Scale Structure and Similarity of Melodies Author(S): James C

Scale Structure and Similarity of Melodies Author(s): James C. Bartlett and W. Jay Dowling Source: Music Perception: An Interdisciplinary Journal, Vol. 5, No. 3, Cognitive and Perceptual Function (Spring, 1988), pp. 285-314 Published by: University of California Press Stable URL: http://www.jstor.org/stable/40285401 Accessed: 04-12-2015 23:43 UTC

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This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions Music Perception ©1988 by the regents of the Spring 1988, Vol. 5, No. 3, 285-314 university of California

ScaleStructure and Similarityof Melodies

JAMES C. BARTLETT & W. JAY DOWLING University of Texas at Dallas

Four experiments explored an asymmetry in the perceived similarity of melodies: If a first-presented melody is "scalar" (conforms to a diatonic major scale), and is followed by a second melody slightly altered to be "nonscalar" (deviating from a diatonic major scale), subjects judge similarity to be lower than if the nonscalar melody comes first. Experiment 1 produced evidence that asymmetric similarity is not due simply to more strongly scalar melodies having greater memorability. Experiment 2 ruled out the hypothesis that asymmetric similarity depends on a task- specific strategy reflecting demand characteristics. Experiments 3 and 4 replicated asymmetric similarity while controlling the number of one- semitone intervals in scalar versus nonscalar melodies. The data are consistent with Garner's principles that stimuli are perceived with reference to sets of alternatives and that good stimuli have few alternatives. Speci- fically, when mélodie* are presented in scalar- nonscalar order, but not when presented in nonscalar-scalar order, the first melody evokes a small set of alternatives which the second melody often violates.

Introduction

A basic fact about melodies is that their tonality, and in particular their use of a restricted set of notes from a diatonic scale, is a highly salient attribute. Even the most nonmusical listener will notice "wrong notes" in atonal melodies, and will judge such melodies as less "pleasant" than strongly tonal melodies. Some aspects of tonality are enormously subtle, and probably perceivable only by experts. However, the conformity of a melody to a diatonic scale- what can be termed its "scalar structure" (Cross, Howell, &CWest, 1985) - appears to be detectable by virtually all listeners brought up in Western culture, even at an early age. The detection of scalar structure of melodies has been supported by sev- eral investigators (see Dowling & Harwood, 1986), including Cross, Ho- well, & West (1983). Cross et al. generated artificial melodies that varied systematically in degree of scalar structure, and they found that musician as well as nonmusician subjects gave generally higher "liking" ratings to the

Requests for reprints may be sent to Dr. James C. Bartlett, Program in Human Develop- ment & Communication Sciences, University of Texas at Dallas, Richardson, Texas 75083- 0688.

285

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions 286 James C. Bartlett & W. Jay Dowling more scalar melodies. Indeed, the ratings of musicians and those of nonmu- sicians were not detectably different.1 A related study by Krumhansl and Keil (1982) had adults and young children aged 6 to 12 years rate melodies for "goodness." The findings suggested that children's sense of tonality, and in particular their sense of which scalar notes were particularly suitable for ending a melody, grew more refined with age. However, even the youngest (6-year-old) subjects gave higher goodness ratings to scalar melodies than to nonscalar melodies. Indeed, Dowling (1988) found that children as young as 3 years old can be more likely to judge that a melody sounds "funny" if it is nonscalar rather than scalar. Although the foregoing evidence supports a sense of scalar structure em- erging early in development, the origins of this sense are not yet understood. One approach to understanding scalar structure is based on the argument (e.g., Dowling, 1978) that children's exposure to diatonic melodies allows them to abstract some sort of scale schema, which thereafter is employed in the encoding of new melodies. Presumably, a melody's fittingness with an internal scale schema- the ease with which it is assimilated to this schema- affects how "good" (or non-funny) it sounds. A second approach to understanding scalar structure assumes that there are purely physical aspects of scales that render scalar melodies "better" or less "funny." Speci- fically, diatonic scales include a reasonably large number of pitch classes (seven) while minimizing the occurrence of semitone intervals- the major diatonic scale (do-re-mi-fa-so- la-ti-do) follows an interval structure (2-2-1-2-2-2-1) containing only two one-semitone intervals. No other scale using seven pitch classes out of 12 equal-tempered semitones has fewer one-semitone intervals, and melodies that violate diatonic scales will generally have more one-semitone intervals than those that match such scales. Since tones that are less than two semitones apart appear to produce interferencein memory (Deutsch, 1982), scalar melodies might sound "better" not because they are readily assimilated to schemata, but rather because they contain small numbers of one-semitone intervals. A third approach to understanding scalar structure is to assume that such structurecontributes to the "goodness" of melodies as gestalts. Due to their organization into phrases and larger structural units, as well as their trans- posability in pitch, melodies have long been viewed as prototypical gestalts (e.g., Boring, 1942; Dowling &cHarwood, 1986). Moreover, research on

1. Cross et al. (1983) initially found that their least scalar melodies evoked high liking ratings. However, this effect was due to the perceived rhythm of the melodies, which tended to place stress on a set of scale-compatible notes in the lowest-scalar-structure condition. When Cross et al. removed this confound by altering the rhythm of their stimuli, the least scalar melodies received low liking ratings, as would be expected.

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions Scale Structure and Similarity of Melodies 287 the factors affecting gestalt "goodness" has clear implications for the perception of melodies. Following Garner's (1970, 1974) conception that "good patterns have few alternatives," we recently suggested that a melody, like other simple visual and auditory patterns, is perceived as belong- ing to a set of alternative stimuli (Dowling & Bartlett, 1981; Bartlett, 1984). The smaller the set of alternative stimuli, the better (more pleasant or stable) the melody. The "wrong notes" heard in a nonscalar melody reflect a subject's perception that, because of these notes, the set of perceived alternatives is large. How might the scalar structure of a melody affect its perceived alternatives? Our notion is twofold: First, the perception of a melody evokes a set of alternatives that share various of its features (e.g., contour, general pitch range, loudness, timbre). This is consistent with the "norm theory" of Kahneman and Miller (1986), who claim that: (a) "the experienced facts of reality [i.e., stimuli] evoke counterfactual alternatives and are compared to these alternatives," and (b) some features of a stimulus are treated as "immutable" in that they "guide and constrain the spontaneous recruitment of alternatives to it" (p. 142). Second, if a melody is perceived as scalar, the set of alternatives evoked by this melody is constrained to fit its musical key. In terms of norm theory (Kahneman &cMiller, 1986), the scale from which a melody's notes are chosen functions as an immutable feature of that melody, constraining the set of alternative melodies to which it is (often implicitly) compared. Note that in the system of European tonal music, the most typical scale pattern is the diatonic scale of seven pitch classes (i.e., seven pitches and their func- tional equivalents at octave intervals), selected from the 12 pitch classes of the chromatic set (i.e., the European "tonal material," Dowling, 1978). Thus, we are suggesting that if a melody is perceived as being scalar, its perceived alternatives are restricted to melodies constructable from the seven pitch classes of a diatonic scale. In contrast, if a melody is perceived as nonscalar, its perceived alternatives are only weakly or not at all constrained by a diatonic scale- they might include melodies based on all 12 pitch-classes of the chromatic set. Since the 12 pitch classes of the chromatic set include the 7 pitch classes of any major diatonic scale, a nonscalar melody would evoke a larger set of alternative melodies than a scalar melody that is otherwise similar (same contour, length, etc.). Indeed, the set of alternatives of a scalar melody may be "nested" within that of a nonscalar melody that is otherwise similar to it (Garner, 1974). The idea that scales constrain alternative sets for melodies can be visual- ized using spatial models of pitch, particularly the "melodic map" of She- pard (1982). One axis of Shepard's spatial model is the cycle of fifths of musical keys, each key generating a diatonic scale. Based on the musical interval of the fifth, the cycle of fifths moves through all possible pitch

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions 288 James C. Bartlett & W. Jay Dowling classesof the chromaticset, makingno repeats(if one startswith F, the cycle continueswith C, G, D, A, E, B, F#, Ctf,Gtf, D(t, A(t [or Bt], and then returnsto F). More important,any set of sevennotes fromcontiguous loca- tions along the cycle constitutethe notes of a diatonicmajor scale. Thus, if we beginwith F and follow the cycleto B (i.e., F, C, G, D, A, E, B), we have the sevennotes of the C majorscale. When the cycle-of-fifthsis "cut open" at some (arbitrary)point to form a one-dimensionalaxis, and combined with a second axis representingpitch height (frequency),we have a two- dimensional"map" for representingmelodies, as shown in Figure1 (note that Ajtis actuallyproximal to F aroundthe cycle of fifths).

