Perception & Psychophysics2000.62 (1), 66-80

Perception of musical tension fornontonal orchestral timbres and its

relation to psychoacoustic roughness

DANIEL PRESSNITZERIRCAM-CNRS, Paris, France

STEPHENMcADAMSIRCAM-CNRS, Paris, France

and Unicersite Rene Descartes, Paris, France

and

SUZANNE WINSBERG and JOSHUAFINEBERGIRCAM-CNRS, Paris, France

Can tension in nontonal music be expressed without dynamic or rhythmic cues? Perceptual theoriesof tonal harmony predict that psychoacoustic roughness plays an important role in the perception ofthis 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 stronger as the perceptual salience of other attributes (suchas high-pitched tones or tonal intervals) was reduced.

An impression of successive tension and release is acommon experience while listening to music. The studyof this intuitive notion is actually fundamental to West-ern music theory and has been a matter ofdebate for bothmusic analysts and cognitive psychologists. Whereas manystudies have helped us to understand tension perceptionin the tonal framework, the compositional practices ofcontemporary composers raise new questions. The useofa musical material that does not draw on the implicitlyshared tonal culture may disorient listeners and, hence,deprive them of the essential landmarks that schemas oftension and release provide for the appreciation ofa mu-sical work. In this study, we propose to investigate theperception of tension levels for nontonal orchestral tim-bres by musician and nonmusician listeners. We hypo-thesized that if tension could actually be perceived insuch a context, a basic psychoacoustic dimension knownas roughness would account for an important part ofthatperception. Roughness is an auditory attribute that has

Part ofthis work was completed thanks to a Fyssen Foundation grantto the first author. The authors thank two anonymous reviewers for ex-tremely useful comments on earlier versions of the manuscript. Corre-spondence concerning this article should be addressed to eitherD.Pressnitzer or S. McAdams, IRCAM, I place Igor Stravinsky,F-75004Paris, France (e-mail: pressnitzer@ircam.frorsmc@ircam.fr).

-Accepted by previous editor, Myron L. Braunstein

been proposed as a sensory basis for musical consonancewithin the tonal system (Helmholtz, 1877/1954).

Comparing tension and roughness for a set of stimuliassumes that there is a parallel between a complex musicalconcept and a basic sensory attribute. This requires apreliminary specification ofthe two terms and of the rea-sons for taking a new perspective in considering themjointly.

Musical Tension in a Tonal ContextThe identification of tension-release schemas is the

starting point for most classical harmonic analyses ofWestern music. The method proposed by the music the-orist Heinrich Schenker (1935/1979), for instance, de-fines hierarchical structural levels that are, in the end, re-ducible to a fundamental Ursatz, which is very similar toa basic pattern oftension and release. The generative the-ory oftonal music (GTTM; Lerdahl & Jackendoff, 1983),which attempts to account for music perception and un-derstanding by principles derived from cognitive psy-chology, holds the existence of a network of tension andrelease to be a fundamental axiom. The links it createsbetween events over time help us to hear a piece in a co-herent way, rather than in the form of a juxtaposition ofisolated sounds. These schemas have also been proposedas a basis for arousal and emotion, underlining anotheraspect of their importance in music listening by trainedor untrained listeners (Langer, 1967; Meyer, 1956).

Copyright 2000 Psychonomic Society, Inc. 66

There exists no simple, universally valid, and widelyaccepted definition of what tension and release actuallyare. To indicate the scope of the notion, let us take thebasic example ofthe authentic cadence in Western tonalharmony. In this succession of two musical events, a dom-inant seventh chord based on the fifth degree ofa majorscale is considered unstable and dissonant, calling for aresolution to a tonic chord based on the first degree, whichis stable and consonant. It is generally accepted that thisinstability constitutes a tension, its resolution a release.The combination of these two is the well-known patternat the conclusion of the vast majority of tonal pieces writ-ten in the 18th and 19th centuries. However archetypal,this example embodies several aspects of the notion ofmusical tension.

Tension is thought to be, in part, linked to the intrinsicconsonant or dissonant aspect of the chords. The domi-nant seventh chord contains a tritone interval, formerlyknown as diabolus in musica (considered to be dissonant,as one may guess), and induces tension. The tonic triadcontains only a perfect fifth and a major third, two con-sonant intervals, and therefore induces very little tension.Attempts were made to ground the idea of intrinsic con-sonance in a feature of the acoustic world: the overtoneseries. That is to say, a set offrequency components withan integer multiple ofa fundamental frequency has beenproposed as a physical basis for the phenomenon (Mer-senne, 1636/1975; Rameau, 1722/1971). Theoriesempha-sizing perception then introduced the concept ofroughnessthat we will discuss below (von Helmholtz, 1877/1954).

Tension can also be thought of in terms ofbeing an ex-pectation, the fulfillment of which brings a release. Fromthis point of view, in the cadence example, the temporalsuccession of the two chords might playa role. The twonotes of the tritone from the dominant chord are unsta-ble and just one semitone apart from the tonic and thethird of the tonic triad, which are stable. Therefore, thetritone is said to resolve on the major third. This idea ofresolution, or good continuation, has been proposed as amusical parallel to the laws ofGestalt psychology (Meyer,1956; Narrnour, 1990).

