melodic anchoring and tone duration · numerous instances of melodic anchoring exist in tonal...

Music Perception © 1994 by the regents of the Winter 1994, Vol. 12, No. 2, 199-212 university of California

Melodic Anchoring and Tone Duration

BERNICE LADEN University of Washington

Bharucha (1984) defined a cognitive principle, melodic anchoring, that outlines the conditions under which tones are perceived as stable points in a melody. He found that temporal order can determine which of two tones is perceived as being more stable. The experiment described in this article extends Bharucha's work by examining melodic anchoring when melody tones are of unequal duration. Listeners (novices and musicians) heard short, tonally ambiguous melodies that were followed by a musical chord. The listener's task was to rate how well the chord seems to fit the melody. A chord by durational pattern interaction was found. The results indicate that although temporal order is a primary factor in melodic anchoring, duration can facilitate or weaken its effect, depending on how the durational pattern aligns with the pitch sequence of the melody.

use a number of compositional devices to establish a tonality. They also use techniques that allow them to deviate from an

established tonality in such a way that adds interest to the music. This article is concerned with one such practice - that of using out-of-key tones followed by in-key tones - and how this practice is perceived by the listener. Nonkey tones create instability that if left unresolved can sound like an error or may leave the listener hanging with anticipation for resolution. Successful composers in the tonal idiom are skilled at resolving such points of instability. What are the particular conditions that allow the listener to perceive this resolution?

Bharucha (1984) reported a comprehensive study on this issue. He defined a cognitive principle, melodic anchoring, that outlines the conditions that favor resolution. He pointed out that the resolution of dissonance is a dynamic process. It requires the establishment of a tonality, the deviation from it, and the return to it. The deviation and return are typi- cally small, a kind of blemish in the tonal fabric of the piece. One of Bharucha's most important findings was that temporal order can deter-

Requests for reprints may be sent to Bernice Laden, Systematic Musicology Division, School of Music (DN-10), University of Washington, Seattle, WA 98195. (e-mail: bladen @ u.washington. edu)

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200 Bernice Laden

mine what is perceived as a stable point in a melody. Stability always follows instability, and not the reverse. In tonally ambiguous melodies, Bharucha found that more recent events are more likely to be perceived as stable, or anchor points.

Numerous instances of melodic anchoring exist in tonal music. Ideal conditions for listeners to perceive resolution occur when an out-of-key tone is followed by an in-key tone, and the musical interval between the two tones is a semitone. For example, in a C-major melody an F# tone is followed by a G. The F# is not a member of the key of C-major - it is out of the tonal context. If randomly inserted into a C-major melody, the Ffl tone is apt to sound like a wrong note. However, an F 9 followed by a G is likely to be perceived as a correct note, although chromatic, because it moves by semitone to a tone that is in C-major. In effect, the G perceptu- ally anchors the Ffl, making it sound stable within the tonal context. Anchoring may either be immediate - the unstable pitch followed immedi- ately by a stable one (F#to G), or delayed - an intervening pitch between the stable and unstable pitch (Ftf-A-G).

Bharucha demonstrated that temporal order determines which of two tones is perceived as more stable - the perceptual anchor point. In two of his experiments (Experiments 1 and 4), subjects heard short melodies composed of interleaved tones from either two or three different chords. In a forced-choice paradigm, the subjects decided which of two chords fit the melody best. In one experiment, subjects heard a melody composed of B- C-D#-E-F#-G. Immediate melodic anchoring predicts that B resolves to C, D# to E, and ¥tt to G. Therefore subjects were expected to prefer the C- major chord over the B-major chord. If the melody were played in reverse, melodic anchoring predicts that the B-major chord would be preferred over the C-major chord.

Bharucha examined delayed anchoring with chord tones interleaved from B-major, C-major, and Db-major chords. The ascending melody used in this condition was Db-B-C-F-Dtf-E-Ab-F8-G. Melodic anchoring predicts a preference for the C-major chord over either Db-major or B-major chords. By delayed anchoring, Db resolves to C, F to E, and Ab to G; by immediate anchoring, B resolves to C, D# to E, and F# to G. Bharucha found anchoring effects for listeners with an average of 3 years of music instruction but no effect was found for listeners who had no formal music instruction. However, his four other experiments elicited a melodic anchoring effect in novices and in moderately trained subjects. Two of these experiments used a recognition memory paradigm (Experiments 2 and 5), and the other two used a chord accompaniment paradigm (Experiments 3 and 6).

