several aspects ofthe data. The first experiment allowed us to exhibit significant Except for Ts' all the timbres that displayed significant differences in tension for nontonal orchestral timbres. differences for tension and roughness in Experiment I The notion of tension-deliberately defined loosely in contained specificities. Moreover, the specificities are the experimental instructions-gave rise to a consensus coherent with the results: T6 and T7 were tense but less among subjects in a musical context that was unfamiliar rough, and they included a prominent high-pitched note to most ofthem. Roughness was also found to be a rele that could induce tension without roughness; T3 con vant criterion by which to judge the timbres. However, sig tained intervals associated with release in the tonal sys nificant differences appeared between the two measures, tem and was judged to be rough but less tense. These fea indicating that factors other than roughness participated tures, in addition to roughness, may have influenced the in tension judgments. The second experiment confirmed tension judgments. The effect ofthe remixing can then be the perception of tension and roughness differences be interpreted as having reduced their perceptual salience. tween the timbres but exhibited almost identical psycho As fewer specificities emerged from the timbres, rough physical scales. The correlation observed indicates that, ness became the main available cue to judge tension. The in this second experiment, it is possible to account for the PCA performed to analyze listening and/or judgment tension judgments by comparisons ofroughness, increas strategies in Experiment I exhibited a secondary com ing roughness inducing greater tension. Ofcourse, a cor ponent contrasting subjects; this component opposes tim relation is by no means a proofofcausality, but other el bres containing a surface specificity to the ones contain ements that appeared in the additional analyses are ing a harmonic specificity. This component can, therefore, coherent with the hypothesis that roughness was a sen be interpreted as a disagreement in listening and/orjudg sory basis for the perceived tension ofthe timbres. ment strategies concerning the impact ofthe specificities The temporal succession ofthe timbres did not have a on tension perception. After the remixing ofthe timbres large influence on the tension judgments. Therefore, it in Experiment 2, the second component disappeared. is mainly the intrinsic aspect ofthe stimuli, which paral Let us, nevertheless, point out that Experiment 2, in lels the tonal concepts ofintrinsic consonance or disso our view, is by no means an improved version ofExper nance, that influenced the tension judgments. Roughness iment I in which possible "flaws" in the stimuli were dis is thought to participate in intrinsic consonance in the covered and then fixed. Our point is not to assert that ten tonal context, and our results extend this interpretation to sion and roughness are equivalent. In the general case, as a nontonal context. was shown by Experiment I, the influence ofroughness The influence ofthe explicit or the implicit accultura combines with several other factors to contribute to the tion oflisteners (all having a "Western" background) did feelings oftension and release experienced by the listen not appear to be influential in a straightforward manner. ers. The transformations made to obtain Experiment 2 That is, no correlation between musical education and stimuli, which basically consisted in homogenizing the judgment strategies could be found. Roughness, as a timbres, suggest that roughness may potentially express basic feature ofsound, is not expected to depend on cul tension in a situation that remains musically realistic. tural factors and is readily available to trained or untrained The comparison between the two experiments allows us listeners. However, this might also be due partly to the fact to specify the conditions under which roughness can be that musicians trained almost exclusively in tonal music come a dominant factor in tension perception. may not have a special strategy for nontonal stimuli. Finally, the correlation between psychophysical scales Remarks on the Experimental Procedure for tension and roughness is not due to a possible confu and Analysis Methods sion between the words tension and roughness. In the ex This study has tried to draw a link between a basic perimental instructions, the definition oftension was left psychoacoustic feature, roughness, and the musically to the appreciation of the listeners, but roughness was important notion of tension. The choice of the stimuli, defined by means ofan example with sound. Roughness therefore, reflects a tradeoff between musical realism 78 PRESSNITZER, McADAMS, WINSBERG, AND FINEBERG and limitation of the number ofexperimental variables. ments (prolongational reduction). For atonal music, Ler On the one hand, the stimuli were extracted from an ex dahl (1989) makes the assumption that the pitch space is isting musical piece. They were