Lastly, the arousal of the expectation could be linkedto cultural habituation: The classic cadence pattern is rec-ognized, and the resolution is expected. Neural nets havebeen able to reproduce the expectancies oflisteners con-cerning tonal music after a preliminary training phase(Bharucha & Olney, 1989). The habituation consists ininternalizing the organization of tonal pitch space (Krum-hansl, 1990). In a study in which tension perception forboth melodies and short chord sequences was investigated,Bigand (1993) confirmed the existence ofexplicit or im-plicit tonal acculturation.

Within the tonal framework, several factors may, there-fore, have an influence on the perception of schemas oftension and release. These influences can be concurrent,as in the case ofa perfect cadence, or contradictory, if thecomposer seeks some kind ofstructural ambiguity. In any

MUSICAL TENSION AND ROUGHNESS 67

case, in the tonal framework, a set of established rulesimplicitly shared by the audience is available to expresstension and release.

Musical Tension in a Nontonal ContextThe problem is very different for a composer who does

not wish to refer to tonality. Let us take, as an example,the genesis of the sequence chosen to be the basis for thisstudy (score shown in Figure 1).

Spectral analyses were performed on recorded notesplayed on a musical instrument-in this case, a double-bass with rapidly changing vibrato depth, speed, andbow pressure. Sets of four to five partials, selected fromamong the strongest components of the analysis withina fixed band of frequencies, were isolated to create areservoir of material. Eight chords from this reservoirform the sequence used in this study. The chords werearranged to create a tension pattern that was needed formusical reasons. Since the chords resulted from a rawacoustic analysis, no classic tonal function could be as-cribed to them. Therefore, the composer chose to definean intrinsic tension value for each of them by means of acomputational algorithm. The greatest common divisorof the constituent frequencies within a tolerance corre-sponding to a sixteenth of a tone was held to be a quali-tative indication of tension: the lower the divisor, themore inharmonic and, therefore, tense the chord wasconsidered to be. Figure 2 displays the output of the al-gorithm, each chord numbered along the abscissa hav-ing a computed value along the ordinate. The shape ofthe curve was also used compositionally to reinforce thistension contour with other musical parameters.

This approach raises several questions. First, is the no-tion oftension still relevant for material without any tonalfunction? Second, in the score, the movements are un-derlined by rhythmic and dynamic differences, whereasthe tension algorithm used only average spectral domaindata and did not take into account these supplementarycues. To be coherent, steady-state timbral differences be-tween the individual chords should be able to convey thetension movements alone. The first aim of this studywas, therefore, to establish whether differences in ten-sion that were not based on tonal, rhythmic, or dynamiccues could actually be perceived by listeners for these or-chestral timbres. In such an unfamiliar context, listenerswould need to rely on universal psychoacoustic cuesuntil style-specific cues could be learned.

RoughnessSuch a psychoacoustic cue may be found in auditory

roughness. Roughness is caused by the perception ofrapidamplitude fluctuations in the range of 20-200 Hz. Simul-taneous tones close in frequency can cause rough beats(e.g., a minor second played in the medium register of thepiano). Experimental studies that have sought to quantifyroughness perception have stressed its close relation to pe-ripheral auditory mechanisms. Beating tone pairs for

68 PRESSNITZER, McADAMS, WINSBERG, AND FINEBERG

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MUSICAL TENSION AND ROUGHNESS 69

10

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Figure 2. The tension measure originally computed by the composer. Timbres(T" etc.) are shown on the abscissa in an order corresponding to their appearancein the musical score. The scale along the abscissa is not continuous, but the linesbetween 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-position (Hutchinson & Knopoff, 1978; Kameoka &Kuriyagawa, 1969a). The studies ofamplitude-modulatedtones (Terhardt, 1974), of amplitude-modulated noise(Fastl, 1977), or of frequency-modulated tones (Kemp,1982) underlined the link of roughness perception withthe low-pass characteristic of amplitude modulation cod-ing by the auditory system (Viemeister, 1977). Other com-putational models have, therefore, been proposed that at-tempt to predict roughness for natural sounds in thetemporal domain, using signal-processing techniques(Aures, 1985). Convergent approaches in the fields of de-velopmental and comparative psychology have shown thatyoung infants (Schellenberg & Trainor, 1996) or membersof other species, such as birds (Hulse, Bernard, & Braaten,1995), were more sensitive to differences in roughness ofsimple intervals than to differences in interval size. Thefinding that different species perceive roughness may berelated to the fact that amplitude modulation coding doesseem to be a basic feature shared by the auditory systemsof both mammals and birds (Langner, 1992). Physiologi-cal correlates to roughness were also found in the dis-charge patterns of auditory nerve units (Tramo, 1996).These results confirm the existence of a basic sound at-tribute tightly linked to peripheral auditory mechanisms.