Bharucha's study provides evidence for anchoring effects in music, although only tones of equal duration were used in the stimulus melodies.

Melodie Anchoring and Tone Duration 201

Evidence for the importance of tone duration in music cognition was reported by Castellano, Bharucha, and Krumhansl (1984) in their study of the perceived tonal hierarchies of North Indian music. They examined differences in tonal hierarchies between Indian and Western listeners. Al- though duration was not manipulated as an independent variable, actual Indian compositions were used as stimuli. Their results indicated a significant correlation between tone duration and probe-tone ratings. Tones that were heard for a longer amount of time in the stimuli were rated higher than those not heard for as long. The correlations were significant for both groups of listeners, with no difference between the groups.

Thus, the purpose of the experiment reported here is to explore melodic anchoring when tones in a melody are of unequal duration. The hypothe- sis tested is that manipulation of duration can either facilitate or inhibit resolution, and this will depend on how duration aligns with temporal order.

Tones of relatively long duration may be processed more than tones of short duration because they occupy cognitive resources for a longer amount of time. So by varying duration, it may be possible either to facilitate or weaken melodic anchoring. If a short-long-short-long-short- long pattern of durations is coupled with a melody composed of the notes B-C-D#-E-F#-G, then C, E, and G may be processed more than B, D#, and ¥tt. In this case, two factors may operate together - durational pattern and

temporal order. Because the durational pattern emphasizes the chord tones of the C-major chord (C-E-G), C-major should appear as a good fit.

According to the temporal order effects reported by Bharucha, the C-

major chord should seem to be a good fit as well. The two factors operat- ing together should result in the C-major chord sounding as a better fit than for a similar melody in which the tones were of equal duration. In this

way, the duration of the tones could facilitate temporal order. If the durational pattern is reversed, then B, D#, and F# should be

processed more than C, E, and G. This durational pattern underscores the chord tones of B major (B-D#-F#), the chord not predicted by melodic

anchoring. In this case, the factors of duration and temporal order may act

against each other. One of two outcomes could result. Subjects might select the B-major chord as the best fitting chord for the melody, or they might still select the C-major chord but feel the chord does not fit as well as when the durational pattern is reversed, or when the melody tones are of equal duration. Thus the effect attributable to temporal order could be weakened.

In two experiments, Bharucha (1984) used a forced-choice paradigm in which subjects heard the melody paired first with one chord and then another. Thus, the listener had to keep in short-term memory the melody paired with the first chord choice while the melody and the second chord

202 Bernice Laden

choice were being presented. Even though Bharucha controlled for order of chord presentation, this method imposes a substantial load on memory, and that may explain why he did not find effects with novice listeners.

The current method attempts to avoid the problem by using a rating response paradigm rather than a forced-choice paradigm. A melody is followed by one chord, and subjects rate, on a scale of 1-7, how well the chord fits the melody. This change should enable novices to do the task more easily because it places fewer memory demands on the listener. If melodic anchoring is robust, its effect should be observed in a rating task. This seems reasonable to assume, if one considers that Bharucha found anchoring effects in novices and experts when using other paradigms.

Materials

The durational patterns and pitch sequences used to construct the melodies are depicted in Figure 1. Although melodies were randomly presented in six different transpositions (i.e., the first tone of each transposition was B, C, Db, D, Eb, and E), responses were collapsed over transposition, and melodies are referred to as if the same set of tones were used for each stimulus.

Two melodic conditions were used: immediate anchoring and delayed anchoring. The immediate anchoring melodies were composed of tones interleaved from two major chords whose roots were separated by a semitone (e.g., B major and C major). The delayed anchoring melodies were composed of tones interleaved from three major chords, each chord separated by either a semitone or tone from the other two chords (e.g., B major, C major, and Db major). Only ascending melodies were used in both the immediate and delayed anchoring conditions. Melodies in either the delayed or immediate anchoring condition were permuted.

