the interplay between metric and figural rhythmic organization

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Journal of Expert mental Psychology:Human Perception and Performance

1998, Vol. 24, No. 5,1546-1561

Copyright 1998 by the American Psychological Association, Inc.0096-1523/9WS3.00

The Interplay Between Metric and Figural Rhythmic Organization

Stephen HandelUniversity of Tennessee, Knoxville

Three experiments investigated the relative importance of figural and metric rhythmic

organizations. Figural organization is determined by the numbers of tones in successive

groups. For figural organization alone, the timings between the onsets of each group are

relatively unavailable, so listeners cannot discriminate between 2 rhythms that have the same

sequence of groups but different timings between the groups. Thus, traditional views argue

that a metric organization is necessary: The timing between adjacent groups is perceived by

means of the strong-weak sequence of beats. These experiments, however, suggest a limited

role for meter. The metric strength of the individual rhythms affected discrimination of pairs of

different rhythms with the same figural organization only when an external meter pulse

accompanied the rhythm and only when the rhythm with the stronger meter was the first of the

pair.

The purpose of the present experiments was to investigatethe roles of the metric (i.e., periodic) and figural (i.e.,

grouping or serial) organizations in the perception of

rhythmic timing patterns composed of identical tones.

Traditionally, rhythmic organization has been thought to

depend on identification of the meter or beat of the passage.

Passages in which such a meter cannot be easily created are

considered to be unstable and therefore difficult to encode

and reproduce. The results of the present experiments argue

that this is an overly simplified conceptualization and

that the metric organization functions only within the

more fundamental figural organization created by element

grouping.

Metric organization is the sense of a regular periodicsequence of subjectively stronger and weaker beats that

characterize music. The meter forms a time-based lattice that

serves to create the rhythmic organization. The meter occurs

at several hierarchical levels at once so that the beats at

higher levels occur at integer multiples of the beats at lower

levels. The strength of any beat is determined by the number

of levels at which the beat appears. For example, consider

four-beat meters based on a repeating unit of 16 elements as

used here. The strong beats would occur at Elements 1,5, 9,

and 13; stronger beats would occur at Elements 1 and 9; and

die strongest beat would occur at Element 1 (Palmer &

Krumhansl, 1990). Notes that fall at the points of the strong

beats become accented, and notes that fall at the points ofweak beats are unaccented. Alternative meters could be

based on units of three, so that for a repeating unit of 12, the

strongest beats would occur on Elements 1,4,7, and 10.

To define strong and weak metric rhythms, I made use of

the rules suggested by Povel and Essens (1985) for se-

I thank Piet Vos, Greg Sandell, and Mari Riess Jones for their

helpful comments on the manuscript and Hancel Woods for his help

in completing Experiment 3.

Correspondence concerning this article should be addressed to

Stephen Handel, Department of Psychology, University of Tennes-

see, Knoxville, Tennessee 37996-0900. Electronic mail may be

sent to [email protected].

quences of identical elements separated by different lengthsof silent intervals. Povel and Essens began by observing that

in a sequence of identical tones, certain tones appear

accented. These include (a) relatively isolated tones, (b) the

second tone of a pair of tones, and (c) the first and last tones

in a series of tones. Povel and Essens continued by arguing

that a strong meter emerges when those accented tones fall at

regular intervals (i.e., beat positions). Empirically (Essens &

Povel, 1985), the most important factor in determining the

ease of reproducing the rhythm and, by inference, in

determining the strength of the meter is that a tone should

occur at the positions of the strong meter beats, and a silence

or rest should not. Theoretically, in determining the best-

fitting meter, Povel and Essens (1985) weighted the lack ofcoincidence of a tone and beat as the most important factor.

On this basis, for rhythms 16 elements long I operation-

ally defined the metric strength of a rhythm by the occur-

rence of tones at the beat positions 1, 5,9, and 13. Thus, the

rhythm X.X.X...X...X... (me Xs represent tone elements, the

dots represent isochronous silent time intervals, and tones

separated by one time unit are heard as forming a single

group) would be strongly metric, because tones fall on the

stronger beats at Elements 1, 5, 9, and 13, but the rhythm

X.X...X..X.X.... would be only weakly metric because tones

fall only at Element 1. From this perspective, rhythms are

not simply metric or nonmetric. Instead, each rhythm is

metric to some degree, depending on the strength of themeter interpretation it evokes. Povel and Essens (1985)

argued that listeners attempt to find a meter to fit a rhythmic

pattern (i.e., a template) and that highly metric rhythms more

easily induce an internal clock that encodes the rhythm in

terms of the meter. In contrast, weak metric rhythms do not

induce an internal clock, and therefore the rhythm cannot be

encoded in terms of a temporal grid in which every element

can be located and timed.

Figural organization is the sense that a sequence of tones

is heard as a series of discrete groups. This organization may

be based on shared acoustic properties such as duration,

pitch, timing, or timbre or may be based on a trajectory such

1546



METRIC AND FIGURAL RHYTHMS 1547

as an ascending or descending scale. In the present context,

the grouping is based on the timing between tones, so that

the groups are composed of tones separated by one silent

intertone interval (one dot in the representation). Bamberger

(1978) and Povel and Essens (1985) termed this figural

grouping because the groups are figures perceived against anordinal ongoing time. The rhythms are organized into

bounded groups of elements that follow one another, but the

tunings between the onsets of the successive groups are not

encoded or compared. For example, the rhythm

X.X..X....X.X... would be coded as 2 tones, silence, 1 tone,

silence, 2 tones, silence (written as 2-1-2-); the lengths of the

silent intervals separating the groups would be coded

roughly, if at all. One would expect a similar rhythm with the

identical figural organization (e.g., X.X....X..X.X..., which is

also coded 2-1-2-) to be easily confused with the former

rhythm because the timing differences between the groups

are not used.

In previous research (Handel, 1992) I demonstrated thatfor weak metric rhythms composed of identical tones

separated by different intertone timings (similar to those

discussed above), listeners heard the rhythms in terms of the

groups of tones and could not accurately judge the timings

between groups. When two different rhythms had the same

figural organization, listeners perceived the two rhythms as

being identical, and discrimination was below chance. In

contrast, when two different rhythms had different figural

organizations, discrimination was quite good.

M y goal in the experiments reported here was to investi-

gate how the figural grouping organization interacts with the

metric organization by using rhythms with stronger as well

as weaker meters. Although all theories of rhythm postulate

that both types of organization jointly determine the emer-

gent rhythm, the precise relationship between the two is

unspecified. For example, Lerdahl and Jackendoff (1983)

suggested that the metric organization dominates shorter

sections of a composition but that the grouping organization

dominates longer sections.

If a strong meter leads to a percept based on a fixed

hierarchical timing structure, then that structure should

preserve the timings both within and between groups of

tones. In general, it should be easier to distinguish between

two different strong metric rhythms or between a strong and

a weak metric rhythm than between two weak metricrhythms. More specifically—and this is the focus of these

experiments—it should be possible to discriminate between

two different rhythms with the same figural organization that

differ in meter. However, if a strong meter does not enhance

rhythmic organization, then the ability to distinguish be-

tween two rhythms should depend on whether their figural

organizations are the same, not on the strength of the meter

of either rhythm. Moreover, if the figural organization is

primary, and the metric organization subsequently elabo-

rates the timing of the figural organization, then the effect of

an imposed external meter pulse should depend on the

specific figural organizations of the two rhythms and should

not improve discrimination among all pairs.

Experiment 1

M y specific purpose in Experiment 1 was to investigate

discrimination among a wide variety of strong and weak

metric rhythms. The goal was to determine if metric strength

affected discrimination of pairs of identical rhythms and

pairs of different rhythms with the same or different figuralorganization(s).

Method

Participants. All 57 participants were undergraduates at the

University of Tennessee who received course credit for their

participation. They were tested in groups of from 1 to 3.

Rhythms. All rhythms were based on five tones embedded in a

repeating pattern of 16 grid elements. The rules used to construct

the rhythms were as follows: (a) A tone always occurred on the beat

at the first element; (b) a tone always occurred on the beat at the

13th element but never occurred on the final three grid elements;

and (c) there was at least one silent element, but no more than three

silent elements, between any pair of adjacent tones. The combina-

tion of these three rules made the longest silent interval three

elements, and one such interval always occurred at the end of the

rhythms. However, there could be other equally long silent

intervals, so that organization according to the gap rule, in which

the longest silent interval ends the rhythm, might be ambiguous

(Garner, 1974; Handel, 1974). However, in practice, this did not

prove to be a problem, and no participant claimed that the rhythms

were transformed from their starting configuration.

I generated all of the rhythms using a 16-element template for

several reasons. First, the number of possible rhythms mat satisfy

the above rules is relatively small, so it is possible to adequately

sample the range of rhythmic complexity. Second, the rhythms

include simple and complex ones, but no one rhythm is so difficult

that it is impossible to pick up in from two to four repetitions.Third, the length of one repetition played at normal tempo is well

within the memory span. Fourth, a 16-element grid is fit perfectly

by either a two- or four-beat meter. The strongest beats occur at

Elements 1 and 9, weaker beats occur at Elements 5 and 13, and the

weakest beats occur at Elements 3,7,11, and 15. A four-beat meter

seems most natural to listeners of Western music: Bolton (1894)

noticed that listeners spontaneously grouped isochronous tones into

units of 4 and 2 as opposed to 3, and Smith and Cuddy (1989) found

that four-beat meters produced better performance man three-beat

meters.