The musical repercussions ofroughness have been ad-dressed as well in some of these studies (Hutchinson &Knopoff, 1978; Plomp & Levelt, 1965; von Helmholtz,1877/1954). The relative roughness of tonal intervals of

harmonic sounds was shown to correspond to their mu-sical consonance. An interval of two simultaneous tonesseparated by a frequency ratio of 2: I (one octave) producesno roughness, as all the partials of the upper note willcorrespond to partials ofthe lower note and will cause nobeats. If the two tones are a just fifth apart (3:2 ratio), afew partials will be mistuned and will produce a littleroughness. If the frequency difference is a tritone (45:32),a greater number of adjacent partials will cause beatsand roughness. It follows that the relationship betweenfrequency ratio and perceived consonance should be dif-ferent if the simultaneous tones do not have harmonicspectra. This effect has been experimentally verified(Geary, 1980; Mathews & Pierce, 1980). Roughness has,therefore, been proposed as a sensory basis on which tonalharmony was built, allowing the development of morecomplex and style-specific rules.

However, most of the experimental results that sup-port this proposition were obtained with simplified stim-uli, and the experimental conditions (most often, directjudgments of consonance or pleasantness) used to ob-tain them could be questionable in a real musical con-text. The contribution ofroughness to tension perceptionin a musical context has, nevertheless, been addressed ina study concerning short chord sequences (Bigand,Parncutt, & Lerdahl, 1996). Roughness, as estimated bymodel simulation, played a role in the tension judgments,together with other factors, such as implicit acculturationto the tonal function of the chords. In addition to study-

70 PRESSNITZER, Me ADAMS, WINSBERG, AND FINEBERG

ing directly the perception of tension in nontonal har-monies, a second aim of this study was to gather rough-ness estimates of complex nontonal musical sounds andto investigate their contribution to tension perception.

EXPERIMENT 1

MethodStimuli. A sequence of eight chords was chosen from Stream-

lines (Fineberg, 1997). The score of this sequence, simplified bythe composer for the needs of the experiment, is shown in Figure I.The chords were played in an ensemble setting (two flutes, clarinet,violin, and viola) by professional musicians who were members ofthe ltineraire ensemble. These chords, sharing a homogeneous reg-ister, were recorded separately with the same duration and increas-

ing-then-decreasing dynamic pattern (dal niente-mf-dal nientei.An example of the temporal and spectral characteristics of one ofthe stimuli is shown in Figure 3. For the sake ofconciseness, the 14other figures corresponding to the other stimuli are not reproducedhere but would be very similar. Thus, the stimuli differed mainly intheir timbral characteristics. and we will refer to them henceforth asorchestral timbres.

Apparatus. The recording took place in IReAM's Espace deProjection concert hall. A pair of Schoeps microphones was placed5 m from the instrumentalists at an elevation of 3 m. The stereo sig-nals were transferred though a Neve V mixing table onto a Sony7050 DAT recorder. They were subsequently digitally transferredand stored on a hard disk at a sampling rate of44.1 kHz with 16-bitresolution through a Digidesign Protools interface.

The experiment used a Soluna SI double-walled sound-insulatedbooth. The stimuli were played by a NeXT station through an ISPW

Viola Flute 1 Flute 2~. -. /

. '. l/plarinet ..· Violin

DSP card, Pro 10 digital-to-analog converters and power amplifier,and AKG K I000 open headphones. The measured sound level wasapproximately 80 dBA, adjustable at the request of the subjects soas to provide the most comfortable listening situation. The experi-ment was conducted in the PsiExp computer environment runningon the NeXT workstation (Smith, 1995).

Subjects. The experimental group was composed of 30 listenersand did not include the authors. The subjects were 17-45 years old(M = 26). They came from widely different backgrounds, someworking at IRCAM, others being recruited from a database of vol-unteers. The group included 9 professional musicians (composersor instrumentalists who had earned money making music over thelast year), 8 amateur musicians (amateur instrumentalists), and13nonmusician listeners (with no musical training whatsoever). Theywere paid for their participation. One nonmusician listener did notfinish the test and was subsequently removed from the results.

Procedure. The experiment included two parts, one concerningtension, the other concerning roughness. In the first part, the eighttimbres were presented in all possible pairs in both orders withoutrepetition (56 combinations). The subjects had to make a forced-choice judgment for each pair. The question they had to answer was,"Between the two sounds ofthis pair, do you hear an evolution from'tension to release' or from 'release to tension' " (translated fromFrench tension and detente). They were allowed to define tensionand release according to any criteria that seemed relevant. After

MUSICAL TENSION AND ROUGHNESS 7 I

three to five test trials, in which no feedback was given, this firststage lasted approximately 30 min. In the second part, listeners' at-tention was directed to one particular sound attribute, roughness.The concept of roughness was introduced through a typical soundexample: a 1000-Hz sine wave that was amplitude modulated at70 Hz, the modulation depth of which could be varied at will. Thisexample was considered to produce no roughness if the modulationdepth was zero, and the maximum roughness was obtainable witha single amplitude-modulated tone when the modulation depth wasone (Zwicker & Fastl, 1990). The subjects were instructed that thedifference in the quality of the tone they heard when moving themodulation depth slider was caused by roughness. Special attentionwas paid to not associating roughness with the dissonant and un-comfortable aspects of the stimuli in the instructions. The 56 pairswere then presented again in random order, and the subjects had tomake forced-choice comparisons concerning changes in roughness.The two parts were always presented in this order (tension judg-ment, then roughness judgment) in order not to induce a bias in ten-sion judgments because of prior knowledge concerning the notionof roughness.

