Recognition of Transposed Melodies: A Key-Distance Effect ... · Since these four experiments share many features, these will be described in a general method section. Table 1 shows

Journal of Experimental Psychology:Human Perception and Performance1980, Vol. 6, No. 3, 501-515

Recognition of Transposed Melodies:A Key-Distance Effect in Developmental Perspective

James C. Bartlett and W. Jay DowlingUniversity of Texas at Dallas

Four experiments examined the possibility of a key-distance effect in a trans-position detection task. Subjects heard standard melodies followed by com-parison melodies presented in the same key, a musically near key or a musicallyfar key. The task was to recognize comparisons that were exact transpositionsof the standards, rejecting nontranspositions. Results suggested a largely in-variant key-distance effect with nontransposition comparisons (lures); same-and near-key lures evoked more false alarms than far-key lures. The variablesof musical experience, age of subject, and familiarity of melody affected thelevel of transposition-recognition performance but did not consistently affectthe size of the key-distance effect. The results support the psychological realityof key distance and are consistent with both musical and nonmusical-auditorytheories of its effects. The key-distance effect was not found with transpositioncomparisons (targets), a result with implications for the separability of key andinterval information in short-term memory for melodies.

Anyone with a good ear for music cansing, whistle, or hum familiar tunes cor-rectly, that is, with the appropriate intervalsamong the notes. Yet, it is surprisinglydifficult for nonmusicians to extract preciseinterval information from unfamiliar melo-dies on a single hearing. Attneave and Olson(1971) asked their subjects to transposeunfamiliar six-note melodies to new keys,using sine-wave oscillators. Their musicallyexperienced subjects were able to do this,but untrained subjects were not. Cuddy andCohen (1976) gave subjects the task of dis-criminating between an exact transpositionof a novel three-note melody and a com-parison melody in which one note had beenchanged. Musically trained subjects at-tained scores of nearly 90% correct on this

This research was supported in part by OrganizedResearch Funds granted by the University of TexasSystem.

The authors thank Jane Aten and the Dallas Inde-pendent School District for assistance in carrying outExperiment 4, and Darlene Smith for comments onan earlier draft of the manuscript.

Requests for reprints should be sent to JamesBartlett, Program in Psychology and Human Develop-ment, University of Texas at Dallas, Box 688, Richard-son, Texas 75080.

task, but untrained subjects performed atabout 60% correct. (Chance was 50%.)Dowling (1978) also gave subjects a trans-position detection task and found chancediscrimination between exact transpositionsof novel melodies to new keys and tonalanswers (i.e., comparison stimuli with thesame contour—patterns of ups and downs—and in the same key as the standardstimuli but shifted in pitch and with differentintervals among the notes). In all of thesetasks with unfamiliar melodies, subjectsseemed to have little trouble reproducingor recognizing the melodic contour, but theyhad a great deal of trouble with the exact-pitch intervals among the notes.

In exploring why subjects have difficultywith pitch intervals, we find it useful todistinguish among the various cues thatmight be used in judging the similaritiesand differences among pairs of melodies.Assuming that two tone sequences have thesame number of notes, go at the same rate,and have the same rhythmic pattern, howcan the listener tell them apart? He mightuse the set of pitches they contain, theircontour, whether they are tonal or atonal,their keys if they are tonal, or whetherthey have the same intervals between notes.

Copyright 1980 by the American Psychological Association 0096-1523/80/0603-0501J00.75

501

502 JAMES C. BARTLETT AND W. JAY DOWLING

These types of cue vary considerably inhow difficult they are to use and do not al-ways operate independently of one another.It is relatively easy to discriminate betweena repetition of a brief melody containingthe same pitches as the standard stimulusand a distorted version having the same con-tour but different pitches (Bowling &Fujitani, 1971). It is also easy to distinguishbetween comparison melodies having thesame contour as the standard and compari-sons with different contour (Dowling, 1978;Dowling & Fujitani, 1971; White, 1960).It is somewhat harder to distinguish be-tween tonal and atonal distortions of a tonalstandard though not as hard for trainedas for untrained subjects (Dowling, 1978).It is easier to detect distortions of intervalsin tonal than in atonal melodies (Frances,1958), but as noted earlier it is difficult todistinguish between the case in which thekey has been changed but the intervalspreserved (exact transposition) and the casein which the intervals have been changedbut the key preserved (tonal answer). Onetheoretical account of this last result is thatimmediately after hearing an unfamiliarmelody, the listener has available twoclasses of information: contour and key (theset of pitches of a modal scale anchoredto a particular tonic).

According to this view there is little repre-sentation of specific interval sizes duringearly stages of learning, but in later stagesrepresentation of interval informationimproves, and listeners are able to recognizetranspositions or to create them themselves.(This account applies to musically untrainedlisteners. Professional musicians doubt-lessly extract interval information muchmore quickly.) There are two consequencesof this account, which are explored in thepresent series of experiments. One is thatwith overlearned, familiar melodies, thescale steps of notes and the intervals be-tween them should be well represented inmemory, and the confusion between trans-positions and nontranspositions shouldbe reduced. This finding is already impliedby the Attneave and Olson (1971) experi-ment; however, these authors sampled onlyone familiar melody (the National Broad-

casting Company [NBC] chimes) and ex-amined only transposition production, notthe confusability between transpositionsand different types of nontransposition ina recognition task. A second consequenceis that key (e.g., C major, G major) mightserve as a cue for melody equivalenceindependently of the intervals themselves.That is, two same-contour melodies shouldsound more similar, and more like transposi-tions, if they are played in the same orsimilar keys. This should hold regardless ofwhether the two melodies are actually trans-positions or merely same-contour itemswith different interval patterns. This key-distance effect on recognition of transposi-tions and rejection of nontranspositions isinvestigated in all four experiments.

Key distance is well defined in westernmusic, and that definition is used here. Twokeys are considered closely related to thedegree to which their diatonic modal scalesshare pitches. Thus, the keys of C major andG major are very close, since their scales(CDEFGABC and GABCDEF#G) sharesix out of seven different pitches. The scalesof C-major and B-major (BC#D#EF#-G#A#B) are distantly related, since theyshare only two pitches (B and E). Theserelationships are coded in a convenientscheme called the "circle of fifths" in whichtwo keys whose tonic centers are a fifthapart (i.e., for which the fifth note in onescale is the first note of the other) share allbut one note. Two jumps around the circleof fifths gives keys that share all but twonotes, and so forth. The circle of fifthsorders all 12 major keys so that distancein either direction around the circle giveskey dissimilarity in terms of shared notes.The sequence of keys is C-G-D-A-E-B-F#(or G")-D6-A6-E6-B6-F-C.