The preceding rules could generate 19 possible rhythms. Three

rhythms were perfectly metric, having tones at Elements 1, 5, 9,

and 13; four rhythms were strongly metric, having tones at

Elements 1, 9, and 13; four rhythms were metric, having tones atElements 1, 5, and 13; and eight rhythms were weakly metric,

having tones only at Elements 1 and 13.

There were 19 pairs that contained two identical rhythms, one

for each of the possible rhythms. To restrict the number of pairs that

contained two different rhythms and to determine if participants

could identify which tone differed between the two rhythms, I

selected the pairs of different rhythms such that the two rhythms of

a pair differed by one tone shifted one grid element. There were 29

such pairs (disregarding the order of the two rhythms).

A total of 48 pairs of rhythms were used in the experiment.

Nineteen pairs contained two identical rhythms (all of the possibili-

ties). Twenty-nine pairs contained two different rhythms: From the

possible set of 29 pairs, 21 pairs were presented in one order, and 4

different pairs were presented in both orders (8 in total). Across the

pairs of different rhythms, the five instances in which the two



1548 HANDEL

rhythms had the same figural organization were included, whereas

the remaining pairs were made up of two rhythms with different

combinations of metric strength. All individual rhythms occurred at

least once, and nearly all of the rhythms occurred equally often as

the first or second rhythm of the pair.

Task. On every trial, two rhythms were presented, and the

participant judged whether the two rhythms were the same ordifferent in terms of the relative timing of the tones. If the

participants thought that the two rhythms were identical, they

circled the word same on the answer sheet. If they thought the two

rhythms were different, they circled one of five equally spaced Xs

that represented the individual tones in order to indicate which one

had changed timing (the participants were instructed beforehand

that only one of the three middle tones could change, so that,

effectively, they were to circle one of the three middle Xs). The first

rhythm was always presented with a higher pitch tone (586 Hz,

triangle waveform), and the second rhythm was always presented

with a lower pitch tone (440 Hz, triangle waveform).Presentation rate. The tones were presented at a moderate rate:

The duration of each grid element was 133 ms, so the length of one

repetition was 2.13 s (16 X 133 ms) and there were 2.3 elements/s.

The interval between Beats 1,5,9, and 13 was about 500 ms, close

to the preferred tempo of major beats (Fraisse, 1982; Parncutt,

1994). Each tone was composed of a 10-ms onset ramp, a 50-ms

steady state, and a 10-ms offset ramp (roughly 50% of the duration

of a grid element).

The rhythms were generated with BRS-Foringer modules and

were prerecorded and presented to participants on cassette tapes.

The experimental session took place in a small room (3 X 4 m)with acoustical ceiling tile. The participants were seated 2.5 m from

two vertically stacked speakers, each of which presented the entire

rhythm. The rhythms were presented at a comfortable listening

level, approximately 65 dB (SPL); participants were allowed to

adjust the loudness if they wished.

Alternation conditions. The rhythm-pairs were presented in

two ways. In the first, each rhythm was presented once, and thenthe pair was recycled three times (i.e., notated AXAXAXAX to

indicate that the presentation would be AA for pairs of identical

rhythms and AB for pairs of different rhythms). In the second, each

rhythm was presented two times, and then the pair was recycled

(i.e., AAXXAAXX). For both conditions, the following rhythm

started at the finish of the three silent grid elements that ended each

rhythm (i.e., at 2.13-s periods). There were no differences between

the repetition of one rhythm and the alternation between differentrhythms. I chose these two conditions to determine if the number of

repetitions and alternations between the two rhythms affected

discrimination.

Experimental design. The design was within subjects: 2 alter-

nation conditions X 48 rhythm-pairs. Each participant was pres-

ented with two blocks of trials, one block for each alternation

condition. For each alternation condition, three different sequences

of the pairs were constructed that roughly counterbalanced order.

The order of presentation of the alternation conditions and the

sequences within each condition were counterbalanced across

participants.

Procedure. Two strategies were used to acquaint participants

with each condition. First, before the actual presentation of each

alternation condition, there were four practice trials that used

simpler four-element rhythms. Two consisted of identical pairs, and

two consisted of different pairs. If participants were confused, then

these rhythms were repeated until participants felt confident.Second, the first two rhythm-pairs were repeated later among the

48 experimental trials (thus, there were actually 50 trials per block).

The participants were not told that these were practice trials, and

the results were not used. There was an 8-s interval between each

trial, during which participants made their responses. Participants

did not receive any feedback. There was a short break between the

two blocks, and the experimental session lasted about 50 min.

Results

For the pairs of identical rhythms, the percentage of

identical responses was the only possible measure. For

the pairs of different rhythms, there were two measures: (a)

the percentage of responses correctly discriminating the two

rhythms and (b) the percentage of responses that correctly

identified which tone had changed timing.

Preliminary analyses indicated that there were no differ-

ences in discrimination among the three orders for each

alternation condition (the average absolute difference was

7%), that there were no differences between the first and

second blocks (79% correct for Block 1; 80% correct for

Block 2), and that there were no differences between the

alternation conditions (the average absolute difference across

rhythms was 3%). Thus, the differences between the control

variables and between the two alternation conditions were so

small that all the results were combined. The percentage

correct is based on two responses from each of the 57

participants (114 responses in total), one from each alterna-

tion condition.

Pairs of identical rhythms. As described in the Method

section, the 19 rhythms and resulting pairs of identical

rhythms logically could be classified into four levels of

metric strength on the basis of whether tones occurred at

Element 5, Element 9, both Elements 5 and 9 (5&9), or

neither Element 5 nor Element 9 (none). The results are

shown in Table 1. Overall, there was a significant difference

between the pairs of identical rhythms, F(18, 1008 = 3.9,p < .005, MSB = 0.11. The pairs were then placed into

groups of equivalent discrimination performance through

the use of 1\ikey's honestly significant difference (HSD)

procedures. These procedures indicated that the 19 pairs

could be placed into three groups and that each group

contained pairs with different metric strength. The first

group contained (a) the three perfectly metric rhythm-pairs

with tones at both Elements 5 and 9 and (b) Rhythm 16. In

this group, discrimination was nearly perfect; 95% of the

responses indicated that the two rhythms were identical. The

second group contained 10 rhythm-pairs, essentially those

for which the percentages correct were in the 80% range.

The third group contained the five rhythm-pairs with percent-ages correct that were below 80%. These latter rhythms

tended to have weaker metrics. In sum, there is some

evidence that metric strength affected discrimination, but the

difficulty of the rhythms varied across a strict metric

categorization.

Pairs of different rhythms. These parrs can be classified

in two ways. The first is according to whether or not the two

rhythms had the same figural organization. There were 5

pairs that had the same figural organization and 24 that did

not. The second is to create a 4 X 4 table defined by the

metric strength of the first and second rhythms (the four

levels being 5, 9, 5&9, or none). For example, one possibil-

ity could be defined by the first rhythm having a tone at




Table 1

Percentages o f Correct Discriminations fo r Pairs of Identical Rhythms

for Experiments 1, 2, and 3

Alternation condition

Rhythm

1. X...X.X.X...X...2. X...X...X.X.X...3. X.X.X...X...X...

M

4. X.X...X.X...X...5 X XX X X...6. X.X..X..X...X...7. X..X..X.X...X...8. X...X.X..X..X...9 X X X X.X...

10. X...X..X.X..X...11. X...X.X...X.X...M

12. X.X...X..X..X...13. X.X..X...X..X...14. X..X...X.X..X...15. X.X...X...X.X...16. X X. X..X..X...17. X..X..X...X.X...18. X..X.X...X..X...19. X..X...X..X.X...M

Metricstrength

5&95&95 & 9

99995555

NoneNoneNoneNoneNoneNoneNoneNone

Experiment 1 :

AXAXAXAX Experiment 2:• AAXXAAXX AAAAXXXX

Perfectly metric

96959294

Strongly metric or metric

888080868275748681

Weekly metric

807574839286827681

84868685

886460

677675

72

66637178

70

Experiment 3:AAXX

97969797

988992

899293

92

83778491

84

Note. Empty cells indicate that a rhythm was not used in an experiment. Indicates whether a tone occurred at Element 5, Element 9, both Elements 5 and 9 (5 & 9), or neitherElement 5 nor Element 9 (None).

Element 5 and the second rhythm having tones at both

Elements 5 and 9 (e.g., X...X..X..X.X... and X...X...X.X.X...).

In such a table, 5 of the 16 cells cannot occur because of the

restriction that the two rhythms differ only in the position of

one element. For example, this restriction eliminates a pair

of rhythms in which one rhythm has a tone at Element 5 but

not at Element 9 and the second rhythm has just the reverse.