Melodies based on two interleaved chords, the immediate anchoring condition, contained six tones. Those based on three interleaved chords, the delayed anchoring condition, contained nine tones. The six-tone melodies were presented with three durational patterns: (1) even tones longest (i.e., the tones of the C-major chord), (2) odd tones longest (i.e., the tones of the B-major chord), and (3) all tones of equal duration. The nine-tone melodies were presented with four durational patterns: (1) tones 3, 6, and 9 longest (i.e., the tones of the C-major chord), (2) tones 1, 4, and 7 longest (i.e., the tones of the B-major chord), (3) tones 2, 5, and 8 longest (i.e., the tones of the Db-major chord), and (4) all tones of equal duration.

There were 36 trial types in the immediate anchoring condition: 5 pitch


Fig. 1. The seven melodies used for immediate and delayed anchoring. The first three melodies follow the principle of immediate anchoring. C-major chord tones are longest in duration in melody 1, B-major chord tones are longest in melody 2, and all tones are of equal duration in melody 3. The last four melodies follow the principle of delayed anchoring. C-major chord tones are longest in duration in melody 1, B-major chord tones are longest in melody 2, Db-major chord tones are longest in melody 3, and melody 4 contains tones of equal duration.

sequences (six permutations of the ascending sequence) x 3 durational patterns (even tones longest, odd tones longest, and equal duration) x 2 target chords (C-major chord, B-major chord). There were 72 trial types in the delayed anchoring condition: 6 pitch sequences (six permutations of the ascending sequence) x 4 durational patterns (tones 1, 4, and 7 longest; tones 2, 5, and 8 longest; tones 3, 6, and 9 longest; and equal duration) X 3 target chords (C-major chord, B-major chord, Db-major chord). In addition, 10 practice melodies were composed. The total number of melodies the subjects heard was 118, including the practice melodies. Melodies were presented in one of two random orders.

204 Bernice Laden

Apparatus

Melodies and target chords were performed in real time under the control of an IBM- AT computer. The computer was interfaced to a Yamaha DX-7 synthesizer with a Roland MPU-401 MIDI (musical instrument digital inter- face) processing unit. A flute preset from the Yamaha DX-7 synthesizer produced all melody and chord tones. Stimuli were presented over a loud- speaker at a comfortable listening level, in a sound-attenuated booth. An IBM computer keyboard was used as a response device, and responses were written to a data file on the computer's hard disk.

Method

SUBJECTS

Two groups of subjects participated: novices and musicians. Twenty-nine novices volunteered for credit toward a psychology course. Novices had received, on average, 3.2 years of voice or instrument instruction: almost 1 year at the high school level and 2.2 years at the elementary school level. One person had just begun lessons at the college level. Five people had taken one music theory class at either the high school or college level. None of them reported being either an amateur or professional musician; none performed in a music ensemble. Twenty-eight of the 29 novices listened to music for an average of 18 hr per week.

Seventeen musicians volunteered to participate for monetary compensation ($5.00). Musicians had to meet one of the following criteria: (1) be a currently enrolled undergradu- ate or graduate student officially accepted as a music major, or (2) possess an undergradu- ate or graduate degree in music. Musicians, on average, had 9.8 years of music lessons: 3.5 years were at the college level, 3.5 years at the high school level, and 2.8 years at the elementary school level. Fourteen were currently taking lessons. Musicians had taken 3.1 years of music theory at the college level and an average of one semester of theory at the high school level. Twelve musicians were currently in a music ensemble and had been in this ensemble for a mean of 4.1 years. The musicians listened to music for an average of 23 hr per week.

PROCEDURE

Subjects first completed a questionnaire concerning their musical background. Then they were tested one at a time in a sound-attenuated booth. Instructions were given both verbally and displayed on a computer monitor. The rating procedure and instructions were modeled after the probe-tone method used by Krumhansl, Sandell, and Ser- geant (1987).

Metronome beats preceded each stimulus primarily to alert the subject to the start of the melody and also to establish a pulse. With or without beats, duration is confounded with accent, as subjective accentuation is a well-known phenomenon. It is assumed that beats preceding the stimulus establish a consistent accent pattern between subjects, thus control- ling for subjective accents. As the timbre and loudness level were the same for all tones, there were no objective cues intended to convey a specific meter.

