TONAL PROFILES OF ARTIFICIAL SCALES: IMPLICATIONS FORMUSIC LEARNING

Sarah C. Creel and Elissa L. Newport

University of RochesterDepartment of Brain and Cognitive Sciences

Rochester, NY, US

ABSTRACTMusic researchers have noted that structurally important tonesin a melody are related to one another by perfect intervals (fifthsand octaves) and occur frequently and in melody-final position.Here we ask whether the latter two cues—frequency and finalposition—have melodic significance for tone collections lackingperfect intervals. Three sets of melodies were generated from awhole-tone scale (C4-A#4). In one condition, E occurred bothfinally and most frequently. In another, E occurred infrequentlybut finally, while G# occurred most frequently. In a thirdcondition, all tones occurred with equal frequency. Participantswere briefly familiarized to one set of melodies, then heard eachmelody from the set, followed by each probe tone, creating arating profile for each set. Participants in all conditions ratedtones that had occurred in the melodies higher than tones thathad not. Frequency and finality both exerted effects. Averagedratings in each condition did not correlate significantly withKrumhansl and Kessler’s [7] major scale profiles, suggestingthat ratings were not an artifact of familiarity with Westerntonal music. The present work this shows effects of frequencyand final position on note significance, without perfect intervalrelationships between the tones.

1. INTRODUCTION

Listeners both within and outside musical cultures perceivedifferences in the prominence of different tones in a collection.In the “probe tone” task [8], listeners are presented with thesame chord sequence or melody multiple times, each timefollowed by a different note of the chromatic scale. The listenerrates each chromatic probe tone for goodness-of-fit to thepreceding melody. Validating music-theoretic predictions,listeners rate tones of greater importance in the key of theexcerpt with higher goodness-of-fit ratings. The highest rating isgiven to the tonic, or central note, of the musical excerpt (suchas the tone C in C major), followed by other tones of the tonictriad (E, G) and the other tones of the scale (B, D, A, F), withnon-scale tones receiving the lowest ratings [7,8]. The highest-rated tones also tend to be the most frequently used tones andtend to appear as the final note of a melody. These effects areevident even in culturally unfamiliar music, though expertise ina particular style leads to more well-formed expectations ofmelodic continuation [2,8,9].

The study of short-term memory (STM), especially serial recalltask performance, is complementary to the probe tone results.Murdock [11] asked participants to memorize lists of words andobtained the now famous “serial position curve,” in which more

recent items are better recalled (as are earlier items whichparticipants have had more time to rehearse). Slobin [12] pointsout that in language acquisition, children may direct attentionpreferentially toward the ends of units. Deutsch [4] found in amatching task (standard tone… distractors… comparison tone)that short term memory for tones was affected by variousproperties of the intervening sequences of distractor tones. Mostpertinent, if the standard tone was repeated in the distractorsequence, memory was facilitated.

In probe tone studies, tones that appear frequently in a melodyare likely to have stronger short-term perceptual representations,and are thus more likely to be rated highly when presented aspost-melodic probes. Similarly, notes which are more recentlypresented (toward the end of the melody) are less likely todecay, and also may receive a greater share of attention over thecourse of learning [12]. Such effects may be the locus of naïveparticipants’ sensitivity [2,9] to the structural properties ofunfamiliar music. The STM model has less explanatory powerfor the effects of expertise on probe ratings; long-term memorymay contribute to greater stability of pitch judgments.