The pairs are shown in Table 2, those with the same

figural organization appearing first followed by those with

different figural organizations. Both types of pairs wereplaced in tables defined by the metric strength of the first and

second rhythms. The rhythm-pairs with different figural

organizations were divided into three groups based on the

relative metric strength of the first and second rhythms: (a)

The metric strength of the two rhythms was equal; (b) the

metric strength of the second rhythm was stronger; or (c) the

metric strength of the first rhythm was stronger. The

percentages of different-rhythm (i.e., correct) judgments and

the percentages of correct element identification are shown.

All of the rhythm-pairs with identical figural organizations

and representative instances of the rhythm-pairs with differ-ent figural organizations are shown (the numbers of pairs are

indicated in parentheses following the instances, and the

ranges of percentages correct are shown following the

average values). Overall, there was a significant difference

between pairs in terms of the percentage of correct discrimi-

nations, F(28,1568) = 20.0,;? < .005, M SB = 0.13, and the

percentage of correct identifications, F(28, 1568) = 12.1,

p < .005, MSE = 0.20. There was no interaction for either

measure.

First consider the same-different figural organization

distinction. There was no overlap in discrimination accuracy

between pairs of different rhythms with the same figural

organization and those with different figural organizations

(Tukey's HSD test). For the five pairs with identical figural

organizations, the mean percentage of judgments that the

two rhythms were different was 52%, nearly identical to

chance performance, and the mean percentage of correct

element identifications was 23%. Thus, even when partici-

pants did perceive the two rhythms as being different, they

were unable to identify which tone had changed (chance

performance being one third of the trials on which listeners

detected a difference, or 17% in this instance). In contrast,

for the 24 rhythm-pairs with different figural organizations,

the mean percentage of judgments that the rhythms differed



1550 HANDEL

Table 2

Experimen t 1 : Percentages of Correct Discriminations a nd of Correct Identifications

of Which Tone Changed Position fo r Pairs o f Different Rhythms

Metric strength

First

rhythm

Second

rhythm Rhythm-pan* Discrimination' Identification'Identical figural organizations

None

None

5

9

None

5

None

None

X.X..X...X..X...X.X...X..X..X...

X..X...X..X.X...X...X..X..X.X...

X...X..X.X..X...X..X...X.X..X...

X.X..X..X...X...X.X..X...X..X...

X..X.X..X...X...X..X.X...X..X...

M

47

50

51

56

54

52

19

20

22

30

24

23Different figural organizations

None

5

9

None

5

9

9

5&9

5&9

None

5

9

5

5&9

5&9

None

5

9

X.X...X...X.X...X..X..X...X.X... (6)

X...X..X.X..X...X...X.X..X..X... (3)

X..X.X..X...X...X..X..X.X...X... (6)

M

X..X..X..X..X...X...X.X..X..X... (2)

X...X..X..X.X...X...X...X.X.X...

X..X..X.X...X...X...X.X.X...X... (2)

M

X..X..X.X...X...X..X X X X

X...X.X.X...X...X...X.X..X..X...

X...X.X.X...X...X..X..X.X...X... (2)

M

83 (70-94)

81 (79-85)

82 (76-91)

83

87 (80-94)

85

87 (80-93)

86

93

94

88 (84-92)

92

51 (37-65)

55 (44-65)

50 (38-61)

52

36 (32-39)

41

42 (32-52)

39

56

60

58 (46-70)

58

'Indicates whether a tone occurred at Element 5, Element 9, both Elements 5 and 9 (5 & 9), or neitherElement 5 nor Element 9 (None). Rhythm-pairs with two possible combinations of metric strengthsare not shown because of sampling among all the rhythm-pairs. The two combinations are (a) 5followed by None, and (b) None followed by 9. The numbe r of instances for combinations ofmetric strength are shown in parentheses following a representative pair. The percentages ofcorrect discriminations and identifications are the averages of all the possible pairs. The lowest andhighest performances across the rhythm-pairs are shown in parentheses following the averages unlessthere was only one possible instance.

was 81% and the mean percentage of correct tone identifica-

tions was 48% (chance performance is 27%).Second, consider the metric strength analysis. What is

clear is that performance did not differ among the combina-

tions of metric strength for the two kinds of different

rhythm-pairs. For the rhythm-pairs with identical figural

organizations, there were no differences between pairs in

which both rhythms had a weak metric and pairs in which

the first rhythm had a strong metric (a tone at Element 9).

For the rhythm-pairs with different figural organizations,




there were no differences that were due to the grouping

according to relative metric strength that is shown in Table 2,

F 2,21) = 2.8,p > .05. Moreover, there were no differences

that were due to the overall metric strength at the following

four levels: (a) none-none; (b) 5-none and none-9; (c) 5-5

and 9-9; and (d) 5-S&9, 9-S&9, 5&9-S, and S&9-9, F(3,

20) = 0.8. There was no simple pattern of outcomes amongthe cells. Consider the two cells that have the greatest

number of rhythm-pairs. Both the average percentage and

the range of percentages were nearly identical for (a) pairs in

which both rhythms had the weakest metric structure (no

tones at Elements 5 or 9) and (b) pairs in which both rhythms

had a strong metric structure (tones at Element 9).

There were differences between pairs of rhythms in the

participants' ability to identify which tone shifted position.

For some pairs of different rhythms, the identification of

which tone had changed timing was relatively poor, al-

though it was easy to discriminate the two rhythms. A typical

example was the following pair of rhythms: X..X..X..X..X...

followed by X...X.X..X..X... In this case, the two rhythmswere judged as being different in nearly all of the trials

(93%), but the choice of the second tone (underlined) as the

one that had changed was at chance (32%). Instead, partici-

pants usually chose the third tone as the one that had moved

(48%). What is characteristic is that in the first rhythm, there

is an isolated tone (separated by two or more silent intervals

on both sides) that shifts one position to form a double group

in the second rhythm. Participants tend to perceive the

second tone of the double group as having shifted, not the

first tone. This result points out the primacy of the initial

tone of the group; it is perceived as being stable and as

defining the timing of the entire group.

Discussion

In sum, the results give little support to the notion that the

metric strength or metric availability influences the discrimi-

nation between this class of rhythms. If the two rhythms of a

pair had the same figural description, then participants

discriminated the two rhythms only at the chance level,

independent of the metric structure. If the two rhythms had

different figural descriptions, then participants were able to

discriminate them easily, but performance again was indepen-

dent of the metric structure. The only evidence that the

metric structure improved discrimination was found for

pairs of identical rhythms: Rhythms with a perfect metricorganization were more accurately perceived as being

identical.

It is possible to detail the relationship between the metric

and figural organizations from two perspectives. The first

perspective involves considering the effect of metric strength

on the five pairs with identical figural organizations. The

rules used to construct the rhythms impose constraints that

limit the possible rhythms. These constraints yield only a

small set of rhythm-pairs with identical figural organiza-

tions, and within this set, the two rhythms tend to have

weaker metrics. In one case, both rhythms have a weak

meter, and in four cases, the rhythms have different strengths.

Performance was equivalent even though it might be ex-

pected that a change in meter would highlight differences in

tuning (much the same as would a transition from tonal to

atonal melodies). This difference in metric strength would be

maximized in the last two pairs, in which the first rhythm

had a strong meter, including a tone at the second strongest

beat at Element 9, and the second rhythm did not. Yet

discrimination was no better than chance.The second perspective involves considering the effect of

figural organization on pairs with identical metric strengths.

In all instances, there was no overlap in discrimination

between pairs with identical figural organizations and pairs

with different figural organizations. Consider the pairs with

the weakest metrics: the none-none pairs. Discrimination

for the pair with identical figural organizations was below

chance, whereas discrimination for the six pairs with

different figural organizations ranged from 70% to 94%.

Now consider pairs with the stronger metrics: 9-none. In

these pairs, the first rhythm had beats at Elements 1, 9, and

13. Nonetheless, discrimination for the two pairs with

identical figural organizations was barely above chance(54% and 56%). In contrast, discrimination for the pair with

different figural organizations was nearly perfect (93%). To

summarize this argument, the difference in discrimination

between pairs with identical and different figural organiza-

tions occurs equally for pairs with weaker metrics and for

pairs with stronger metrics. Thus, the predominance of the

figural organization is not limited to weaker metric rhythms.

Even a quick perusal of the outcomes suggests that

discrimination is affected by many factors. For example,

discrimination involving Rhythm 16, X..X..X..X..X..., is

quite good even though the four-beat metric is weak.

Possibly, this rhythm is organized according to a three-beat

metric despite the fact that such a meter would not split therhythm evenly. In this case, the pairs containing Rhythm 16

should be considered highly metric. A reanalysis of the pairs

of rhythms with different figural organizations in which

those pairs containing Rhythm 16 were omitted did not

change any of the outcomes: There was no differencebetween the groups defined by relative metric strength (in

Table 2) or by overall metric strength as defined above.

Thus, the evidence for a three-beat meter is equivocal. The

rhythms might simply be organized according to the even

spacing of the tones without a meter being induced at all

(without a sense of stronger and weaker beats).

