Psychological Review1978, Vol. 85, No. 4, 341-354

Scale and Contour: Two Components of a Theoryof Memory for Melodies

W. Jay BowlingUniversity of Texas at Dallas

This article develops a two-component model of how melodies are stored in long-and short-term memory. The first component is the overlearned perceptual-motorschema of the musical scale. Evidence is presented supporting the lifetime sta-bility of scales and the fact that they seem to have a basically logarithmic formcross-culturally. The second component, melodic contour, is shown to functionindependently of pitch interval sequence in memory. A new experiment is re-ported, using a recognition memory paradigm in which tonal standard stimuli areconfused with same-contour comparisons, whether they are exact transpositionsor tonal answers, but not with atonal comparison stimuli. This result is con-trasted with earlier work using atonal melodies and shows the interdependenceof the two components, scale and contour.

Remembering melodies is a basic process inthe music behavior of people in all cultures.This behavior may involve production, aswith the singer performing a song for an audi-ence or the participant in a significant socialevent trying to remember the appropriatesong. Or it may involve recognition, as withthe listener whose comprehension of the laterdevelopments in a piece depends on memoryfor earlier parts. In this article, I concentrateon two components of memory that contributeto the reproduction and recognition of melo-dies, namely, melodic contour and the musicalscale. I maintain that actual melodies, heard

Earlier versions of this article were presented atthe Music Educators National Conference, WesternDivision, San Francisco, 1975, and the meeting ofNew American Music, Tangents III, University ofWyoming, 1977. Support for the experiment reportedhere was provided in part by a Biomedical SciencesSupport Grant to the University of Texas at Dallasfrom the National Institutes of Health.

I thank Dane Harwood, Darlene Smith, JamesBartlett, Drew Harare, Mark Goedecke, CynthiaNull, Kelyn Roberts, and Klaus Wachsmann for help-ful discussions and comments. And I especially wishto thank Mantle Hood for bringing the data onIndonesian tunings to my attention.

Requests for reprints should be sent to W. JayDowling, Program in Psychology and Human De-velopment, University of Texas at Dallas, Richardson,Texas 75080.

or sung, are the product of two kinds of un-derlying schemata. First, there is the melodiccontour—the pattern of ups and downs—thatcharacterizes a particular melody. Second,there is the overlearned musical scale to whichthe contour is applied and that underlies manydifferent melodies. It is as though the scaleconstituted a ladder or framework on whichthe ups and downs of the contour were hung.

Two examples epitomize the behavior thistheory addresses. First, if people in our West-ern European culture hear a melody fromsome non-Western culture using a non-West-ern scale, their reproductions of that melodywill use their own Western scale, preservingthe contour of the original melody. The scalefunctions as a classic example of a sensori-motor schema controlling perception and be-havior. In this example, the non-Westernmelody is assimilated to the Western schema(Frances, 19S8, p. 49). Part of the educationof ethnomusicologists is directed toward free-ing them from their native schemata so thatthey can hear accurately the pitches of non-Western music.

The second example involves the use ofmelodic contour in the structure of pieces ofmusic. One way a composer can tie a piecetogether is to repeat the same contour at dif-ferent pitch levels, at different relative place-

Copyright 1978 by the American Psychological Association, Inc. 0033-295X/78/8504-0341$00.75

341

342 W. JAY DOWLING

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Figure J. Section A shows examples from Beethoven's Piano Sonata opus 14 no. 1, illustratinguse of the same melodic contour with different interval sizes. (Intervals between notes are shownbelow the staves in semitones. Excerpts are labeled with measure numbers.) Section B is anAmerican Indian example from Kolinski (1970, p. 91).

merits on the scale, or even on different scales.The repetition provides unity without becom-ing boring through being too exact. Figure 1Ademonstrates Beethoven's use of this devicein his Piano Sonata opus 14 no. 1. Such adevice relies on the listener's ability to recog-nize the melodic contour through transforma-tions of pitch. That such processes are notconfined to Western music is shown by Kolin-ski's (1970) example from the Flathead In-dians (see Figure IB). Adams (1976) hasprovided a guide to the uses of contour con-ceptualizations in ethnomusicology.

In what follows, I will discuss (a) scalesof pitch and their characteristics and (b)melodic contours and their independence inmemory. (Independence is here used in thesense of referring to cases where one remem-bers one thing without remembering a relatedthing.) I will also present a new experimentthat illustrates performance in memory formelodies consistent with the present two-component theory.

Musical Scales

Several aspects of musical scales as theyfunction in various cultures are of particular

interest to the psychologist. First, scales con-sist of discrete steps of pitch, typically fiveor seven to the octave. This limitation wouldseem to match quite well the limitations ofpeople as information processors. Second,musical scales of pitch are approximatelylogarithmic with respect to frequency, a factthat bears directly on the problem of pitchscaling in psychophysics. Third, musical scalescan be slid continuously up and down in pitchwithout distorting their relative interval sizes.They serve as highly stable sensorimotorschemata with great flexibility of application.

Discrete Scale Steps

With few exceptions, the cultures of theworld use discrete changes of pitch along amusical scale in creating their melodies. Sincethe singing voice and many early instrumentsare capable of producing a continuous varia-tion of pitch, how is it that the music of theworld moves by discrete steps? Helmholtz(1954) raised this question, and some of theanswers he suggested are appealing even to-day. The ultimate biological functions of dis-crete steps are as obscure as the functions ofmelody or of music itself. However, given that

MEMORY FOR MELODIES 343

we have melody, discrete scale steps can bevery useful. Helmholtz argued that the di-vision of the pitch continuum into discretesteps is desirable in order that the degree ofmelodic and rhythmic movement might beimmediately apparent to the listener. If pitchmoved continuously in a melody, he argued,it would be much more difficult to decide ex-actly how much the pitch had changed orwhat rhythmic, temporal units had elapsed.In fact, such a decision could be made onlyon the basis of a fixed set of discrete refer-ence points anyway. That is, the listenerwould have to learn some form of scale as acognitive framework through which to dealwith the melodies he hears, continuous or not.