Analysis methods. Using the forced-choice judgments as a basis,the eight timbres were ordered along a linear psychophysical scale,to allow a comparison with the composer's predicted tension. ABradley-Terry-Luce (BTL) analysis was performed (David, 1988).This method makes the assumption that each timbre has a true value

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Figure 4. Psychophysical scales for tension (solid lines) and roughness (dashed lines) for Experiment I. The timbres arelabeled along the abscissa; the results of the BTL analysis and the standard deviations estimated by bootstrap are displayedalong the ordinate. Empty circles represent the BTL values, and dots the means of bootstrap replications. The scales arenot continuous, the lines between the points having been added for visual clarity. The scales are arbitrary and representthe contrast between items.

72 PRESSNITZER, McADAMS, WINSBERG, AND FINEBERG

according to tension or roughness. It is this value that we try to es-timate. During any experimental comparison between two timbres,listeners do not compare the true values but, rather, two associatedrandom variables whose distributions are centered on the true val-ues. In the BTL hypothesis, the distribution ofthe random variablesis approximated by a hyperbolic secant law with constant variance(this yields a cumulative distribution similar to the cumulative nor-mal, differing only at the tails). The proportions ofjudgments ob-served are then used to estimate the true values.

The result of the BTL analysis is a single tension or roughnessvalue for each timbre. To test whether the subjects judged that stim-uli indeed differed with respect to tension or roughness, the differ-ences along the psychophysical scales were compared with thestandard deviation (SD; 68% of the central cases) of the results, asin an analysis ofvariance (ANOYA). However, an ANOYA assumesa normal error distribution, which is not necessarily the case here.A bootstrap analysis was therefore made, in which the SDs were es-timated by using an empirical distribution obtained by means ofre-sampling with replacement from the sample (Efron & Tibshirani,1993). A bootstrap sample size of 100 was used, which is adequatefor estimates of SD. The SDs are displayed in Figure 4 around themean of the bootstrap values. The departure of the error from nor-mality is noticeable by the asymmetry of the error bars about theBTL value.

A test of the null hypothesis between two items at a given risk ais usually achieved by examining the confidence intervals at 1 - 2aattached to each of them. If the confidence intervals overlap, thenull hypothesis cannot be rejected. Therefore, the statistical crite-rion we will adopt for inferring a significant difference between val-ues at p < .05 is the comparison of the absolute difference betweenthe values with the 90% confidence intervals, defined as ±1.645 *SD (Efron & Tibshirani, 1993).

ResultsThe results are displayed in Figure 4. Let us consider

first the tension measure (solid lines). The highest ten-sion value was obtained by timbre TI , whereas the lowestvalue was produced by T5• On the BTL psychophysicalscale, the absolute difference between these two ex-tremes is more than an order ofmagnitude (10 times) big-ger than the SD attached to the judgments. Using the sig-nificance criterion based on confidence intervals, thedifferences between the extremes of the psychophysicalscale are significant. Therefore, all the stimuli were notrandomly judged as being equally tense. Closer exami-nation of the psychophysical scale for tension indicatesthat there were two broad groups: One, which includedTI , T2, T4 , T7, was judged as being more tense, and theother, which included T3 , T5 , T6 , T8 , as being less tense.The differences within the groups are not significant,whereas the difference between any pair oftimbres acrossgroups is significant.

The psychophysical scale for roughness (dashed lines)can be examined in a similar fashion. The difference be-tween the most rough timbre, T2 , and the least rough tim-bre, T6 , is an order of magnitude greater than the SDs.Significant differences in roughness were, therefore,perceived between our complex orchestral sounds. Thedetailed examination shows that the roughness valueswere more regularly distributed along the psychophysi-cal scale than were the tension values.

A comparison between the two psychophysical scalesindicates that they differ for several timbres. With the non-

overlap of the 90% confidence intervals between theroughness and the tension values as the statistical infer-ence criterion, differences are significant for T3, 75, T6 ,and T7 . Specifically, T6 and T7 are judged as being tensebut not rough, whereas T3 and T5 are judged as beingrough but less tense.

Additional AnalysesInfluence of presentation order. The order of pre-

sentation is not considered in the BTL analysis: Eachpair oftimbres was presented in both sequential orders tothe listeners, on separate trials, and the judgments for thesame pair were collapsed in a global proportion. Thegeneral influence of presentation order was, therefore,specifically tested to check whether it had an effect onlisteners' judgments. An order sensitivity coefficient (ose)was defined as the percentage of trials in which the firsttimbre ofa pair was chosen as being more tense or rough.Ifpresentation order had no influence on judgments, thefirst element of a pair would be "chosen" as often as thesecond one across trials, and the coefficient should beequal to 50%. The statistical test for the ose was definedas follows: If the 50% value is included in the confidenceinterval at a given risk, order is considered as having nosignificant effect.