The duration of tones varied so that relatively long tones occurred on a pulse and the pattern of long and short tones repeated throughout a melody (e.g., short-long-short-long-


short-long). Both the pulse and the pattern of durations were predictable, and they were consonant with each others in that tones of relatively long duration always occurred on the pulse. When the melody began, the metronome beats ceased.

The melody was followed by a 2-s pause. Then, the metronome beats and melody were repeated, followed by a 1.5-s delay. Finally, the target chord was played for 1.5 s. The subject's task was to rate how well the target chord seemed to fit the melody. A 7-point rating scale was used, with 1 corresponding to "fits poorly" and 7 corresponding to "fits well." Subjects responded by pressing a key on a computer keyboard.

Results

The immediate and delayed anchoring conditions were analyzed sepa- rately by using a repeated measures analysis of variance. A test of simple effects was done when appropriate. An analysis of variance showed presentation order had no effect [F(l,44) = 1.41, p = .24].

IMMEDIATE ANCHORING DATA

Musical experience had no effect [F(l,44) = 1.38, p = .25]. This indicates that the overall mean scores between the two groups were similar regardless of musical background. The mean for musicians was 4.90, whereas novices had a mean of 4.68.

There was a main effect of target chord [F(l,44) = 54.6, p < .001]. This is because the C-major target chord was rated higher (5.53) than the B- major target chord (4.05) regardless of durational pattern. This result

supports Bharucha's findings that the pitch sequence is biased more toward one tonal interpretation than the other.

As expected, there was no main effect of durational pattern [F(2,88) =

.3, p = .49]. Mean ratings for durational patterns 1, 2, and 3 were 4.84, 4.80, and 4.73, respectively.

There was a significant durational pattern by target chord interaction [F(2,88) = 11.5, p < .001]. Mean target chord ratings by durational

table 1 Mean Ratings for Immediate Anchoring, Two Target Chords by Three

Durational Conditions

Chord Emphasized by Durational Pattern

C Major B Major Equal Duration Target Chord 12 3 Mean

C major 5.87 5.17 5.56 5.53 B major 3.81 4.44 3.89 4.05 Mean 4.84 4.81 4.73

206 Bernice Laden

pattern are listed in Table 1. In durational pattern 1, the chord tones of C major are longest, in pattern 2 the B-major chord tones are longest, and pattern 3 uses tones of equal duration. Each target chord received its highest rating when it followed the melody whose durational pattern stressed the tones of that chord. The C-major target was rated highest (5.87) when it followed durational pattern 1. The B-major target chord was rated highest (4.44) for pattern 2. To examine these results more closely, difference scores were calculated by subtracting the ratings of the isochronous condition from the ratings of the two other durational conditions, on a subject-by-subject basis. The resulting adjusted mean ratings under the two durational conditions are depicted in Figure 2.

A post-hoc test of simple main effects indicated significant differences due to the durational pattern for both the C-major target chord (p < .01) and for the B-major target chord (p < .001). Figure 2 shows that when the durational pattern increased the ratings for one target chord, it decreased the ratings for the other target chord.

Although there was no difference in the means of the responses due to musicianship, there was a difference in the range of ratings between musicians and novices (3.4-6.4 vs. 4.1-5.4, respectively). This is indicated by a significant musicianship by target chord interaction [F(l,44) = 36.2, p < .001]. Despite the fact that both groups were instructed to develop a rating strategy that enabled them to use the full range of the 7-point rating scale,

Fig. 2. A graph of the target chord ratings as a function of durational patterns 1 (C-major chord tones emphasized) and 2 (B-major chord tones emphasized). The rating for the isochronous (equal duration) pattern has been subtracted from patterns 1 and 2 in order to illustrate better the effect of tone duration. An adjusted rating of 0 would indicate that target chords' ratings were no different from ratings in the isochronous condition.


the musicians appeared to use a strategy that enabled them to use a wider range of the scale than the novices did.

DELAYED ANCHORING DATA

Musical experience did not have a significant effect [P(l,44) = 1.2, p = .28]. The mean for musicians was 4.30, and the mean for novices was 4.50.