The modern cognitive psychologist caneasily carry Helmholtz's argument one stepfurther. Granting that we need discrete scalesteps to comprehend melodic movement, howmany should there be? Miller's (1956) classicarticle suggested that human beings are lim-ited in their categorical judgment capabilityto using 7 ± 2 categories on any one dimen-sion. Most cultures fall within this range, us-ing five or seven distinct scale step categorieswithin the octave. As will be discussed below,the system of categories repeats cyclicallyevery octave. Thus, in Miller's terms, a pitchwould be categorized in terms of two dimen-sions: one for pitch level within the octave(often called chroma) and the other for oc-tave level. Certain cultures that would seemat first sight to provide exceptions to thispattern turn out on closer inspection not to.For example, the music of India typicallyuses many very narrow intervals of which 22are available within an octave. However,melodies are basically constructed out ofscales having seven or so focal pitches, andthe other neighboring tones are used as auxil-iary tones around these focal pitches for thepurposes of ornamentation.

At this point, I need to introduce a con-ceptual scheme for talking about musicalscales. This scheme has four levels of abstrac-tion from the pitches of actual melodies andshares certain features with the conceptualschemes of Hood (1971) and Deutsch (1977).I have discussed it in greater detail in an-other paper (Bowling, Note 1). The most

abstract level is that of the psychophysicalscale, which is the general rule system bywhich pitch intervals are related to frequencyintervals of tones. I will argue that the ap-propriate form for the psychophysical scaleis approximately logarithmic, owing to thefundamental place of octave judgments in hu-man auditory processing. The second level isthat of tonal material, which includes the setof pitch intervals in use by a particular cul-ture or within a particular genre. In Westernmusic, the tonal material would include theset of semitone intervals of the equal tem-pered chromatic scale but not anchored to anyparticular frequency. The third level is thatof the tuning system, which consists of a se-lection of a subset of the available pitch in-tervals from the tonal material that are usedin actual melodies. In Western music, the tun-ing system might consist of the set of intervalsrepresented by the white notes of the piano—the set of intervals with the ascending cycle(in semitones) of [2, 2, 1, 2, 2, 2, 1] repeat-ing every octave. This set of intervals canbecome the basis of any of the heptatonicmodes (that is, the modes with seven notesper octave): major, minor, or the medievalchurch modes. The set of intervals of theblack notes on the piano [2, 3, 2, 2, 3] canalso function as a tuning system for the West-ern pentatonic modes.

The most concrete level is mode. In goingfrom tuning system to mode, two things hap-pen. First, an anchor for the frequencies isestablished, and what were pitch intervals atthe more abstract levels get translated intothe pitches of notes. Second, a tonal focus inthe tuning system is selected, and a tonalhierarchy is established on the tuning sys-tem. (The tonal hierarchy determines whichnotes in the mode are more important anddynamic tendencies of the notes as they func-tion in melodies.) These two operations areusually combined in Western music under therubric of "selecting a tonality," for example,taking the intervals of the white-note tuningsystem and selecting the key of C-major, A-minor, Eb-major, or C-dorian. Since mode inmy system overlaps considerably with theterm scale as used in the phrases musical scaleand diatonic scale, I will often use scale in

344 W. JAY DOWLING

what follows as a synonym for mode. I wantto caution the reader, however, that scale isalso used in ways that are not synonymouswith my use of mode, for example, in thephrase chromatic scale, which is more nearlysynonymous with my term tonal material. Myuse of scale is informal; a strictly formal sys-tem would use only mode. I use the termtonal to refer to melodies using the notes ofwell-known modes. And I should caution thereader that what I have to say here is mostlyirrelevant to the dispute among proponentsof tempered, Pythagorean, and other "natu-ral" tuning systems well discussed by Ward(1970).

Logarithmic Scale

The musical scales of most cultures repeatthemselves cyclically every octave. Tones anoctave apart are treated as equivalent in somesense and are typically given the same name(C, D, E; do, re, mi; or Barang, Sulu, Data[Indonesian]). Tones that are psychologi-cally and musically an octave apart have aratio between their fundamental frequenciesof approximately 2/1. (The "approximately"will be discussed below.) Ward (1954) hasshown that Westerners are quite precise in

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setting two pure tones (presented alternately)to the subjective interval of an octave. Thisis all that is required to produce a logarithmicpsychophysical scale of pitch: Tones at equaldistances along the subjective pitch scale(namely, an octave apart) should be relatedby equal 'frequency ratios.

Complications arise because the subjectiveoctave usually represents a frequency ratiojust slightly greater than 2/1. Ward (1954;replicated by Burns, 1974, using non-Westernsubjects and by others [Sundberg & Lind-qvist, 1973] using Westerners) found thatthrough the midrange of up to frequenciesof about 900 Hz, the frequency ratio of asubjective, pure-tone octave was about 2.02/1.This ratio still leads to an approximatelylogarithmic scale. Ward's results are plottedin the curve of Figure 2, which shows thetuning of successive octaves as cumulative de-viations from the 2/1 frequency ratio inlogarithmic units (hundredths of a semitone,or cents). (A semitone represents a frequencyratio of 21/12/1). Octaves having a 2/1 fre-quency ratio would be represented in Figure2 as a horizontal line. Straight segments ofthe curve with positive slope represent loga-rithmic pitch scales with a greater than 2/1frequency ratio to the octave.

340

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Figure 2. Cumulative tuning deviations of octaves in cents (hundredths of a semitone) as afunction of the fundamental frequency of the upper note in the octave for Burmese harp (Xs;Williamson & Williamson, 1968) and for Indonesian gamelans using sUndro (circles) and pilog(triangles) tuning systems, (The Indonesian data are based on Hood [1966; filled symbols; # = 2]and Surjodiningrat, Sudarjana, & Susanto [1969; open symbols; JVs = ll and 10 for sUndro andptlog, respectively]. The solid line is based on Ward's [1954] data for pure-tone octave judgments.)