Fig. 1. A portion of Shepard's (1982) melodic map, unrolled onto a two-dimensional sur- face with the dimensions of pitch height (ordinate) and key distance around the cycle of fifths (abscissa). Filled circles represent the seven pitches of the C-major scale, and the verti- cal line separates scalar from nonscalar pitches. Open circles and arrows indicate (a) the scalar melody C-B-D-G-E-A-C, and (b) the nonscalar melody C-B-D(t-G-E-A-C.

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions Scale Structure and Similarity of Melodies 289 The melodyshown in Figure1 A beginsand ends on C, and containsnei- therflats nor sharps,and so it clearlymatches the key of C. This fact is high- lightedon the melodicmap by meansof a verticalline delimitingthe notes of the C-majorscale. All notes of the melodyfall to the left of the line, and this capturesthe notion that scalar structurelimits the set of alternatives perceivedfor a melody. If the melodywere transposedinto a differentkey (e.g., G), its map-positionwould be changed,but its "shape"would be the sameand againit would fall into a compactmap region. Thus, strongly scalar melodies in any diatonic key occupy restrictedregions of the melodic map. The hypothesiswe are forwardinghere is that the perceivedalternatives for stronglyscalar melodies occupy the samerestricted map regionsas the melodiesthemselves. In contrast,as shown in Figurelb, weakly scalar and nonscalarmelodies will tend to coverthe full lateralextent of the map, and we suggestthat theirperceived alternative melodies will also coverthe entiremap range.Thus, we have a way of visualizingthe notion that a set of alternativesfor a scalarmelody is smallerthan that of a nonscalarmelody and is "nested"within that of a nonscalarmelody. The idea that scalarmelodies evoke small sets of perceivedalternatives, andthat the alternativesets evokedby scalarmelodies can be nestedwithin those evoked by nonscalarmelodies, has been supportedby a finding of asymmetricsimilarity (Tversky, 1977). Dowling and Bartlett(1981) con- structedpairs of five-notemelodies, each pair consisting of a scalarmelody accompaniedby a relativelynonscalar mate. The scalarmelody was a random permutationof the firstfive notes of the C-majorscale, alwaysbegin- ningon middleC (262 Hz). Its nonscalarmate was physicallyidentical, except that one note was changed by one semitone to fall outside of the C-majorscale (e.g., a D mightbe replacedby Djt).Subjects' task was either to rateeach pair for similarity,or to ratetheir confidence that eachpair was "same"versus "different" (although in fact all pairswere different).Both similarityand same-differentratings were made using a six-point scale, and average ratings were higher (i.e., judged similarity/samenesswas greater)when the nonscalaritem came first (nonscalar-scalarpairs) than when the scalaritem came first(scalar-nonscalar pairs). Asymmetric simi- larityhas been found outsidethe music domain (Handel& Garner,1966; Tversky, 1977), and even within the music domain the effect is not re- strictedto melodies- asymmetricsimilarity has been found with single pitches presentedin a tonal context (Krumhansl,1979), as well as with chordsequences (Bharucha & Krumhansl,1983). However,the effect ob- tainedwith melodiesis most directlyrelevant here. In interpretingasymmetrical similarity of melodies, we follow Garner (1974; Handel & Garner, 1966) in assumingthat asymmetriesreflect a "nesting"relation in the sets of alternativesevoked by two stimuli.That is, asymmetricrelatedness between two stimulioccurs when the set of alterna-

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions 290 James C. Bartlett & W. Jay Dowling tives evoked by one stimulus includes the second stimulus,but not vice versa.Turning to the paradigmof Dowling and Bartlett(1981), the idea is thatif a firstmelody evokes a set of alternatives,and if a subsequentmelody falls outside this set of alternatives,an impressionof dissimilarityresults. This state of affairsshould be much more probablewith scalar-nonscalar pairs- the initial melodies of such pairs have sets of alternativescon- strainedby their key, and the second melodies in such pairs should fre- quentlyfall outside of these sets. In contrast,violations of alternativesets shouldbe rarein the case of nonscalar-scalarpairs. The initialmelodies of such pairs are likely to have large sets of alternatives,including not only other nonscalarmelodies, but also scalarmelodies. And since the second, scalar,melodies share many features of theirfirst-presented mates, they are likelyto fall within the sets of alternativesevoked by theirmates. Towardthe generalgoal of evaluatinga perceived-alternativeshypothesis for effectsof scalarstructure of melodies,the presentresearch was a fur- therexploration of asymmetricsimilarity of scalarand nonscalar melodies. Our aim was to determinewhether asymmetricsimilarity was better explained by a perceived-alternativeshypothesis than by three competing views. First,we addressedthe possibilitythat asymmetricsimilarity results fromscalar melodies being generally more memorable than nonscalarmelodies (Experiments1 and 2). Second,we examinedthe notion that asymmetricsimilarity is the productof a task-specificstrategy as opposedto the intrinsicallyperceptual process of inferringalternative sets for melodies (Experiments2 and 4). Third, we tested the hypothesisthat the greater numberof one-semitoneintervals in nonscalarmelodies than in scalarmelodies is sufficientto explain asymmetricsimilarity (Experiments 3 and 4). Sincethe four experimentsthat testedthese views were fairlysimilar in de- signand procedure, it is usefulto presenta GeneralMethod section prior to detailsof the individualexperiments.

General Method

SUBJECTS

Undergraduates at the University of Texas at Dallas served in these experiments for par- tial course credit. This population has a mean age of 29.4 years, and consists of 64% fe- males. Based on prior findings that moderate amounts of prior musical experience affect certain aspects of melody processing (Dowling & Harwood, 1986), subjects in each experiment were separated into two groups, "moderately experienced" and "inexperienced." Moderately experienced subjects had 2 years or more of musical training, including lessons on an instrument or voice, and playing in instrumental ensembles (but not choral singing). Those subjects had an average of about 5 years training approximately 10 to 15 years prior to the experiment. Inexperienced subjects had less than 2 years musical training.

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions ScaleStructure and Similarityof Melodies 291

STIMULI

The stimuliconsisted of pairsof seven-notemelodies. On eachtrial, subjects would hear a pairof melodiesin which one of the notes was alteredin pitch by one semitone.Melodies wereeither scalar or nonscalar,and were combined in fourtypes of pairsas shownin Table 1. In Experiments1 and 2, all four possibletypes of pairswere used: pairsin which both melodieswere scalar (SS),pairs in which both melodieswere weakly scalaror nonscalar (NN), pairsin whichthe firstmelody was scalarand the secondwas not (SN), and pairsin whichthe secondmelody was scalarand the firstwas not (NS).In Experiments3 and4 only SN and NS pairswere employed.Note that for both SN and NS pairs, the one-semitone changewas suchas to alterthe scalestructure of the melody(A(t might be substitutedfor A). For SS and NN pairshowever, the one-semitonechange did not affect scalarstructure (E mightbe substitutedfor F). The stimuliwere basedon 24 or 48 seed melodies,all beginningand endingwith middle C (fundamentalfrequency, 262 Hz). The interveningfive pitches were all differentand con- sistedof fivepitches of the C-majordiatonic scale other than C. EitherE or F was includedin thisset of pitches,but not both. Sincethere are only sevenpitches in the scale,this meant that the fivepitches in the middleof the melodywere drawn from the set A-B-D-G pluseither E or F. Thesefive possibleintervening pitches gave 5! = 120 possiblemelodies. For each ex- perimentwe randomlyselected the seed melodiesfrom the set of 120 possiblemelodies. A constrainton selectionwas thatthe melodiccontour (pattern of upsand downs in pitch)was differentfor each seed melody. An SN pairwas constructedfrom a seedmelody by recordingthe seedmelody twice, first with no change(scalar) and then with a nondiatonicnote substitutedfor a diatonicnote (nonscalar).The diatonicand nondiatonicnotes alwaysdiffered by one semitone.An NS pairwas constructedin the sameway as an SN pair, exceptit was the secondmelody that was recordedunchanged and the firstthat was recordedwith the nondiatonicnote. An SS pairwas constructedby recordingthe seedmelody twice, once with no changeand once with an E substitutingfor the F or viceversa (depending on whetherthe seedmelody contained an E or F). An NN pairwas constructedin preciselythis same fashion,except that a diatonic pitch (besidesthe E or F) was replacedby a nondiatonicpitch in both membersof the pair (forexample, A)t for A). Note thatthe two melodiescomprising each pair always differed by only one semitonein a single serial position. This one-semitonechange did not cause a changein the melodiccontour of the melodies. Eachexperiment consisted of from two to five blocks of 24 melodypairs. Eachof the pairswithin a blockwere constructed from a uniqueseed melody. There was randomassign-

TABLE1 Examples of Melody Pairs Used in Experiment 1

Item Type First Melody Second Melody SS CBDGEAC CBDGFAC NN CBDttGEAC CBDtfGFAC SN CBDGEAC CBDttGEAC NS CBDttGEAC CBDGEAC

note: S = scalar,N = nonscalar.