Although the major goal of these experi-ments is to examine the key-distance effect,we are also concerned with the effects ofthe age and experience of listeners. Musicaltraining has typically been associated withgood performance on transposition pro-duction and recognition tasks (Attneave &Olson, 1971; Cuddy & Cohen, 1976; Dow-ling, 1978), showing that sophisticated sub-jects are better at extracting information

RECOGNITION OF MELODIES 503

about muscial intervals. However, little isknown concerning the effects of training onkey distance and similarity. There are twoconceivable outcomes. One possibility(suggested by Dowling, 1978) is that themore experienced subjects have more firmlyinternalized the tonal system of their cultureand will therefore show a correspondinglygreater effect of key distance. An alternatepossibility is that since the system of keysin western music is based on similarityin terms of shared pitches, and the numberof shared pitches is a purely physical vari-able that should need no cultural trainingto be effective, there should be little effectof experience on discrimination betweenkeys. The finding of Dowling and Fujitani(1971) that even with atonal melodies thesharing of pitches was a powerful vari-able suggests that shared pitches are indeedimportant. Experiments 1,2, and 3 manipu-late experience as a dichotomous variable(more or less than 2 yr of training), andExperiment 4 is a replication of Experiment3 with children of ages 5-10. This latterage range was chosen because work byZenatti (1969) and others suggests thatsensitivity to mode differences developsduring this period.

One additional variable, presentationrate, is explored in Experiment 1. In onecondition the 6 note/sec rate of Dowling(1978) is replicated, and in the other a muchslower rate of 1 note/sec is used. We did notexpect rate to interact with the key-distanceeffect but thought that it might interactwith experience. That is, it seemed plausiblethat less experienced subjects might do rela-tively better at the slower rate at which theirless practiced encoding skills would beeffective.

General MethodSince these four experiments share many features,

these will be described in a general method section.Table 1 shows the salient features of these experimentsin comparison with those of Dowling and Fujitani(1971) and Dowling (1978).

SubjectsUndergraduates at the University of Texas at Dallas

served in Experiments 1, 2, and 3 to fulfill a course

requirement. The subjects' mean age was 29.2 yr,and their mean amount of musical training was 3.5 yr,defined as lessons on an instrument or voice orparticipation in an instrumental ensemble. For pur-poses of data analysis, subjects were dichotomizedinto inexperienced (less than 2 yr of training) andexperienced (2 yr or more of training) groups. Sub-jects with some training but less than 2 yr were rare,and the mean amount of training of the inexperiencedand experienced groups was .17 yr and 6.8 yr, re-spectively. Many of the subjects had served in similarmusic recognition experiments during the precedingyear. The subjects served in group sessions, and thesame group of subjects served in both Experiments 2and 3. Approximately 65% of each group in eachexperiment was female.

StimuliThe stimuli were produced on a freshly tuned

Steinway piano, tape recorded, and presented tosubjects over loudspeakers at comfortable listeninglevels. Timing was controlled by a Davis timer, whichemitted barely audible clicks at intervals of .33 secor 1.00 sec (Experiment 1) or .67 sec (Experiments 2,3, and 4). The interstimulus interval (ISI) was keptconstant throughout all four experiments and was 4.0sec. This ISI was longer than the 2.0-sec intervalused by Dowling (1978) so that the pair of stimuliin the slow condition of Experiment 1 might be sepa-rated sufficiently so as not to run together.

ProcedureSubjects were instructed that this was an experiment

on memory for melodies. On each trial of the experi-ment, they heard a pair of melodies. The subjects'task was to judge whether the two melodies werethe same or different and to respond using a four-levelconfidence scale. Subjects wrote their responses se-quentially on a sheet of paper. Separate sheets wereused for the two conditions of Experiment 1. Sub-jects had 6.0 sec to respond on each trial, and theonset of each trial was announced by the experi-menter's voice saying the trial number 2.0 sec beforethe start of the standard stimulus.

Before the start of each session, the subjectslistened to examples of each trial type used in theexperiment, constructed out of familiar melodies notused in the rest of the experiment. The reasonseach type of lure was different from the standardwere explained, and the experimenter emphasized thatthe subjects were to respond same only to exacttranspositions. The set of examples began and endedwith an example of exact transposition.

Experiment 1

In Experiment 1 standard stimuli werefollowed by six types of comparison stimuli(see Table 1): transpositions (T); tonallures in the same key as the standard (LS),


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in a nearly related key (LN), or in a far key(LF); atonal lures with the same contour asthe standard (At); and different contourtonal lures (D). The Interval Changecolumn in Table 1 gives the number ofintervals in the comparison that were dif-ferent from the corresponding intervals inthe standard, counted as types, not tokens.That is, if an interval were repeated, itwas only counted once. In the sense usedhere, the first phrase of "Mary Had a LittleLamb" contains two intervals, the firstphrase of "Frere Jacques" contains threeintervals, and the first phrase of "TwinkleTwinkle Little Star" contains two intervals.Ascending and descending intervals be-tween the same pitches (e.g., do-re andre-do) were counted only once. Unisonswere disregarded. The Note Change In-ferred column in Table 1 gives the numberof pitches in the comparison not containedin the diatonic scale of the standard, forexample, an F# when the standard was inthe key of C. These were counted as types,so that repeated notes were counted onlyonce. The Note Change Actual column inTable 1 gives the percentage of notes inthe comparison that did not appear in thestandard and were counted as tokens. InExperiment 1, only the zero entries underInterval Change for T stimuli and underNote Change Inferred for LS stimuli werecontrolled directly. The other values variedas a consequence of the operation of theother constraints imposed on the stimuli.Note, for example, that among tonal luresthe farther removed the key, the more actualand inferred note changes there are.