MEMORY FOR MELODIES 345

Figure 2 also shows some measurements ofnon-Western instrument tunings: a set froma Burmese harp (Williamson & Williamson,1968) and several sets from Indonesian game-lans (Hood, 1966; Surjodiningrat, Sudarjana,& Susanto, 1969). Gamelan refers to both theorchestra and the set of instruments, con-sisting chiefly of gongs and marimbas. Thecorrespondence of the tunings and Ward'scurve is very good, especially considering thesorts of systematic deviations within the oc-tave in gamelan tunings discussed by Hood(1966). One reason that the fundamental fre-quencies of gamelan tunings are free to ap-proximate the tunings of subjective octaves isthat there is not the same attempt as foundin the West to make fundamentals of highertones match upper partials (overtones) oflower tones. One reason for this is that acous-tically gongs have very irregular series ofupper partials.

Western pianos are tuned to octaves thatare slightly greater than 2/1 ratios, but thedeviation is smaller than that for subjectivepure-tone octaves (Martin & Ward, 1961).The reason for the deviation is that pianostrings are not ideal, frictionless, vibratingbodies but have a certain amount of stiffness.This stiffness is most pronounced at the upperand lower extremes of the keyboard, wherethe ratio of the diameter to the length of thestring is relatively large. The stiffness of thestrings leads the frequencies of upper partialsto be progressively sharper than true har-monics (which stand in integer ratios to thefundamental). Hence, tuning upper funda-mentals to partials of lower notes will lead tostretched octaves, but they are not so severelystretched as those of the human ear. OurWestern emphasis on consonance of simul-taneous tones leads us to prefer this pianotuning over one in which melodic successionwould be given precedence. (See Plomp &Levelt, 1965, for a discussion of the contribu-tion of coincidence of upper harmonics to theconsonance of complex tones.) These con-siderations also suggest that for the same rea-sons, a cappella choirs and string quartetswill tend to use a 2/1 octave, especially dur-ing slow passages.

The precision of judgment of Ward's

(1954) subjects is a very good reason for pre-ferring a quasi-logarithmic scale to other can-didates for the psychophysical scale relatingpitch to frequency (Ward, 1970), Other rea-sons include the above cross-cultural data andthe fact that one of Ward's (19S4) subjectswho had absolute pitch produced the samescale by note labeling as with the octavejudgment method. Another strand of evidenceis provided by Null (1974), who obtained alogarithmic scale using a slightly modifiedmagnitude estimation method. One of thecleverest corroborations of the log scale isprovided by an experiment of Attneave andOlson (1971). They observed that musicallyuntrained subjects had difficulty in producingtranspositions of arbitrarily selected pitch in-tervals. Then, they hit upon the idea thatcertain interval sequences might be over-learned even by the uninitiated, for example,the National Broadcasting Company (NBC)chimes. They found that the NBC chimes hadalways been presented at the same pitch level—on the notes G-E-C in the middle register,an acronym for the General Electric Corpora-tion. They asked subjects to produce the pat-tern at various pitch levels above and belowthe original. The scaling question was, Wouldtranspositions follow a log scale, or a powerfunction, or something else? Subjects over-whelmingly responded with transpositionsalong a logarithmic scale. Thus, given a mean-ingful task, untrained subjects use a loga-rithmic scale for pitch.

Attneave and Olson's subjects demonstratehow stable the tonal scale system is through-out life once it is learned. So do Frances's(1958) subjects, who found it easier to noticechanges on rehearing tonal melodies thanatonal. Tonal scales constitute one of the mostdurable families of perceptual-motor schematathat have been observed in psychology, rank-ing perhaps only after the schemata of natu-ral language in their stability and resistanceto change in adult life. In fact, the same kindsof categorical perception phenomena foundin the phonetics of a language seem to holdfor musical scale pitch judgments (Burns,1974). It would probably surprise mostAmerican psychologists how early in life theseperceptual-motor schemata are acquired. Im-

346 W. JAY DOWLING

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Figure 3. Sections A-E are examples of stimuli fromthe present experiment. (A is the sample tonal stan-dard stimulus; B is the target stimulus, the exacttransposition of the standard; C is the tonal an-swer lure, which remains in the key of the standardbut at a different pitch level; D is the atonal lurewith the same contour as the standard; and E is therandomly different lure.) Sections F-I are examplesof atonal stimuli from Experiment 1 of Dowlingand Fujitani, 1971. (F is the sample standard stimu-lus; G is the target stimulus, the exact transpositionof the standard; H is the same-contour lure; and Iis the randomly different lure. All staves are notatedwith a treble clef understood. Intervals in semitonesare shown under each stave.)

berty (1969) found that 8 year olds are ableto notice shifts of scales within a melody fromone key to another a semitone or two higher.They found shifts of mode that left the under-lying pattern of intervals unchanged (as in thetonal answer stimuli of the experiment re-ported below) much more difficult. Zenatti(1969) found that 8 year olds can recognizethree-note tonal melodies much better than

atonal. Five year olds find tonal and atonalmelodies equally difficult because they havenot yet thoroughly internalized the scale.Eleven year olds find both types equally easy.But with four- and six-note melodies, evenadults find the atonal more difficult, in agree-ment with Frances (1958).

In this discussion of musical scales, I havenot tried to incorporate Shepard's (1964)helical theory of pitch scales. I wish to note,however, that I believe the present theorycompatible with his. It only requires that thehelix be sprung somewhat to allow for Ward'senlarged subjective octaves. I believe Shep-ard's demonstration of the auditory barberpole could be replicated using Ward's quasi-logarithmic scale. The issue of the acceptanceof the helical model as a pitch scale has notbeen settled, however. For example, Deutsch(1972) has demonstrated that in the recog-nition of familiar tunes, chroma (the qualityof C-ness, D-ness, or E-ness; do-ness, re-ness,or mi-ness) does not suffice as a cue to tuneidentity.

Memory for Melodic Contour

For everyone except the small percentageof the population having absolute pitch, well-known melodies must be stored as sequencesof pitch intervals between successive notes(Deutsch, 1969). In this section, I have as-sembled evidence that memory for the con-tour (the ups and downs of the melodicintervals) can function separately from mem-ory for exact interval sizes. That is, the con-tour is an abstraction from the actual melodythat can be remembered independently ofpitches or interval sizes. This is true for mel-odies in both short-term and long-termmemory.