An important question concerns the role of learning indetermining what tones in a collection are structurally important.Are certain tones (for example, by virtue of their intervallicinterrelationships) preferred a priori, with increased frequencyof use and placement at the end of a melody resulting from thispreference? Or are frequency and recency the cues which leadthe listener to perceive certain tones as structurally important?Two highly distinct views of tonality perception offer differentweightings of the role of learning. Butler and colleagues [1]propose a theory of the calculation of tonal center that consistsof three hypotheses. The primacy hypothesis states that listeners,given only a single note, will perceive that note as tonic until astronger candidate comes along. The rare-interval hypothesissuggests that pitch intervals which occur less often (betweenfewer pairs of notes in a scale) are more valuable in finding thetonal center, as they provide unambiguous information to theidentity of the major scale. The temporal order hypothesis statesthat familiar orderings of scale tones are more informative forkey identity. This view seems to imply that once the intervallictemplate for a scale is learned, note frequency is a relativelyunimportant cue. This fails to explain how a listener becomesaware that she is listening to a major-mode composition in thefirst place; presumably, some other process or cue indicates this,and analysis of order and rare-interval information proceedsaccording to this assumption. This view predicts that the absenceof rare intervals should dampen one’s sense of tone importance(produce an undifferentiated tonal profile). A differentperspective is that of Krumhansl and colleagues [7,2,9]. On theirview, listeners are highly sensitive to the frequency of

2.3 Procedure

PsyScope [3] software was used to present the stimuli.Participants in each condition initially received 36 trials oflistening exposure (3 exposures of each melody) before anyprobe tone judgments were made. Following exposure, theywere instructed to listen to each melody, followed by a probetone (after a 500-ms pause), and to rate how likely it was thatthe probe tone had been contained in the preceding melody. Thefirst 12 trials of randomly-chosen melody followed byrandomly-chosen probe tone were discarded as practice trials.The remaining 144 combined all melodies with all 12 probetones in random orders which were different for eachparticipant.

3. RESULTS AND DISCUSSION

First, all ratings of a single probe tone for a single participantwere averaged together to yield an average rating for thatparticipant. This resulted in a single 12-value probe-tone profilefor each participant. Then, planned ANOVAs were conducted ineach condition separately for several contrasts of interest. Toassess the possible influence of major-scale familiarity onratings, correlations between averaged ratings in each condition(Figure 1) and all major-scale profiles7 were calculated.

3.1 Tone comparisons

We hypothesized that if participants were able to discern thestructure of the scale being used, then they should rate tonesoccurring in the melodies more highly than tones not occurringin the melodies. Accordingly, in all conditions, participantsrated tones present in the stimuli higher than tones not present(F1(1,11) = 40.82, F2(1,11) = 12.12, F3(1,11) = 60.01, all p <.01).

A second hypothesis was that, if participants were sensitive tofrequency-of-occurrence information, they should rate morehighly the tones which occurred more often. Therefore, wecompared ratings of tones which occurred four times to toneswhich occurred twice, and tones which occurred twice to thoseoccurring only once. In the frequent=final condition (Figure 1a),the most frequent tone (E, also the final tone) was rated morehighly than twice-occurring tones (F(1,11) = 103.36, p < .001),though twice-occurring tones were not rated more highly thansingly-occurring tones (F(1,11) = 1.55, ns). Similarly, in thefrequent≠final condition (Figure 1b), the most frequent tone(G#) was rated more highly than the second most, but theseconds were not rated higher than the singly-occurring tones(F(1,11) = 9.35, p < .05; F(1,11) = 2.72, ns).

A third hypothesis was that, if frequency of occurrence andfinality exerted separate effects on ratings, then both frequentand final tones should have been rated highly. Indeed, in thefrequent≠final condition, the final tone E, in addition to themost frequent G#, received higher ratings than the average ofthe other tones present (F(1,11) = 6.13, p < .05), and the ratingsE and G# were indistinguishable (F(1,11) = .33, ns). Bycontrast, in the frequent=final condition, only E received ratingsabove the average of other occurring tones, and exceededratings for G#, in this condition only a singly-occurring tone(F(1,11) = 57.69, p < .001).

To address the concern that spurious results might have beengenerated from tone preferences unrelated to the characteristicsof the tones used in the experiment, we examined the controlcondition (Figure 1c). Informal visual inspection leads to theobservation that participants seemed to prefer midrange tones.This is not unlike previous results [8] with non-musicians, inwhich tones proximal in pitch to the pre-probe note were ratedmore highly. Statistically, while the tone G# was rated higherthan other occurring tones (F3(1,11) = 8.52, p < .05), E was not(F3(1,11) = .05, ns). This G# preference appears to be a range-mediality effect, as corroborated by a test showing that F#, alsoa range-medial tone, also outrated the other occurring tones(F3(1,11) = 17.24, p < .01). In neither of the other conditionswas there any such preference for F# (F1(1,11) = 5.75, p < .05 inthe opposite direction, F2(1,11) = .03, ns). We use these data asconfirming evidence that the results in the first two conditionstruly reflected effects of both recency (final position) andfrequency-of-occurrence information.