There was a main effect of target chord [P(2,88) = 49.7, p < .001]. The C-major target chord was rated highest, 5.25. This rating was signifi- cantly higher (p < .01) than the mean rating of either the B-major target chord (3.95) or the Db -major target chord (4.01). The higher rating for C major indicates that the melody was biased toward C major, as predicted by the principle of melodic anchoring and reported previously by Bharucha. Durational pattern was not significant [F(3,132) = 1.3, p =

.26]. Means for patterns 1, 2, 3, and 4 were 4.38, 4.34, 4.38, and 4.51, respectively.

There was a durational pattern by target chord interaction [JF(6,264) =

8.5, p < .001]. Mean target chord ratings by durational pattern are listed in Table 2. In pattern 1, the chord tones of C major were longest, in

pattern 2, the tones of B major were longest, in pattern 3, the tones of D major were longest, and in pattern 4, all tones were of equal duration.

A post-hoc test of simple effects indicated that durational pattern signifi- cantly affected ratings for the three target chords: C major (p < .001), B major (p < .05), and Db major {p < .001). Although the C-major target was always rated more highly than the other two target chords, C major received its highest rating (5.61) when the chord tones of C major were emphasized in the melody. A similar pattern can be seen for the two other targets. B major received its highest rating (4.19) when the chord tones of B major were emphasized in the melody. Db major received its highest rating (4.40) when the chord tones of Db major were emphasized in the

table 2 Mean Ratings for Delayed Anchoring, Three Target Chords by Four

Durational Conditions

Chord Emphasized by Durational Pattern

C Major B Major Db Major Equal Duration Target Chord 12 3 4 Mean

C major 5.61 5.08 4.95 5.34 5.25 B major 3.80 4.19 3.79 4.02 3.95 Db major 3.74 3.75 4.40 4.16 4.01 Mean 4.38 4.34 4.38 4.51

208 Bernice Laden

melody. Difference scores for the three nonisochronous durational conditions are plotted in Figure 3.

Although there was no main effect of musicianship, there was a significant musicianship by target chord interaction [F(2,88) = 20.6, p < .001]. As explained in the results for the immediate anchoring condition, this interaction can be attributed to the difference in the range of the responses between the musicians and the novices (3.3-5.9 vs. 4.0-5.3).

Discussion

The results provide a replication of previous findings in addition to uncovering a few more details concerning the conditions that favor melodic anchoring. The results for the condition in which melody tones were of equal duration concur with Bharucha's (1984) earlier findings that temporal order affects what listeners perceive to be anchor points in ambiguous melodies. The higher ratings for the C-major chord indicate that the tones C, E, and G were perceptual anchors. Each of these tones was second in the interleaved chord tone pairs. If temporal order did not have an effect, then ratings for chords in the equal-duration condition would have been the same.

The absence of a main effect of durational pattern was expected. This is

Fig. 3. A graph of the target chord ratings as a function of durational patterns 1 (C-major chord tones emphasized), 2 (B-major chord toness emphasized), and 3 Db-major chord tones emphasized). The rating for the isochronous (equal duration) pattern has been subtracted from patterns 1, 2, and 3 in order to illustrate better the effect of tone duration. An adjusted rating of 0 would indicate that target chords ratings were no different than ratings in the isochronous condition.


explained by the differences in chord ratings for each durational pattern. When one chord received a relatively high rating, the other chord ratings decreased. When the ratings were collapsed over target chord, the varia- tions averaged out so there was virtually no difference attributable to duration alone.

However, the interaction of durational pattern with target chord indicates that duration, as well as temporal order, can affect listeners' perception of the resolution of tonal instabilities. Each chord received its highest rating when the associated melody tones had the longest duration. This supports the notion that the amount of cognitive processing a tone receives is proportional to its duration and could have implications for the representation of duration in models of music cognition. Bharucha and Stoeckig (1986, 1987) proposed that the music cognitive system can be modeled as a spreading activation network. In the MUSACT model developed by Bharucha (1987), the most recent events are the most active and hence have a greater effect on cognition. This account agrees with the finding that melodic anchoring is due in large part to temporal order.