There are several possible explanations of why these

results did not show any effect of the metric structure.1. The discrimination task may not have been sufficiently

sensitive. The percentage correct for pairs with differentfigural organizations ranged from around 80% to 85%, and

this may have represented a ceiling effect that masked any

effects of the metric structure. Povel and Essens (1985) used

a reproduction task, and Smith and Cuddy (1989) used a

reaction time task; both of these may have allowed meter

effects to occur. However, even the more sensitive measure

used here, the identification of which tone changed timing,

did not show any differences, and a ceiling effect is unlikely

to have affected that result.

2. The metric structure may not have been apprehended

strongly. There are two parts to this argument. First, the



1552 HANDEL

single or double alternation may have precluded the building

up of the metric structure of either rhythm. These alternation

conditions were chosen because they produced the best

discrimination in previous work (Handel, 1992), but neither

one gives the listener repeated looks at the possible

organizations to induce the metric organization of each

rhythm. Second, these are relatively hard rhythms to pick up.On the whole, none of them follows simple rules, so the

meter may have been relatively hidden. The rhythms with

the strongest metric structure are the simplest because of the

tone locations, so it is difficult to tease out clearly the

contribution of the metric structure.

Taken together, the rapid alternations and the difficulty of

the rhythms might argue that the metric structure did not

affect discrimination because listeners could not pick up and

make use of the meter. To counter these objections, in

Experiment 2 I changed the methodology to try to enhance

the perception of the metric structure.

Experiment 2

The goal in Experiment 2 was to investigate further the

role of metric structure in the discrimination of rhythms. The

results of Experiment 1 seemed to show that the effect of

metric structure was minimal. Participants organized the

rhythms according to the figural grouping structure, and the

grouping structure, in turn, determined discrimination. In

Experiment 2, I tried to bring the metric structure into

perceptual prominence by making two changes in the

methodology.

The first change was to the alternation condition. In

Experiment 2, the first rhythm was repeated four times, and

then the second rhythm was repeated four times (i.e.,AAAAXXXX). The rationale for this was that playing each

rhythm four times in a row would allow the listener to pick

up the meter more easily. It is possible that the single and

double alternations used in Experiment 1 forced listeners to

concentrate on the figural structure.

The second change was to introduce a short-duration,

low-pitch pulse tone to time the first rhythm, in much the

same way that a percussion accompaniment occurs on the

meter beat in a performance. Two approaches were used. In

the first approach, the pulse occurred at Elements 1,5,9, and

13 of the first rhythm whether or not a rhythm tone occurred

at those elements. Thus, it was possible to have a pulse

without a tone. There were no pulse tones for the secondrhythm. I did not use pulse tones for the second rhythm

because I was afraid that participants would use the derived

strategy of simply attending to the coincidence of pulse and

tone in the two rhythms to determine if they were the same

or different (pulse tones were used for both rhythms in

Experiment 3). This condition is termed the meter-rhythm

condition because the pulse timed the underlying meter of

the first rhythm. In the second approach, the pulse occurred

at Elements 1, 5, 9, and 13 only when a tone also fell on

those elements. The purpose of this condition was to

eliminate the possible confusion when a pulse occurred

without a tone and to emphasize the link between the meter

pulses and tones. Because tones always occurred on Ele-

ments 1 and 13, the difference between the two conditions

could occur only at Elements 5 and 9. As in the meter-

rhythm condition, the pulse occurred only on the first

rhythm. This condition is termed the accent-rhythm condi-

tion because the pulse accented the tones at the metric

positions.

Theoretically, the pulse could improve discriminationequally for strong and weak metric rhythms by providing a

timing reference. Furthermore, this reference would exist

whether or not the tones and pulses coincided. However,

perceptually, it is probably easier to use such a reference

when the pulses and tones coincide, as they do for the

stronger metric rhythms, than it is when the pulses and tones

fall on different grid elements, as they do for the weaker

metric rhythms. In these latter cases, one might expect the

effect of the pulse to be variable, depending on the exact

timings of the pulses and tones.

To summarize, the purpose of Experiment 2 was to

determine whether repeating each rhythm four times and

introducing a pulse would emphasize the metric structuresufficiently for the strength of the metrical organization to

affect discrimination.

Method

Participants. All 61 participants were undergraduate volun-

teers at the University of Tennessee who received course credit for

their participation. Different participants were used in each experi-

ment. The participants were tested in small groups of from 1 to 3.

Rhythms. The rhythms were the same type as those used in

Experiment 1. A total of 27 pairs of rhythms were used. Thirteen

pairs contained two identical rhythms. These were selected from

the possible set of 19 (see Experiment 1) so that there was a roughlyequal distribution of metric strength: Three pairs had tones at

Elements 5 and 9, at Element 9, or at Element 5, and four pairs did

not have tones at either of these metric elements. Fourteen pairs

contained two different rhythms. Five of these pairs contained two

different rhythms that had the same figural organization, and the

remaining nine pairs had rhythms with different combinations of

metric strength. All rhythms were used.

Task. The task was the same as that used in Experiment 1.

Presentation conditions. The rhythms were presented at the

same rate that was used in Experiment 1, roughly 2.3 elements/s.

The first rhythm was presented four times and then the second

rhythm was presented four times. The timing of the alternation was

the same as that used in Experiment 1. In contrast to Experiment 1,the first rhythm was presented with a lower pitch tone (400 Hz

triangle wave), and the second rhythm was presented with a higher

pitch tone (600 Hz, triangle wave). The high and low pitch tones

had a steady-state duration of 50 ms and 10-ms/lO-ms rise/fall

times, as in Experiment 1. The pulse was a 100-Hz sine wave

presented for 35 ms: 15 ms steady state and 10-ms/lO-ms rise/fall

transients. All of the other conditions were identical to those in

Experiment 1.Experimental conditions. There were three conditions. In the

first, termed rhythm-rhythm, each rhythm was presented alone

without an accompanying pulse. This condition was identical to the

situation in Experiment 1 (with the exception of the alternation

method) and served as a replication. In the second condition,

termed meter-rhythm, the pulse tone occurred on Elements 1, 5, 9,

and 13 for the four repetitions of the first rhythm. If there was a

rhythm tone, the pulse and tone started synchronously, although the



METRIC AN D FIGURAL RHYTHMS 1553

tone continued after the pulse. If there was not a rhythm tone, the

pulse was heard alone. In the third condition, termed accent-

rhythm, the pulse occurred on Elements 1,5,9, and 13 of the first

rhythm only if a tone occurred. The timing for the pulse and tone

was identical to that in the meter-rhythm condition.

Experimental design. The design was within subjects: 3 condi-

tions X 27 patterns. The 27 patterns within a condition werepresented in a single block, and the blocks were presented to the

participants in the identical order: rhythm-rhythm, meter-rhythm,

and accent-rhythm. This order was chosen to maximize the effect

of the external pulse. The rationale was that the rhythm-rhythm

condition would serve as a reference, allowing participants to

become familiar with the rhythms. Following this, participants

could make use of the pulse to perceive the timing structure of the

rhythms without having to become familiar with the rhythms. The

accent-rhythm condition was presented last because it seemed

somewhat unrepresentative of natural rhythms and I did not want it

to create negative transfer to either the rhythm-rhythm or meter-

rhythm conditions. For each block, three different sequences of

rhythms were constructed that roughly counterbalanced the order

of the pairs of rhythms.

As in Experiment 1, before each block, participants were

presented with four simple examples, and the first two trials in each

block were replicated later within the block. The timing of the trials

was the same as that used in Experiment 1, and there was no

feedback. There were short breaks between the conditions, and the

experimental session took about 50 min.

Results

The outcomes were analyzed according to the samestrategy used in Experiment 1. The results for pairs ofidentical rhythms are considered first, followed by the

results for the pairs of different rhythms. Preliminaryanalyses indicated that performance for the three orders ofeach condition was equivalent. For the rhythm-rhythmcondition, the percentage correct ranged from 74% to 71%;

for the meter-rhythm condition, it ranged from 72% to 70%;and for the accent—rhythm condition, it ranged from 76% to70%. On this basis, I combined the results for the threeorders for each experimental condition. The percentagescorrect are based on 61 responses, one per participant.

Pairs of identical rhythms. There were no differencesamong the three experimental conditions, F(2, 120) = 1.15,

and there was no interaction between rhythm and condition,F(24, 1440) = 1.85. The percentages of correct judgments

for the rhythm-rhythm, meter-rhythm, and accent-rhythmconditions w ere 76%, 73%, and 75 %, respectively. Overall,there was a significant difference among the rhythm-pairs,F(12, 720) = 15.4, p < .001, MSB = 0.19. The bestdiscrimination occurred for the three rhythms with thestrongest metric structure (i.e., with tones at Elements 1, 5,9, and 13) and for Rhythm 4. For these rhythms, thepercentage correct averaged 86% . For the remaining pairs (9in total), there were no differences as a function of experimen-tal condition or metric strength. Here the average percentagecorrect was 69%. Thus, the significant effect occurredprimarily between rhythm s with the strongest metric and allthe others. The percentages of correct judgments averaged

across experimental conditions are shown in Table 1.