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions 292 James C. Bartlett & W. Jay Dowling ment of seed melodies to condition (for example, SS, NN, SN, NS), with the constraint that each condition occurred equally often in each block. The melody pairs were presented over loudspeakers using high quality stereophonic equipment.

PROCEDURE

Subjects served in group sessions and were introduced to the experiment by means of instructions that included four examples of the types of melody pairs they would hear. Sub- jects were asked to listen to each pair of melodies carefully and to rate (for example) the similarity of the melodies in the pair on a six-point scale going from "6" ("very similar") to "1" ("very different"). Subjects responded on an answer sheet printed with blanks num- bered with the appropriate number of trials. Subjects also completed a brief questionnaire concerning age, sex, and musical experience.

Experiment1

The aim pursuedin Experiment1 was to determineif the finding of asymmetricsimilarity could be explainedby a simplememorability hypothesis. It frequentlyis claimedthat morestrongly tonal melodiesare more easily rememberedthan less tonal or atonal melodies,although relevant data arescarce (but see, e.g., Frances,1958/1988). Makingthe workingassump- tion that this claim is true, and that it extendsfrom tonal structurein gen- eralto scalarstructure in particular,the asymmetricsimilarity effect can be easily explained.First, consider scalar-nonscalar pairs: Since the notes of the first (scalar)melody are verywell remembered,the alterationin a note of the second (nonscalar)melody is easily detected,producing an impression of low similarity.Now, consider nonscalar-scalarpairs: Since the notes of the first(nonscalar) melody are rememberedrelatively poorly, the alterationin a note of the second (scalar)melody is not easilydetected, pro- ducingan impressionof relativelyhigh similarity. The memorability hypothesis is compatible with either a schema- assimilationview or the memory-interferenceview of effectsof scalarstruc- tureon processingof melodies(see Introduction). That is, the low memorability of nonscalarmelodies might be attributedeither to their less than perfectmatch to existingscale schemata,or to the semitoneintervals - and memoryinterference - suchmelodies produce. Hence, in testingthe memorabilityhypothesis, we areproviding information relevant to thesebroader hypothesesfor scalarstructure of melodies. In orderto test the memorabilityhypothesis, Experiment 1 includedthe SN and NS conditionsused in our priorstudies, along with two additional conditions; SS and NN (see Table 1). Although all melody pairs were changedby only one semitonein one serialposition, the memorabilityhy- pothesespredicts that this semitonemismatch will be more easily detected when the firstmelody is scalarthan when it is nonscalar.Hence, the rated

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions Scale Structure and Similarity of Melodies 293 similarity of SS pairs should be as low as that of SN pairs and lower than that of NS and NN pairs. The perceived-alternatives hypothesis does not make the same predictions. Since the melodies of an SS pair are in the same key, and also are identical save for one note changed by a semitone, the second melody in such a pair need not mismatch the perceived alternative set of the first. If there is no such mismatch, similarity ratings made to SS pairs should be higher than those made to SN pairs and at least as high as those made to NS pairs, in direct contradiction to the memorability hypothesis. On the assumption that two nonscalar melodies do not produce alternative-set violations, the rated similarity of NN pairs also should be high. As a test of generality of whatever findings emerged, we followed Dowl- ing and Bartlett (1981) in asking half of the subjects to rate the similarity of each melody pair and the remainder to rate their confidence that the melodies of each a pair were exactly the same versus changed. Subjects were not informed that all melodies were changed in one note.

METHOD

Subjects

Twenty-eight subjects served in Experiment 1, with 13 in the inexperienced group and 15 in the moderately experienced group.

Stimuli

Stimuli were produced on a freshly tuned Steinway piano. Timing was controlled by the clicks of a metronome set at 72 beats/min, which were barely audible on the tape. Melodies proceeded at a rate of three notes per metronome beat, or 3.6 notes/sec. Melodies were played "legato," with little time between note offsets and onsets, and the seventh note of each melody was held for a full metronome beat. (That is, the last note was three times as long as each of the first six notes.) One metronome beat separated the standard and comparison melodies on a trial. Each trial began with a warning consisting of the spoken trial number two beats (1.67 sec) before the onset of the first melody. Subjects had eight beats (6.67 sec) to respond before the start of the next trial. Melodies were constructed from the set of pitches between the F|t below middle C and the F above. Standard and comparison melodies on a trial always differed in exactly one pitch, which was altered by one semitone. There were four types of trials: SS, NN, SN, and NS. The melodies on SS and NN trials differed by the interchange of the pitches E and F. The melodies on SN and NS trials differed by the substitution of nondiatonic pitches for diatonic ones: A| for A, C| for D, or F# for G (randomly determined and occurring equally often). These substitutions of nondiatonic pitches had the effect of making the N melodies either strictly nonscalar (in that the melody could not be interpreted in any diatonic scale), or relatively nonscalar (in that the melody could not be interpreted within the C major scale im- plied by all melodies of the experiment, all of which began and ended on C). The substitutions involving Aft and C)t produced strict nonscalarity through the creation of adjacent one-semitone intervals (AJ-B-C and B-C-C(t). The substitutions involving F# produced strict nonscalarity in those melodies containing F due to the creation of two tritone (six-

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions 294 JamesC. Bartlett& W. JayDowling semitonerelationships within the set of pitches(i.e., B-F and C- Fjt).The substitutionsin- volvingF)t produced relative nonscalarity in thosemelodies containing E insteadof F. Thisis becauseF|t in conjunctionwith the pitchesC, D, E, G, A, and B is compatiblewith the G- majordiatonic scale, and hence not strictlynonscalar. However, F| in thatcontext is percep- tually jarringdue to its intervalof a tritone with the initial and final Cs of the melody, therebyproducing relative nonscalarity. Thus, strict nonscalarity occurred in five-sixthsof the N melodies,whereas relative nonscalarity occurred in one-sixth. Procedure

Therewere 96 trialsarranged in fourblocks of 24 each.Each block consisted of a random arrangementof six occurrenceseach of the fourtrial types (SS, NN, SN, NS). Subjectsserved in groupsessions, and different sessions performed the blocksin differentorder, counterbal- ancedso that approximatelyequal numbers of subjectsperformed each blockin each ordi- nal position.The sameseed melodieswere repeatedin each block, but a givenseed melody was testedin eachof the fourdifferent types of trialin differentblocks. Seven of the subjects at each experiencelevel rated the stimuli for similarity(on the six-point scale described above),and the remainderjudged the degreeto whichthe comparisonstimulus on eachtrial appearedto be the sameor different(with six responsecategories: very sure different, sure different,different, same, sure same, very sure same, going from"1" to "6").

RESULTS

Each subject's responses were used to compute the average similarity or same-different rating for SS,SN,NS, and NN items (S = scalar, N = nonscalar). These individual-subject data were subjected to an analysis of vari- ance (ANOVA) which included the between-subjects variables of Rating type (similarity/same-different) and Musical experience (moderate/none), and the within-subjects variables of First melody type and Second melody type. The alpha level was .05. The ANOVA showed main effects for both First melody and Second melody, F (1,24) = 40.2 and 39.1, MSe = .069 and .215, respectively. It also showed interactions between First melody and Musical experience, F (1,24) = 4.96, MSe = .069, Second melody and Musical experience, F (1,24) = 5.98, MSe = .215, and between First and Second melody, F (1,24) = 14.6, MSe = .147. The rating-type variable produced no main effect and participated in no reliable interactions. As shown in Table 2, in which the data have been collapsed over the rating-type variable, the SS and NS pairs produced the highest ratings, and the SN pairs produced the lowest ratings, with the NN pairs falling in between. A set of planned F tests confirmed that there was no reliable difference between the ratings to SS and NS pairs (F < 1), whereas the ratings to both reliably exceeded the ratings to SN pairs, (JF(1, 24) = 36.6 and 54.3 for the SS-SN and NS-SN comparisons, respectively, with MSe = .260 and .192). The ratings to the NN pairs differed reliably from ratings to each of the other three pairs (F (1, 24) = 8.21, 10.1, and 29.3, and MSe = .092, .101, and .167, for the comparisons with SS, NS, and SN pairs, respectively).

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TABLE 2 Average Ratings of Melody Pairs by Subjects in Experiment 1

Type of Melody Pair Scalar- Scalar- Nonscalar- Nonscalar- Musical Experience Scalar Nonscalar Scalar Nonscalar

Inexperienced 4.41 3.85 4.39 4.28 Moderately 4.65 3.56 4.76 4.32 Experienced Mean 4.53 3.71 4.58 4.30

note: Data from the Similarity Rating Group and Same-Different Rating Group have been collapsed in this table (there being no significant effect of rating task in the ANOVA). Both similarity and same-different ratings were based on a l-to-6 scale (6 = most similar or most confidence in identity of melodies).