The ose is restricted to the interval [0, I], and the useof its SD to estimate a confidence interval would requirea transformation. To avoid that, the confidence intervalwas estimated by bootstrap and 90% percentiles. A boot-strap sample size of 2,000 was chosen to estimate theconfidence interval, defined as 90% ofthe results aroundthe central case (Efron & Tibshirani, 1993). Presentationorder was found to have a small but significant influenceon tension judgments (ose = .44; ose E [.42 .47];p < .05).Order ofpresentation also slightly influenced roughnessjudgments (ose = .47; ose E [.46.49]; p < .05). Despitethe marginal significance, the bias is small, and we in-terpret this analysis as an indication that order had onlyminor importance for both tension and roughness judg-ments. From a practical perspective, the bias is smallenough to justify the BTL analysis that disregards pre-sentation order.

Listening and/or judgment strategies. The exami-nation of the agreement between listeners is a means toestimate whether all the subjects responded in the sameway or whether different strategies appeared among them.This examination is all the more important because oursubject group included professional musicians as well asamateur and nonmusician listeners, who were requiredto judge a complex notion such as tension. A relationshipbetween strategies and subgroups ofsubjects having dif-ferent musical education would indicate the influence ofmusical training on the experimental task.

A principal component analysis (PCA; Hotelling,1933) was performed to study the tension judgmentsacross subjects. Each listener was considered as a vari-able (as is the case in Q-factor analysis). The scores at-tributed to each timbre, defined as the sum ofmore tensejudgments across the experimental trials for a given lis-

Listeners

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Figure 5. Results of the principal component analysis for thetension judgments of Experiment I. Top panel: Listener coeffi-cients for the two first principal components. Professional musi-cians are denoted as P, amateurs as A, and nonmusicians as N.Bottom panel: the component scores for each of the timbres aredisplayed. Timbres are denoted as T. to Ts, as in Figure 4.

tener, were considered to be the observations. The cor-relation matrix between listeners could essentially be de-scribed by two principal components, accounting togetherfor 75% of the variance. The other components, explain-ing less variance than did the original variables, are notconsidered any further.

The first component is, by definition, the main dimen-sion of the data. It accounts here for 56% ofthe variance,

MUSICAL TENSION AND ROUGHNESS 73

and all the subjects have comparable coefficients for thisdimension (see Figure 5). In addition, the examinationof the component scores shows that the order of the tim-bres from left to right corresponds to the ordering by in-creasing tension given by the BTL analysis (Figure 4) .Thus, there is a consensus among the listeners as to theordering of the timbres along the first dimension, sinceall the listeners have essentially the same coefficients withrespect to this dimension.

The coefficients of the individual listeners are regu-larly spread along the second component, indicating dif-ferences among the subjects. However, the distributionof subjects according to their degree of musical training(P, professional; A, amateur; and N, nonmusician; seethe procedure details) shows no particular cluster of onecategory. Therefore, this dimension cannot be explainedin terms of differences in explicit musical education (asmeasured by our criterion). Concerning the timbrescores, the component opposes Ts' T6 , and T7 to T3 andT4 . An interpretation for this component will be pro-posed in the General Discussion section.?

EXPERIMENT 2

Fusion and SpecificitiesLet us consider again the way the timbres were com-

posed. Because of the use of spectral analyses of naturalsounds, the score contains many notes that have quasi-harmonic relationships. For instance, for T7 (see Figure 3),the viola and the flute are almost one octave apart. Theharmonics of the different instruments overlap to a greatextent. The feeling that derives from this technique, whichis central to the composer's aesthetic, is that offusion be-tween the instruments. It would be difficult for us to de-fine acoustically what is meant by the word fusion. Letus just point out qualitatively that a systematic interroga-tion of the subjects after Experiment 1 showed that noneof them was able to name the five instruments used. Lackof segregation has been shown to be related, for exam-ple, to difficulty in identifying simultaneously presentedvowels (de Cheveigne, McAdams, Laroche, & Rosen-berg, 1995).

However, careful listening to the timbres reveals thepresence of salient features in some of them. Timbres T6 ,T7 , and Ts contain a high flute note that was to be playedat a moderate dynamic (see the score in Figure 1). In therecorded performance, these notes emerge from the tim-bres (see, for instance, the amplitude of the Flute 2 com-ponent in Figure 3) and give rise to what we call a sur-face specificity. For T3 and T4 , intervals with a harmonicfunction can be discovered in the score (for instance, inT3 , a perfect fifth between the flutes and an almost majorthird between the clarinet and the second flute). Theseintervals evoke a strong syntactic function in the tonalsystem. In the composer's original intention, they shouldhave been blended into the global timbre, but the rela-tive balance between the instruments made them salientin our recordings. This constitutes what we call a har-monic specificity.

74 PRES SNITZER, McADAMS, WINSBERG, AND FINEBERG

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

A new experiment was designed in which modifica-tions of the acoustic stimuli were done under the com-poser's supervision to obtain better fusion, according tohis vocabulary. A multitrack recording was used to makea new version of the timbres in which the relative levelof each instrument, as well as the evolution of the levelsover time, was modified. Again, no systematic acousticcriterion for fusion can be proposed. Nevertheless, theacoustic analyses of the new version of T7 are shown asan example in Figure 6. In this case, the remixing hadthe effect of correcting the balance between the instru-ments, most notably between Flute I, Clarinet, and Flute 2.The waveform also displays a more regular envelope, theattacks ofthe different instruments having been smoothed.