Retrieval from Short-term Memory

The contours of brief, novel atonal mel-odies can be retrieved from short-term mem-ory even when the sequence of exact intervalscannot. This point is illustrated by an ex-periment by Dowling and Fujitani (1971, Ex-periment 1). They used a short-term recogni-tion memory paradigm in which the standard

MEMORY FOR MELODIES 347

stimulus on each trial was a randomly gen-erated five-note melody having small pitchintervals between successive notes. The com-parison stimulus followed the standard aftera brief pause. Three types of comparison mel-odies were the same as the standard in bothcontour and pitch intervals, or had the samecontour but different intervals, or were dif-ferent in both contour and intervals (i.e.,were novel random sequences). These are il-lustrated in Figure 3, Sections F-I. Differentgroups of subjects had the task of distinguish-ing among the following types of comparisonmelody: exactly the same versus random, ex-actly the same versus same contour, and samecontour versus random. Half the subjects weregiven comparisons starting on the same pitchas the standard; the other half had com-parisons whose starting note was transposedto another pitch level. The results showed thatwhen the comparison starts on the same pitchlevel as the standard, exact-same comparisonsare easily distinguished from either randomcomparisons or same-contour, different-inter-val comparisons. In other words, it was easyto reject any comparison stimulus that didnot contain exactly the same pitches as thestandard. When the comparison melodies weretransposed, however, exact-same targets andsame-contour comparisons were easily dis-tinguished from random ones but almost im-possible to tell apart. Listeners responded onthe basis of the presence or absence of thecontour and were unable to recognize thesameness of intervals when these were addedto the contour.

Thus, when the listener is trying to retrievean exact set of intervals from memory, thebest he can do under the above conditions isretrieve the contour. It is critical to this re-sult that the target melodies be atonal, thatis, not using the pitches of a musical scalefamiliar to the subjects. Frances (1958) foundalterations in tonal melodies easier to detectthan alterations in atonal melodies. A majortheme in the present article is that there aretwo components at work in the normal processof melody recognition: contour and scale.Bowling and Fujitani (1971, Experiment 1)explored the extreme case where the role ofthe scale had been all but eliminated. They

found contour recognition to be completelydominant over pitch interval recognition.However, one would not expect the same re-sult with tonal melodies. The overlearnedscale framework should make recognition ofthe difference between a tonal target melodyand an atonal lure having the same contourmuch easier. (These stimuli are illustrated inFigures 3B and 3D.)

Distinguishing between a tonal melody anda tonal lure having the same contour as thefirst melody but starting on a different noteof the same modal scale should be very dif-ficult. The relationship 'between this last pairof melodies is the same as that of a fugue sub-ject and its tonal answer. Such a pair is il-lustrated by Figures 3A and 3C. There aretwo ways to think of the tonal answer interms of the conceptual scheme of tuning sys-tem and mode.

1. We might think of the tonal answer asconsisting of the same set of diatonic inter-vals translated into a new mode. The intervalpattern of the tuning system (in Figure 3, thewhite notes of the piano) remains fixed at thesame pitch level, while the tonality of themelody in the sense of its starting pitch levelis moved to a new place in the tuning system.Thus, both the standard and the tonal answerin Figure 3 (A and C) have the diatonic in-tervals [ + 2, -1, + 2, +1], but the first isin C-major and the second is in A-minor.

2. The tonal answer might be thought ofas remaining in the same mode as the stan-dard, which is exactly the way a tonal answeris treated in a fugue. In that case, the pitchesof the mode remain fixed while the startingpitch of the melody is shifted to a differentdegree of the scale. Both melodies in Figure3 (A and C) would remain in C-major, andthe difference between them would be that thestandard begins on the first degree and thetonal answer on the sixth degree of the modalscale.

I prefer the second of these characteriza-tions for describing the cognitive processinginvolved in the experiment presented below.This is because the time interval between thepresentation of the standard and the tonal an-swer is short. The standard is coded as beingin a particular major mode. When the listener

348 W. JAY BOWLING

hears the tonal answer immediately followingthe standard, nothing in that comparison pat-tern demands that he change mode. There-fore, he hears the tonal answer in the samemode as the standard. Diatonic interval pat-tern (contour in a restricted sense) and modecan function as features of the standard.Tonal answers would then be difficult to dis-tinguish from standard stimuli because theyshare these two features. Exact transpositionsforce the listener to change mode in midtrial.Exact transpositions share the feature ofhaving the same intervals as the standardswhen measured in semitones (that is, at thelevel of tonal material). The experiment thusbrings these sets of feature similarities intoconflict with each other.

Lest too persuasive an argument here makethe results of the experiment seem a foregoneconclusion, let me introduce a plausible the-ory that makes a different prediction fromthe two-component scale-contour theory. Itcould be, according to this theory, that con-tours are not stored in memory independentlyof interval sizes. Dowling and Fujitani gottheir result because they used unnaturalatonal melodies. Atonal intervals are difficultto remember, both because listeners have nothad much practice with them and becausethey do not occur as part of an overlearnedscale schema. However, if we replicate Dowl-ing and Fujitani using tonal materials, wewill get a very different result. The intervalsequences of tonal standard melodies will beeasily learned because they fall on a well-known scale. Thus, changes in those intervalswill be easily noticed whether the change isto an atonal melody or to a tonal melody inanother mode. The listeners should at leastdo better than chance in discriminating ex-act transpositions from tonal answers. (Togive this theory its due, I should note thatpilot work with a few professional musiciansconvinces me that they can perform in theway just described).

The two-component theory, on the otherhand, claims that even with tonal melodies,contour (in the sense of ups and downs mea-sured in diatonic intervals) and interval sizes(measured in semitones at the level of tonalmaterial) are stored independently, the latter

simply as a mode label. Tonality can func-tion as a cue to distinguish a tonal melodyfrom an atonal one. But changes in intervalsize that leave tonality intact will be difficultto notice.

Experiment on Tonal Melodies

This experiment is based on the paradigmof Dowling and Fujitani (1971, Experiment1). It copies the conditions of that experi-ment in which comparison melodies weretransposed (i.e., began on a different pitchfrom the standard melodies) and in which thesubject's task was to recognize only exacttranspositions of the standards. The most im-portant difference between the two experi-ments is that in Dowling and Fujitani, allmelodies were atonal; while in the presentexperiment, all but one type of comparisonmelody were tonal. Other differences in methodderived from differences in the availableequipment, subject populations, and the de-sirability of equalizing expected interval sizebetween tonal and atonal melodies used inthe present experiment. Since the most com-parable conditions in the two experiments—those of distinguishing targets from randomlydifferent comparisons—gave roughly compara-ble results (81% and 84% vs. 89%), the ef-fects of changes in these other variables areapparently negligible for purposes of estab-lishing the qualitative results toward whichthis study is directed.