Pairs of d i f f e r e n t rhythms. For all parrs, the percentage

of judgments that the two rhythms were different and thepercentage of correct note identifications are shown in Table3 as a function of condition and of the metric strength of thefirst and second rhythms. As in Experiment 1, pairs withidentical and different figural organizations were separated.

Overall, for both the percentage of judgments that the tworhythms were different and the percentage of judgments thatcorrectly identified wh ich element had changed timin g, therewere significant differences between rhythm-pairs, F(13,

780) = 17.5, p < .005, MS B = 0.21, and F(13, 780) = 9.7,

p < .005, MS B = 0.22, respectively; no differences betweenconditions, Fs(2, 120) = 1.4 and 0.5, respectively; and asignificant Rhythm-Pair X Condition interaction, F(26,

1560) = 3.1,p < .005, MSB = 0.15, andF(26,1560) = 2.7,p < .005, MSB = 0.15, respectively.

The Rhythm X Condition interaction is the crux of theresults. Consider first the rhythm-rhythm condition, equiva-lent to the situation in Experiment 1. Here there was no

overlap in discrimination accuracy between rhythm-pairswith the same figural organization and rhythm-pairs withdifferent figural organizations (Tukey's HS D test). Therewere no differences among the pairs with identical figuralorganizations and no differences among the parrs withdifferent figural organizations. Neither the relative noroverall metric strength affected discrimination. For pairswith identical and different figural organizations, the percent-ages of correct discriminations were 50% and 84%, respec-tively, and the percentages of correct identifications of thetone that changed position were 19% and 41%, respectively.

These percentages were nearly identical to those for thesame pairs in Experiment 1.

Consider next the meter-rhythm and accent-rhythm con-ditions. These results are quite different from those of therhythm-rhythm condition, and there was a striking interac-tion between pairs with the same figural organization andpairs with different figural organizations as a function of themetric strength of the first and second rhythms. For the parrswith the same figural organization, there were tw o distinctoutcomes. If the first rhythm had the weakest metricstructure, with tones at Elements 1 and 1 3 but not atElements 5 or 9, then discrimination w as below chance. Thepercentages of correct different judg men ts for the meter-

rhythm and accent-rhythm conditions were 46% and 40%,respectively (this difference was not significant). However,

if the first rhythm had a stronger metric structure, with a toneat Elements 5 or 9, then the pulse in the meter-rhythm andaccent-rhythm conditions generated significantly better per-formance. The percentages of correct different judgm entsfor the meter-rhythm and accent-rhythm conditions were72% and 69%, respectively.

For the pairs with different figural organizations, with twoexceptions, discrimination was excellent. The percentage ofcorrect different judgmen ts was 76%, and the percentageof correct element identifications averaged 39%. As wasfound for the, rhythm-rhythm condition, there were noeffects that were due to metric strength. Even excluding thetwo pairs with the poorest discrimination, the percentage

correct was slightly h igher for the rhythm-rhythm condition.



1554 HANDEL

Table 3

Experiment 2: Percentages of Correct Discriminations Discr.) and of Correct

Identifications Ident.) of Which Element Changed Position for Pairs

of Different Rhythms

Experiment condition

Metric strength*

Firstrhythm

Secondrhythm Rhythm-pair

Rhythm-rhythm

Discr. Ident.

Meter-rhythm

Discr. Ident.

Accent-rhythm

Discr. Ident.

Identical figural organization

None

None

5

9

None

5

None

None

X.X..X...X..X...

X.X...X..X..X...

X..X...X..X.X...X...X..X..X.X...

M

X...X..X.X..X...

X..X...X.X..X...

X.X..X..X...X...X.X..X...X..X...

X..X.X..X...X...

X..X.X...X..X...

M

44

49

47

43

57

57

52

14

20

17

18

23

19

20

53

38

46

75

75

67

72

16

18

17

39

31

31

34

36

44

40

61

67

80

69

14

20

17

25

25

30

27

Different figural organization

None

5

9

None

5

5

5&9

None

5

9

5

5&9

None

9

X..X..X...X.X...

X..X..X..X..X...

X.X...X..X..X...X.X...X...X.X...

X...X.X..X..X...X...X.X...X.X...

X..X..X.X...X...X..X.X..X...X...

X.X...X.X...X...X.X...X..X...X...

M

X..X..X..X..X...X...X.X..X..X...

X...X..X..X.X...X...X...X.X.X...

M

X...X.X...X.X...X..X..X...X.X...

X...X.X.X...X...

X..X..X.X...X...

M

85

74

82

87

92

84

90

87

88

77

84

81

Indicates whether a tone occurred at Element 5,Element 5 nor Element 9 (None).

43

33

39

41

48

41

48

23

36

44

54

49

Element 9,

85

52

62

84

82

73

82

79

81

74

84

79

43

20

31

43

38

35

36

36

36

34

55

45

84

53

54

83

82

72

80

84

82

79

92

86

55

26

23

46

48

39

26

33

30

35

61

48

both Elements 5 and 9 (5 & 9), or neither

_ _ „* < • _ _ _«i *___ _ _ ?̂ *t.

Thus, the pulse did not improve discrimination if the two

rhythms had different figural organizations.

There were no differences among the three conditions in

the participants' ability to identify which tone had changed

position. More important, the

percentages of

correct identifi-

strength in Table 3. There are large differences among the

pairs. But, in general, participants were unable to identify

more accurately that a tone had moved from a strong to a

weak metric position than the reverse.




Discussion

These results, completely consistent with those from

Experiment 1, clarify the role of the metric structure in

rhythm perception. The meter did improve discrimination

for pairs of identical rhythms, but the effect was more

complicated for pairs of different rhythms. To follow theform of the Discussion in Experiment 1, let us first consider

the effect of metric strength on the five pairs of rhythms with

the same figural organization. For the rhythm-rhythm pairs,

performance hovered about chance even if the initial rhythm

had tones at the strongest metric beats (at Elements 1 and 9).

Thus, these results perfectly replicate those of Experiment 1.

For the meter-rhythm and accent-rhythm pairs, the external

pulse brought about a fixed temporal grid that enabled

listeners to distinguish between two rhythms with the same

grouping or figural organization but with different timings

between the groups. However, the pulse improved discrimi-

nation only if the pulse coincided with the tones of the initial

rhythm. The pulse made the metric structure of the initialrhythm more available so that the timings between adjacent

groups could be encoded relative to the meter. However,

when the pulse did not coincide with any of the three internal

tones of the first rhythm (the first two pairs in Table 3), the

pulse did not affect discrimination even if the second rhythm

had a stronger meter.

Now consider the effect of the figural organization on the

pairs with the same metric strength. For the rhythm-rhythm

pairs, the results replicate those in Experiment 1. For all

comparisons, discrimination for pairs with different figural

organizations was well above chance, in contrast to the

chance performance for all pairs with identical figural

organizations. For the meter-rhythm and accent-rhythmpairs, the results differed because there was overlap among

pairs with different and identical figural organizations.

This asymmetry, in which a transition from stronger to

weaker structure produces better performance than does a

transition from weaker to stronger structure, has been foundin other kinds of auditory processing. For example, Jones

and Boltz (1989) found that a hierarchic (i.e., stronger

meter) to nonhierarchic (i.e., weaker meter) transition yielded

better performance than the opposite sequence. Bharucha

and Pryor (1986) found a similar asymmetry in temporal

discrimination. Krumhansl, Bharucha, and Castellano (1982)

showed that harmonic discrimination was better if the first

melody was strongly tonal and the second atonal than thereverse, and Bartlett (1993) demonstrated that listeners

could detect changes in melodic contour more easily if the

tonal contour preceded the atonal contour.

Jones and Boltz (1989) argued that all of these kinds of

results can be subsumed under the concept of expectancy.

The initial melody, rhythm, or sequence of tones creates a

trajectory about subsequent events. Stronger meters (or

more tonal melodies) more tightly constrain the range of

expectancies so that rhythmic or tonality deviations can be

more easily perceived (expectancy is roughly analogous to

Garner's, 1974, notion of inferred sets). Nonetheless, it

seems reasonable that the structure of the second sequence,

by inducing a set of expectancies or possible alternatives,

ought to affect discrimination. But that was not the case here.

There are two possible reasons: (a) The second rhythm was

being directly compared with the first rhythm without being

encoded, or (b) the fact that there was no pulse for the

second rhythm made the metric strength less prominent for

the listener.

Experiment 3

What is known at this point is that the metric strength

influences discrimination in only one context: if the two

different rhythms have the same figural organization, if the

first rhythm has the stronger inherent meter, and if the metric

elements of the first rhythm are marked by a pulse. I

designed Experiment 3 to investigate two issues further.The first issue is why the effects of the metric structure are

so limited. One possibility is that because the pulse never

occurred for the second rhythm, the effect of the pulse in the

first rhythm was weakened and any possible effect of the

metric strength of the second rhythm was negated. For thisreason, in one condition in Experiment 3 I had the pulse

occur on elements 1, 5, 9, and 13 for both rhythms (termed

the meter-meter condition) in order to continue the metric

structure across the second rhythm. These outcomes can be

compared with those when the pulse occurred for the first

rhythm only (meter-rhythm) or not at all (rhythm-rhythm).

