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MELODICPATTERNSANDTONALSTRUCTURE:CONVERGINGEVIDENCEARTICLEJANUARY1991DOI:10.1037/h0094138

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Psychomusicology, 70, 107-126 1991 Psychomusicology

MELODIC PATTERNS AND TONAL STRUCTURE: CONVERGING EVIDENCE

Lola L. Cuddy Queen's University at Kingston

Perception of tonal structure conveyed by three-note melodic patterns was stud-ied. Patterns were the major triad, the minor triad, the diminished triad, and a pattern consisting of three notes in adjacent locations on the cycle of fifths. Pitch contour was either ascending (unidirectional) or reversing (changing direction). The first experiment involved a variant of the probe-tone technique in which lis-teners were asked to rate each note of the chromatic scale as a key-note or tonal center for each pattern. The second experiment collected listener's judgments of structural goodness and of major/minor quality for each pattern. In both experi-ments, the greatest amount of perceived structure was associated with the major triad with ascending pitch contour. The data support the notion that the pitch relationships of the major triad represent a cognitive prototype for the Western idiom.

This article reports two investigations of the perception of tonal structure in short melodic patterns. On this topic, there is a great deal of empirical evidence to support the notion that the perception of tonal structure is influenced by music knowledge [for reviews, see Dowling & Harwood (1986); Frances (1958/ 1988); Handel (1989); Krumhansl (1990,1991)]. Descriptions of music knowl-edge include abstract schematic representations of the hierarchical relations among pitches that characterize the structure and syntax of the Western har-monic idiom (Bharucha, 1984; Dowling, 1978; Krumhansl, 1990; Shepard, 1982). Recently, however, Butler (1989,1990) has disputed the interpretation of much of the empirical evidence, and has thereby questioned certain funda-mental principles on which psychological theories of tonal structure are based.

The dispute is addressed, in the present experiments, by considering Butler's (1989, 1990) criticisms of a report by Cuddy and Badertscher (1987). Cuddy and Badertscher (1987) evaluated the tonal structure conveyed by three me-lodic contexts by means of the probe-tone technique developed by Krumhansl and colleagues (e.g., Krumhansl & Kessler, 1982; Krumhansl & Shepard, 1979). The contexts in the Cuddy and Badertscher (1987) study were a major triad pattern, an ascending major scale, and a diminished triad pattern, and listeners were asked to rate how well each of the 12 tones of the chromatic scale com-pleted the pattern. Tonal structure was assessed in terms of recovery of the tonal hierarchythe extent to which probe-tone judgments reflected both a focal tone or tonic, and structural relations among other tones with respect to the tonic (Krumhansl, 1983; Krumhansl, 1990; Krumhansl & Kessler,1982; see also Lerdahl, 1988). The evidence collected by Cuddy and Badertscher (1987) was that the major triad context conveyed a greater sense of tonal structure than the other two contexts. It was suggested that the major triad was prototypic of tonal structure.

Cuddy 107

Our notion of the prototypic nature of the major triad is consistent with a

description provided by Krumhansl (1990): "The basic idea is that within cat-

egories certain members are normative, unique, self-consistent, simple, typi-

cal, or the best exemplars of the domain.... They are reference points to which

other category members are compared.... [Certain patterns] seem somehow

'better'than others, because they are simpler, more regular, or more symmet-

ric" (Krumhansl, 1990, p. 17). Moreover, the major triad appears to fulfill a

criterion for the tonal-harmonic scheme described by Jones (e.g., 1981, 1982).

as representative of an ideal prototype. Jones (1982) notes that the "tonal-

harmonic scheme reflects a listener's sense of the stable harmonic context and,

in particular, of the tonal center of a piece" (p. 2). The priority assigned to the

major triad is consistent with empirical evidence (e.g., Krumhansl & Kessler,

1982; Roberts & Shaw, 1984), with psychoacoustical theories of sensory con-

sonance (following Helmholtz, 1863/1954), and with music theory in the Schenkerian

tradition (Schenker, 1906/1954).

In recent commentaries, however, Butler (1989, 1990) has contested the

Cuddy and Badertscher (1987) results on several grounds. First, he argues that

the probe-tone technique they used to assess tonal structure is unreliable. He

argues that it is not meaningful to identify probe-tone judgments of pattern

completion with perceived tonal structure. According to Butler (1989, 1990),

the instructions for the typical probe-tone procedure are so vague that the lis-

tener is free to set any one of a number of response criteria. Butler (1989)

suggests, however, that probe-tone judgments might reliably demonstrate ef-

fects such as primacy and recency effects traditionally associated with free

recall.