MethodThe two conditions of Experiment 1 each consisted

of 72 trials. In the fast condition, the duration of aquarter note (see Figure 1) was .17 sec and in the slowcondition 1.0 sec. Each standard and comparisonstimulus consisted of five notes of which the fifth hadtwice the duration of the first four. Thus, stimuliwere 1.0 sec long in the fast condition and 6.0 seclong in the slow.

Stimuli were constructed in the same way as de-scribed by Dowling (1978). Each of the 16 possiblecontour patterns of five-note melodies appeared in astandard stimulus four or five times in the 72 trialsof a condition. Contours were randomly assigned totrial types, and trial types were randomly assigned

to trial numbers within four blocks of 18 trials. Withineach block all trial types were as equally representedas possible. All standard stimuli started on middle C(F0 = 262 Hz, where F stands for fundamental fre-quency) and were in the key of C major. The melodieswere generated as a random walk on the tonal scale,using the randomly selected contour and probabilitiesof diatonic scale step sizes of P(±l step) = .67 andP(±2 steps) = .33. This gave an expected intervalsize of 2.3 semitones, which is roughly the same asthe mean interval size for the familiar tunes used inthe other experiments.

Figure 1 shows examples of the different types ofcomparison stimuli used in Experiment 1. In the 72trials, there were 18 transpositions, 12 tonal lures inthe same key, 9 in a near key, 9 in a far key, 12 atonal,and 12 different contour. Half of the comparisonsbegan on A below middle C, the other half on theE above, randomly determined and balanced within

Experiment

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Experiment 2

Oh, Sutanna

Figure 1. Examples of stimuli used in Experiment 1(top) and Experiment 2 (bottom).


each trial type. T stimuli were simply transposed tothe key of A or E and so began on the first scale stepor tonic of those keys. (See the column labeled ScaleStep of Reference in Table 1). T stimuli retained boththe diatonic and physical interval sizes of the standards.LS stimuli stayed in the key of C major and so changedphysical interval sizes measured in semitones from thestandards but not diatonic interval sizes. They beganon either the sixth (A) or third (E) scale step of C major.For LN stimuli, A and E became the second scalesteps of the keys of G and D, both nearly related to C.For LF stimuli, A and E were the fourth scale stepsof the keys of E and B, both relatively distant from C.

The At stimuli were generated using the same con-tours as the standards but with an interval distributionthat introduced nondiatonic intervals while retainingthe same expected interval size of 2.3 semitones:P(±\ semitone) = .17; P(±2 semitones) = .33; P(±3semitones) = .50. The constraint was added (and notpresent in Dowling, 1978), that not only should inter-vals be randomly selected but the resulting tone se-quences should be impossible in any western mode,including the harmonic and melodic minors.

Different contour stimuli were generated in the sameway as standards, with two out of the four intervaldirections randomly selected for change from thecontour of the standard and with the constraint thatno contour appear more than once as a D comparisonstimulus in the 72 trials. D stimuli were in the keysof A or E and thus began on the first scale step in thosekeys. Changes in interval size are irrelevant and nottabulated because of the changes in direction.

The fast and slow conditions used the same stimuluspairs on like trial types, but the trials were presentedin different random orders in the two conditions.Twenty-four subjects served in Experiment 1, andall subjects did both the fast and the slow conditionsin separate sessions separated by a 5-min break.Fourteen subjects did the conditions in the order

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Stimulus Type

Figure 2. Probability of a recognition response (hitsto targets and false alarms to all other items) as a func-tion of stimulus type and musical experience of subject(panel A) and presentation rate (panel B). (exp =experienced; inexp = inexperienced.)

fast-slow, and 10 subjects, in the reverse order.Half of the subjects with each order were experiencedand the other half inexperienced.

Results

For scoring purposes the four confidencelevels were collapsed into the two categories,same and different, with two responsetypes going into each category. The falsealarm data (i.e., responses of same to anybut the T stimuli) were fed into a four-wayanalysis of variance with lure type (LS, LN,LF, At, D), experience, presentation rate(fast, slow), and test order (fast-slow, slow-fast) as factors. The largest effect was thatof lure type, F(4, 80) = 67.24, p<.001,M5e = .029. The other significant maineffect was that of rate, F(l, 20) = 6.21,p < .05,MSe = .024, with fewer false alarmsat the slow rate. There were significantinteractions between Lure Type x Rate,F(4, 80) = 2.75, p < .05, M5e = .022; luretype x experience, F(4, 80) = 2.95, p < .05,M5e = .029; and Experience x Rate xOrder,F(l, 20) = 5.74,p < .05,MSe = .024.No other effects approached significanceexcept for a marginal interaction betweenExperience x Rate, F(l, 20) = 4.11, p<.06, MSe = .024.

Figure 2 displays the most importantamong these results. In both panels ofFigure 2, the main effect of lure type canbe seen clearly, with D and At stimuli pro-ducing fewer false alarms than the tonallures. Planned comparisons between ad-jacent pairs of lure types showed significantdifferences at the .05 level for D versus At,7(23) = 4.15, At versus LF, r(23) = 5.61, LFversus LN, f (23) = 2.11, but not for LNversus LS, ?(23) = .77. A post hoc com-parison showed a highly significant differ-ence for LF versus LS, f(23) = 3.41, p <.001. To determine the generalizability ofthese effects over items, we did a parallelset of t tests over items rather than oversubjects. All of the foregoing significanteffects were supported at the .05 levelexcept for LF versus LN. Thus, the resultssupport a key-distance effect; nontransposi-tions in far keys (LF items) were easier toreject than tonal answers (LS items) and


Table 2Probabilities of Responding Same to Targetsand Lures in Experiment 1

Targets Lures

Experience Order

Inexperienced

Experienced

Note. S = slow;

F-SS-F

F-SS-F

F = fast.

.66

.55

.71

.63

.70

.59

.80

.82

.42

.48

.41

.37

.50

.42

.47

.49

possibly easier to reject than nontransposi-tions in near keys (LN items).

The Lure Type x Experience interactionshown in Figure 2A was analyzed by five/ tests, comparing experienced to inexperi-enced subjects on each type of lure. Of thesefive tests, only two indicated a reliable ex-perience effect, D, /(22) = 2.41, and LF,t(22) = 2.33. Note that these differences arein opposite directions—Experienced sub-jects made more false alarms to LF itemsand fewer false alarms to D items. Ex-perienced subjects also made significantlymore hits to transpositions than inexperi-enced subjects, t(22) = 2.20.