Using tonal melodies in this paradigmmakes possible the introduction of one moretype of comparison melody: the tonal answer.In this type, the comparison begins on a dif-ferent pitch from the standard but stayswithin the same diatonic scale. Thus, the pitchintervals between tones will generally bechanged, but the melody will still be tonal.Figure 3 shows examples of this and the othertypes of comparison stimuli used in the pres-ent experiment and that of Dowling andFujitani.

Method

Subjects. Twenty-one students at the Universityof Texas at Dallas served in four separate group

MEMORY FOR MELODIES 349

sessions, most of them receiving extra credit inupper level psychology courses for their participa-tion. Subjects were divided into groups on the basisof a postexperiment questionnaire. Subjects in theexperienced group had 2 or more years of musicaltraining (including studying an instrument or voiceor playing an instrument in an ensemble but ex-cluding taking music courses or singing in choir).In the inexperienced group, subjects had less than2 years training. Means for the two groups were5.0 and .14 years training, respectively. The meanage of subjects was 30.4 years and was comparablein the two groups. There were three males and sevenfemales in the experienced group and seven malesand four females in the inexperienced group (a dif-ference that probably reflects a tendency to givefemales music lessons in our culture). Performanceof males and females in the two groups was roughlycomparable, with a slight superiority of experiencedmales.

Procedure. Subjects were instructed that this wasan experiment in memory for melodies. On each trial,they heard a pair of brief melodies, and their taskwas to say whether the two were the same or dif-ferent. For this purpose, they responded using afour-category scale with responses of "sure same,""same," "different," and "sure different." There were48 trials in the experiment and they wrote their re-sponses on a sheet of paper provided. The experi-menter explained that all comparison stimuli, eventhose that were the same, would start on a differentnote from the standard. What was important in de-termining sameness was that not only the ups anddowns but also the distances among the notes bethe same. The experimenter referred to the possi-bility of singing "Happy Birthday" starting on dif-ferent notes as an illustration of how the same mel-ody could occur at different pitch levels as long asthe distances among the notes remained the same.The experimenter presented one example of each ofthe types of stimulus pairs. After responding to ques-tions, the experimenter then presented the 48 trials.

Stimuli. Stimuli were played on a freshly tunedSteinway piano and recorded on tape. They werepresented to subjects over loudspeakers at comforta-ble listening levels via high-quality reproductionequipment. The timing of stimuli was controlled bya Davis timer producing clicks every .67 sec, whichwere barely audible on the tape. In all stimuli, therate of presentation of the quarter-note values ( J )of Figure 3 was 3 tones per sec. Thus, each stimuluswas 2 sec in duration. There was a 2-sec blank in-terval between standard and comparison stimuli oneach trial and a 5-sec response interval followingthe comparison stimulus. A warning, consisting ofthe experimenter's voice announcing the trial num-ber, preceded the onset of each trial by 2 sec.

All standard stimuli began on middle C (funda-mental frequency of 262 Hz). There are 16 possiblecontours for five-note sequences, providing unisonsare excluded. The contours of the standard stimulion each of the 48 trials of the experiment were se-lected by using three successive random permutations

of the order of the 16 contours. Thus, each contourappeared as a standard exactly three times in theexperiment. The interval sizes between notes of thetonal stimuli were chosen with the following proba-bilities of diatonic scale steps: P (±\ step) = .67 ;P (±2 steps) = .33.

There were four types of comparison melody. Eachof these four types occurred equally often in thethree blocks of 16 trials (randomly determined). Allcomparison melodies began on either the E aboveor the A below middle C (randomly determined).These transpositions were chosen as being moderatelydistant from C both in pitch level (+4 and —3semitones) and in shared pitches (three and four,respectively). (Frances, 1958, has shown "remote"transpositions in the latter sense harder to recog-nize than "near" transpositions.) Target comparisonstimuli (see Figure 3B) were exact transpositions tothe standards to the key of E or A. They retainedexactly the interval sizes of the standards. Tonalanswer comparison stimuli (see Figure 3C) were luresthat started on E or A but that remained in C, thesame key as the standard, and had the same con-tour and diatonic intervals. Thus, the interval sizesin semitones did not remain the same as in the stan-dard, while the tonal scale remained the same.

Atonal same-contour comparison stimuli (see Fig-ure 3D) were lures that retained the contour of thestandard but that used intervals randomly selectedwithout regard for tonal scales. The probabilities ofinterval sizes of the atonal lures were P (±1 semi-tone) = .17, P (±2 semitones) = .33, and P (±3 semi-tones) — .50. (These probabilities were chosen sothat the expected interval size of a tone sequencewould be 2.33 semitones. This is comparable to theexpected interval size of 2 .27 semitones for the tonalsequences. The latter figure was calculated as aweighted average of the diatonic interval sizes, with-out regard for starting pitch. The fact that all stan-dard stimuli began on C, immediately next to a1-semitone interval, would lower this estimate slightlyin the present case.) The random different stimuli(see Figure 3E) were lures having different con-tours from the standards (randomly selected) anddifferent diatonic scale intervals selected just as withthe standards.

Data analysis. The four-category confidence judg-ments were used to generate individual memory op-erating characteristics (MOC) for each subject foreach of the three types of stimulus comparisons. Hitrates were given by responses to the target stimuli.These hit rates were plotted separately against threesets of false alarm rates given by responses to tonalanswer, atonal contour, and random lures to givethree areas under the MOC for each subject. Areasunder the MOC can be interpreted as an estimate ofwhat the proportion correct would be in the casewhere chance performance is .50 (Swets, 1973).Areas under the MOC were evaluated using an un-weighted-means analysis of variance for unequal cellsizes due to the unequal numbers of experiencedand inexperienced subjects.