Second, Butler (1989, 1990) has accompanied his criticisms of the probe-

tone technique with criticisms of current approaches to the study of the percep-

tion of tonal structure. In their place, Butler offers an alternative account based

on logical analysis of the interval content of music patterns, the "recognition of

critical intervallic relationships as they unfold throughout the musical perfor-

mance" (1989, p. 233).

Butler (1989) cites, as compatible with his own approach, Browne's (1981)

analysis of the diatonic pitch set in terms of its interval-class content. Browne

(1981) points out that within the diatonic pitch set of seven pitch-classes, there

are 21 interval classes. There are two minor seconds (or major sevenths), five

major seconds (or minor sevenths), four minor thirds (or major sixths), three

major thirds (or minor sixths), six perfect fourths (or perfect fifths) and one

tritone (augmented fourth or diminished fifth). The frequency of occurrence

with which each interval class occurs in the diatonic set may be summarized by

the vector .

Next, Browne (1981) points out several properties of the vector, the most

important of which is the principle of unique multiplicity. "The diatonic set

contains a full range of intervallic ubiquity. The six interval-classes occur from

one to six times, and each of them a unique number of times. This constitutes a

full spread of possibilities from 'rarity' to 'common-ness'a maximum pos-

sible hierarchization" (p. 6). Note that "rarity" and "common-ness" in this analysis

refer to frequency of occurrence in the interval vector, not to frequency of

108 Psychomusicology Fall 1991

occurrence in music. Frequency of occurrence in theiMerKalmecttoadifteFr quency of occurrence of intervals in music are not in!e^efeie

The interval content of the minor triad logically implicates three diatonic keys; the interval content of the fifths pattern logically implicates five diatonic keys. From the perspective of logical analysis of interval content, neither pattern should 'elicit girtunambiguous sense of tonal center and accompanying struc-tutalrKiera#ehymnd, therefore, neither should be as strong an indicator of tonal sff^iur&tothe diminished triad.

(o Ihdre is, however, evidence suggestive that the minor triad pattern and the fiflfc pattern might yield a reasonably strong sense of tonal structure. With respect to minor triads, it has been shown with the probe-tone technique that harmonic minor triads strongly instantiate the tonality of the root of the triad (Krumhansl & Kessler, 1982); minor triads suggested a single key to listeners to a greater extent than did diminished triads, which tended to be interpreted in terms of both the major and minor keys in which the chord functioned harmoni-cally. Cohen (1991) reported a study in which listeners were asked to listen to excerpts from the Bach Preludes and to sing the scale of the key suggested by the excerpt. For each of the six Bach Preludes in the minor key, the four opening notes outlining the minor triad signaled the minor tonality for listeners.

With respect to fifths patterns, the evidence is indirect. Cross, Howell, and West (1985) reported experiments in which listeners heard three-note patterns, including fifths patterns (pitch-class sets of the type ), and rated the goodness-of-fit of a single tone following each pattern. The single tone was either a member of one of the scales logically implicated by the pattern or was an out-of-scale note. For the fifths patterns, listeners readily rejected, as "wrong," the note that did not fit within any of the five scales implicated by the patterns. Moreover, the authors found that fifths patterns were more effective contexts for producing rejections of nonscale notes than were three-note patterns con-taining the rare interval of the tritone (patterns implicative of only one diatonic scale). Cross, Howell, and West (1985) concluded that "the lower the logical scale specificity, the stronger the scalar schema" (p. 137). The authors are careful to explain that scale identity may not be the same as key identity. How-ever, to the extent that scale identity contributes to perceived tonal structure, the implications of their conclusion appear to be opposite to Butler's (1989, 1990) proposals.

A final point deals with the order in which the notes of the pattern were presented. In the present experiments, all patterns were realized either as three notes with ascending pitch contour or three notes with reversing pitch direc-tion, i.e., a change in pitch contour. The reversing pitch contour for the dimin-ished triad exemplified an ordering that should, according to Butler (1989), be especially conducive to the recovery of a tonal center. On the other hand, the application of the Gestalt principle of "good continuation" to music patterns (Deutsch, 1982, p. 101) leads to the prediction that tonal structure will be more readily detected for patterns with a unidirectional pitch contour than for pat-terns with more complex contours. Cuddy and Cohen (1976) found that major triad patterns with unidirectional pitch contour were more easily recognized under transposition than were major triad patterns with a contour that changed

110 Psychomusicology Fall 1991

direction. The main aspects of the method for the two experiments will be described next, followed by the specific description of each.

General Method Listeners

Listeners were volunteers from the university community who had attained at least Grade VIII Royal Conservatory level of performance in voice or an instrument. This level is comparable to the practical component of the Grade 12 music curriculum in Ontario schools. A typical listener had received music training at the level of a junior in an undergraduate music program. No listener was a professional musician. Listeners ranged in age from 16 to 30; the ratio of females to males was 2:1. They were paid $3.00 per session for participation.