Figure 2B displays the effect of presenta-tion rate and the Lure Type x Rate inter-action. The generally lower false alarm ratesat the slow rate carry over to lower hitrates to T stimuli. This suggests that themain effect of rate is due to a criterionshift and not to greater accuracy. This sup-position is borne out by the lack of anysignificant rate effect in the analysis of areascores reported later. We explored the LureType x Rate interaction with five t tests,one for fast versus slow rates for eachtype of lure. Only the test for LF itemsshowed a reliable effect, t(23) = 3.26. Thus,the data suggest that the key distance effectis stronger for slow than for fast stimuli andstronger with inexperienced than experi-enced subjects.

The three-way interaction of Experience xRate x Order was unexpected and ispuzzling. This interaction is representedin Table 2 along with corresponding data onhits. One reasonable description of the

pattern is as follows: Fast presentation ratewas always associated with both higher falsealarm rates and higher hit rates, except withinexperienced subjects in the slow-fasttest order. We attribute this pattern to apractice effect. For inexperienced subjectspractice with slow melodies facilitatesaccurate performance on the later test withfast melodies, whereas practice with fastmelodies does not help much.

Area scores. In the present experi-ments, we have found response rates re-ported in terms of hits and false alarms suchas those analyzed earlier to be more inform-ative than discrimination measures suchas area under the memory-operating charac-teristic (MOC; Swets, 1973). However,since Dowling (1978) reported his data interms of area scores, we also show thepresent data in that form for comparison.Table 3 shows area under the MOC cal-culated using the four categories of con-fidence level responses, comparing hit ratesto T items with each of the five false alarmrates. Comparison of the means in rows 3and 6 of Table 3 shows that the presentresults conform to those of Dowling. Dis-

Table 3Areas Under the Memory-OperatingCharacteristic for Experiment I ComparedWith Those of Dowling (1978)

Study andexperience

Dowling(1978)

IE

MExperi-

ment 1IE

M

Tvs.LS

.49

.48

.49

.50

.57

.54

Tvs.LN

———

.48

.57

.53

Tvs.LF

———

.58

.62

.60

Tvs.At

.59

.79

.69

.66.78.72

Tvs.D

.81

.84

.83

.76

.87

.82

Note. I means inexperienced; E means experienced;T means exact transpositions of the standard stimuli;L refers to tonal stimuli that share contour but notintervals with standard stimuli in the same (LS), near(LN), or far (LF) keys relative to the keys of the stand-ards; At means atonal stimuli that share contour withthe standard stimuli; D means stimuli with differentcontours from standard stimuli.


crimination between T and LS items is nearchance, whereas discrimination betweenT items and both At and D items is sub-stantially above chance. These results alsoshow that discrimination between T and LNitems is about the same as that betweenT and LS items, whereas the T versus LFdiscrimination is somewhat better. The areascores for LN and LF items differed sig-nificantly by a t test, r(23) = 4.56, p < .01.

The effects of experience differed in thetwo experiments. Whereas Dowling (1978)found a sizable experience effect with onlyAt items, t tests on the present area-under-MOC data indicated significant (p < .05)experience effects for every item typeexcept LF. Experiments 2 and 3 providefurther looks at experience effects. It shouldbe noted that the pattern of experienceeffects in Table 3 (area scores) are consis-tent with those indicated by the "raw"response probabilities shown in Figure 2.In Figure 2 it can be seen that more experi-enced subjects showed higher hit rates thanless experienced subjects but did not showhigher false alarm rates, except with LFitems. Thus, experience affected dis-crimination between targets and betweeneach type of lure except LF items.

Discussion

The most important finding of Experi-ment 1 was that LF items—same-contourtonal-comparison items in a far key fromthe standard—are harder to reject than LSitems and probably LN items as well. SinceLF items are tonal, their relatively highrejection rate cannot be due to a strategy ofrejecting atonal items. If these LF itemssound different from their standard stimuli,it is because of the relatively distant rela-tionship of their keys and those of the stand-ards. If key distance is responsible for per-ceptual dissimilarity between LF lures andstandards, then it should also affect thesimilarity of targets in near and far keys.Experiments 2, 3, and 4 introduce a dis-tinction between TN and TF stimuli, that is,between targets transposed to near and farkeys, respectively. The key-distance effectshould lead hit rates to be lower for TF items

than for TN items because of their dis-similarity to the standard stimuli.

Experiments 2, 3, and 4 test the replica-bility of the key-distance effect with familiarmelodies. One expectation we had was thattranspositions would be much more ac-curately recognized with familiar melodies,since the intervals of those melodies wouldbe thoroughly overlearned. We expectedthis effect of familiarity to appear with in-experienced subjects as well as with experi-enced ones, as suggested by the success ofAttneave and Olson's (1971) inexperiencedsubjects in reproducing the intervals of thefamiliar NBC chimes. An effect of familiar-ity on the size of the key-distance effectwas considered an open question. On theone hand, it seemed possible that subjectscould effectively separate interval informa-tion from key information when hearing atune with a previously established repre-sentation in long-term memory. If so, keydistance would have no effect with familiarmelodies. On the other hand, familiaritymight simply improve the extraction ofinterval information without affecting itsseparability from key information. In thislatter case, key-distance effects should befound with both familiar and unfamiliarmaterials (unless precluded by ceiling orfloor effects).

Experiment 2 was a test of the key-distance effect with both near- and far-keytargets and lures. It was a simplification ofExperiment 1 in that we did not think furtherreplication of the ease of rejection of Atand D items was necessary. Along with thissimplification we decided to control directlythe number of interval changes in lures andthe number of inferred note changes infar-key items. This is shown in Table 1,which also indicates those cases in whichkey or scale step of reference was allowedto vary to contrive exactly three changes ininterval or note. Examples of the types ofstimuli used in Experiment 2 are shown inFigure 1.