Out of the six plannedF tests, only one produceda reliableeffect involving the musicalexperience variable. This was the F test comparingthe NS and SN conditions, in which the Melody pair type x Musical experience interactiongave F (1, 24) = 7.70, MSe = .192, replicatingthe findingsof Dowling and Bartlett(1981). As shown in Table2, the size of the difference between the NS and SN conditionswas greateramong the more experiencedsubjects.

DISCUSSION Contraryto the memorabilityhypothesis, the similarity/same-different ratingsfor SS pairs were significantlyhigher than those for SN pairs, and were as high as the ratings for NS pairs. This pattern fits well with the perceived-alternativeshypothesis: SS pairs, like NS pairs, should not produce mismatcheswith perceivedalternative sets. Hence, both sorts of pair shouldbe ratedas more similarthan SN pairs,which shouldproduce mismatcheswith perceivedalternative sets. A possibledifficulty for the perceivedalternatives view is that NN pairs receivedlower ratingsthan SS and NS pairs.This effectwas not predicted, though the SS-versus-NNdifference fits a number of prior studies by Krumhansland her colleagues (e.g., Krumhansl, 1979; Bharucha & Krumhansl,1983). Using single notes as well as chords and chord sequences,these studieshave shown greatersimilarity among stimuli central to a prevailingkey than amongthose distantfrom a prevailingkey.

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Experiment 2

The aim pursuedin Experiment2 was to determineif the asymmetric similarity effect is due to automatic processes versus task-specific strategies. Facedwith the data from Experiment1, it is possibleto arguethat the low similarityand same-differentratings made to SN pairs reflectsa specific strategythat subjectsadopt in orderto cope with the demandcharacteris- tics of certaintasks. Forexample, charged with ratingpairs of melodiesfor similarity or sameness/differenceand finding all pairs approximately equallysimilar or confusable(all have just a one-semitonechange in one note), subjectsmight: (a) attemptto extract a sense of key from the first melody, (b) judge whetherthis key is violated by the notes of the second melody, and (c) take key violations as evidencefor dissimilarityor difference, all as a task-specificstrategy. Since key violationswould be morefre- quentlydetected in SN pairsthan in the othertypes of pairs,the low ratings of the formerwould be handled.To evaluatethis strategyargument, we decidedto exert more control over subjects'processing strategies through use of a well-definedtask: Subjects were askedto judgepairs of melodiesas sameversus different in melodiccontour (the patternof ups and downs in pitch),under conditions in which accuracycould be meaningfullyassessed. Contourof melodiesis a highly salientfeature, as evidencedby the fact that even inexperiencedsubjects can make same-differentjudgments with respectto this featurewith high levels of accuracy(Dowling & Fujitani, 1971; Dowling & Harwood, 1986). Furthermore,sameness or difference in the contourof two melodiesis physicallyindependent of theirtonalities or keys. Thus, there is simply no reason why listeningfor changesin key shouldbe used as a strategyfor makingcontour judgments. However, if the alternativesevoked by a first-presentedmelody are necessarily constrained by key, and if a second-presentedmelody that violates these alternatives necessarilycreates an impressionof difference,relations of scale structure mightaffect contour judgments. Specifically, SN pairs,in which violations of the alternativeset are most likely to occur, shouldbe judgedmore often as differentin contourthan NS and SSpairs, in which set violationsare un- likelyto occur.This patternshould hold even in casesin which contourac- tuallyis unchanged.

METHOD

Subjects

Fifty-two subjects served in Experiment 2, with 35 in the inexperienced and 17 in the moderately experienced groups.

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Stimuli

Stimuliwere producedusing the "clarinet"voice of a YamahaPortasound synthesizer, whichwas connecteddirectly to a tape recorder.Timing was controlledby the built-inmet- ronomeof the synthesizerset to blinkat 60 beats/min,which produced no audiblesignal on the tape. Melodiesproceeded at a rateof two notes per metronomebeat, or 2.0 notes/sec. Melodieswere played "legato,"with little time betweennote offsets and onsets, and the seventhnote of eachmelody was held for a full metronomebeat. (Thatis, the last note was twiceas long as eachof the firstsix notes.)Two metronomeeats (2 sec)separated the standardand comparisonmelodies on a trial.Subjects had 5.0 sec to respondbefore the startof the next trial.The seed melodieswere constructed using the pitchesranging from the G below middleC to the G above.A givenmelody contained either the high G or the low G, not both. As in Experiment1, therewere four tonality conditions: SS, NN, SN, andNS. The melodiesof SSand NN pairsdiffered by the interchangeof the pitchesE and F. The melodiesof SN andNS pairsdiffered by the substitutionof nondiatonicpitches for diatonicones: A)t for A, or D|t for D (randomlydetermined and occurringequally often). While all melodypairs containeda one-semitonechange of one note, half of these pairsalso containeda contour change.Changes in contourwere accomplished by substitutingthe G abovemiddle C for the G below, or vice versa (randomlydetermined and occurringequally often). Samecontour trialsused either the high or low G, randomlydetermined.

Procedure

Subjectsreceived 48 melodypairs arranged in two blocksof 24. Eachblock consisted of a randomarrangement of threeoccurrences each of the eightpair types (SS, NN, SN, andNS, all with same or differentcontour). Items were also counterbalancedacross two lists with respectto scalarstructure of comparisonmelody, so thata seedtested as a SStrial in one list was testedas a SN trialin the otherlist; andsimilarly for NN andNS trials.Subjects partici- patedin groupsessions, and theirtask was to rateeach melody pair for similarity,and also for samenessversus difference in contour,using a six-pointscale in both cases (6 = most similarand sure-same-contour,1 = least similarand sure-different-contour).The contour judgmentsare of most interest,but we wantedto test the replicabilityof the patternof similarityratings found in Experiment1.

RESULTS

The analysisof similarityratings was similarto that of Experiment1. The majorchange was that same-versus-differentContour of pairswas an additionalfactor in the ANOVA. Further,due to the slight unevennessin cell sizes, the counterbalancingvariable of List was also includedas a factor. The outcome of the ANOVA resembledthat of Experiment1 in that therewere reliablemain effects of Firstmelody and Secondmelody, F (1, 48) = 5.96 and 37.6, MSt = .271 and .302, respectively,as well as a First x Secondmelody interaction, F (1,48) = 5.95, MSe = .284. It can be seenin Table3 that similarityratings were once againhighest in the SSand NS conditions,lowest in the SN condition,and intermediate in the NN condition.It also can be seenin the tablethat Contourhad a largemain effect, F

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TABLE 3 Average Similarity Ratings of Melody Pairs by Subjects in Experiment 2 Contour and Scalar Structure Condition Same Contour Different Contour

Musical Experience SS SN NS NN SS SN NS NN

Inexperienced 4.54 4.21 4.52 4.35 3.19 2.78 3.26 3.01 Moderately 4.59 4.11 4.64 4.27 3.35 2.62 3.24 3.15 Experienced Mean 4.57 4.16 4.58 4.31 3.27 2.70 3.25 3.08

note: SS stands for scalar-scalar pairs, SN for scalar-nonscalar pairs, NS for nonscalar-scalar pairs, and NN for nonscalar-nonscalar pairs.

(1, 48) = 197.0, MSe = .816: Same-contouritems receivedsubstantially highersimilarity ratings than different-contouritems. Althoughthe counterbalancingvariable of List produced a main effect, F (1, 48) = 4.12, MSe = 1.93, it did not enterinto reliableinteractions. A differencefrom Experiment1 was that therewere no statisticallyreli- ableeffects involving the Musicalexperience variable. Table 3 shows only a very small tendency for the differencebetween NS and SN pairs to be greaterin the moderatelyexperienced group than in the inexperienced group. A secondANO VA was performedon the averagecontour ratings, which also weremade on a six-pointscale (6 = suresame, 1 = suredifferent). The outcomewas somewhatdifferent than that performedon the similarityratings:Whereas we once againobtained a maineffect of Secondmelody, F (1, 48) = 50.9, MSe = .289, therewas no main effectfor Firstmelody and no First x Second melody interaction.There was of course a Contourmain effect,F (1,48) = 173.2, MSe = .176, which in this ANOVA was qualified by a Contour x Secondmelody interaction, F (1,48) = 5.90, MSe = .380. The counterbalancingvariable of List producedno main effect, and al- thoughit interactedwith Firstmelody, F (1,48) = 4.52, MSe = .270, it did not qualifyany of the aforementionedstatistically reliable effects. Again, Musicalexperience entered into no reliableeffects. Althoughaverage contour ratings have the advantageof beingcompara- ble to averagesimilarity ratings, it is usefulalso to examineproportions of "same-contour"judgments (ratings of 4, 5, or 6) to same-contouritems (hits) and different-contouritems (false alarms). An ANOVA was performedon the proportionsof same-contourdecisions, and the resultswere