Patterns

Test patterns were eight diatonic patterns of three successive notes span-ning six or seven semitones. For the first four patterns, the pitch contour as-cended; for the remaining four, the pitch contour reversed direction. Within each contour (ascending and reversing), there were four patternsthe major triad, a pattern of fifths (as described above), the minor triad, and the dimin-ished triad. The patterns with ascending contour are exemplified by C4E4G4, C4

F4G4, D4F4 A4, and B3D4F4, respectively. The patterns with reversing contour are exemplified by E4G4C4, G4C4F4, A4D4F4, and D4F4B3, respectively.3 In the experiments, the patterns were transposed to different, randomly selected, fre-quency locations within the overall range B3 to D5.

Fourteen practice patterns were also constructed. They were three-note diatonic patterns within the range of an octave, and all were different from the test patterns.

Apparatus and General Procedure

Sine-tones for each pattern were produced by a DMX-1000 signal proces-sor under control of a LSI 11/23 host computer. The sampling rate was 19.3 kHz. The duration of each tone in each pattern was .33 s with 25 ms rise time and fall time. Frequency values for the tones were determined according to the system of equal temperament, with A4 = 440 Hz. The amplitude of each tone was set according to the Fletcher-Munson loudness contours. The overall level was adjusted to that judged comfortable by the listener, about 65 dB SPL.

In the experiments, the experimental conditions were randomly ordered across trials, and the entire set of trials presented as a single block. The order of trials, and the frequency location of the pattern presented on each trial, were randomized independently for each listener. The patterns were delivered through Sennheiser HD-424 headphones to the listener seated in a sound-proof booth. Responses were entered on a Zenith Z19 console located in the booth and stored in the host computer for analysis. Trials were self-paced; after responding to a trial, the listener pressed the "enter" key on the terminal to initiate the next trial.

In both experiments, listeners were told that there were no "right" or "wrong" answers to the tests. They were asked to respond in terms of their own auditory

Cuddy 111

"feelings or impressions." Therefore, no feedback was provided on either prac-

tice or test trials.

Experiment I

In the first experiment, listeners were asked to judge the suitability of each

of the 12 notes of the chromatic scale as a tonic or key center for each of the test

patterns.

Method

Thirteen listeners were tested. On each trial, a test pattern was presented

and was followed, after a delay of Is, by a 1-s presentation of a single tone

called a key-probe. There were 12 key-probes for each test pattern. Each key-

probe was coded in terms of pitch-class distance, from 0 to 11, from the first

note of the pattern. Each pitch-class distance was tested once for each pattern.

The timbre of the key-probes was that of a "Shepard tone" (Shepard, 1964;

see also Cuddy & Badertscher, 1987), a complex of octave equivalents for

which the amplitude envelope is shaped to obliterate a clear sense of pitch

height. Listeners were asked to rate the suitability of the key-probe as a tonic or

key-note for the pattern on a scale of " 1 " to "6," where " 1 " represented "very

good " and "6" represented "very poor." They were told that the timbre of the

key-probe would be different from that of the pattern, the purpose being to

remind them not to rate the key-probe for melodic continuity or completion but

as an abstract key-center for the pattern.

Nine practice patterns were each paired with each of five randomly se-

lected key-probes. Practice trials consisted of the 45 pairings of patterns and

probes presented in random order for ratings by listeners. Practice trials were

followed by test trials in which each of the test patterns was paired with each of

12 key-probes. In the test trials, two patterns and their pairings with the 12 key-

probes were replicated (major triad pattern with ascending contour and fifths

pattern with reversing contour). The replication trials were randomly inter-

leaved with all other trials and allowed an assessment of internal reliability.

Five additional practice patterns were embedded among the test patterns in

order to encourage the listener to expect a variety of diatonic patterns. The

order of pairings of patterns and probes, and location of the pattern within the

frequency range, were independently randomized across trials for each lis-

tener.

Each session consisted of 45 trials in the practice phase followed by 180

trials in the test phase and lasted about one hour.

Results and Discussion

For each test pattern, a set of mean ratings across the 13 listeners was

obtained for each of the 12 pitch-classes of key-probes. This set of ratings will

be called the key-probe profile for the pattern.