Experiment 2 also contrasted the recogni-tion of first phrases of familiar melodies withrecognition of unfamiliar stimuli. The un-familiar melodies were constructed so thateach had the same rhythmic pattern as one


of the familiar melodies but a differentmelodic pattern. Due to contraints onstimulus construction (see later), it was im-possible to assign melodies randomly to trialtypes. Therefore, every effort was madeprior to Experiment 2 to assign stimuli sothat melodies in each trial type would be ofroughly equal familiarity. As a final check,we had the subjects of Experiments 2 and 3rate each of the familiar melodies for famil-iarity at the end of the experimental session.Mean percent familiarity judgments rangedfrom 88 to 96 over the four trial types.We searched thoroughly for correlations,both across items and across subjects, foreffects of familiarity on recognition per-formance and found none.

Experiment 2

MethodThere were 40 trials in Experiment 2. There were

four types of trials (TN, TF, LS, and LF), and therewere five instances of each trial type with both familiarand unfamiliar melodies. The order of the 40 trialswas randomized with the constraint that familiarmelodies and their same-rhythm unfamiliar counter-parts not appear consecutively. A given familiarmelody and its unfamiliar mate both occurred in thesame trial-type category. The duration of the mostfrequent note in each of these melodies was set at.67 sec—a quarter-note duration in Figure 1. Themodal stimulus was 5.33 sec long, with a range of2.67 sec-9.33 sec. The familiar melodies wereselected on the basis of subjective familiarity tosubjects in prior research. All were in major keys.

The assignment of familiar melodies to trial typeswas constrained by logical possibilities available witheach melody. For example, since the first phrase of"Twinkle Twinkle Little Star" contains just twointervals (counted as types), it could not appear asan LS or LF stimulus, since those categories requirethree interval changes (see Table 1). It should benoted that since TN stimuli could not contain anypitches not implied by the C-major scale of the stand-ard, they could have been called TS if that categorywere not logically impossible in music theory. Con-struction of the yoked-control unfamiliar melodieswas constrained by the same need to use the melodyin the assigned trial category and also by the require-ment of producing an overall mean interval size of2.3 semitones. Apart from those constraints, the un-familiar melodies were simply constructed to soundalright—that is, to be reasonably good gestalts. Noattempt was made to randomize note or intervalselection. A little experimentation with the con-straints listed or implied earlier will convince thereader that such an attempt would have boggled themind of a J. S. Bach or a large computer. But the

result was a set of unfamiliar stimuli that was probablymore musically meaningful than the stimuli of Experi-ment 1.

Fifteen subjects served in Experiment 2—7 inex-perienced and 8 experienced.

Results

Table 4 gives the proportions of sameresponses to targets and lures in Experiment2, collapsed across confidence levels as inExperiment 1. A four-way analysis of vari-ance was performed on these data, with thefactors of familiarity, interval change (targetvs. lure), key change, and experience. Theonly significant main effect was that ofinterval change, F(l, 13) = 273.0, p < .001,M5e = .035, indicating successful discrimi-nation between targets and lures. There wasa significant interaction between IntervalChange x Experience, F(\, 13) = 8.89, p <.02, M5e = .035, supporting the tendencyfor experienced subjects to outperform in-experienced subjects. There was also asignificant interaction of Interval Change xFamiliarity, F(l, 13) = 46.4, p<.001,MSe = .023, supporting the predicted trendfor better interval discrimination withfamiliar melodies. Of most interest, therewas an Interval Change x Familiarity xKey Change interaction, F(l, 13) = 4.98,p < .05, MSe = -029. This interaction isclear in rows 3 and 6 of Table 4, collapsingover experience. It can be attributed to the

Table 4Probabilities of Responding Same to Targetsand Lures in Experiment 2

Familiarityand

experience

UnfamiliarIE

M

FamiliarIE

M

Targets

TN

.69

.70

.70

.971.00.99

TF

.74.75.75

.861.00.93

LS

.49.40.45

.29

.15

.22

Lures

LF

.29

.20

.25

.34

.03

.19

Note. I means inexperienced; E means experienced;TN and TF refer to transpositions to near and far keys,respectively; LS and LF refer to same-contour imita-tions in same and far keys, respectively.


relatively high false alarm rates to LS itemswith unfamiliar melodies. In fact, of the fourcomparisons testing for the key-distanceeffect within the categories of familiar-unfamiliar and target-lure, only the testbetween unfamiliar LS and LF items wassignificant, t(l4) = 2.63. None of the fourt tests was significant when performed overitems rather than subjects, but this can beattributed to the small number of items (five)used in each category. Since Experiments 1and 3 both support the key-distance effecteven with items taken as the random factor,we are confident that the key-distance effectgeneralizes over items.

Discussion

Experiment 2 replicated the key-distanceeffect, but only in terms of false alarm ratesto unfamiliar items. Experiment 3 was de-signed as a further test of the key-distanceeffect concentrating on just familiar melo-dies. Experiment 2 also demonstratedclearly that interval changes in familiarmelodies are much easier to detect thaninterval changes in unfamiliar ones. Both ex-perienced and inexperienced subjects ap-pear to have melodic interval sizes storedin their long-term memories for those tunesthey know, and those interval sizes can beretrieved iin such a way as to help themdetect changes of interval size when theyoccur.

Experiment 2 replicated the positiveeffect of musical experience on perform-ance; experienced subjects were better atthe transposition detection task. However,the qualitative nature of this experienceeffect differed in the two experiments. InExperiment 1, the more experienced sub-jects tended to show a smaller key-distanceeffect, whereas in the present study, thekey-distance effect was, if anything, largerfor more experienced subjects. (Only ex-perienced subjects showed a trend towarda key-distance effect with familiar lures.)Experiments 3 and 4 provide additionalinformation on this point.

Experiment 3

Experiment 3 was conducted with thesame subjects as Experiment 2—It simply

followed in the same session after a 5-minbreak. Experiment 3 had two purposes.First, it provided a more extensive test ofthe key-distance effect with familiar melo-dies, using more melodies and adding LNitems between LS and LF as in Experi-ment 1.

A second purpose of Experiment 3 was toprovide a task that could be used to comparethe performance of children and adults withrespect to the key-distance effect. Pilotwork showed that the unfamiliar materialsof Experiment 1 were much too difficultfor the children to disclose differences dueto detection of interval changes. We there-fore constructed a set of stimuli usingfamiliar melodies, which we could use inparallel experiments with adults and chil-dren, namely, Experiments 3 and 4.