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions Scale Structure and Similarity of Melodies 299 highlysimilar to that performedon contourratings. The maineffect of Sec- ond melodywas reliable,as also was that of Contour,F (1, 48) = 38.3 and 174.0, MSc = .023 and .080, respectively).A minor differencefrom the ANOVA of contourratings was that the Secondmelody x Contourinter- action was only marginallyreliable, F (1, 48) = 3.37, MSe = .031. There were no effectsinvolving either List or Musicalexperience. Despitesome differencesin the outcomesof ANOVAs, the actualpattern of means of the similarityratings, contour ratings, and proportionsof same-contourjudgments were actuallyquite similar.As shown in Table 4, contourratings and same-contourjudgments resembled similarity ratings in showinghighest scores in the SSand NS conditions,and lowest scoresin the SN condition. The principaldifference was that with the contour ratings and same-contourdecisions, the four pair-conditionswere closer to- getherwith different-contouritems than with same-contouritems (thiswas reflectedby the Second melody x Contour interactionsin the contour- judgmentsANO VAs, but not in the similarity-judgmentANOVA). We note that an ANOVA of the contour-ratingsto different-contouritems only showed a main effect of Second melody tonality, F (1, 48) = 11.3, MSe = .241. A similar ANOVA of same-contour-judgment proportions also showed this effect. DISCUSSION

A strong predictionof the perceived-alternativeshypothesis was con- firmedin this experiment.We replicatedthe findingthat SS and NS pairs have highersimilarity than SN pairs, and found in addition,as predicted, thataverage same-versus-diff erent contour ratings as well as proportionsof same-contourjudgments showed generallythis same pattern. Given the

table 4 Average Contour Ratings and Proportions of Same-Contour Decisions in Experiment 2

Contour and Scalar Structure Condition Same Contour Different Contour

Type of Rating SS SN NS NN SS SN NS NN Contour 4.10 3.53 4.24 3.70 2.58 2.27 2.46 2.29 Ratings Same-Contour .68 .53 .71 .59 .28 .20 .26 .21 Decisions

note: SS stands for scalar-scalar pairs, SN for scalar-nonscalar pairs, NS for nonscalar- scalar pairs, and NN for nonscalar-nonscalar pairs.

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions 300 James C. Bartlett ÔCW. Jay Dowling veryhigh salienceof the contourattribute in immediatememory for melodies,we findit impressivethat contourjudgments were sensitiveto our ma- nipulationsof scalarstructure. The fact that contourjudgments were sensi- tive in this way suggestsquite stronglythat SN pairs,as opposedto SS and NS pairs,produce strong impressions of dissimilarity,apart from subjects' consciousstrategies. Just as in Experiment1, NN pairs in this experimentapparently were perceivedas reliablyless similarthan SS and NS pairs. Sinceit is not obvi- ous that NN pairs would produceviolations of perceivedsets of alternatives, this outcome is somewhatpuzzling - we take up this matterin the GeneralDiscussion.

Experiment 3

In Experiment3 we questionwhether the physicalproperty of semitone intervalsexplains the asymmetricsimilarity effect. We havementioned that one-semitoneintervals are moreprevalent in nonscalarmelodies than they are in scalarmelodies. One-semitoneintervals might have a varietyof effects, includingthat of reducingmemorability of melodies.Experiment 1 was a test of the hypothesisthat low memorabilityof nonscalarmelodies, possiblyresulting from their one-semitone intervals, explains the asymmetric similarityphenomenon. Although we failedto findevidence in support of this hypothesis,other effects of one-semitoneintervals might yet account for asymmetricsimilarity. For example, assume that (a) numerousone- semitone intervalsmake a melody sound abnormal,and (b) a relatively abnormal-soundingstimulus tends to be perceivedas dissimilarnot only to other stimuliin general,but to the stimulusthat precededit in particular. This would explainwhy nonscalarmelodies, in which one-semitoneintervals are relativelyfrequent, are perceivedas dissimilarto scalarmelodies when the scalar-nonscalar order is used. Thereare other possibleaccounts of asymmetricsimilarity that point to the prevalenceof one-semitoneintervals in nonscalarmelodies. In orderto evaluatethis entire class of accounts, we examinedwhether asymmetric similaritywould generalizeto conditions in which neitherthe scalar nor nonscalarmelodies contained any one-semitoneintervals. The perceivedalternatives hypothesis- which makes no specific reference to one- semitoneintervals - predictsthat asymmetricsimilarity should generalize to melodieslacking one-semitone intervals. In contrast,if one-semitonein- tervalsare criticalto the findingof asymmetricsimilarity, such generaliza- tion shouldnot occur. The ideal materialsto use in this studywould be melodypairs in each of which: (a) one melodywas scalarwhereas the otherwas strictlynonscalar,

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions ScaleStructure and Similarityof Melodies 301 that is, inconsistentwith all diatonic majorscales (regardlessof key), (b) neithermelody contained any semitoneintervals, and (c) the two melodies differedin just one note alteredby one semitone.Unfortunately, we were unable to develop such pairs, and so we adoptedthe strategyof relaxing constraint"a," while maintainingconstraints "b" and "c."2Specifically, the "nonscalar"melodies used in this experimentall were merelyrelatively nonscalaras opposed to strictlynonscalar (see Method section of Experi- ment 1). That is, all "nonscalar"melodies were compatiblewith a diatonic majorscale (G major),but they were incompatiblewith the particularscale (Cmajor) suggested by the startingand endingnotes (C),as well as all other melodypairs in the study.Although this solutionis less thanideal, note that to the extent that "nonscalar"melodies might be perceivableas scalar,the studywas biasedagainst the findingof asymmetricsimilarity. Hence, if Ex- periment3 supportsasymmetric similarity, the perceivedalternatives hy- pothesiswill be stronglyfavored.

METHOD

Subjectsand Procedure

Fifty-sixsubjects served in Experiment3, with 26 in the inexperiencedgroup and 30 in themoderately experienced group. They served in groupsessions, and performed the taskof listeningto each of 120 melodypairs, and ratingthe similarityof each pair on a six-point scale. Stimuli

Stimuliwere produced by a Commodore64 computervia its 6581 SoundInterface De- viceand recorded directly on tape.Timing was controlledby the computerwith an accuracy of .017 sec. Melodiesproceeded at a rate of 2.6 notes/sec.Each note was 0.32 sec in duration, with an onsettime of about24 msecfollowed by a decayto a level 0.27 of peak ampli- tude (decayconstant = 48 msec).Internote intervals were 0.06 sec in length.A 2-sec interval separatedthe standardand comparisonmelodies on a trial, and subjectshad 8 sec to respondbefore the startof the next trial. Eachof the 24 seedmelodies used the six pitchesof the keyof C rangingfrom the E below middleC to the E above,excluding B andF (i.e, E [low],G, A, C, D, E [high]).Note thatthis pitch set includesno semitoneintervals. The seven-noteseed melodiesalways began and endedon C, whichnever occurred within the five "internal"notes.

2. Producingstrictly nonscalar melodies by shiftingjust one pitch (constraint"c") while satisfyingthe constraintof no semitoneintervals ("b"), with melodiescontaining six differ- entpitches, is virtuallyimpossible. The two principalways to makea melodystrictly nonsca- larare: (1 ) to includetwo adjacentone-semitone intervals (violating constraint "b"), and (2) includingtwo pairsof tones in the tritone(6-semitone interval) relationship. Since we had eliminatedthe note B fromall melodies(required by constraint"b"), which is the only note standingin a tritonerelation (with F) within C major,our scalarmelodies had no tritone intervals.Thus, altering just one pitch(constraint "c") could produce a patterncontaining at mostone tritone.These considerations demanded that we settlefor relativerather than strict nonscalarity.

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Unlike Experiments I and 2, here we used only two types of melody pairs, SN and NS. The two melodies comprising an SN or NS pair always differed in one note - the G in the scalar melody was replaced by an F# in its "nonscalar" mate. Since none of the melodies contained an F, the use of Fj in the "nonscalar" melodies could not produce any semitone intervals. Thus, there were no semitone intervals in either scalar or "nonscalar" melodies. Because we were using only two types of melody pair, we were able to employ more ex- tensive counterbalancing than in Experiments 1 and 2. Each of the 24 seed melodies was used to construct five SN pairs and five NS pairs. Within each set of five pairs, the serial positions of notes 2 through 6 were shifted so that the altered note (G to F(j or vice versa) occurred once at serial position 2, once at serial position 3, once at serial position 4, once at serial position 5, and once at serial position 6. Each of the five pairs from each seed melody was assigned to one of five blocks of the list. Hence, the list included 120 melody pairs, orga- nized into five successive blocks, each block including one melody pair made from each of the 24 original seed melodies. Across the five blocks, each seed melody was represented by a pair with the changed note occupying each of the five internal serial positions. Further, a seed was tested either as an SN pair in three blocks and an NS pair in two, or as an SN pair in two blocks and an NS pair in three. There were two different versions of the 120-pair list, each version used with half (28) of the subjects. The lists were identical save for the ordering of pairs: Each NS pair on version 1 of the list was played as an SN pair on version 2, and vice versa.