The eight panels of Figure 1 show the set of mean ratings obtained for each

of the eight test patterns. For purposes of illustration, the various transpositions

of each pattern have been collapsed to a single frequency locationthe note-

112 Psychomusicology Fall 1991

C4 E

4 G

4

Major Triad Ascending

I 1 I I I I I I I I I I DbAbEbBb F C G D A E B F #

5 -

CFG 4

y\. 5

<

Fifth Patterns Ascending.

i i i i i i i i i i i i DbAb EbBb F C G D A E B F #

4 -

5 "

C Eb4 G4

kA .^ Minor Triad Ascending

i i i i i i i i i i i i DbAbEbBb F C G D A E B F #

4 -

5 "

eEb4Gb4

WW-Diminshed Triad Ascending

I I I I I I I I I I I I DbAbEbBb F C G D A E B F #

1

2 - I

3 -

4

5 H

E4 G4 C4

Major Triad Reversing

I I I I I I I I I I I I DbAb EbBb F C G D A E B F #

Q4 C 4 F 4

Fifth Patterns Reversing 6 i i i i i i i i i i i i

1 DbAb EbBb F C G D A E B F I

2 -

3 "

5 -

G4CEb4

Minor Triad Reversing

I I I I I I I I I I I DbAbEbBb F C G D A E B F #

E b 4 G b 4 C 4

4 - 1

Diminshed Triad Reversing

i i i i i i i i i i i i DbAbEbBb F C G D A E B F #

KEY-PROBE ORDERED BY CYCLE OF FIFTHS

Figure 1. Key-probe profiles for the eight test patterns (Experiment 1). From

top to bottom, the panels represent major triads, fifths patterns, minor triads,

and diminished triads. The left-hand column is ascending pitch contour, the

right-hand column is reversing pitch contour. The note names for the key

probes on the horizontal axis align with the notes of the specific exemplar of

each pattern given within each panel.

Cuddy 113

names exemplified in each panel. The vertical axis of each panel is mean rating.

The horizontal axis is key-probe ordered according to the cycle of fifths. The

note-names for the key-probes are assigned with respect to the exemplar of

each pattern, described further below. Exemplars for the left- and right-hand

panels are paired so that in each row key-probe profiles refer to the same pitch

content. Two panels, representing the profiles for the major triad pattern with

ascending contour and the fifths pattern with reversing contour, include the

data for replicated patterns.

The left-hand column of Figure 1 shows the mean ratings for patterns with

ascending contours. Each pattern is illustrated by an exemplar that begins on

C4, and the names of the key-probes on the horizontal axis correspond to the

note-names of the particular exemplar. The key-probe C corresponds to C4 in

the exemplars and thus corresponds to the first note of the patterns in the left-

hand column. For example, for the major triad pattern with ascending contour,

both replications, the key-probe assigned the highest rating for the exemplar

C4 E4 G4 was the key-probe C. Across the transpositions of the pattern, the key-

probe assigned the highest rating for the major triad pattern with ascending

contour was the pitch class of the first note (first serial position).

The right-hand column shows the data for patterns with reversing contours.

The exemplar for each panel in the right-hand column is the reversal of the

exemplar in the corresponding left-hand column. The key-probe C in each panel

in the right-hand column corresponds to C4 in the exemplar, and, as well, to the

serial position at which C4 occurred in the exemplar. Thus it can be seen, for

example, that for the major triad pattern with reversing contour, the key-probe

assigned the highest rating for the exemplar E4G4C4 was the key-probe C. Across

the transpositions of the pattern, the key-probe assigned the highest rating for

the major triad pattern with reversing contour was the pitch class of the last note

of the pattern (third serial position).

Inspection of Figure 1 reveals that for major triad patterns, fifths patterns,

and minor triad patterns, ratings for key-probes on either side of the key-probe

given the highest rating tended to decrease in a fairly regular fashion. Ratings

for key-probes appeared systematically related to distance on the cycle of fifths;

ratings tended to decrease as distance of the key-probe increased, in either

direction, from the key-probe given the highest mean rating. For the diminished

triad patterns (bottom panels of Figure 1), ratings did not appear to be system-

atically related to distance on the cycle of fifths.

The ratings collected for each test pattern were subjected to ANOVA (one-

factor repeated measures, conducted separately for each pattern). Table 1 shows

the results of the ANOVA. The rows in Table 1 represent the different patterns;

the columns represent the two different orders of presentation. The upper entry

in each cell is the value of the F-ratio, based on 11 and 132 df. The middle entry

is 82, the component of the numerator of the F-ratio that is an estimate of the

variability of the treatment (population) means (Myers, 1979, p.84). The lower

entry is the estimate of error variance. The second entries on each line for the

major triad pattern with ascending contour and fifths pattern with reversing

contour are the results for the replication of the pattern represented by the cell.

114 PsychomusicologyFall 1991

The correlations between profiles for replicated patterns were highly signifi-

cant (for the major triad pattern with ascending contour, r (10) = .87; for the

fifths pattern with reversing contour, r (10) = .90, both/?