350 W. JAY BOWLING

Table 1Areas Under the Memory OperatingCharacteristic of the Experiment Comparedwith Similar Conditions of Dowling andFujitani's (1971} Experiment 1

Group

Target Targetvs. vs. Target

tonal atonal vs.answer contour random

ExperiencedInexperienced

Dowling andFujitani

.48

.49

—

.79

.59

.53

.84

.81

.89

Results

Table 1 shows the mean areas under theMOC for the two groups and the three stimuluscomparisons. The main effect of stimuluscomparison type was significant, F(2, 38) =77.35, p < .001. Distinguishing between tar-gets and tonal answer lures was very difficult,with chance performance in both groups. Dis-tinguishing targets from atonal same-contourlures was somewhat easier, and distinguishingtargets from random lures was easiest of all.The Experience X Stimulus Type interactionwas significant, F(2, 38) = 8.01, p < .001,mainly reflecting a difference of ability indistinguishing targets from atonal same-con-tour lures. The main effect of experience ap-proached significance at the .05 level. Thismodest effect is consonant with the modestcorrelations found by Dowling and Fujitanibetween performance on their task and ex-perience.

General Discussion of Short-term Recognitionof Melodies

The present results illustrate the importanceof scale as well as contour in short-term rec-ognition memory for melodies. This point isbrought out by comparison with the resultsof Dowling and Fujitani (see Table 1). Bothstudies found that the two melodies are rela-tively easy to distinguish in that they havedifferent contours, with performance in the.80s. Dowling and Fujitani's subjects found itdifficult to distinguish between two atonalmelodies with the same contour but different

interval sizes, performing at around thechance level of .50. In the present experiment,subjects found it easier to reject an atonalcomparison melody when it was preceded bya tonal standard melody. This was especiallytrue of experienced subjects who presumablyhave a firmly internalized modal system.What subjects in the present experimentfound extremely difficult, performing atchance, was distinguishing between exacttranspositions of comparison melodies to newtonal keys and shifts of the contour along thesame diatonic scale as the standard. Both ex-perienced and inexperienced subjects hadtrouble with this task. Phenomenologically,the comparison stimuli in Pairs A-B andA-C of Figure 3 sound "natural," while thecomparison in Pair A-D sounds "strange."

This result illustrates the separateness ofthe functions of contour and mode. The func-tion of mode is not to fix a set of intervalsin semitones as belonging to a melody. If itwere, tonal answers would not be confusedwith exact transpositions. The mode is simplya framework on which the contour may behung. For brief melodies heard only once, thepoint on the modal scale where the melodybegins is not taken into account. What sub-jects seem to account for is that both themode and the contour are the same in thetwo melodies.

This result should not be taken to meanthat diatonic scale intervals are somehow psy-chologically equal. The concept of subjectiveequality applies best to the level of the psy-chophysical scale. The aesthetic purpose ofusing differently sized pitch intervals in mo-dal scales would be lost if all the intervalsin the mode were subjectively the same. Dif-ferent intervals are used because they pro-vide melodic interest. Melodies are translatedinto different modes because that is more in-teresting than reiterating them in the samemode. Musicians find tuning systems that useonly subjectively equal intervals dull becausethey deny a major source of melodic variety.This is the principal criticism of the "whole-tone scale" with which Debussy and othersexperimented around the turn of the century.

Moreover, Frances (1958, Experiment 2)found evidence that makes the subjective

MEMORY FOR MELODIES 351

equality of modal intervals difficult to believein. Frances mistuned certain notes on a pianoand then placed these notes in various melodiccontexts. He found that when the mistuningwas in the direction of the dynamic tendencyof the tone in its modal context, the altera-tion was much less likely to be noticed thanwhen the mistuning was in the opposite di-rection. This means that the subjective inter-val size changes with modal context. Suchchanges would be consonant with the theorythat diatonic intervals tend to be subjectivelyequal provided that the changes due to con-text make large intervals (in the sense of thepsychophysrcal scale and tonal materiallevels) smaller and small intervals larger.However, Frances got the opposite result. Inall of his cases, it was small intervals thatbecame smaller.

The confusion of target melodies and tonalanswers does not occur with well-known mel-odies stored in long-term memory. Attneaveand Olson (1971) have shown that with fa-miliar melodies, exact interval sizes are pre-cisely remembered. In fact, familiar melodiescan be used as mnemonics for retrieving scaleintervals, as when a music student uses thesong "Over There" to remember descendingmajor sixths ( — 9 semitones) or the song"There's a Place for Us" for ascending minorsevenths ( + 10 semitones). But even for fa-miliar melodies, the contour and mode canfunction independently, as when "FrereJacques" or "Twinkle, Twinkle" are sung ina minor key or when their contours are recog-nized in spite of distorted interval sizes(Bowling & Hollombe, 1977).

That memory for exact interval sizes of fa-miliar melodies is so good raises the questionof how such melodies are stored. They cannotbe stored simply as contour plus scale, sincethat would leave the skips unspecified. "Twin-kle, Twinkle" and the "Andante" theme fromHaydn's Surprise Symphony would be storednearly identically: the contour [0, +,0, +,0,—, ±, 0, —, 0, —, 0, — ] (where 0 = unison,+ = up, and — = down) beginning on thetonic and in the major mode. What is neededis a way of specifying skips along the diatonicscale. What I will suggest is a three-valueddimension of quasi-linguistic marking. Inter-

vals of one diatonic step will be unmarked;two-step intervals will be marked "s" for skip;and larger leaps will be marked "be," wherex gives the number of steps. In this system,"Twinkle, Twinkle" becomes [0, +]4, 0, +,0, -, -, 0, -, 0, -, 0, -], while Haydn's"Andante" becomes [0, +s, 0, +s, 0, -„, +,0, —„, 0, — s, 0, — 8]. This system takes ad-vantage of the fact that relatively narrow in-tervals predominate in the music of the world(Bowling, 1968). Of the 26 intervals in thefirst two phrases of the two songs just cited,12 are unisons (0 steps), 7 are one step (un-marked), 6 are two steps (marked "s"), and1 is four steps (marked "14").