This removes a potential cue for auditory segregation(Bregman, 1990). After the remixing ofthe eight timbres,a procedure similar to that in Experiment I was used toestablish psychophysical scales for tension and roughness.

MethodStimuli. New versions ofthe timbres employed in Experiment I

were used. The same performances were selected, but the relativebalance between the instruments' volumes, as well as their tempo-ral evolution, was modified by remixing. An artificial room effectwas added with a Lexicon processor, to reproduce the natural roomcolor present in the stimuli of Experiment I.

Apparatus. The multitrack recording on a 33.24A Sony multi-track recorder was made with five Neuman KM 140 cardioid mi-crophones, placed 50 ern from each performer's instrument. The

MUSICAL TENSION AND ROUGHNESS 75

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76 PRES SNITZER, McADAMS, WINSBERG, AND FINEBERG

percentiles. The result in this second experiment was r =.94; r E [.84.96], whereas the first experiment gave r =.53; r E [.32 .73]. With the exception of the significantdifference for Ts (for which we find no plausible interpre-tation), these results suggest that roughness could nowbe sufficient to explain tension perception of the remixedtimbres.

Replication of the Additional AnalysesThe additional analyses performed on the results of

Experiment 1 were repeated for the new experimentaldata. Order ofpresentation was found to have significantinfluence neither on tension judgments nor on roughnessjudgments.

The peA analysis revealed a quasi-unidimensionalsolution, with a first consensus component that reflectedthe BTL psychophysical scale explaining 73% ofthe vari-ance. The second component, accounting for only 15%of the variance, explains not much more variance thando any of the original variables. This indicates that, inthis second experiment, the tension judgments could al-most exclusively be explained in terms of the consensusdimension.

MODEL SIMULATION

A computational model of roughness (Hutchinson &Knopoff, 1978) was tested to try to reproduce the exper-imental results. The model considers a set of frequenciesand amplitudes U;, a j) intended to represent the spectralcomposition ofa given sound. For each possible pair (i,j)of components, a partial roughness rij is computed ac-cording to their frequency difference. All the partial rough-nesses, normalized by the amplitudes, are then summed

to give the global roughness that constitutes the modeloutput. The corresponding analytic formula developedby Parncutt can be found in Bigand et al. (1996).

This model has theoretical weaknesses. The calcula-tion of roughness between two frequency components isactually derived from experimental results (Plomp &Levelt, 1965), but the influence of differences in ampli-tudes between interacting components, as well as thesimple addition between partial roughnesses, is not. Thisextrapolation of data concerning equal amplitude tonepairs to tone complexes is likely to be incorrect (Kame-oka & Kuriyagawa, 1969a; Vos, 1986). This model wasnevertheless tested, because its input is in a form similarto that of the composer's original algorithm. More gen-erally, it is well adapted to musical notation, wherechords can be represented by a list of component notes(frequencies).

To simulate our empirical findings, the data fed intothe model should be the notes written in the score, withall the amplitudes equal. However, a spectrum also has tobe associated with each note, because beats between par-tials are an essential source of roughness (Kameoka &Kuriyagawa, 1969b). Therefore, hypothetical spectra withfour partials and a 12dB/oct rolloffwere chosen. This rep-resents a schematization of the stimuli but remains plau-sible, considering the register and instrumentation used(see Figures 3 and 6).

The computed roughness values are shown in Fig-ure 8. The correlation between the BTL analysis of ex-perimental roughness judgments of Experiment 1 andcomputed roughness is (r = .83; r E [.73 .90],90% con-fidence interval estimated by bootstrap percentiles). Forthe roughness psychophysical scale obtained in Experi-ment 2, the correlation is (r = .88; r E [.81 .94]). The ex-

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

.2

'"'"g..Q

.15be::l0....

"Cs::l

.1S-oU

.05

8764 5Timbres

321O'----'----'----.L..---'----'__-L-_--L__--'-----'

Figure 8. Model calculation of roughness for the eight timbres. The roughnessscale is arbitrary.

perimental roughness judgments are, therefore, generallyconcordant with the model simulation.

With respect to using the model as a compositionaltool, it is also possible to qualitatively compare its outputwith the composer's original tension predictions, shownin Figure 2. Considering roughness as a tension indica-tor, the model is globally better at predicting the experi-mental judgments; timbre T7 , for instance, was predictedas bearing a low tension value but was experimentallyjudged as being both tense and rough. The model repli-cates this finding.

GENERAL DISCUSSION

Tension and RoughnessThe first experiment allowed us to exhibit significant

differences in tension for nontonal orchestral timbres.The notion of tension-deliberately defined loosely inthe experimental instructions-gave rise to a consensusamong subjects in a musical context that was unfamiliarto most of them. Roughness was also found to be a rele-vant criterion by which to judge the timbres. However, sig-nificant differences appeared between the two measures,indicating that factors other than roughness participatedin tension judgments. The second experiment confirmedthe perception of tension and roughness differences be-tween the timbres but exhibited almost identical psycho-physical scales. The correlation observed indicates that,in this second experiment, it is possible to account for thetension judgments by comparisons ofroughness, increas-ing roughness inducing greater tension. Ofcourse, a cor-relation is by no means a proof ofcausality, but other el-ements that appeared in the additional analyses arecoherent with the hypothesis that roughness was a sen-sory basis for the perceived tension of the timbres.