Table 2

Correlations between key-probe profiles and standardized profiles around the

cycle of fifths (Experiment 1). The correlation for the best-fitting standardized

profile is underlined

Pattern: Major triad ascending

Standardized major key profile

Db Ab Eb Bb F C G D

-.13 .04 .06 .30 .79 .80 .20 -.24

Exemplar: C4 E

4 G

4

A

-.43

E B

-.54 -.49

-.23 -.20 .26 .31 .65 .79 .27 -.33 -.52 -.42 -.41

F#

-.34

,56

Pattern: Major triad reversing

Standardized major key profile Db Ab Eb Bb F C G D

-.11 .13 -.03 .07 .69 TL .11 -.22

Pattern: Fifths pattern ascending

Standardized major key profile Db Ab Eb Bb F C G D

-.09 .14 -.36 .60 M .63 .12 -.33

Pattern: Fifths pattern reversing

Standardized major key profile

Bb F C G D

.74 J9 .26 -.15 -.39

.54 J 3 .24 -.37 -.48

Standardized minor key profile

bb f c g d

.47 J 5 .26 .32 .48

Exemplar: E4G4C4

.20

.34

db

,51

.21

.32

ab

-.35

.32

.27

eb

-.09

A E

-.23 -.31

Exemplar:

A E

-.63 -.72 -

Exemplar:

A E

-.60 -.64 -

-.43 -.45 -

a e

-.05 -.38 -

B F#

,40 -.46

: C4F4G4

B F#

,58 -.34

G4 C4 F4

B F#

,52 -.22

,50 -.21

b f#

,41 -.48

-.26 -.29 -.08 .43 .85 .18 .09 .34 .06 -.36 -.66 -.31

Exemplar: C4 Eb

4 G

4 Pattern: Minor triad ascending

Standardized minor key profile db ab eb bb f c g d

-.08 .07 -.21 .06 .49 J% .03 -.30

Pattern: Minor triad reversing

Standardized major key profile

Db Ab Eb Bb F C G D

.38 .84 ,86 .37 .12 -.01 -.32 -.68

Pattern: Diminished triad ascending

Standardized minor key profile

db ab eb bb f c g d

.01 .22 .21 -.09 .09 .52 -.40 -.55

Pattern: Diminished triad reversing

Standardized major key profile

Db Ab Eb Bb F C G D

.60 .63 .09 -.14 -.09 -.16 -33 -.35

Note: For r(10) = .71, p < .005.

a e

.06 .08

Exemplar:

A E

.69 -.53

Exemplar:

a e

.06 -.08

Exemplar:

A E

.27 -.26

b f#

-.30 -.53

G4C4Eb4

B F#

-.29 -.06

C4Eb4Gb4

b f#

.03 -.02

Eb4Gb4C4

B F#

.02 -.25

116 Psychomusicology Fall 1991

The next analysis examined the relationship between the key-probe pro-files reported in Figure 1 and the standardized profiles for major and minor keys derived by Krumhansl and Kessler (1982). The standardized profiles are a set of ratings obtained for the major and for the minor key by averaging the probe-tone profiles for several key-defining contextschords and chord cadences. Krumhansl and Kessler (1982) demonstrated that an abstract representation of key relationships may be recovered from the standardized profiles and expressed as two circular configurationsthe cycle of fifths and the cycle of thirds, re-spectively.

A best-fitting standardized profile was sought for each of the key-probe profiles in Figure 1. The ratings for each key-probe profile were correlated with the ratings for the standardized profiles for each of the 12 major and 12 minor keys. The highest positive correlation was determined, and the key of the stan-dardized profile yielding the highest correlation, if significant, was selected as the best-fit. Because of the large number of correlations involved, the criterion for significance was set at .005, higher than the conventional level.

Table 2 shows the set of correlations for the entire cycle of keys around the best-fitting key. The correlation for the best-fitting key is underlined. The as-signment of key-names in Table 2 corresponds to the exemplar of each pattern given in the table and also in each panel of Figure 1.

Two sets of correlations are provided for the major triad pattern with as-cending contour and fifths pattern with reversing contour, one set for each replication of the pattern. In addition, for the fifths pattern with reversing con-tour exemplified as G4C4 F4, F major was the best-fitting key for one replica-tion, f minor was the best-fitting key for the other. Both cycles, therefore, are given in Table 2. It can be seen that both F major and f minor are possible selections for best-fitting key for this exemplar.

No best-fitting key was found for either diminished triad pattern according to the above criterion for significance, probably because, as noted above, dif-ferences among key-probe ratings for these patterns were not reliable. The cycles containing the nearest fitting keys for the diminished triad patterns are included in the table. It may be noted that the key of Db, the diatonic key logically implicated by the pattern Eb4 Gb4 C4, is weakly implicated in the correlational data.