RESULTS

An initial look at the data showed that the average similarity rating for SN pairs was 4.09, while that for NS pairs was 4.34. The difference appeared small, and we wondered if it might be clarified by considering the position in the melodies of the altered notes (the changed-note position varied from 2 through 6- positions 1 and 7 always contained Cs). Hence, we performed an ANOVA including the within-subjects variable of Changed note position along with the within-subjects variable of Melody pair type (SN vs. NS), and the between-subjects variables of List version and Musical experience. Neither the List nor Musical experience variables produced reliable main effects or entered into reliable interactions. However, the ANOVA showed a main effect for Melody pair type, F (1, 52) = 15.2, MSe = .517, a main effect for Changed note position, F (4,208) = 3.22, MS = .172, and a Melody pair type x Serial position interaction, F (4,208) = 3.92, MSe = .143. As shown in Table 5, the asymmetrical similarity effect was statistically reliable for changed notes at serial positions 3 through 6, though not at serial position 2. Since the asymmetric similarity effect was relatively small, we were concerned with its generalizability over different melody pairs. Consequently, we performed a second ANOVA on the effects of Changed note position and Melody pair type using items rather than subjects as the random variable. Melody pair type was a within-items variable, whereas Changed note position was a between-items variable; there were 24 melody pairs in each Changed note position condition. The main effect of Changed note position was no longer reliable, but the main effect of Melody pair type and the Mel-

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TABLE 5 Average Similarity Ratings for Melody Pairs Changed in Serial Positions 1 through 6 in the Scalar-Nonscalar and Nonscalar-Scalar Conditions Scalar Structure Condition Serial Position Scalar-Nonscalar Nonscalar-Scalar Diff. 2 4.25 4.27 -.02 3 4.02 4.23 -.21a 4 4.16 4.44 -.28a 5 4.02 4.33 -.31a 6 4.02 4.42 -.40a

aDifferencegave p < .05 by t test.

ody pair type x Changednote position interactionboth were once again significant, F (1,115) = 39.8 and F (4,115) = 2.65, respectively, MSe = .099 in both cases.

DISCUSSION

The purposeof Experiment3 was to examinethe existenceof asymmetric similaritybetween scalar and nonscalar melodies with the factor of semitoneintervals removed. The resultsof the experimentconfirmed asymmetricsimilarity, showing that the presenceof semitoneintervals in melodies, and the greaternumber of such intervalsin nonscalarthan scalarmelodies, is not a necessary prerequisitefor this effect to occur. This is consistentwith the perceived-alternativeshypothesis, which makesno ex- plicitreference to semitoneintervals as a factorin asymmetricsimilarity. Notwithstandingthat semitoneintervals in nonscalarmelodies are not necessaryto produceasymmetric similarity, it is noteworthythat the magnitude of asymmetricsimilarity was rather small in this experiment- averagingover serialposition, its magnitudewas only .25 on the 6-point scale.This could mean either of two differentthings. First, the prevalenceof semitoneintervals in nonscalarmelodies might have contributedto asymmetricsimilarity in Experiments1 and 2. If so, the absenceof suchintervals in the presentexperiment would have reducedthe effectin magnitude.Sec- ond, as remarkedpreviously, the "nonscalar"melodies used in this experiment were merely relativelynonscalar as opposed to strictly nonscalar. Hence,they occasionallymight have been heardas scalar.This would have weakenedasymmetric similarity.

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Experiment 4

The generalaim of this finalexperiment was to establishmore firmly the criticalfinding of Experiment2. That criticalfinding was that nonscalar- scalarpairs were not only judgedmore similar than scalar-nonscalarpairs, but also were more often judgedas having the same contour.This effect observedwith contourjudgments was importantin rulingout the idea that task-specificstrategies produce asymmetric similarity. However, if the ef- fectproved limited in its generalizability,a task-specificstrategy hypothesis mightbe resurrected. We examinedtwo specificissues. The first was whethercontour judg- mentswould show the asymmetricsimilarity effect with the factorof semitone intervalscontrolled. Experiment 3 controlledsemitone intervals, and obtainedonly a small asymmetryin similarityjudgments. We wonderedif controllingfor semitoneintervals would removethe asymmetryin contour judgments. The secondissue was whethercontour judgments would show asymmetric similaritywhen subjectsdo not also makesimilarity judgments. Experi- ment2 useda dual-taskprocedure whereby subjects responded to eachmelody pair with both a similarity rating and a same-different contour judgment.This dual-taskprocedure might have producedtask demands suchthat ratingpairs for similarityinfluenced contour judgments. If so, the asymmetryeffect shown with the contourjudgments might have been an artifactand not trulycontrary to a task-specificstrategy hypothesis.

METHOD

Subjects and Procedure

Forty subjects served in group sessions. There were 21 subjects in the inexperienced group and 19 in the moderately experienced group. They received a list of 120 melody pairs, and judged whether the melodies of each pair had the same or different contour, using a six- point scale as in Experiment 2(6 = sure same contour, 1 = sure different contour).

Stimuli

Stimuli were produced as in Experiment 3, except for the following changes: First, all seed melodies included the pitch B as well as E, G, A, D, and C (serial positions 1 and 7). This meant that all melodies- both scalar and nonscalar- contained exactly one one-semitone interval; that between B and C. The note B was included because: (a) we wanted to maintain the use of six different pitches per melody as in Experiments 1 through 3, and (b) the contour changes (see below) prevented the use of both the upper and lower E within the same melody (the tactic of Experiment 3). Second, half the SN and NS melody pairs contained a change in contour. Contour changes were accomplished by substituting the E above middle C in one melody for the E below middle C in the other, or vice versa (randomly determined and occurring equally often). Same contour trials used either the high or low E, randomly determined.

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Third, the melodies were presented at the (slightly reduced) rate of 2.0 notes/sec. Each note was 0.44 sec in duration, with internote intervals of 0.06 sec. As before, a 2-sec interval separated the standard and comparison melodies on a trial, and subjects had 8 sec to respond before the start of the next trial. The 120-trial list comprised five 24-trial blocks in which a melody pair derived from each of the 24 seed melodies appeared a single time. Across the five blocks, each seed melody was: (a) represented by a pair with the changed note occupying each of the five internal serial positions (2 through 6), and (b) presented in the SN order in three blocks and in the NS order in two, or as in the SN order in two blocks and the NS order in three (as in Experiment 3). In addition, a seed was tested three times as a same-contour item and twice as a differentcontour item, or else vice versa. Finally, there were four different versions of the 120-trial list, and across these four versions, items were counterbalanced with respect to both melodypair type (SN vs. NS) and contour condition (same vs. different). Each of the four list versions was used with a subgroup of 8 to 12 subjects. After partitioning based on musical experience, there were between three and seven subjects in each of the eight cells (2 Experience levels x 4 List versions). Because of the varying cell sizes we report an AN OVA of the results using List version as a variable.

RESULTS

As in Experiment2, we performedseparate ANOVAs of subjects'average contourratings, and of the averageproportions of same-contourdecisions (i.e., averageproportions of ratingsof 4, 5, and 6 on the six-point scale).Both ANOVAs includedthe counterbalancingvariable of List version and as well as Musicalexperience of subjects,with Melody pair type (SNvs. NS) andsame-versus-different contour as within-subjectsvariables. Due to the inclusionof the contourvariable, we collapsedover the variable of changednote positionto avoidthe impracticallysmall number of six ob- servationsper cell. The ANOVA of the contour ratingsproduced a robust main effect for Melodypair type, F (1,32) = 21.1, MSe = .125, a morerobust main effect for same-versus-differentContour, F (1, 32) = 221.4, MSt = .781, and a strong interaction between these two variables, F (1, 32) = 22.6, MSt = .050. As shown in Table 6, contour ratings were higher in the nonscalar-scalarcondition than in the scalar-nonscalarcondition, especially for same-contouritems. This is identical to the pattern that was shownin Experiment2 (Table4). The ANOVA of contour ratings also showed a same-versus-different Contourx Musicalexperience interaction, F (1, 32) = 4.44, MSe = .781, reflectingthe fact that the moderatelyexperienced subjects exceeded the inexperiencedsubjects in average contour ratings to same-contouritems (4.52 vs. 4.17), but fell below inexperiencedsubjects in averagecontour ratingsto different-contouritems (2.08 vs. 2.33). This patternreflects simply slightlygreater accuracy in makingcontour ratings on the part of the moreexperienced subjects.