Experiment 3 incorporated some method-ological refinements, which can best bedescribed with reference to Table 1. InExperiment 3 the reference scale steps towhich the tonal lures were moved werecontrolled precisely, and the shift in pitchof the starting notes of both targets andlures was carefully counterbalanced acrosskey distance and item type. In Experiment1, reference scale step was completely con-founded with key distance. That may havebeen an innocuous confounding, but it isconceivable that shifts of comparisons to thefourth degree of the scale make intervalchanges easier to detect than shifts to thethird or sixth degree of the scale. Withthe randomly generated materials of Experi-ment 1, this confounding was a virtualnecessity—or at least the set of rulesnecessary to eliminate the confounding andstill preserve random generation would havebeen very long. In Experiment 2 switchingto familiar tunes and yoked-control con-structions took us away from the com-plexities of random generation, and wechose to control the number of intervalchanges and the number of note changesprecisely. The price we paid for that wasthat we had to use whatever key and refer-ence scale step would work with the com-parison stimulus. At the very least thisintroduced noise into the data and at worstmight have involved unknown confoundsthat we would have no means of assessing.


In Experiment 3 we exerted precise controlover the keys and reference scale steps ofcomparison stimuli and monitored theresulting pattern in terms of interval changesand note changes. Note changes checkedout reasonably well in that there were sub-stantially more changes for far keys thanfor near keys, and the values of TN andLN, and TF and LF, were close. For inter-val changes, which we wanted to hold con-stant for all lure stimuli, the range acrossitem types was 3.4-3.8 changes, which wasbetter than the range in Experiment 1 of2.2-2.9 changes.

Method

There were 25 trials in Experiment 3: 5 each of 5trial types. The trial types were TN, TF, LS, LN,and LF. All standard stimuli were familiar melodieshaving the same timing characteristics as in Experi-ment 2, except that here the first two phrases of eachmelody were used. The modal stimulus was 10.67sec long, and the range was 5.33-16.0 sec. (Twophrases were used to make the task easier for thechildren of Experiment 4). At the end of the session,the subjects rated the familiarity of all 25 tunes usedin the experiment. They were presented again witheach tune and were asked to give its title or some ofthe words or name its appropriate occasion, or failingthat to state whether it sounded familiar. The resultsof these two kinds of response were closely parallel,so only the percentage of subjects responding at thelooser criterion will be reported. The mean percentof subjects familiar with the tunes used for the TN andTF categories were 72% and 79%, respectively, andfor the LS, LN, and LF categories, 94%, 91%, and89%, respectively. The a priori attempt to equalizefamiliarity across key distance was therefore success-ful, and the decision to bias familiarity, if it were tobe biased at all, against targets was also successful.

Unlike Experiments 1 and 2, the standard stimuliin Experiment 3 were randomly assigned to all 12different keys, with the constraint that all keys appearat least twice. For simplicity of exposition, we willdescribe the changes of key of the comparison stimulirelative to C major. (This description is as though weconstructed each trial in C major to begin with andthen randomly transposed the various trials to dif-ferent keys.) The reference note or tonic of the com-parison melody was always one or two semitonesabove or below C; that is, B" (A#), B, D" (C#), or D.(We say "reference note" rather than "starting note"because not all familiar tunes start on the first degreeof the scale.) Altogether five stimuli were shifted toD (+2 semitones), eight to D" (+1 semitone), sevento B (-1 semitone), and five to B6 (-2 semitones).Of those shifted to D, three were TN and two wereLS. Of those shifted to Db, three were TF, three wereLN, and two were LF. Of those shifted to B, twowere TF, three were LS, and two were LN. Of those

shifted to B6, two were TN and three were LF. Fortranspositions the two near keys were B" and D major,both of which share five-sevenths of their pitches withC major. The far keys were B and D6 major, bothof which share two sevenths of their pitches with Cmajor. Note that the TN stimuli, whose scale stepreference is one, simply shifted to Bs or D; and theTF stimuli, again referenced to the first scale step,shifted to B or D6. The LS stimuli stayed in C majorand shifted to either the second (D) or seventh (B)scale step. The LN stimuli went into either A or Dmajor, using the second (B) or seventh (C#) scalestep, respectively. The LF stimuli went into B major,in which A# is the seventh scale step and C# thesecond.

Results

Table 5 shows proportions of positiveresponses as a function of item type andexperience, collapsed into two responsecategories as in the analysis of Experiments1 and 2. As in Experiment 2 discriminationbetween targets and lures with familiarmaterials was good, with uniformly high hitrates for both groups of subjects, and sowe did an analysis of variance on just thefalse alarm data. (In passing, we note thatthere is no evidence for a key-distance effectwith the targets, but this may be due toceiling effect.) In this 3 x 2 (Lure Types xLevels of Experience) analysis, the maineffect of lure type was significant, F(2,26) = 3.52, p < .05, M5e = .017, and repre-sented essentially a key-distance effect. At test over items supported the differencebetween LS and LF items, ?(8) = 2.69,

Table 5Probabilities of Responding Same to Targetsand Lures in Experiments 3 and 4

Targets Lures

Experience & age TN TF LS LN LF

Inexperienced adults .89 .89 .23 .11 .03Experienced adults .93 .95 .05 .05 .00

M .91 .92 .14 .08 .02Kindergarten .67 .58 .65 .57 .55Grades 1 & 2 .58 .54 .60 .60 .36Grade3 .70 .62 .53 .48 .35

M .65 .58 .59 .55 .42

Note. LN refers to same-contour imitations in nearkeys. TN and TF refer to transpositions to near andfar keys, respectively; LS and LF refer to same-con-tour imitations in same and far keys, respectively.


p < .05. This result contrasts with the non-significant key distance effect with familiartunes of Experiment 2. The effect of experi-ence approached significance, F(l, 13) =3.91, p < .07, MSe = .023. The interactionhad an F ratio close to 1.