In order to document this predominanceof small diatonic intervals more fully and toshow that using the present system of mark-ing would put considerably less load on mem-ory than would remembering literally everyinterval size, 1 counted all the intervals inthe collection of 80 Appalachian songs bySharp and Rarpeles (1968). I chose this col-lection because it was compiled by carefulscholars from an almost exclusively vocal tra-dition that does not use harmonizing accom-paniments. The collection is just about theright size to produce stable data, and thesongs in it were selected without any obviousbiases regarding the phenomenon under in-vestigation. I first categorized the 80 songsinto those using heptatonic modes (sevennotes to the octave; 46 songs) and those us-ing pentatonic modes (five notes to the oc-tave; 34 songs). For convenience, and be-cause the existence of a system of hexatonicmodes is not indisputable, I treated the 21songs that used only six notes of the scale asheptatonic (an example of such a song is"Twinkle, Twinkle"). This decision would ifanything bias the interval count against smalldiatonic intervals, since a hexatonic stepacross the note omitted from the heptatonicmode was counted as a skip. (It is interestingthat the note omitted from the heptatonicmode was always one of the pair of notes inthe underlying tuning system that stands inthe unique 6-semitone interval to each other—B or F in the white-note tuning system—and that the 6-semitone interval did not occurin any of the heptatonic songs.) A subsequent

352 W. JAY BOWLING

Table 2Percentages of Diatonic Intervals ofDifferent Sizes in the 80 Songs of Sharpand Karpeles (1968}, with UnisonsOmitted

Mode type

Interval size indiatonic steps

2 3 4 >4

Heptatonic(46 songs,1,544 intervals)

Pentatonic(34 songs,1,334 intervals)

56 30 8 3 2

81 15 2 1 1

check on the data showed that separating thehexatonic songs from the heptatonic has anegligible effect on the frequency distribu-tion of interval sizes.

The songs were strophic. That is, more orless the same melody was repeated for theseveral verses. For present purposes, each in-terval in one strophe of each song was countedonce. Where the rhythm differed from stropheto strophe (because of different words), Iused the rhythm of the first strophe.

Unisons accounted for 23% and 25% ofthe intervals in the heptatonic and pentatonicmodes, respectively. Taking unisons and un-marked diatonic steps together accounted for66% and 86% of all the heptatonic andpentatonic intervals. Omitting unisons fromconsideration allows us to see what percent-ages of + and — intervals need to be marked"s" or "1." Table 2 shows these data. Forboth mode types, the unmarked intervals ac-count for over half the cases. Only 13% ofheptatonic and 4% of the pentatonic intervalsneed to be coded as leaps.

Moreover, the leaps are used in generallypredictable ways in the songs. Of 202 leapsof three or more steps in the heptatonic songs,106 (52%) occurred in one of the followingtwo contexts: (a) pick-up notes at the startof a phrase or leaps to the start of a newphrase (as between the second and thirdphrases of "Twinkle, Twinkle"; 75 instances)and (b) passages in which the same intervaland rhythmic pattern including the leap wasrepeated in the same song (as in the first and

penultimate phrases of "Twinkle, Twinkle";31 instances). The occurrence of leaps is alsoredundant with mode. Among the pentatonicmodes, for example, the mode whose ascend-ing intervals in semitones are [2, 3, 2, 2, 3]had only 1% leaps in its songs versus 4%for the other modes. And each mode has itsown pattern of more and less probable leaps.For example, no leaps were observed betweenthe seventh and fourth degrees of the majormode (the 6-semitone interval).

The scarcity of leaps and their redundantusage when they do occur reduces considera-bly the load on memory. Therefore, it seemsplausible to characterize the memory storageof the pitch material of an actual melody asa combination of mode and contour, includ-ing a specification of the starting pitch levelin the mode and the marking of skips andleaps. It is important to note that this anal-ysis is restricted to the pitch material. Withreal melodies, rhythm must play an importantpart in memory. Kolinski (1969) in his anal-ysis of variants of the song "Barbara Allen"provides numerous instances in which thevery same contour and mode, with a changein rhythm, become a different song, often inanother culture. For example, a change inrhythm turns one of the variants into thesextet from Lucia di Lammermoor. In fact,it is artificial even to think of rhythmlessmelodies. In the state of our knowledge, thisis a necessary artificiality, since the problembecomes enormously complex when rhythm isadded.

Thinking

Rather than just holding a melodic phrasein short-term memory, subjects in Bowling's(1972) study on melodic transformations hadto turn it upside down, backwards, or both.Recognition follows that order of increasingdifficulty. Of interest here is the fact thatsubjects were able only to recognize the mel-odic contour when so transformed and notthe exact interval sizes.

Long-term Memory

In addition to being preserved in short-term memory, melodic contours also seem to

MEMORY FOR MELODIES 353

be retrievable from long-term memory inde-pendently of interval sizes. White (1960) dis-torted familiar melodies such as "YankeeDoodle" and "On Top of Old Smokey" bychanging the pitch intervals between notesby doubling them, adding a semitone, andso on. While the undistorted melodies wererecognized 94% of the time, melodies sub-jected to these contour-preserving transforma-tions were recognized at about the 80% level.Other contour-preserving transformations suchas setting all intervals to 1 semitone produceda greater decrement in performance (toaround the 65% level). However, contour-destroying transformations produced evengreater decrements. For example, randomizingthe intervals or subtracting 2 semitones fromthem even when this changed their sign pro-duced performance in the 45-50% range. (Itis difficult because of sampling problems tosay what the chance level in White's task was,though it was undoubtedly in the 10-20%range. The rhythmic patterns of the tunespresented alone on one pitch were recognizedwith 33% accuracy.)

Bowling and Fujitani (1971, Experiment2) refined somewhat White's approach usingfive familiar tunes whose first two phrasescould be stylized into the same rhythmic pat-tern. They used three kinds of distortion:preservation of contour, preservation of con-tour plus relative interval size (i.e., thegreater-than/less-than relationships of succes-sive intervals were preserved), and preserva-tion of the underlying harmonic structure ofthe melody while destroying contour. Thecontour-preserving distortion produced a dec-rement in performance from 99% (undis-torted) down to 59%. Preserving the relativeinterval sizes only boosted this a little (to66%). Destroying contour led to a perform-ance of 28%. (Chance level was probablybetween 20% and 30%).