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TABLE 6 Average Contour Ratings and Average Proportion of Same-Contour Decisions in Experiment 4

Same Contour Different Contour Scalar- Nonscalar- Scalar- Nonscalar- Type of Rating Nonscalar Scalar Nonscalar Scalar Contour 4.19 4.60 2.18 2.27 Ratings Same-Contour .69 .77 .16 .18 Decisions

A finaloutcome of the ANOVA of contourratings was a three-wayinteraction of Melody pair type x same-versus-differentContour x List version, F (3, 32) = 6.54, qualifiedby the four-wayinteraction involving Mu- sical experience,F (3, 32) = 8.75, MSe = .050 in both cases.Perusal of the data suggestedthat, for reasonswe cannotexplain, the moderatelyexperienced subjectsreceiving one of the four lists did not show the tonalitycon- dition effect, whereas the inexperiencedsubjects receiving this same list showed a particularlylarge tonality condition effect. We view this pattern as a flukeand will not discussit further. The ANOVA of the proportionsof same-contourjudgments (Table 6, Row 2) producedthe samepattern of effectsas that of contourratings. The only exceptionwas that the Musicalexperience x Contourinteraction did not attainsignificance (p > . 10). Thus,the interactionobtained with the averagecontour ratings should be interpretedcautiously. To confirmthe reliabilityof our majorfindings over items, we performed an additionalANOVA on the contourratings, using items as the random factor.The two factorswere Melodypair type and Contour,both of which produced reliable main effects, F (1, 119) = 48.4 and 1405.3, and MSe = .199 and .364, respectively.The interactionwas also reliable,F (1, 119) = 13.5, MSe = .222, confirming the pattern of the subjects-as- randomANOVAs.

General Discussion

These four experimentshave extended prior evidencefor asymmetric similarityof scalarand nonscalarmelodies - pairs of more and less scalar melodiesare perceivedas more similarwhen the less scalarmelody comes first.At the same time, the presentstudies have strengtheneda perceived-

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions Scale Structureand Similarity of Melodies 307 alternatives hypothesis for the processes underlying a person's sense of scale. According to the perceived alternatives hypothesis, the ordinary process of perceiving a melody involves its implicit comparison to a set of alternative melodies (cf. Garner, 1974). This set of perceived alternative melodies preserves some of the original melody's attributes (i.e., those of its attributes that are perceived as "immutable," Kahneman & Miller, 1986). To perceive a melody as scalar or "in key" is to perceive its key, or the set of pitch-classes that constitute this key, as one of its immutable attributes. Hence, to perceive a melody as scalar or in key is to compare it to a set of alternative melodies based on the pitch classes of its key. To perceive a melody as nonscalar, or as containing "wrong notes," is to compare it to a larger set of alternatives based on a larger set of pitch classes, perhaps all 12 pitch classes of the chromatic set. The preceding analysis implies that if two melodies are highly similar, but differ in their scalar structure, their sets of alternatives are likely to be "nested" (Handel & Garner, 1966). That is, the alternatives of the less scalar items are likely to include the scalar item, but not vice versa. Since nesting implies asymmetric relatedness, the phenomenon of asymmetric similarity is accommodated nicely. Specifically, we have argued that when a scalar and nonscalar melody are presented with the nonscalar melody first, the second melody is perceived as falling outside the alternative set of the first. The consequence is a global impression of difference which affects the perceived similarity of the melodies, as well as other judgments such as same-versus-changed contour. The perceived-alternatives hypothesis made three clear predictions that distinguished it from other views. A first prediction concerned melody pairs which differed in the same way as scalar-nonscalar and nonscalar-scalar pairs, but which consisted of two scalar items: Such scalar-scalar pairs should produce no perception of second melodies violating perceived alternatives of first melodies. Hence, no global impression of difference should occur. In line with this reasoning, Experiment 1 showed that scalar-scalar pairs were rated as being equally as similar as nonscalar-scalar pairs, and as more similar than scalar-nonscalar pairs. Confirming this prediction was important not only for supporting the perceived alternatives hypothesis, but for ruling out the competing idea that asymmetric similarity reflects the poor memorability of nonscalar melodies. Such poor memorability might be a result of two factors: (a) the assim- ilation of nonscalar melodies to internal scale schemata (Dowling, 1978), or (b) memory interference involving semitone intervals (Deutsch, 1982), which are more prevalent in nonscalar than scalar melodies. In either case, melody pairs in which both items are scalar should receive low similarity ratings. Since in fact such pairs received high similarity ratings, both the

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions 308 James C. Bartlett & W. Jay Dowling schema-assimilationand memory-interferencenotions were compromised by the study'sfindings. Although it is plausiblethat nonscalarmelodies are moredifficult to rememberthan scalar melodies, and that scaleschemata as well as memoryinterference might contributeto this memorabilitydiffer- ence, the availabledata rule againstthe idea that differentialmemorability providesthe explanationfor the asymmetricsimilarity effect. Thus, in re- jectingthe memorabilityhypothesis, we are not assertingthat schemata and/orone-semitone intervals play no role in melody processing.We are simply suggestingthat our data requirethe concept of perceivedalternatives in additionto these otherideas. A secondprediction of the perceivedalternatives hypothesis was that the asymmetricsimilarity effect, as well as the high similarityof scalar-scalar pairs,should be reflectednot only in similarityjudgments - which mightbe subjectto task-specificstrategies - but in judgmentsregarding an attribute of melodiesthat is logicallyindependent of scalarstructure. One such attribute is melodic contour, and Experiments2 and 4 confirmedthat nonscalar-scalarpairs were more often judged as sharingcontour than scalar-nonscalarpairs, especially when contourwas actuallyidentical. Ex- periment2 showed in additionthat scalar-scalarpairs were judgedto be matchingin contouras often as nonscalar-scalarpairs and moreoften than scalar-nonscalar pairs. These findings were criticalfor establishingthe va- lidity of the similarityratings used in Experiments1 and 3. Without the convergingfindings of the contourjudgments, it would have been arguable that a task-specificstrategy for judgingsimilarity was responsiblefor the asymmetricsimilarity effect. Armedwith these findings,we can conclude that the processesunderlying asymmetric similarity are automaticif not mandatory- they appearto affectperceived similarity regardless of the listener'stask or intentions. A thirdprediction of the perceivedalternatives hypothesis concerns the troublesomefactor of one-semitoneintervals, which are generallymore prevalentin nonscalarmelodies than in scalarmelodies. There probably exist a varietyof reasonswhy an imbalancein one-semitoneintervals might contributeto asymmetricsimilarity. However, the perceived-alternatives view implies asymmetricsimilarity when this imbalanceis corrected.In- deed, Experiments3 and 4 employedscalar and nonscalarmelodies that were equated for one-semitone intervals, and showed once again that nonscalar-scalarmelody pairs are ratedas more similar,and are more often judged as having the same contour, as comparedto scalar-nonscalar melody pairs. Althoughwe were unableto use strictlynonscalar melodies in these studies,being forcedto use melodiesthat were only relativelynonscalar(i.e., incompatiblewith the prevailingkey of C), this (necessary)limi- tation of our experimentaldesign could only weakenthe findingof asymmetricsimilarity. In fact, we observedthat the effectwas ratherweak, but

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions Scale Structure and Similarity of Melodies 309 that it was nonethelessreliable (Experiment3), and even generalizedto contourjudgments (Experiment 4). It thereforeappears that thereis asymmetricsimilarity when semitoneintervals are controlled.There clearlyis moreto asymmetricsimilarity than a confoundingof scalarstructure with semitoneintervals. Althoughthe datain handare largely consistent with a perceivedalternatives notion, we see two potentialproblems for the survivalof this notion. The firstproblem is empirical;it concernsthe relativelylow similarityof melody pairs in which both members are nonscalar. Such nonscalar- nonscalarmelody pairs were examined in Experiment1, in which their rated similaritywas approximatelyintermediate between that of scalar- nonscalarpairs (whichwere the least similar)and that of scalar-scalarand nonscalar-scalarpairs (whichwere the most similar).Such pairs were also examinedin Experiment2, in which their rated similaritywas relatively lower, that is, closer to scalar-nonscalarpairs than to scalar-scalarand nonscalar-scalarpairs. Indeed, looking at the contourratings and proportionsof same-contourjudgments of Experiment2 (Table4), the nonscalar- nonscalar pairs appeared quite similar to the (least similar) scalar- nonscalarpairs. The ANOVAsof averagecontour ratings and proportions of same-contourdecisions supported this observation- both ANOVAs supporteda maineffect of Secondmelody type, with no maineffect of First melodytype and no interaction(the ANOVA of the similarityratings - in Experiment2 as well as Experiment1 - supportedall threeeffects). Thus, the contourratings and same-contourjudgments suggested less perceived similaritywhen the second melody was nonscalar,regardless of whether the firstmelody was scalaror nonscalar.This is not what a perceivedalter- nativeshypothesis, as formulatedheretofore, would lead one to predict- the simplestperceived-alternatives hypothesis implies no violationsof perceived alternativeswith nonscalar-nonscalarpairs. Hence, the perceived similarityof suchpairs should be high, perhapsas high as nonscalar-scalar and scalar-scalarpairs. In orderto handle the relativelylow similarityof nonscalar-nonscalar pairs, the perceived-alternativeshypothesis requires elaboration. Perhaps the simplestelaboration is to assumethat nonscalarnotes in otherwisescalar melodiesare essentiallyambiguous - they can be interpretedeither as trulyout-of-key notes, or as pitch-alteredversions of in-keynotes. Figure2 usesShepard's (1982) melodicmap to illustratethis point. A nonscalarnote might be interpretedas falling outside the scale-definedmap region con- tainingthe othernotes (Figure2a), or it mightbe interpretedas a variantof a scalarnote with its pitch alteredby one semitone(Figure 2b). It is intui- tivelycompelling that when a nonscalarnote in an otherwisescalar melody is initiallyencountered, it has a jarringquality which indicatesits interpre- tation as an out-of-keynote (Figure2a). However, after subsequentkey-