For major triad patterns, fifths patterns, and minor triad patterns, the vari-ance shared between the key-probe profile and a standardized profile was greater than the residual variance. There was, however, a systematic effect in the re-sidual variability of the key-probe profiles that lends itself to musical interpre-tation. For profiles best fit by a major key, the key-probe corresponding to the subdominant was rated higher than the key-probe corresponding to the mediant. The direction of this difference is opposite to the direction of the difference in the standardized profile for the major key. The finding may mean that key-probe ratings are slightly drawn along the cycle of fifths toward the key in which the tonic note performs a dominant function. (This result is also evident in Table 2.) The profile for the major triad chord contains a similar tendency (Krumhansl & Kessler, 1982).

Cuddy 117

A further correlational analysis was conducted to examine an alternative

account of the obtained variability in key-probe ratings. The alternative ac-

count was that ratings simply reflected the tones contained in the pattern. Two

sets of predictors were derived and will be referred to as the unweighted version

and the weighted version, respectively, of a pattern-content model. For the

unweighted version, it was assumed that key-probes were rated according to

whether or not the pitch-class of the key-probe matched the pitch-class of one

of the notes that occurred in the test pattern. Thus, the values entered for the

unweighted predictor were " 1 , " for the notes that occurred in the test pattern,

and "0" for all other notes. For the weighted version, it was assumed, in addition

Table 3

Correlations between key-probe profiles and predictors based on unweighted

version (upper entry in each cell) and weighted version (lower entry in each

cell) of a pattern-content model (Experiment 1)

Pattern

Major triad

Fifths

Minor triad

Diminished triad

Pitch contour

Ascending

.47, .58

.60, .65

.89

.81

.58

.68

.67

.68

Reversing

.45

.49

.68, .63

.72, .68

.62

.62

.32

.41

Note: For r(10) = .71, p < .005.

to the above, that greater weight was assigned to the first and last note of the

pattern (i.e., the first and third serial position). The values for the weighted

predictor were "2" for the first and third serial position of the pattern," 1" for the

middle position, and "0" for all other notes. Correlations between the key-

probe ratings and the predicted values for each version of the pattern-content

model are shown in Table 3.

The format of Table 3 is identical to Table 1. The upper entry in each cell is

the correlation obtained between key-probe ratings and the unweighted predic-

tor values.The lower entry in each cell is the correlation obtained between key-

probe ratings and the weighted predictor values. The second entries on each

line for the major triad pattern with ascending contour and fifths pattern with

reversing contour are the results for the replication of the pattern represented by

the cell.

118 Psychomusicology * Fall 1991

Table 3 reveals a slight advantage of the weighted version of the pattern-

content model over the unweighted version for eight of the ten pairs of correla-

tions. (Correlations were higher, on the average, by about .05). Even so, the

weighted version of the pattern-content model did not suggest a more promis-

ing account of the key-probe profiles than an account based on the standardized

profiles. Correlations for the weighted version of the pattern-content model

were lower than those obtained for the best-fitting standardized profile in all

cases except the diminished triad pattern with ascending contour. Moreover,

for the weighted version of the pattern-content model, only two correlations

were significant beyond the .005 level.

A comparison between the underlined correlations in Table 2 and the cor-

relations in Table 3 suggests that tonal hierarchy predictors usually accounted

for a greater amount of the variability in key-probe ratings than did predictors

based solely on pattern-content. This suggestion was followed by conducting

hierarchical regression on the entire set of key-probe profiles (10 patterns x 12

probes). The weighted version of the pattern-content model was entered first

into the regression and accounted for 36% of the variance (p < .001). The best-

fitting standardized profile was entered second and accounted for an additional

20% of the variance (p < .001). Thus, there was systematic evidence that the

key-probe ratings were not merely indicative of pattern-content, but also con-

tained information about tonal structure.5

The results of the first experiment suggest that the major triad pattern with

ascending contour occupied a privileged position among the patterns tested.

This pattern was associated with the greatest amount of differentiation among

the key-probe ratings. It was followed, in amount of differentiation among key-

probe ratings, by the major triad with reversing contour, and the fifths patterns.

Much weaker differentiation among key-probe ratings occurred for minor and

diminished triad patterns. This ordering did not correspond to the ordering of

the number of keys logically implicated by the patterns.

Experiment II

In the first experiment, it was found that key-probe ratings for major triad

patterns, fifths patterns, and minor triad patterns implicated tonal centers and

tonal hierarchies. The major triad pattern with ascending contour was a par-

ticularly effective context in that it yielded the strongest differentiation among

key-probes and the clearest indication of tonal structure. In the second experi-

ment, converging evidence for this finding was sought. Rather than assessing

structure through the analysis of key-probe ratings, the second experiment col-

lected direct judgments of structural quality or "goodness" for the patterns

(Cuddy, Cohen, & Mewhort, 1981; Garner, 1974), and judgments of major/

minor quality.