(Although participants usually could determine if the two

rhythms were different for the meter-meter condition by

simply determining if the coincidences of pulses and tones

were identical in the two rhythms, no participant explicitly

reported using this derived strategy).

The second issue concerns the generality of the asymme-

try in outcomes that is due to the relative metric strengths ofthe two rhythms when there is a pulse. I argued for this

asymmetry in Experiment 2 by comparing across rhythm-

pairs. For example, discrimination was at chance for Pair A,

in which the meter was weak-strong, but discrimination was

very good for Pair B, in which the meter was strong-weak.

Because any pair of rhythms have unique timing characteris-

tics, it is impossible to argue unambiguously that a strong-to-

weak meter transition always yields better discrimination.

For this reason, each pair of different rhythms with the same

figural organization was presented twice, the second time

with the order of presentation of the two rhythms reversed. If

there is a general asymmetry created by the interaction of

relative metric strength and pulse, then discrimination of

each combination of rhythms should be better if the rhythm

with the stronger metric is presented first than if the rhythm

with the weaker metric is presented first. In pairs in which

both rhythms have equal metric strength, there should be

little difference between the two orders of the rhythms.

Method

Participants. All 67 participants were undergraduates at the

University of Tennessee who received course credit for their

participation. They were tested in groups of from 1 to 3.

Rhythms. The rhythms were the same type as those used in

Experiments 1 and 2. There were 36 pairs of rhythms in all.

Thirteen pairs had two identical rhythms; these were the same pairs



1556 HANDEL

used in Experiment 2. Twenty-three pairs had two different

rhythms. These can be broken into two sets. The first set consisted

of the five pairs of different rhythms used previously that had the

same figural organization. Each pair was presented in the two

possible orders to generate a total of 10 pairs. The second set

consisted of 13 pairs that had different figural organizations. These

pairs were chosen to match the metric strengths of the pairs with theidentical figural organizations.

Task. The task was simpler than the one used in Experiments 1

and 2. In Experiment 3 participants judged whether the two

rhythms were identical or different on a 4-point scale (1 = very

sure identical, 2 = fairly sure iden tical, 3 = fairly sure different,

and 4 = very sure different). In deriving the percentage correct, I

considered judgments of 1 and 2 to be identical judgments and 3

and 4 to be different judgments. I switched the response in order

to maximize performance so that any possible improvement that

was due to the meter could be found, and I felt that trying to

identify the tone that changed position could be distracting.

Presentation conditions. The rhythms were presented at the

same rate used previously, roughly 2.3 elements/s. The first rhythm

wa s presented two times, and then, without a break, the second

rhythm was presented two times. This alternation condition waschosen to make the task more difficult so that any improvement that

was due to the meter would not be obscured by a ceiling effect. The

rhythms were generated with the MIDI software package MIDI-

LAB for the IBM PC. The sounds were generated with a Seiko

DS-250 keyboard, and the piano timbre was used. The first rhythm

was presented with a lower pitch tone (440 Hz), and the second

rhythm was presented with a higher pitch tone (660 Hz). Each tone

was 75 ms in duration. The pulse was a 99-Hz tone presented for

40ms.

Experimental design. The design was within subjects: 3 condi-

tions X 36 pairs of rhythms. The rhythms were presented in three

blocks according to condition and across subjects; the order of

presentation of the conditions was counterbalanced. For each

condition, the rhythms were placed into four sequences thatcounterbalanced order. The procedures were the same ones used in

Experiments 1 and 2. There were short breaks between the three

conditions, and the experimental session took about 75 min.

Results

Preliminary results indicated that there were no differ-ences that were due to the sequence order within each

condition. The maximum difference in the percentage cor-

rect between the sequences for any condition was 11%.

Moreover, there were no differences in percentage correct

that were due to the order of the blocks. The percentages

correct for Blocks 1, 2, and 3 were 77%, 82%, and 82%,

respectively. On this basis, the results were averaged oversequences and order. The percentages correct are based on

67 responses, one per participant.

Pairs of identical rhythms. There was a small significant

difference among conditions, F 2, 132) = 3.9, p < .025,

MSB = 0.09, a significant Rhythm X Condition interaction,

F(24, 1584) = 2.6, p < .005, MSB = 0.07, and a significantdifference among rhythm pairs, F(12, 792) = 9.8, p < .005,

M SB = 0.08. For the three rhythms in which tones occurred

at all four meter elements, discrimination was nearly perfect.

The percentages correct for the rhythm-rhythm, meter-

rhythm, and meter-meter conditions were 99%, 95%, and

96%, respectively. Discrimination was equivalent for the six

rhythms in which tones occurred at Elements 1,5, and 13 or

at Elements 1,9, and 13. (The only exception was Rhythm 4:

The percentage correct equaled that for rhythms with the

strongest meter). The percentages correct for the rhythm-

rhythm, meter-rhythm, and meter-meter conditions were

89%, 91%, and 96%, respectively. Discrimination was

poorer for the four rhythms that had tones only at Elements 1

and 13. The percentages correct for the rhythm-rhythm,

meter-rhythm, and meter-meter conditions were 88%, 78%,

and 84%, respectively. Over all pairs, the differences among

conditions were small, averaging 2%. For this reason, the

percentage correct for each rhythm was combined across

conditions and is shown in Table 1.

On the whole, discrimination for the pairs of identical

rhythms mirrors that in the first two experiments, although

the percentage correct is higher in Experiment 3. What is

common across the three experiments is that it was easier to

identify two strongly metrical rhythms as being identical.

What differs in Experiment 3 from Experiments 1 and 2 is

the hint of an interaction between metric strength and pulse

condition. Discrimination was identical across the various

pairs of identical rhythms for the rhythm-rhythm condition

without any external pulse, but discrimination was more

difficult (i.e., participants were more likely to hear the two

rhythms as being different) for the less metrical rhythms for

conditions with an external pulse.

Pairs of different rhythms. Fo r these pairs, there were asignificant rhythm effect, F(22, 1452) = 33.0, p < .005,

MSB = 0.22, a condition effect, F(2, 132) = 4.1, p < .025,

M SB = 0.21, and a Rhythm X Condition interaction, F(44,

2904) = 4.3, p < .005, MSB = 0.15. The Rhythm X

Condition interaction is the main focus of the results (as in

Experiment 2). This interaction can be understood from

three perspectives.First, consider the overall difference between the 10 pairs

with identical figural organizations and the 13 pairs with

different figural organizations. As found in Experiments 1

and 2, there were large differences in the percentage

of correct discriminations for the rhythm-rhythm and

meter-rhythm conditions, F(l, 21) = 58.0, p < .001, and

F(l, 21) = 6.5, p < .02, respectively. Discrimination was at

the chance level for pairs with identical figural organizations

(52%) and well above chance for pairs with different figural

organizations (77%). These percentages are nearly identical

to those found in Experiment 2. In contrast, there was no

difference in discrimination for the meter-meter condition

because discrimination for the parrs with identical figuralorganizations improved sharply (63%) compared with dis-

crimination for pairs with different figural organizations

(77%),F(1,21) = 2.5 /».05.

Second, consider the 10 pairs of different rhythms with

the same figural organizations. For the two pairs in which the

tw o rhythms had equal metric strengths (la and Ib in Table

4) and the four pairs in which the rhythm with the weaker

metric preceded the rhythm with the stronger metric (2a-

5a), discrimination was at the chance level or lower and was

essentially equal for the three conditions. The only excep-

tions occurred for Pairs Ib and 5a for the meter-meter

condition. In contrast, if the stronger metric rhythm pre-

ceded the weaker one (2b-5b), discrimination was much



METRIC AND FIGURAL RHYTHMS

Table 4

Experiment 3: Percentages o f Correct Discriminations fo r Pairs of Different Rhythms

1557

Metric strength

Firstrhythm

Second Pairrhythm no.

Experimental condition

Rhythm-pair Rhythm-rhythm Meter-rhythm Meter-meter

Identical figural organization

None

None

None

5

9

None

None

None

5

9

None (la)

(Ib)

5 (2a)

(3a)

9 (4a)

(5a)

None (2b)

(3b)

None (4b)

(5b)

None (6)

(7)

5 (11)

(12a)

9 (13a)

(14a)

None (12b)

None (13b)

(14b)

X.X..X...X..X...X.X...X..X..X...

X.X...X..X..X...

X.X..X...X..X...

M

X..X...X.X..X...X...X..X.X..X...

X..X...X..X.X...X...X..X..X.X...

X.X..X...X..X...

X.X..X..X...X...

X..X.X...X..X...X..X.X..X...X...

M

X...X..X.X..X...

X..X...X.X..X...

X...X..X..X.X...X..X...X..X.X...

X.X..X..X...X...

X.X..X...X..X...

X..X.X..X...X...X..X.X...X..X...

MDifferent figural

X.X...X..X..X...

X.X...X...X.X...

X..X..X...X.X...X..X..X..X..X...