3.2 Correlations with major scales

We also examined the question of major scale influence bycalculating correlation coefficients of the average profile in eachcondition with Krumhansl and Kessler’s [7] major scale profiles.Given the strength of the major third (M3) relationship betweentones in the artificial stimuli and between the first two tones ofthe tonic triad in the major mode, one might reasonably expectsome similarity to exist in ratings for the current stimulusprofiles and major scale profiles. However, these 36 correlationsranged from r = .-.32 to r = .49, and none achieved statisticalsignificance, suggesting that there is not an influence ofsimilarity to any major scale evident in the ratings provided byour listeners. This compares with correlations between averagedobtained profiles in each condition and the frequencies ofoccurrence of the tones in that condition of r1 = .89 (p< .0001),r2 = .66 (p = .0165), and r3 = .82 (p= .0004), for first, second,and third conditions respectively.

4. CONCLUSIONS

Previous probe tone studies [8,2,9] showing positive correlationsof frequency of occurrence with tone goodness-of-fit ratingshave examined natural musical stimuli, or artificial stimuli [10]including perfect intervals (P5s). In this experiment, we utilizedartificial musical stimuli which lacked any perfect intervals, andfound that listeners showed effects similar to previous probetone studies: they rated frequent tones as more important thaninfrequent tones, and rated occurring tones more highly thannon-occurring tones. Melody-final tones were also given highratings. Though it is perhaps problematic to equate tonepreferences with judgments of tonal center, we suggest based onour results that the importance of arbitrarily-chosen tones in aset may be augmented by the addition of the cues of recency andfrequency. A perfect fifth or octave interval, or rare pitchintervals, neither of which were present in our stimuli, may notbe necessary for recognition of important tones in a set.

We also found that listeners’ responses were not highlycorrelated with tonal profiles for any major scale. This differsfrom previous research [2,9] finding that ratings of unfamiliarmusical stimuli are similar to ratings for Western tonalstructures. Our results likely reflect a greater dissimilaritybetween our stimuli and Western tonal stimuli than between

Western and non-Western natural musical stimuli, as well as thelisteners’ sensitivity to frequency of occurrence and recency oftones.

Our results are consonant with the STM literature [4,11]. Iftones are rated more highly when they are better recognized,and they are recognized more accurately when they occur moreoften in the preceding context (or have occurred very recently),it stands to reason that recent and frequent probes are givenhigher ratings. The extent to which these expectations may beinternalized and generalized to new situations is not yet known.Recency and frequency may not necessarily be instructive inreal music learning, but if they were it would more readilyexplain such phenomena as malleability of tonal perception (asseen in studies of the effects of expertise in non-Westernmusical styles [2,9]), and, comprehension of multiple tonalsystems (e.g. the major/minor dichotomy, or more dissimilarsystems such as classical and jazz styles).

Future work using artificial musical stimuli will focus on therole of learning (in the long term) in perception of musicalmicrostructure, and on the roles of other cues in ascertainingtone importance, such as familiarity of interval size. A currentproject in our lab is exploring the role of simple-ratio intervalsize, using stimuli contructed from a whole-tone scalecontaining either 4:5-ratio major thirds (M3s), or M3s that arestretched or compressed relative to the simple-ratio M3. Willthe simple ratio aid listeners in determining the relativeimportance of tones? The aim of this exploration is to discoverboth the malleability and the limits of human tonal perception,aiding our understanding of human cognition and suggestingnew directions for musical creativity.

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We are grateful to Dick Aslin, Davy Temperley, and BetsyMarvin for helpful comments on this research.

This research was supported in part by a NSF GraduateResearch Fellowship to SC, and NIH grant DC00167 and NSFgrant SBR-9873477 to EN.