recorded with live instru flat and replaces the stability rules by salience rules to ments in a concert-like situation and, in a second condi obtain similar reductions. Both the tonal and the atonal tion, were remixed in a situation habitually found in the time-span reduction theories have been experimentally preparation of recorded music. The question of finding tested, with contrasting results (Dibben, 1994). Whereas a tension hierarchy was motivated by a preoccupation enter listeners were able to match a reduction to its original for tained by the composer during the writing ofthe piece. tonal pieces, results were close to random in the atonal On the other hand, the timbres were homogeneous in condition. The author proposed several reasons for this register and dynamics, which may represent a limitation latter outcome, but the suggested conclusion is that the with respect to other musical situations. For instance, one inability to match original pieces and reduced versions is may wonder how salient the tension cues linked to rough inherent to the music tested (excerpts from Schoenberg ness would still be when placed in competition with cues opuses II and 19). Hierarchical levels ofstructure would ofa different nature, such as rhythm, dynamics, or regis be impossible to extract when listening to atonal music, tral extremes. The interactions ofmelodic and harmonic and the only tension and release movements perceptible factors were also not addressed here. These interactions in this context (thanks to associations between sound are important in the context ofpolyphonic music, where events) would, therefore, be of lesser importance (Dib it has been claimed that auditory streaming processes in ben, 1996). fluence the perception ofroughness and tension (Wright Our results bring new elements to bear on this con & Bregman, 1987). clusion. The experimental judgments of orchestral tim Forced-choice paired comparisons were used to avoid bres showed that tension and release movements could direct magnitude estimation judgments. These judg actually be perceived by listeners in a musical context ments would have been hard to define without introduc not related to tonality. Another study gave a converging ing terms not necessarily relevant to a musical context. set of results by exhibiting a similar range of variation Furthermore, the complexity of the stimuli could have for tension judgments within tonal and nontonal musical made the task difficult for listeners. This design led us to excerpts and a significant effect of timbre on the judg adopt nonparametric statistical analysis methods in order ments (McAdams & Pressnitzer, 1996; Paraskeva & to make as few hypotheses on the outcome ofthe data as McAdams, 1997). A difference between the present study possible: The bootstrap technique was used to examine and those ofDibben (1994, 1996) is that, here, the under the stability ofthe BTL results. lying structural harmony was approached in terms of The analyses attributed a single tension value to each timbre, rather than in terms ofnotated pitch events.' Tim timbre. Ofcourse, this is not supposed to mean that there bral quality alone, without a reference to a pitch space exists an absolute intrinsic tension for the timbres inves organization, was sufficient to convey intrinsic move tigated. It should be emphasized that the hierarchy is rel ments of tension and release between pairs of sounds. ative. The individual estimated tension values can be The question is now whether the local properties inves thought ofin a fashion similar to that ofthe relative con tigated (such as roughness) are able to convey tension sonance and dissonance values traditionally ascribed to and release movements on larger time scales. It would be individual tonal chords. Although the level of "accept ofgreat interest to test whether originals and reductions, able" dissonance has varied over the history of tonal similar to the ones proposed by Lerdahl (1989) but based music, it does not preclude perception ofsensory conso on timbra1 salience rules, including roughness, could be nance as a potential basis for tension perception (Breg matched by listeners. man, 1991). Schoenberg (1911/1978), for example, pre Timbre as potential form-bearing structure has inter ferred to refer to dissonances as "remote consonances"! ested composers, from the experiments of Berlioz and Debussy to Schoenberg's Klangfarbenmelodie, and more Perception ofTension in Nontonal Music recently, those who belong to the musique spectrale Theories of nontonal tension are far less numerous trend (Murail, 1984; Pressnitzer & McAdams, 1999). than theories of tonal tension. On the one hand, com Cognitive psychology has expressed the condition upon posers have proposed theories of nontonal tension that which a multidimensional attribute such as timbre could often have a close relationship to their own musical styles, be the basis for building musical form-mainly in terms as a codification of personal practices. A theory that is of the possibility of categorization and recognition of