X. X X X X .X...X.X..X..X...

X..X..X...X.X...X...X.X...X.X...

X.X...X..X..X...X.X...X.X...X...

X X X X XX..X..X.X...X...

M

X...X.X...X.X...X..X..X...X.X...

X.X...X.X...X...

X.X...X..X..X...

X..X..X.X...X...X X X X X...

M

41

50

46

45

33

38

36

38

56

57

53

65

58organization

73

93

91

85

86

91

88

74

91

96

87

32

63

48

19

29

41

40

33

70

75

77

75

74

47

85

72

77

77

88

80

73

93

95

87

49

72

61

32

26

62

65

46

80

69

92

77

80

45

69

91

84

83

82

85

87

96

97

93

(table continues)



1558 HANDEL

Table 4 (continued)

Metric strength3

First Secondrhythm rhythm

Pairno.

Experimental condition

Rhythm-pair Rhythm-rhythm Meter-rhythm Meter-meter

Different figural organization

5

9

5 8a)

8b)

9 9)

10)

X...X.X..X..X...X...X.X...X.X...

X...X.X..X..X...

X.X...X.X...X...

X.X..X..X...X...

X..X..X.X...X...X..X.X..X...X...

58

7

8

77

76

42

6

62

70

6

66

71

65

60

Indicates whether a tone occurred at Element 5, Element 9, both Elements 5 and 9 (5 & 9), or neither

Element 5 nor Element 9 (None).

better and there were large differences between the condi-

tions. For the rhythm-rhythm condition, discrimination

improved from 38% to 58% although performance was

above chance only for Pair 5b. For the meter-rhythm and

meter-meter conditions, the improvement was much more

dramatic (from 33% to 74% and from 46% to 80%,respectively) and discrimination of all four pairs was above

chance. These results are shown in Table 4.

Th e discrimination performance for the four pairs going

from a weaker to a stronger metric breaks into two classes.

Performance was better for the meter-rhythm condition an dconsiderably better for the meter-meter condition for Pairs

4a and 5a than for Pairs 2a and 3a. Probably, in the twoeasier pairs, the tone that changed moved to Element 9,

which created a stronger metric than in the two other cases in

which the tone moved to FJement 5, which created a weaker

metric. There was no such difference for the rhythm-rhythm

condition, which demonstrates the potential usefulness of

the meter if the figural organization does not discriminate

two different rhythms. The difference in discrimination between

the meter-rhythm and meter-meter conditions for Pairs 4a

and 5a illustrates that a pulse that accompanies the stronger

meter of the second rhythm can improve discrimination.

Third, consider the 13 pairs in which the two rhythms haddifferent figural organizations. For the rhythm-rhythm con-

dition, discrimination for all pairs (with the exception of Pair8a) was equivalent. There was no effect of metric strength.

Moreover, as described above, discrimination for all of these

pairs was better than that for pairs with the identical figural

organization. For the meter-rhythm and meter-meter condi-

tions, discrimination was far more variable, and the effect of

metric strength was inconsistent. Discrimination was poor-

est when the two rhythms in a pair had the identical metric

strength even if both rhythms had strong meters (Pairs 9 and10). Discrimination improved when the two rhythms h addifferent metric strengths and was maximum when thestronger metric was the first rhythm of the pair. Tw orhythm-pairs were significantly more difficult than theothers (Pairs 6 and 8a), and performance on them equaled

that for pairs with identical figural organizations. These two

pairs were the same ones that produced poorer discrimina-

tion in Experiment 2.The identical pattern of results was found even for the best

25% of the participants. These participants, although they

performed more accurately across all the pairs, also were

unable to discriminate Pairs la-5a for the rhythm-rhythm

and meter-rhythm conditions and Pairs la-3a for themeter-meter condition.

Discussion

These results support the contention that for these rhythms

and tasks, the metric structure operates within the figural orgrouping structure. If the figural organizations of tworhythms are different, then adding an external pulse will no timprove and may even degrade discrimination. However,

the metric structure can help listeners discriminate two

different rhythms with identical figural organizations. Butthe metric structure cannot operate backward in time.

Unless the timing of the tones of the initial rhythm fits themeter (i.e., tones occur synchronously with the pulse at beat

elements), discrimination will not improve. In fact, if thetones of the initial rhythm do not fit the meter, the pulse will

not act as a temporal grid and will make discrimination more

difficult. Thus the effect of an external meter pulse is context

dependent.

General Discussion

The results of these three experiments help to delimit the

role of the metric structure. The notion of a meter underlying

the perception of every rhythm, or that metric rhythms areprototypical, i s seductive, bu t that notion may overstate theimportance of a meter in discrimination.

For the rhythms used in these three experiments, listeners

appear to initially place the tones into groups based on theshortest interval, and those groups form the basis of thefigural organization. If two rhythms have different figuralorganizations, either i n terms of the number of tones in each

group or in terms of the order among the groups (e.g., 1-3-2as opposed to 3-1-2), then listeners easily perceive that the




two rhythms are different. If the figural organizations are the

same, then listeners must use the timing between the onsets

of the initial elements of each group to discriminate the

rhythms. It is here that the meter can provide a grid to time

the intervals between successive groups. What is surprising

is the relative difficulty listeners have in making use of the

possible grids. When these rhythms were presented withouta pulse, there was little evidence that the occurrence of tones

at the metric elements affected discrimination. The strength

of the inherent meter produced by the timing of the tones did

not create a grid that allowed participants to compare

timings across groups. When these rhythms were presented

with a pulse, the pulse improved discrimination only if the

initial rhythm was strongly metric so that the pulse occurred

synchronously with tones. Otherwise, the pulse did not

improve discrimination and actually impaired it, even though

it should logically have instituted the same underlying

metric and timing relationships. In sum, in certain instances

the meter can be used to distinguish among rhythms with

identical figural organizations by creating a temporal grid, inthe same way that melodic tonality can be used to distin-

guish among equivalent melodic contours by creating a

harmonic template or that facial features can be used to

distinguish among equivalent profiles by creating expressive

prototypes.

Generality of Results

Comparisons across experiments. One relevant issue

concerns whether the results reported here can be attributed

to general experimental design effects, response biases, or

both. For example, Yee, Holleran, and Jones (1994) reported

that performance for highly skilled participants changed as a

function of the types of rhythms included within an experi-

mental session. It is unlikely that such design effects could

explain these results even though the three experiments used

a variety of presentation conditions, including different

response modes, pulse conditions, and alternation condi-

tions, and used a different set of participants in each

experiment. I argue this on two grounds. First, performance

was remarkably consistent across experiments, particularly

for the critical different pairs with identical figural organiza-

tions. Consider the five pairs that occurred in all three

experiments, which are the first five pairs shown in Table 2.

The range in the percentage of correct discriminations for

these pairs for the rhythm-rhythm condition across the three

experiments is 6%, 5%, 13%, 4%, and 11%. The range in the

percentage of correct discriminations for these pairs for the

meter-rhythm condition between Experiments 2 and 3 is

21%, 19%, 5%, 2%, and 8%. Second, the use of alternative

pulse conditions (meter-rhythm and meter-meter) led to

new response patterns for those conditions without changing

the responses to the other conditions within Experiments 2

and 3. The meter-rhythm condition (in Experiment 2)

yielded better discrimination for strong-to-weak meter pairs

but did not change the discrimination for the rhythm-rhythm

condition. The meter-meter condition (in Experiment 3)

yielded better discrimination for pairs in which the second

rhythm had a tone at Element 9 (Pairs 4a and 5a in Table 3)

but did not affect discrimination for the rhythm-rhythm and

meter-rhythm conditions.

It is also unlikely that response biases affected the

outcomes. In each of the three experiments there was a

higher percentage of different pairs (60%, 52%, and 64% for

Experiments 1,2, and 3, respectively) than of identical pairs.

Thus, purely on the basis of frequency, participants shouldhave responded different if they were uncertain. But

participants judged different pairs with identical figural

organizations as identical, going against the probability

expectancy. I believe that participants' initial hypothesis in

this task is that the two rhythms are identical and that they

judge them as different only when they perceive a timing

change. Thus, when the participants do not pick up the

variation in the between-groups timing for two different

rhythms with identical figural organizations, they judge the

rhythms as being the same.

Alternative meters. Participants may be using alterna-

tive meters in perceiving these rhythms. In that case, the

analyses based on four-beat meters would not be relevant formany pairs. Rhythm 16 (in Table 1) could be organized

according to a three-beat meter because the tones fall on

Elements 1, 4, 7, 10, and 13. Similarly, Rhythms 7 and 17

begin with tones on Elements 1,4, and 7. In all three of these

rhythms, however, the interval between the onset of the final

tone at Element 13 and the onset of the next repetition at

Element 1 is four elements, so a strict three-beat meter

would progressively fall out of phase with the rhythmic

tones across repetitions. This difference in timing is quite

noticeable (399 ms vs. 532 ms). Nonetheless, to avoid the

possibility that the classification of Rhythm 16 as weakly

metric biased the results, I redid all of the analyses of pairs

of different rhythms in Experiments 2 and 3 and omittedpairs involving Rhythm 16. The results did not change for

any analysis. However, there is some evidence, particularly

in Experiment 3, that pairs of different rhythms involving

Rhythm 16 were easier to discriminate. Overall, the percent-

age of correct discriminations for pairs involving Rhythm 16

was 88%, whereas the percentage of correct discriminations

for the other different pairs with different figural organiza-

tions averaged 72%. What makes the conclusion that

participants were using a three-beat meter comparison

problematic is that Rhythm 16 has a unique figural organiza-

tion of five individual elements and differs from all of the

other rhythms, which have at least one group of two or more

elements. For this reason, the discrimination could be madewithout any perception of meter at all.