Method

There were two successive parts to the experiment; 18 listeners partici-

pated in both parts. Listeners had not participated in the first experiment. In the

first part, listeners were asked to rate the perceived structural goodness of each

Cuddy 119

pattern on a 6-point scale. It was suggested to listeners that structural goodness

referred to the degree to which the notes held together as a "good form" or

coherent pattern. On the 6-point scale, " 1 " represented "very high structure,

cohesiveness, or good form" and "6" represented "very low structure, cohe-

siveness, or good form." In the second part, listeners were asked to rate each

pattern on a 6-point scale for "major/minor quality" where " 1 " represented

"very strong major quality" and "6" represented "very strong minor quality."

Both parts of the experiment began with practice trials in which each of the

practice patterns were presented once and rated. The practice trials were fol-

lowed by the experimental trials. The set of experimental trials contained an

example of each test pattern plus the two replicated patterns and five patterns

Table 4

Ratings of structural goodness for eight stimulus patterns (Experiment 2).

The upper entry in each cell is mean rating; the lower entry is standard

error of the mean. On the rating scale, "1" represented "very high" and

"6" represented "very low"

Pitch contour

Pattern Ascending

1.83,2.17

.23, .27

2.83

.27

2.61

.27

3.22

.28

Reversing

3.00

.26

2.56,2.61

.26, .25

3.78

.26

4.06

.27

Major triad

Fifths

Minor triad

Diminished triad

from the set of practice patterns. As noted above, the order of presentation of

the patterns, and the frequency location within the range, were both indepen-

dently randomized for each listener.

Each session, therefore, consisted of 9 trials in the practice phase and 15

trials in the test phase for ratings of structural goodness, then 9 trials in the

practice phase and 15 trials in the test phase for ratings of major/minor quality.

The entire session lasted less than half-an-hour.

Results and Discussion

Table 4 shows the mean rating of structural goodness for each of the eight

test patterns (upper entry in each cell) and the standard error of the mean (lower

entry in each cell). The format of Table 4 is the same as that of Table 1. Inspec-

tion of Table 4 yields the following observations, supported by tests of orthogo-

nal contrasts within the ANOVA.

120 Psychomusicology Fall 1991

Major triad patterns and fifths patterns received higher ratings of structural

goodness than minor triad and diminished triad patterns, F (1,17) = 19.59, p <

.001. Differences within the set of means for major triad patterns and fifths

patterns depended on pitch contour. For patterns with ascending pitch con-

tours, the major triad pattern received higher ratings than the fifths pattern, F

(1, 17) = 6.54, p < .02; for reversing contours, the means were reversed, but

were not significantly different, F (1, 17) = 1.22,p > .20.

Differences within the set of means for minor and diminished triad pat-

terns appear to favor higher ratings for minor triads than for diminished triads,

but the differences were not significant (for ascending contours, F (1, 17) =

2.37, p > .10; for reversing contours, F (1, 17) = .60 ns). For both minor and

Table 5

Ratings of major I minor quality for eight stimulus patterns (Experiment 2). The

upper entry in each cell is mean rating; the lower entry is standard error of the

mean. On the rating scale, "1" represented "very strong major quality" and

"6" represented "very strong minor quality"

Pattern

Pitch contour

Ascending

1.39,

21,

2.89

.29

5.33

.25

5.33

.22

1.39

.22

Reversing

2.83

.32

2.50,2.17

.29, .26

4.83

.25

5.06

.24

Major triad

Fifths

Minor triad

Diminished triad

diminished triad patterns, patterns with ascending pitch contour received higher

ratings than patterns with reversing contours, F (1, 17) = 15.30, p < .001. The

two means collected for each replicated pattern were similar (for the major triad

patterns with ascending contour, F (1,17) = 3.40, p > .05; for the fifths patterns

with reversing contour, F (1,17) = .06 ns). The set of standard errors was stable;

moreover, standard errors were not systematically related to mean ratings.

Table 5 shows the results for the ratings of major/minor quality. The for-

mat of Table 5 is identical to that of Table 1. Inspection of Table 5 yields the

following observations, supported by tests of orthogonal contrasts within the

ANOVA.

Major triad patterns and fifths patterns were judged to convey a strong

sense of major key; minor and diminished triad patterns were judged to convey

a strong sense of minor key. The difference in ratings was highly significant, F

(1, 17) = 90.18,/? < .0001. The differences between major triad and fifths pat-

Cuddy 121

terns were similar in direction to those found for ratings of structural goodness.

For patterns with ascending pitch contours, the major triad received higher

ratings of major quality than the fifths pattern, F (1, 17) = 20.55, p < .001; for

reversing contours, the means were reversed, but were not significantly differ-

ent, F (1,17) = 1.78,/? > .15).