I (Laden, 1989) developed a model that extended the MUSACT model of music cognition and was instantiated as a computer simulation. The simulation, referred to as Listener, is based on the assumption that non-

pitch factors act to modulate processing and that duration is important to tonal processing. In Listener, a tone that is longer in duration than adja- cent tones will cause more activation to spread through the network sim-

ply because of its length. Tones of particularly long durations may cause activation to saturate to a ceiling level. Listener has a change-detection mechanism to account for possible effects of subjective accent and a work-

ing memory component. What is of interest here is Listener's output in

response to the melodic anchoring task. Stimuli from the immediate and delayed anchoring experiment were

input to the model in a vector format in which each vector represents a unit of time. Tones of relatively long duration were represented by several vectors, and as a consequence of this, longer tones spread more activation

through Listener's network. When the activation values output from Listener are compared with

subjects' responses as reported in this research report, the Pearson correlation between the two sets of data is .9 (p < .02) for immediate anchoring stimuli and .9 (p < .01) for delayed anchoring stimuli. Subjects' data and Listener's normalized output are plotted in Figures 4 and 5. Note the similar-

ity between the shapes of the plots. In response to the immediate anchoring task, Listener always rated the C-major target chord higher than B major. C

major received its highest rating when the chord tones of C major were

emphasized, and a similar result can be observed for B major. In response to the delayed anchoring task, Listener always rated the C-major target chord

210 Bernice Laden

Fig. 4. A comparison between the normalized activation output from Listener and the target chord ratings from human subjects, for the immediate anchoring task.

highest. The C-major and Db-major chords received their highest rating when their respective chord tones were emphasized by the durational pattern. B major received its highest rating in the isochronous condition, and its second highest rating when its chords tones were emphasized. Thus, the simulation's data shows a high correlation with the subjects' data, but not a perfect rank-order correlation. Nevertheless, it appears that no explicit representation of duration is needed to model durational effects, provided that activation is proportional to the duration of a musical tone.

Although musicians and novices had similar patterns of results, there was a primary difference. The novices had a narrower range of responses than the musicians had. The ambiguity of the melodies was such that even though all subjects were instructed to use the full 7-point rating scale, novices appeared to have a difficult time discerning large differences between the stimuli. Indeed, the chromatic melodies sound ambiguous, which may have made the task quite difficult for the novices. Despite the


Fig. 5. A comparison between the normalized activation output from Listener and the target chord ratings from human subjects, for the delayed anchoring task.

narrow range of responses, reliable effects were obtained. Therefore, the rating paradigm offers an alternative to, and perhaps an improvement over, the forced-choice paradigm used by Bharucha, particularly in those situations in which one wants to test the novice listener.1

1. Work for this article was undertaken as part of the author's doctoral dissertation. The author thanks the School of Music Systematic Musicology Division for subject funds and the Psychology Department for use of the subject pool. Penny Yee, Glen Gould, and several anonymous reviewers provided helpful comments on an earlier draft.

References

Bharucha, J. J. Anchoring effects in music: The resolution of dissonance. Cognitive Psychol- ogy, 1984, 16, 485-518.

Bharucha, J. J. MUSACT: A connectionist model of musical harmony. Proceedings of the

212 Bernice Laden

Ninth Annual Conference of the Cognitive Science Society. Hillsdale, NJ: Erlbaum, 1987,508-517.

Bharucha, J. J., & Stoeckig, K. Reaction time and musical expectancy: Priming of chords. Journal of Experimental Psychology: Human Perception & Performance, 1986, 12, 403-410.

Bharucha, J. J., & Stoeckig, K. Priming of chords: Spreading activation or overlapping frequency spectra? Perception & Psych op hysics, 1987, 41(6), 519-524.

Castellano, M. A., Bharucha, J. J., & Krumhansl, C. L. Tonal hierarchies in the music of North India. Journal of Experimental Psychology: General, 1984, 113(3), 394-412.

Krumhansl, C. L., Sandell, G. J., & Sergeant, D. S. The perception of tone hierarchies and mirror forms in twelve-tone serial music. Music Perception, 1987, 5(1), 31-78.

Laden, B. A model of tonality cognition which incorporates pitch and rhythm. Unpub- lished doctoral dissertation, University of Washington, Seattle, 1989.

melodic anchoring and tone duration · numerous instances of melodic anchoring exist in tonal...

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