Melodic contours of familiar tunes can berecognized even though the distortion of in-terval sizes is very great. Deutsch (1972)showed that distorting a tune by adding orsubtracting one or two octaves from each pitchmade it very difficult to recognize. But if theoctave distortion is carried out with a preser-

vation of contour, performance is remarkablyimproved (Dowling & Hollombe, 1977).

One final consideration is that long-termmemory has the function in musically non-literate societies of preserving the musical cul-ture, including the melodies. What we wouldexpect from the present theory is that vari-ants of a tune would share certain similarities,namely, those that arise from very similarcontours being hung on the underlying scaleframework in various ways. This variationmight occur for three principal reasons: for-getting of the original intervals, the desire tocreate interesting innovations by manipulatinginterval relationships (as shown in Figure1), and changes of instruments and scale sys-tems that necessitate transformations of mel-odies (as in the case of adapting a non-West-ern melody to a Western scale). All of theseprocesses are probably operating, for example,in the variations of the tune "Barbara Allen"studied by Seeger (1966) and Kolinski(1969). The most striking result of Seeger'sstudy of 76 variants of "Barbara Allen" inthe U.S. Library of Congress is that theyfall into families based on the sharing ofclosely related contours. These contours fallonto their scales in various ways, producinga profusion of similar but interestingly variedmelodies.

Reference Note

1. Dowling, W. J. Musical scales and psychophysicalscales: Their psychological reality. In T. Rice &R. Falck (Eds.), Cross-cultural approaches tomusic: Essays in honor of Mieczyslaw Kolinski.Manuscript in preparation.

References

Adams, C. R. Melodic contour typology. Ethno-musicology, 1976, 20, 179-215.

Attneave, F,, & Olson, R. K. Pitch as medium: Anew approach to psychophysical scaling. AmericanJournal of Psychology, 1971, 84, 147-166.

Burns, E. M. Octave adjustment by non-Westernmusicians. Journal of the Acoustical Society ofAmerica, 1974, 56, S25. (Abstract)

Deutsch, D. Music recognition. Psychological Re-view, 1969, 76, 300-307.

Deutsch, D. Octave generalization and tune recogni-tion. Perception &• Psychophysics, 1972, 11, 411-412.

354 W. JAY BOWLING

Deutsch, D. Memory and attention in music. In M.Critchley & R. A. Henson (Eds.), Music and thebrain. London: Heinemann, 1977.

Dowling, W. J. Rhythmic fission and the perceptualorganization of tone sequences. Unpublished doc-toral dissertation, Harvard University, 1968.

Dowling, W. J. Recognition of melodic transforma-tions: Inversion, retrograde, and retrograde inver-sion. Perception &• Psychophysics, 1972, 12, 417-421.

Dowling, W. J., & Fujitani, D. S. Contour, interval,and pitch recognition in memory for melodies.Journal oj the Acoustical Society of America,1971,49, S24-S31.

Dowling, W. J., & Hollombe, A. W. The perceptionof melodies distorted by splitting into several oc-taves: Effects of increasing proximity and melodiccontour. Perception & Psychophysics, 1977, 21,60-64.

Frances, R. La. perception de la musique. Paris: Vrin,1958.

Helmholtz, H. von On the sensations oj tone. NewYork: Dover, 1954.

Hood, M. Slendro and pelog redefined. Selected Re-ports, UCLA Institute of Ethnomusicology, 1966,1(1), 28-48.

Hood, M. The ethnomusicologist. New York: Mc-Graw-Hill, 1971.

Imberty, M. L'acquisition des structures tonales chezI'enjant. Paris: Klincksieck, 1969.

Kolinski, M. "Barbara Allen": Tonal versus melodicstructure, part II. Ethnomusicology, 1969, 13, 1-73.

Kolinski, M. Review of Ethnomusicoiogy oj the Flat-head Indians by Alan P. Merriam. Ethnomusicol-ogy, 1970, 14, 77-99.

Martin, D. W., & Ward, W. D. Subjective evalua-tion of musical scale temperament in pianos. Jour-nal of the Acoustical Society oj America, 1961, 33,582-585.

Miller, G. A. The magic number seven, plus or minustwo. Psychological Review, 1956, 63, 81-97.

Null, C. H. Symmetry in judgments oj musical pitch.Unpublished doctoral dissertation, Michigan StateUniversity, 1974.

Plomp, R., & Levelt, W. J. M. Tonal consonanceand critical bandwidth. Journal oj the AcousticalSociety oj America, 1965, 38, 548-560.

Seeger, C. Versions and variants of the tunes of"Barbara Allen." Selected Reports, UCLA Insti-tute oj Ethnomusicology, 1966, 1(1), 120-167.

Sharp, C., & Karpeles, M. Eighty English folk songsfrom the southern Appalachians. Cambridge, Mass.:MIT Press, 1968.

Shepard, R. N. Circularity in judgments of relativepitch. Journal of the Acoustical Society of America,1964, 36, 2346-2353.

Sundberg, J. E. F., & Lindqvist, J. Musical octavesand pitch. Journal oj the Acoustical Society ojAmerica, 1973, 54, 922-929.

Surjodiningrat, W., Sudarjana, P. J., & Susanto, A.Penjettdikan dalam pengukuran nada gamelangamelan djawa terkemuka di Jogjakarta danSurakarta. Jogjakarta, Indonesia: UniversitasGadjag Mada, 1969.

Swets, J. A. The relative operating characteristicin psychology. Science, 1973, 182, 990-1000.

Ward, W. D. Subjective musical pitch. Journal oj theAcoustical Society oj America, 1954, 26, 369-380.

Ward, W. D. Musical perception. In J. V. Tobias(Ed.), Foundations of modern auditory theory(Vol. 1). New York: Academic Press, 1970.

White, B. W. Recognition of distorted melodies.American Journal oj Psychology, 1960, 73, 100-107.

Williamson, M. C., & Williamson, R. C. The con-struction and decoration of one Burmese harp. Se-lected Reports, UCLA Institute o-f Ethnomusicol-ogy, 1968, 1 ( 2 ) , 45-76.

Zenatti, A, Le developpement genetique de la per-ception musicale. Monographies Francoises de Psy-chology, 1969, No. 17.

Received September 19, 1977 •