Does feedback f f e c t discrimination? It is possible that

discrimination would have been better, particularly for pairs

of different rhythms with the same figural organization, if

participants had been given feedback. This feedback would

have allowed the participants to learn to attend to the

relevant timing information between groups. Although I

could not provide feedback for each trial because of the

available equipment, I attempted to test this possibility with

a fourth experiment in which I provided intensive pretrain-

ing on the rhythms. Before participants began a block of

trials for one condition, four different kinds of pairs of

rhythms were demonstrated and explained: (a) pairs of

identical rhythms that participants misjudged rarely; (b)



1560 HANDEL

pairs of identical rhythms that participants misjudged some-

times (discrimination usually was good for identical rhythms);

(c) pairs of different rhythms that participants misjudged

rarely; and (d) pairs of different rhythms with the same

figural organization that participants judged correctly at less

than chance. For each kind of rhythm, several examples

were presented auditorily while participants looked at avisual representation of the rhythms indicating which ele-

ment had shifted (similar to the representations shown in the

four tables). After the participants stated that they could hear

that the rhythms were identical or different and could

explain the visual representations, the experimental trials

were started. To keep the experiment simple, I used only the

rhythm-rhythm and meter-meter conditions. The orders of

the rhythm-pairs and conditions were counterbalanced, and

the presentation conditions were identical to those in Experi-

ment 3. A total of 40 undergraduate students participated.

In spite of the extensive pretraining, discrimination was

identical to that in Experiment 3. The most important results

concern the pairs of different rhythms with the same figuralorganizations. For the meter-meter condition, if the rhythm

with the stronger meter preceded the one with the weaker

meter, the percentage of correct discriminations was 87%,

but the percentage of correct discriminations for the reversed

pair was only 40%. (The analogous percentages from

Experiment 3 were 80% and 46%). For the rhythm-rhythm

condition, if the rhythm with the stronger meter preceded the

one with the weaker meter, the percentage of correct

discriminations was 64%, but the percentage of correct

discriminations for the reversed pair of rhythms was 40%.

(The analogous percentages from Experiment 3 were 58%

and 38%). Thus, although the pretraining may have im-

proved discrimination slightly for the stronger-to-weakermetric pairs, it did not improve performance for the more

difficult weaker-to-stronger metric pairs. Overall, the pattern

of results was identical to that in Experiment 3. Specifically,

the pulse improved discrimination only if the stronger metric

rhythm was the first (i.e., presumably the reference) rhythm.

Otherwise, discrimination for the meter-meter and rhythm-

rhythm conditions was equivalent and remained below

chance for rhythms with the identical figural organization.

Is the figural organization always predominant? In this

context, the figural organization determined whether two

rhythms were perceived as identical or different. These

results are contrary to the belief that the meter underlies

rhythmic perception and that the figural organization repre-sents a weaker or less organized percept. There are several

possible reasons for the present outcome. First, the partici-

pants were unselected and probably relatively untrained, and

metric organization improves with musical training (e.g.,

Yee et al., 1994). Second, the discrimination task itself might

have minimized the usefulness of the meter, and the

alternation between rhythms might have made the meter

difficult to perceive. Third, the pairs of different rhythms

with identical figural organizations tend to have weaker

meters. Rhythms with stronger meters might have allowed

participants to discriminate between two different rhythms

with identical figural organizations. Fourth, the intervals

between the onsets of adjacent tones are based on only oneunit of 133 ms, and the ratios between different onset

intervals were 1:2:3, which do not readily fit any simple

meter.

Any one or any combination of these possibilities could

account for the weak effect of metric strength. Nonetheless, I

do not believe that they undercut the conclusion that the

figural organization is primary. A meter can resolve the

temporal relationships among the figural groups, but themeter could not exist without the figural groups. The meter is

an emergent property of the auditory grouping in the same

way that symmetry is an emergent property of visual

grouping.

Is a Concept of Meter Necessary?

The concept of a meter is deeply ingrained in music

theory and empirical research. Nearly every theorist argues

for the multilevel nature of a regular beat and the interplay

between the metric and grouping structure (Yeston, 1976).

Moreover, the most influential recent treatment of the

subject, by Lerdahl and Jackendoff (1983), argued that the

metric and grouping structures are independent.

Similarly, there are extensive findings in both motor and

music research that there is a basic temporal unit that is used

to create all of the intervals. Fraisse (1982) summarized

research demonstrating that when participants reproduce

intervals between three or four tones, the intervals are

systematically distorted so that they approach one of two

values: a short interval that is roughly one half the length of a

long interval. Povel (1981) and Povel and Essens (1985)

argued that listeners attempt to create an internal clock (i.e.,

a meter) when listening to a rhythm. Rhythms that are easily

encoded are those in which accented tones fall at equal

intervals, and listeners are assumed to search for a clock that hits the accented tones. In addition, Jones and coworkers

(Jones, 1993) have argued for a model of rhythmic attending

in which the presence of a regular pattern of strong and weak

beats allows the listener to extrapolate the passage and

identify the important structural elements. Finally, Collier

and Wright (1995) suggested that there are innate prefer-

ences for specific rhythmic ratios and that musicians can

scale these ratios faster or slower. But even experienced

musicians find it difficult to learn complex ratios, and none

could scale these complex ratios. What this all means is mat

there is a consensus that rhythmic production is based on a

temporal unit (or possibly two independent units) and that

this unit is subdivided or multiplied to produce the variousintervals in a passage. Using this unit as a reference,

performers can stretch or contract durations to produce the

desired artistic effect (Clarke, 1985).

The problem, then, is to reconcile the overwhelming

evidence for the importance of a meter in reproduction tasks

to the relatively small effects found for a meter in the present

discrimination tasks. One way is to make use of ideas frominformation theory that Garner (1974) used to explain

differences in recall and discrimination tasks. All theorists

have explicitly or implicitly argued that the meter simplifies

rhythms by making them temporally predictable (and thus,

in Garner's terms, making the inferred set smaller). Thus,

there is a simple contingency between the beats and thetones that fall on the beats. The interval between strong beats




is always the same, and this allows the listener to extrapolate

the beat and tonal rhythm into ttie future (cf. Jones & Yee,

1993). This regularity allows the person producing a rhythm

to preplan a repetitive motor response for the strong beats

and to attend to the more irregular intermediate weaker

beats. The memory load is reduced, and therefore we would

expect that reproduction of metric rhythms would be moreaccurate than reproduction of nonmetric rhythms. However,

the simple contingency among the stronger beats of metric

rhythms makes them less differentiated, and therefore we

would expect discrimination among metric and nonmetric

rhythms to be equivalent because of two competing factors.

On the one hand, it is easier to encode metric rhythms

because of the simple contingencies, and that should im-

prove discrimination. On the other hand, the simple contin-

gencies make the metric rhythms more similar, and that

should make discrimination more difficult. In these experi-

ments, the pulse improved discrimination, presumably by

allowing participants to more efficiently encode the metric

rhythm so that it could be better differentiated from thefollowing nonmetric rhythm. This argument points out once

again the contextual nature of rhythmic organization: The

usefulness of any organization depends on the specifics of

the task, and different concepts may be necessary as the task

varies.

From this perspective, the better reproduction of metric

rhythms occurs not because they are metric, but because

they are simpler, and simpler would be the preferred

explanation because it is applicable in a broader domain.

There is an inevitable confound here in that metric rhythms

are necessarily simpler because the strong beats occur at

equal temporal intervals and are therefore more easily

predicted. I do not believe that this is merely a semanticissue because it goes to the heart of whether rhythms are

simply one type of pattern. If this is the case, then concepts

applicable to a broad cross-section of visual and auditory

perceptual phenomena, such as regularity, symmetry, good

continuation, common fate, and similarity, might suffice to

explain rhythm perception without the need for rhythm-

specific concepts.

Although I have argued previously that both visual and

auditory events are perceived within a hierarchical space-time framework and that it is possible to form many

equivalences for these sorts of concepts (Handel, 1988), the

ubiquitous theme-plus-variation structure of music tends to

make the concept of periodicity (i.e., a metric beat) synony-

mous with repeatability, and that need not be true for the

visual world. We do need a concept of meter (if only to

emphasize the motoric and affective components of rhythm),

but the effect of the metric regularity can be understood only

within the context of the listening task, and different tasks

will require different concepts.

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Received August 20,1996

Revision received August 8, 1997

Accepted September 15 1997 •

the interplay between metric and figural rhythmic organization

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