The temporal succession of the timbres did not have alarge influence on the tension judgments. Therefore, itis mainly the intrinsic aspect of the stimuli, which paral-lels the tonal concepts of intrinsic consonance or disso-nance, that influenced the tension judgments. Roughnessis thought to participate in intrinsic consonance in thetonal context, and our results extend this interpretation toa nontonal context.

The influence of the explicit or the implicit accultura-tion oflisteners (all having a "Western" background) didnot appear to be influential in a straightforward manner.That is, no correlation between musical education andjudgment strategies could be found. Roughness, as abasic feature of sound, is not expected to depend on cul-tural factors and is readily available to trained or untrainedlisteners. However, this might also be due partly to the factthat musicians trained almost exclusively in tonal musicmay not have a special strategy for nontonal stimuli.

Finally, the correlation between psychophysical scalesfor tension and roughness is not due to a possible confu-sion between the words tension and roughness. In the ex-perimental instructions, the definition of tension was leftto the appreciation of the listeners, but roughness wasdefined by means of an example with sound. Roughness

MUSICAL TENSION AND ROUGHNESS 77

estimations were then obtained in two distinct ways (anexperimental evaluation and a model simulation) thatgave converging results. Lastly, the significant differencesobserved in Experiment I between tension and roughnessshow that the subjects were indeed able to differentiatetension and roughness.

Comparison Between the Two ExperimentsExperiment I displayed significant differences be-

tween psychophysical scales for tension and roughness,differences that generally disappeared in Experiment 2.Our interpretation of this is based on the specificitiesmentioned earlier. Although the status of these speci-ficities is hypothetical, this hypothesis allows us to ac-count for several aspects of the data.

Except for Ts' all the timbres that displayed significantdifferences for tension and roughness in Experiment Icontained specificities. Moreover, the specificities arecoherent with the results: T6 and T7 were tense but lessrough, and they included a prominent high-pitched notethat could induce tension without roughness; T3 con-tained intervals associated with release in the tonal sys-tem and was judged to be rough but less tense. These fea-tures, in addition to roughness, may have influenced thetension judgments. The effect ofthe remixing can then beinterpreted as having reduced their perceptual salience.As fewer specificities emerged from the timbres, rough-ness became the main available cue to judge tension. ThePCA performed to analyze listening and/or judgmentstrategies in Experiment I exhibited a secondary com-ponent contrasting subjects; this component opposes tim-bres containing a surface specificity to the ones contain-ing a harmonic specificity. This component can, therefore,be interpreted as a disagreement in listening and/or judg-ment strategies concerning the impact ofthe specificitieson tension perception. After the remixing of the timbresin Experiment 2, the second component disappeared.

Let us, nevertheless, point out that Experiment 2, inour view, is by no means an improved version of Exper-iment I in which possible "flaws" in the stimuli were dis-covered and then fixed. Our point is not to assert that ten-sion and roughness are equivalent. In the general case, aswas shown by Experiment I, the influence of roughnesscombines with several other factors to contribute to thefeelings of tension and release experienced by the listen-ers. The transformations made to obtain Experiment 2stimuli, which basically consisted in homogenizing thetimbres, suggest that roughness may potentially expresstension in a situation that remains musically realistic.The comparison between the two experiments allows usto specify the conditions under which roughness can be-come a dominant factor in tension perception.

Remarks on the Experimental Procedureand Analysis Methods

This study has tried to draw a link between a basicpsychoacoustic feature, roughness, and the musicallyimportant notion of tension. The choice of the stimuli,therefore, reflects a tradeoff between musical realism

78 PRESSNITZER, McADAMS, WINSBERG, AND FINEBERG

and limitation of the number of experimental variables.On the one hand, the stimuli were extracted from an ex-isting musical piece. They were recorded with live instru-ments in a concert-like situation and, in a second condi-tion, were remixed in a situation habitually found in thepreparation of recorded music. The question of findinga tension hierarchy was motivated by a preoccupation enter-tained by the composer during the writing of the piece.On the other hand, the timbres were homogeneous inregister and dynamics, which may represent a limitationwith respect to other musical situations. For instance, onemay wonder how salient the tension cues linked to rough-ness would still be when placed in competition with cuesofa different nature, such as rhythm, dynamics, or regis-tral extremes. The interactions of melodic and harmonicfactors were also not addressed here. These interactionsare important in the context of polyphonic music, whereit has been claimed that auditory streaming processes in-fluence the perception of roughness and tension (Wright& Bregman, 1987).

Forced-choice paired comparisons were used to avoiddirect magnitude estimation judgments. These judg-ments would have been hard to define without introduc-ing terms not necessarily relevant to a musical context.Furthermore, the complexity of the stimuli could havemade the task difficult for listeners. This design led us toadopt nonparametric statistical analysis methods in orderto make as few hypotheses on the outcome of the data aspossible: The bootstrap technique was used to examinethe stability of the BTL results.