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Fig. 2. Melodies represented as in Figure 1 : (a) the melody C-D- G- E-A)t-B-C in which the A)t is interpreted as an out-of-key pitch; (b) the same melody in which A)t is interpreted as a within-key variant of A. consistent notes, the nonscalar note tends to be remembered as a variant of an in-key note matching the prevailing key context. Bharucha's (1984) work on anchoring can be seen as illustrating a special case of this principle- the case where a nonscalar note is immediately or almost immediately followed by a scalar note only one-semitone removed in pitch. Returning to ratings of nonscalar-nonscalar pairs, the preceding argu- ments have an interesting implication: At the time that the subject is comparing the two melodies (i.e., during or after presentation of the second melody), the nonscalar note of the first presented melody may have been interpreted as scalar, whereas the nonscalar note of the second-presented melody is likely to be interpreted as nonscalar, with the consequence that

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions Scale Structure and Similarity of Melodies 311 perceivedsimilarity is low. Althoughthis reasoningis post hoc, futurere- searchmight fruitfully address the cognitiveprocesses that produceand re- solve the ambiguous"meanings" of nonscalarnotes. A second threatto the perceivedalternatives notion is more theoretical than empirical.A differentand apparentlycontradictory perspective on asymmetricsimilarity melodies derives from Tversky 's (1977) set-theoretic account.According to Tversky,asymmetrical similarity between two stimuli can occurif two conditionsare met: First,the two stimulimust be une- qualin "salience"such that the featuresof one must be morenoticeable or prominent,or greaterin number,than those of the other. Second, there mustbe "asymmetryof focus" (selectiveattention) on one of the two stimuli, so thatits distinctivefeatures are more heavily weighted in the judgment of similarity.If a pairof stimulidiffer in salience,similarity should be lower if thereis selectivefocus on the moresalient of the two. Tverskygoes further to arguethat "good form" contributesto the salienceof a stimulus (i.e., stimulithat are good gestaltshave highly salient features),and also mar- shals evidence (Rothkopf, 1957; Wish, 1967) that when subjects make same-differentjudgments to pairs of auditorysequences, they selectively focuson the firstsequence of a pairat the expenseof the secondsequence of a pair.If we assumethat scalarmelodies are possessedof good form, it follows they shouldalso have a high degreeof salience,which would produce the findingof lower similarityfor scalar-nonscalarpairs - in which the more salient stimulusreceives selective focus - than for nonscalar-scalar pairsin which the less salientstimulus receives selective focus. A problemwith the set-theoreticargument, as formulatedabove, concernsthe claimthat a nonscalarmelody is necessarilyless salientthan a scalar melodywith which it is paired.Intuitively, the nonscalarmelody of a scalar-nonscalarpair sounds strikinglywrong and ugly, which is not the samething as havinglow salience.Rather than arguingthat scalarstructure affects salience, we propose that the set of alternativesevoked by a melody- the regionof the melodicmap that encapsulatesthis melody- can act as a "feature"affecting similarity judgments. A corollaryclaim is that while the small set of alternativesevoked by a scalarmelody is violated by its nonscalarmate, the largeset of alternativesevoked by a nonscalarmelody is not violated by its scalarmate. Thus, the alternative-setof a scalar melodyfunctions as a "distinctivefeature," whereas the alternative-setof a nonscalarmelody either functions as a "commonfeature" or does not function as a featureat all. If we follow Tversky(1977) in proposingthat featuresof the firstmelody are weighted more heavily than featuresof the second, we have an account of asymmetricsimilarity of melodies: A more scalarmelody and a less scalarmelody are perceivedas less similarif the morescalar melody, the one whose set of perceivedalternatives functions as a distinctivefeature, is presentedfirst and thereforereceives selective focus.

This content downloaded from 129.110.242.50 on Fri, 04 Dec 2015 23:43:44 UTC All use subject to JSTOR Terms and Conditions 312 James C. Bartlett & W. Jay Dowling This accountis compatiblewith Tversky's(1977) set-theoreticframework, the main changebeing that it does not appealto "salience."It also is compatible with spatial models of musical pitch, especiallythat of Shepard (1982, Figure1), suggestingthat set-theoreticand spatialmodels need not be viewed as conflicting. A finalmatter to discussconcerns the contourratings and same-contour judgmentsin Experiments2 and 4. Both studiesshowed that judgedsame- ness of contour was higher for nonscalar-scalarpairs than for scalar- nonscalarpairs. However, these effectswere apparentlystronger for same- contouritems than different-contour items (thiswas evidencedby a Second melodytype x Contourinteraction in Experiment2, and by a Melodypair type x Contour interactionin Experiment4). A possible explanationis that our scalar-structuremanipulations affect perceived similarity of melodies, which in turn affectscontour judgments in two ways. First,high perceivedsimilarity causes a bias to judgetwo melodies"same." Second, perceived similarityactually improves the ability of subjectsto comparethe two melodies- melodiesperceived as essentiallysimilar might more accu- ratelyjudged for same-versus-differentcontour than melodiesperceived as different.These two effectswould reinforceeach otherwith same-contour items,but would work againsteach otherwith different-contouritems (for which "same-contour"judgments are errors). An implicationof the precedinganalysis is that the accuracyof discrimi- nating same- from different-contour pairs should be higher in the nonscalar-scalarcondition than in the scalar-nonscalarcondition. To test this possibility,we used subjects'contour ratings to derivearea-under-the- MOC scores (Swets, 1973) for the nonscalar-scalarand scalar-nonscalar conditionsin Experiments2 and 4 (Areaunder the MOC scoreswere com- putedfrom the ratingdata suppliedby each subjectwithin each condition). The resultingmeans are shown in Table 7, wherethere is a trendfor better discriminationin the nonscalar-scalarcondition. This trend is reliable. ANOVAs comparingthe scalar-nonscalar and nonscalar-scalarcondi- tions showed a main effect of Melody pair type in Experiment2, F (1, 48) = 7.41, MSe = .015, as well as in Experiment4, F (1, 45) = 14.0, MSe = .003 (the latterANOVA showedinteractions between Melody pair type and List,and amongMelody pair type, List, and Musical Experience - these interactionsreflect the same anomalouspattern described previously in the Results section of Experiment4). Thus, the evidenceis reasonably clearthat the orderingof scalarand nonscalarmelodies affects not only the overall tendency to make same-contourjudgments, but the accuracyof those judgmentsas well. This is suggestivethat strongperceived similarity between two melodies has two differenteffects; that of producinga bias toward"same" judgments, and that of improvingcomparisons of the melodies. Futureresearch must furtherexamine the ways in which tonalityin-

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TABLE 7 Mean Area under MOC Scores for Same- versus Different-Contour Discrimination in Experiments 2 and 4

Scalar-StructureCondition

Experiment Scalar-Nonscalar Nonscalar-Scalar

Experiment 2 .73 .78 Experiment 4 .81 .85

note: Area under MOC scores generally vary from .50 (chance discrimination) to 1.0 (perfect discrimination).

formationenters in to contourjudgments. It seemsfair to say that no exist- ing theories,aside from the perceived-alternativeshypothesis, would have predictedthat scalarstructure might be involvedin such judgments. Futureresearch on scalarstructure of melodiesshould includeconverg- ing operationson the perceivedalternatives for scalarand nonscalarmelodies. Asymmetricsimilarity is but one source of evidence- albeit a strik- ingly counterintuitivesource - that scalar melodies have few perceived alternatives.3

References

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3. We thank Reid Hastie for valuable comments on this research, and Deborah Dayboch for initially calling our attention to the phenomenon.

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