Experiment 4

Experiments 1, 2, and 3 have clearlydemonstrated a key-distance effect in thedetection of interval changes in transposedmelodies, at least indicating higher falsealarm rates when tonal lures are closer tothe key into which the lure has been trans-formed. The key-distance effect seems to bea robust phenomenon not consistentlydependent on the familiarity of the muscialstimuli or the muscial training of the listen-ers. Experiment 4 explores the possibilitythat the key-distance effect might be largelyindependent of the age of the listeners.Children of ages 5-8 performed the trans-position detection task with the same stimuliused in Experiment 3. This age rangeseemed most appropriate to investigate,since previous studies had found importantchanges in performance on melody recogni-tion tasks during that period. Zenatti (1969)had children say which note of a melodyhad been changed in pitch. She found thatwith three-note melodies the average successrate on this rather difficult task went from25% (around chance) at age 5 to about 50%at age 9. Imberty (1969) has shown thatalready by the age of 8, children are sensi-tive to changes of mode (major vs. minor)and key when these are introduced in themidst of a somewhat familiar melody.

MethodExperiment 4 used the same materials as Experi-

ment 3. The main differences in procedure were thatsubjects were run individually and the experimenterrecorded their responses. Only the responses sameand different were used, since pilot attempts to usethe four-response system with kindergarteners raninto problems.

Three groups of subjects participated. There were23 kindergarten students of mean age 5.6 yr at thetime of testing, 11 first and second graders of meanage 6.9 yr, and 12 third graders of mean age 8.6 yr.All subjects had participated for the better part of 1school yr in federally funded music enrichment

programs for inner-city children and so were if any-thing more sophisticated musically than their peers.(This sophistication is substantiated by tests of melodicmemory with similar groups.) Although the groupswere by definition selected for academic achievementbelow national norms, the research just cited showssubstantial gains in reading scores by children in theseenrichment programs, and so we believe a fair charac-terization of these subjects is that they were probablyabout average in academic performance for their ages.

Results

Table 5 shows proportions of same re-sponses to the stimuli of Experiment 4 bychildren of different ages. An analysis ofvariance of the hit data showed no effects.For a description of overall discrimination,rather than area under the MOC (which fortwo-category data would be rather unstable),we did an analysis of A' (Grier, 1971) data.This showed only an effect of age, with theolder subjects performing better, F(2, 43) =4.18,/j < .05, MSe = .007. (In calculating A',TN was compared with LN, and TF withLF, LS being dropped from the analysis.)The analysis of variance on false alarm datashowed a significant key-distance effect,F(2, 86) = 9.18, p<.001, MSe = .037.There were no other significant effects. (At test over items for LS vs. LF gave asignificant difference by a one-tailed test,f(8) = 1.91.) Notice that with the youngestchildren there was only a key-distanceeffect, with no evidence of discrimination.This is consonant with the findings of Riley,McKee, Bell, and Schwartz (1967) that forchildren of this age, the pitch of tones in apair is much more salient than the intervalbetween them.

General Discussion

Figure 3 shows false alarm data from allfour experiments. The main point of interestis that the key-distance effect is apparentin all sets of data. The key-distance effectdid not appear as we expected in hit data,but it appeared in false alarm data acrossage and experience without qualitative dif-ferences. In fact the performance of adultswith unfamiliar melodies (Experiment 1)closely parallels the performance of childrenwith familiar melodies (Experiment 4). This


constant effect of key distance on falsealarms is the most important finding of thesestudies, Although the key-distance effectdid not occur for some subjects in certainconditions (for experienced subjects withunfamiliar materials in Experiment 1 and forinexperienced subjects with familiar tunesin Experiment 2), the accumulated datasuggest that the key-distance effect is notconsistently dependent on age or musicaltraining. Training, whether of the formalsort that differentiates our experiencedsubjects from the inexperienced or of theinformal sort that leads people to know a fewfamiliar tunes of their culture, generallyleads to superior performance in detectingchanges in interval sizes when melodiesare shifted in pitch. But the key-distanceeffect appears qualitatively over a widerange of task difficulty and is even presentwith kindergarteners, who are not able tosolve the transposition detection task at all.

It should be noted that professionalmusicians might perform flawlessly on ourtask, showing no key-distance effect due tofloor and ceiling effects (although profes-sionals would also be able to verbalize keydistance, even if they did not show it indiscrimination failures). Still it is interestingthat intelligent adults with some degree ofmusical experience find transpositionrecognition difficult and are especially proneto confusion between transpositions andsame-contour comparisons in a similar key.In this type of short-term memory task,sensitivity to key distance seems easier andmore natural than sensitivity to melodic-interval size.

The observed invariance of the key-distance effect strongly supports the psy-chological reality of key and mode in musicmemory (Dowling, 1978). At the same time,this invariance across such a wide range ofage and experience raises the possibilitythat key-distance effects result from theprocessing of auditory information inmemory in ways that have little to do withmusic. The simplest possible auditorytheory attributes the key-distance effect toshort-term memory for absolute pitch(Deutsch, 1975). In our experiments keydistance is correlated with the number of

.5

.4

0)V)co

S.2o>

0 -

a expt I -unf

aexpt 2-unf

expt 2-fam

expt 3 -f am

I

LF LN LSStimulus Type

Figure 3. False alarm rates to LF, LN, and LS luresfor familiar and unfamiliar standards in Experiments(expt) 1-4. (The data from all experiments arecollapsed over experience and age groups. unf =unfamiliar; fam = familiar.)

new pitches in the comparison, which didnot occur in the standard (Table 1). Forexample, in Experiment 1 LS comparisonsintroduced on the average 2.58 new pitchesout of 5 (52%), LN items introduced 3.22,and LF items introduced 4.44. Paralleltrends occurred with the lure types in Ex-periments 2 and 3. Hence, one might explainthe key-distance effect in terms of repeatedand nonrepeated pitches, that is, the greaterthe number of new pitches in a comparisonstimulus, the more different it sounds, andthe lower the probability of a response ofsame. To evaluate this pitch-repetition ac-count, we performed correlations acrossitems between new pitches in the compari-son and the false alarms it generated forLS, LN, and LF items grouped together.In Experiments 1 and 4, this correlationwas not significant, being close to zero inExperiment 1. However, the correlationsfor Experiments 2 and 3 did reach signifi-

514 JAMES C. BARTLETT AND W. JAY DOWLINO

cance with a one-tailed test at the .05 level,giving r(18) = -.39 and r(13) = -.49, re-spectively. The pitch repetition view canneither be accepted nor rejected on thisevidence.