more generally relevant and, therefore, concerned with vectors in a timbre space (McAdams, 1989; McAdams & experimental testing is the extension of the GTTM to Cunibile, 1992). Our study is an indication that timbre atonal music by Lerdahl (1989). may also be a privileged support for harmony, thanks to The GTTM reduces a musical piece-at different lev the dimension of roughness. els-to structural units by way ofa time-span reduction. The reduction is made according to stability rules that CONCLUSION are based on the hierarchical relationships that exist in the tonal pitch space. This reduction is then supposed to Two experiments have shown that the fundamental be the basis ofthe perception oftension and release move- musical concept oftension-release schemas can be con- MUSICAL TENSION AND ROUGHNESS 79

veyed by orchestral timbres, even when no harmonic HUTCHINSON, W., & KNOPOFF, L. (1978). The acoustic component of function corresponding to the Western tonal system can Western consonance. Interface, 7,1-29. be defined for them. Different factors influenced these KAISER, H. F. (1958). The varimax criterion for analytic rotation in fac tor analysis. Psychometrika, 23, 187-200. schemas: tonal references, heard both by musicians and KAMEOKA, A., & KURIYAGAWA, M. (1969a). Consonance theory: nonmusicians, or surface characteristics resulting from Part. I. Journal ofthe Acoustical Society ofAmerica, 45, 1451-1458. performance variables, such as the emergence of high KAMEOKA, A, & KURIYAGAWA, M. (\969b). Consonance theory: pitched tones. However, when these features were re Pt. II. Journal ofthe Acoustical Society ofAmerica, 45,1459-1469. KEMP, S. (1982). Roughness of frequency-modulated tones. Acustica, duced in salience, roughness became a noteworthy di 50,126-133. mension. This sound attribute, in close relationship with KRUMHANSL, C. L. (1990). Cognitive foundations ofmusicalpitch. Ox peripheral auditory mechanisms, was highly correlated ford: Oxford University Press. with the musical notion oftension. Its simulation with a LANGER, S. K. (1967). Mind: An essay on human feeling (Vol. I). Bal predictive model may be considered. Roughness, as a di timore: Johns Hopkins University Press. LANGNER, G. (1992). Periodicity coding in the auditory system. Hear mension oftimbre, could open up a way ofthinking ofnon ing Research, 60,115-142. tonal harmonies on the basis ofperceptual phenomena. LERDAHL, F. (1989). Atonal prolongational structure. Contemporary Music Review, 4, 65-87. REFERENCES LERDAHL, F., & JACKENDOFF, R. (1983). A generative theory oftonal music. Cambridge, MA: MIT Press. AURES, W.(1985). Ein Berechnungsverfahren der Rauhigkeit [A rough MATHEWS, M. v., & PiERCE, 1. R. (1980). Harmony and nonharmonic ness calculation method], Acustica, 58, 268-281. partials. Journal ofthe Acoustical Society ofAmerica, 68, 1252-1257. BHARUCHA, J. J., & OLNEY, K. L. (1989). Tonal cognition, artificial in McADAMS, S. (1989). Psychological constraints on form bearing di telligence and neural nets. Contemporary Music Review, 4, 341-356. mensions in music. Contemporary Music Review, 4, 181-198. BIGAND, E. (1993). The influence ofimplicit harmony, rhythm and mu McADAMS, S., & CUNIBILE, J. (1992). Perception oftim braI analogies. sical training on the abstraction of tension-relaxation schemas in Philosophical Transactions ofthe Royal Society ofLondon : Series B, tonal music phrases. Contemporary Music Review, 9,123-137. 336, 383-389. BIGAND, E., PARNCUTT, R., & LERDAHL, F.(1996). Perception ofmusi McADAMS, S., & PRESSNITZER, D. (1996). Psychoacoustic factors to cal tension in short chord sequences: The influence of harmonic musical tension in Western nontonal music [Abstract]. International function, sensory dissonance, horizontal motion, and musical train Journal ofPsychology, 3, 148. ing. Perception & Psychophysics, 58,125-141. MERSENNE, M. (1975). Harmonie universelle. Paris: S. Cramoisy. BREGMAN, A. S. (1990). Auditory scene analysis: The perceptual orga (Original work published 1636) nization ofsound. Cambridge, MA: MIT Press. MEYER, L. B. (1956). Emotion and meaning in music. Chicago: Uni BREGMAN, A. S. (1991). Timbre, orchestration, dissonance, et organi versity ofChicago Press. sation auditive. In 1. 8. Barriere (Ed.), Le timbre. metaphore pour la MURAIL, T. (1984). Spectra and pixies. Contemporary Music Review, 1, composition (pp. 204-215). Paris: Christian Bourgois. 