The analyses attributed a single tension value to eachtimbre. Ofcourse, this is not supposed to mean that thereexists an absolute intrinsic tension for the timbres inves-tigated. It should be emphasized that the hierarchy is rel-ative. The individual estimated tension values can bethought of in a fashion similar to that of the relative con-sonance and dissonance values traditionally ascribed toindividual tonal chords. Although the level of "accept-able" dissonance has varied over the history of tonalmusic, it does not preclude perception of sensory conso-nance as a potential basis for tension perception (Breg-man, 1991). Schoenberg (1911/1978), for example, pre-ferred to refer to dissonances as "remote consonances"!

Perception of Tension in Nontonal MusicTheories of nontonal tension are far less numerous

than theories of tonal tension. On the one hand, com-posers have proposed theories of nontonal tension thatoften have a close relationship to their own musical styles,as a codification of personal practices. A theory that ismore generally relevant and, therefore, concerned withexperimental testing is the extension of the GTTM toatonal music by Lerdahl (1989).

The GTTM reduces a musical piece-at different lev-els-to structural units by way of a time-span reduction.The reduction is made according to stability rules thatare based on the hierarchical relationships that exist inthe tonal pitch space. This reduction is then supposed tobe the basis of the perception oftension and release move-

ments (prolongational reduction). For atonal music, Ler-dahl (1989) makes the assumption that the pitch space isflat and replaces the stability rules by salience rules toobtain similar reductions. Both the tonal and the atonaltime-span reduction theories have been experimentallytested, with contrasting results (Dibben, 1994). Whereaslisteners were able to match a reduction to its original fortonal pieces, results were close to random in the atonalcondition. The author proposed several reasons for thislatter outcome, but the suggested conclusion is that theinability to match original pieces and reduced versions isinherent to the music tested (excerpts from Schoenbergopuses II and 19). Hierarchical levels of structure wouldbe impossible to extract when listening to atonal music,and the only tension and release movements perceptiblein this context (thanks to associations between soundevents) would, therefore, be of lesser importance (Dib-ben, 1996).

Our results bring new elements to bear on this con-clusion. The experimental judgments of orchestral tim-bres showed that tension and release movements couldactually be perceived by listeners in a musical contextnot related to tonality. Another study gave a convergingset of results by exhibiting a similar range of variationfor tension judgments within tonal and nontonal musicalexcerpts and a significant effect of timbre on the judg-ments (McAdams & Pressnitzer, 1996; Paraskeva &McAdams, 1997). A difference between the present studyand those of Dibben (1994, 1996) is that, here, the under-lying structural harmony was approached in terms oftimbre, rather than in terms ofnotated pitch events.' Tim-bral quality alone, without a reference to a pitch spaceorganization, was sufficient to convey intrinsic move-ments of tension and release between pairs of sounds.The question is now whether the local properties inves-tigated (such as roughness) are able to convey tensionand release movements on larger time scales. It would beofgreat interest to test whether originals and reductions,similar to the ones proposed by Lerdahl (1989) but basedon timbra1 salience rules, including roughness, could bematched by listeners.

Timbre as potential form-bearing structure has inter-ested composers, from the experiments of Berlioz andDebussy to Schoenberg's Klangfarbenmelodie, and morerecently, those who belong to the musique spectraletrend (Murail, 1984; Pressnitzer & McAdams, 1999).Cognitive psychology has expressed the condition uponwhich a multidimensional attribute such as timbre couldbe the basis for building musical form-mainly in termsof the possibility of categorization and recognition ofvectors in a timbre space (McAdams, 1989; McAdams &Cunibile, 1992). Our study is an indication that timbremay also be a privileged support for harmony, thanks tothe dimension of roughness.

CONCLUSION

Two experiments have shown that the fundamentalmusical concept of tension-release schemas can be con-

veyed by orchestral timbres, even when no harmonicfunction corresponding to the Western tonal system canbe defined for them. Different factors influenced theseschemas: tonal references, heard both by musicians andnonmusicians, or surface characteristics resulting fromperformance variables, such as the emergence of high-pitched tones. However, when these features were re-duced in salience, roughness became a noteworthy di-mension. This sound attribute, in close relationship withperipheral auditory mechanisms, was highly correlatedwith the musical notion of tension. Its simulation with apredictive model may be considered. Roughness, as a di-mension oftimbre, could open up a way ofthinking ofnon-tonal harmonies on the basis of perceptual phenomena.

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NOTES

I. The critical band is a general concept defining the frequency res-olution of the auditory system and is directly influenced by the biome-chanics ofthe basilar membrane (Scharf, 1970).

2. A factor analysis was not performed after the PCA, for the fol-lowing reason. A criterion, such as varimax (Kaiser, 1958), rotates theaxes to make the subjects' loading on each factor either very high or verylow. Such a rotation would alter the consensus among the subjects as tothe ordering ofthe timbres along the first dimension. Our objective wasmainly to assess this consensus; therefore, the axes were not rotated.

3. It must be acknowledged that even in the original version of theGTTM (Lerdahl & Jackendoff, 1983, p. 297), timbre was considered asa candidate contributor to nontonal tension perception. However, thesalience rules proposed in Lerdahl (1989) were defined for a collectionof pitches and not for one sound event that had a homogeneous "tim-bre." In any case, they did not include roughness as a relevant criterion.

(Manuscript received March 4, 1997;revision accepted for publication September 18, 1998.)