We prefer the view that key-distanceeffects reflect musical schemata that are tosome degree culture specific but acquiredearly in life. According to this view alistener hearing a melody assimilates it to aninternal schema that represents a particularmode in his culture. This modal scale istemporarily anchored to a specific pitchlevel, thus representing what we are callinga key. The mode-key schema governs ex-pectations for the pitches of subsequentnotes in the melody. The occurrence of anew pitch is disruptive only if it violatesthe schematic representation of the key.Thus, it should not be the occurrence ofnew notes per se that causes an impressionof dissimilarity but rather the occurrence ofnotes foreign to the mode-key schema.However, we have no direct evidence thatmode schemata influence performance inshort-term memory tasks such as those usedhere. A critical test of a pitch similarityversus a mode schema account might in-volve a rigorous control of the number ofnew pitches that distinguish LN and LFcomparisons from standard stimuli. Thendifferences in false alarm rates to LN andLF comparisons having the same number ofnew pitches could not be attributed toabsolute pitch memory and would supportthe schema view. Such an experiment re-mains to be done.

The present results raise another questionthat is completely independent of the pitch-repetition versus mode-schema issue. Thisquestion concerns the relative retentioncharacteristics of key and scale informationversus melodic-interval information. It isfrequently stated that people do not gener-ally remember the absolute pitches inmelodies for appreciable lengths of time butthat long-term memory for melodies in-volves memory for only interval sizes.Dowling (1978) took this view, and Deutsch(1975) stated thatwe recognize a transposed melody much more readilythan we recognize the key it was played in. Memory

for the abstracted relationships between the componenttones of the melody must therefore be more enduringthan memory for the tones themselves, (p. 122).

Few would quarrel with these words, yet thepresent experiments show that with shortretention intervals detection of key similar-ity appears much easier than detection ofinvariance of melodic-interval size. It wouldappear that the relative importance of keyinformation in memory falls drastically asretention interval is lengthened, whereasthe relative importance of interval informa-tion increases. This question, too, awaitsfurther research.

A final issue concerns our failure to ob-serve a significant key-distance effect withtargets in Experiments 2, 3, and 4. Ceilingeffects on target recognition might explainthis failure with familiar melodies and adultsubjects in Experiments 2 and 3 (Tables 4and 5), but target recognition was .75 orlower with unfamiliar melodies and adultsubjects (Experiment 2) and with familiarmelodies and children (Experiment 4). Yet,a reliable key-distance effect was neverobtained with targets. We see three possibleexplanations for this invariance of targetrecognition. The first1 is that subjects mightperceive the tonality and key of transposi-tions more easily than those of lures usedin these experiments. Transpositions (aswell as standards) often began on the tonicof their key, and, when they did not, thetonic was usually the first accented note ofthe melody. This was less often true of LS,LN, and LF items, and it is plausible thatsubjects had more difficulty extracting in-formation about key from lures than fromtargets. It is possible that a key-distanceeffect occurs only when there is success-ful extraction of key information from astandard stimulus and failure to extract keyinformation from a comparison. In suchcases, subjects might be influenced by thecompatibility between the key of the stand-ard and the notes of the comparison stimulus.This compatibility between key of standardand notes of comparison would be strongerfor LS and LN items than for LF. In con-

1 We thank an anonymous reviewer for suggestingthis alternative.


trast, when subjects are able to extract keyinformation from both standard and com-parison stimuli, they might be able toseparate key information from interval in-formation and to base their decisions solelyon the latter. A second possible explanationfor the absence of a key-distance effectwith targets is the relatively small range ofkey distance sampled with these stimuli.Whereas the key distance of lures variedfrom same-key to far-key, that of targetsvaried only from near-key to far-key. (Asmentioned previously, music theory doesnot allow the possibility of a transpositionin the same key as a standard.) A thirdexplanation is that a large shift in key be-tween a standard and a transposition makesthe interval matches more noticeable to thelistener. A near-key transposition will cer-tainly sound similar to its standard, butlisteners might be unable to analyze thesource of this similarity. Knowing that theirtask is to recognize transpositions only,they may often reject such near-key itemsbecause they are unsure that intervalmatches are contributing to the similaritythey experience. A far-key transpositionmight be less confusing in this respect. Lis-teners might be aware of the changed key (orchanged notes), so that any similarity theydetect can be attributed to interval matches.Hence, the greater noticeability of intervalmatches with far-key transpositions mightmask the key-distance effect with theseitems. The present research has clearlyraised more questions than it has answered,and the most puzzling of these concern the

mechanism by which subjects separateinterval matches from other sources ofsimilarity between melodies.

ReferencesAttneave, F., & Olson, R. K. Pitch as medium: A

new approach to psychophysical scaling. AmericanJournal of Psychology, 1971,54, 147-166.

Cuddy, L. L., & Cohen, A. J. Recognition of trans-posed melodic sequences. Quarterly Journal ofExperimental Psychology, 1976, 28, 255-270.

Deutsch, D. The organization of short-term memoryfor a single acoustic attribute. In J. A. Deutsch(Ed.), Short-term memory. New York: AcademicPress, 1975.

Dowling, W. J. Scale and contour: Two componentsof a theory of memory for melodies. PsychologicalReview, 1978,85, 341-354.

Dowling, W. J., & Fujitani, D. S. Contour, interval,and pitch recognition in memory for melodies.Journal of the Acoustical Society of America, 1971,49, 524-531.

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

Grier, J. B. Nonparametric indexes for sensitivityand bias: Computing formulas. PsychologicalBulletin, 1971, 75, 424-429.

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

Riley, D. A., McKee, J. P., Bell, D. D., & Schwartz,C. R. Auditory discrimination in children: Theeffect of relative and absolute instructions on re-tention and transfer. Journal of ExperimentalPsychology, 1967, 73, 581-588.

Swets, J. A. The relative operating characteristic inpsychology. Science, 1973, 182, 990-1000.

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

Zenatti, A. Le developpement genetique de la per-ception musicale. Monographies Francoises dePsychologie, 1969 (Whole No. 17), 1-110.

Received June 25, 1979 •

Documents

Recognition of Transposed Melodies: A Key-Distance Effect ... · Since these four experiments share many features, these will be described in a general method section. Table 1 shows