157-171. DAVID, H. A. (1988). The method ofpairedcomparisons (2nd ed.). Lon NARMOUR, E. (1990). The analysis and cognition ofbasic melodic struc don: Charles Griffin & Company. tures: The implication realisation model. Chicago: University ofChi DE CHEVEIGNE, A., McADAMS, S., LAROCHE, J., & ROSENBERG, M. cago Press. (1995). Identification ofconcurrent harmonic and inharmonic vow PARASKEVA, S., & McADAMS, S. (1997). Influence oftimbre, presence/ els: A test ofthe theory ofharmonic cancellation and enhancement. absence oftonal hierarchy and musical training on the perception of Journal ofthe Acoustical Society ofAmerica, 97, 3736-3748. musical tension and relaxation schemas. In Proceedings ofthe 1997 DIBBEN, N. (1994). The cognitive reality ofhierarchical structures in tonal International Computer Music Conference (pp. 438-441). Thessalo and atonal music. Music Perception, 12, 1-25. niki: Aristole University ofThessaloniki. DIBBEN, N. (1996). Perceptual facilities in atonal music: Implications PLOMP, R., & LEVELT, W. (1965). Tonal consonance and critical band for the listening experience. In 8. Pennycook & E. Costa-Gioni width. Journal ofthe Acoustical Society ofAmerica, 38, 548-560. (Eds.), Proceedings ofthe Fourth International Conference on Music PRESSNITZER, D., & McADAMS, S. (1999). Acoustics, psychoacoustics Perception and Cognition (pp. 55-58). Montreal: McGill University. and spectral music. Contemporary Music Review, 19,33-60. EFRON, 8., & 1'IBSHIRANI, R. J. (1993). An introduction to the bootstrap. RAMEAU, J. P. (1971). Treatise on harmony reduced to its naturalprin London: Chapman & Hall. ciples (P Gosset, Trans.). New York: Dover. (Original work published FASTL, H. (1977). Roughness and temporal masking patterns of sinu 1722) soidally amplitude modulated broadband noise. In E. F.Evans & 1.P SCHARF, B. (1970). Critical bands. In 1.V. Tobias (Ed.), Foundations of Wilson (Eds.), Psychophysics and physiology ofhearing (pp, 403 auditory theory (Vol. I). London: Academic Press. 415). London: Academic Press. SCHELLENBERG, E. G., & 'TRAINOR, L. J. (1996). Sensory consonance and FINEBERG, 1. (1997). Streamlines. Paris: Editions Max Eschig. the perceptual similarity ofcomplex-tone harmonic intervals: Test of GEARY, J. M. (1980). Consonance and dissonance ofpairs ofinharmonic adult and infant listeners. Journal ofthe Acoustical Society ofAmer sounds. Journal ofthe Acoustical Society ofAmerica, 67, 1785-1789. ica, 100, 3321-3328. GREENWOOD, D. D. (1991). Critical bandwidth and consonance in rela SCHENKER, H. (1979). Free composition (E. Oster, Trans.). New York: tion to cochlear frequency-position coordinates. Hearing Research, Longman. (Original work published 1935) 54, 164-208. SCHOENBERG, A. (1978). Theory ofharmony (R. E. Carter, Trans.). HELMHOLTZ, H. L. F. VON (1954). On the sensations oftone as the London: Faber and Faber. (Original work published 1911; trans. from physiological basis for the theory ofmusic (2nd ed.; A. J. Ellis, 3rd ed., 1922) Trans.). New York: Dover. (Original work published 1877; trans. from SMITH, B. (1995). PsiExp: An environment for psychoacoustic experi 4th ed., 1885) mentation using the IRCAM Musical Workstation. In Proceedings of HOTELLING, H. (1933). Analysis of a complex of statistical variables the Societyfor Music Perception and Cognition Conference '95 (pp. 83 into principal components. Journal ofEducational Psychology, 24, 84). Berkeley, CA. 417-441,498-520. l'ERHARDT, E. (1974). On the perception ofperiodic sound fluctuation HULSE, S. H., BERNARD, D. J., & BRAATEN, R. F. (1995). Auditory dis (roughness). Acustica, 30, 201-212. crimination ofchord-based spectral structures by European starlings TRAMO, M. J. (1996). Neural representations oftonal harmony [Abstract]. (Sturn us vulgaris). Journal ofExperimental Psychology: General, International Journal ofPsychology, 3, 187. 124,409-423. VIEMEISTER, N. F.(1977). Temporal factors in audition: A system analy- 80 PRESSNITZER, McADAMS, WINSBERG, AND FINEBERG

sis approach. In E. F.Evans & 1.P.Wilson (Eds.), Psychophysics and 2. A factor analysis was not performed after the PCA, for the fol physiology ofhearing (pp. 419-429). London: Academic Press. lowing reason. A criterion, such as varimax (Kaiser, 1958), rotates the Vos, J. (1986). Purity ratings oftempered fifths and major thirds. Music axes to make the subjects' loading on each factor either very high or very Perception, 3, 221-258. low. Such a rotation would alter the consensus among the subjects as to WRIGHT, 1.K., & BREGMAN, A. (1987). Auditory stream segregation and the ordering ofthe timbres along the first dimension. Our objective was the control ofdissonance in polyphonic music. Contemporary Music mainly to assess this consensus; therefore, the axes were not rotated. Review, 2, 63-92. 3. It must be acknowledged that even in the original version of the ZWICKER, E., & FASTL, H. (1990). Psychoacoustics.facts and models. GTTM (Lerdahl & Jackendoff, 1983, p. 297), timbre was considered as Berlin: Springer-Verlag. a candidate contributor to nontonal tension perception. However, the ZWICKER, E., FLOTTORP, G., & STEVENS, S. S. (1957). Critical band width salience rules proposed in Lerdahl (1989) were defined for a collection in loudness summation. Journal ofthe Acoustical Society ofAmerica, of pitches and not for one sound event that had a homogeneous "tim 29, 548-557. bre." In any case, they did not include roughness as a relevant criterion.

NOTES

I. The critical band is a general concept defining the frequency res olution ofthe auditory system and is directly influenced by the biome (Manuscript received March 4, 1997; chanics ofthe basilar membrane (Scharf, 1970). revision accepted for publication September 18, 1998.)