The slight differences between means for minor and diminished triad pat-

terns were not significant (all contrastsp > .15). The two mean ratings collected

for each replicated pattern were similar (means for the major triad patterns with

ascending contour were identical; means for the fifths patterns with reversing:

contour were not significantly different; F (1, 17) = 1.06, p> .30). The set of

standard errors was stable; moreover* standard errors were not systematically

related to mean ratings.

In both parts of the experiment; the major triad pattern with ascending

contour was assigned a privileged position. Of all patterns tested, this pattern

was associated with the highest degree of structural quality in the first part of

the experiment and the strongest conveyor of major quality in the second part

(both overall, and in comparison to other major and fifths patterns).

Differences between the two parts of the experiment may also be noted. In

particular, the perceptual structure of minor and diminished triad patterns was

judged to be weak to moderate but the minor quality of these patterns was

judged to be clear and strong.

The reliability of the replications; and the stability of the standard errors in

both parts of the experiment, are indicators of the consistency of listeners^

response strategies for both tasks. Had minor and diminished triad patterns

elicited a greater variety of individual strategies than major triad and fifths

patterns, significantly greater between-subject variability would be expected

for the former patterns than fbr the latten

General Discussion

The initial motivation for the present experiments was to search for con-

verging evidence to support the distinction drawn between tonal structures

conveyed by the major and the diminished triad (Cuddy & Badertscher, 1987).

Cuddy and Badertscher's (1987) data showed that a major triad pattern was

more effective in recovering the tonal hierarchy than a diminished triad pattern.

In the first experiment reported here, key-probe profiles for the major triad

patterns revealed a clear sense of key center, and contained information about

the tonal hierarchy of the key. Key-probe profiles for the diminished triad pat-

terns did not yield reliable evidence of a sense of tonal structure. In the second

experiment, both structural quality and the sense of major modality were rated

significantly higher for the major triad patterns than for the diminished triad

patterns. These differences between the major triad and diminished triad pat-

terns are convergent with the differences reported by Cuddy and Badertscher

(1987). Altering the order of the notes in the triads, in the present experiments,

did not reverse these findings, but, rather, preserved the direction of the differ-

ences.

122 Psychomusicology Fall 1991

Supplementary evidence was provided by the testing of fifths patterns and

minor triad patterns. Findings for the fifths patternthe most ambiguous of all

patterns tested in terms of number of keys implicatedyielded data that re-

sembled the data for major triad patterns. Key-probe profiles yielded evidence

of a strong tonal center. Ratings of structural quality and major modality were

almost as high as those for major triad patterns and significantly higher than

ratings for the diminished triad patterns.

Key-probe profiles for minor triad patterns also yielded a sense of tonal

center, but, compared to key-probe profiles for major triad patterns, the distinc-

tion between key-probes was much weaker. Minor triad patterns were judged to

be of moderate to weak structural quality, but to yield a strong sense of minor

modality. The association of weak or ambiguous tonal structure with minor

quality (also found for diminished triads) is worth pursuing; it may bear on the

affective character of minor triads and modes. Major triads are associated with

positive affect, minor with negative affect (Crowder, 1984, 1985; Crowder &

Kastner, 1989). Meyer (1956) has commented that the minor mode "is both

more ambiguous and less stable than the major mode" (p. 226). The association

of the minor mode with negative affect (i.e., anguish and suffering) he attributes

to the "deviant, unstable character" (p. 228) of the mode; it is "quasi-chromatic

and changeable" (p.224).

Examination of the results for all four patterns tested yielded no support for

any account that attributes perceived tonal structure of a pattern primarily to the

number of diatonic keys logically implicated. Moreover, there was no support

for the possibility that key-probe ratings for all four patterns merely reflected

pattern content. Key-probe ratings for major triad, fifths, and minor triad pat-

terns also contained evidence of sensitivity to tonal structure conveyed by the

patterns.

Overall, the evidence supports the notion that the degree of tonal structure

conveyed by short melodic patterns is dependent on the ease with which a

pattern can be mapped on a stable, abstract, internally consistent representation

of the hierarchical pitch relationships of Western tonal music. A pattern such as

the major triad, which contains both psychoacoustic and cognitive cues that are

prototypic of the pitch structure of Western tonal music, readily accesses this

representation. Of the remaining patterns tested, results for the fifths patterns

most closely resembled results for the major triad patterns. This finding sug-

gests that the fifths patterns deviated least from the prototype and accessed an

internal representation of tonal relationships more readily than did the remain-

ing patterns.

The present data (Experiment 1), Cuddy and Badertscher (1987), and Krumhansl

and Kessler (1982) all converge on the finding that the major triad most strongly

instantiates the key of its root. This clear sense of tonal center doubtlessly

facilitates the recovery of the hierarchical relationships among tones within

that key, and relationships of that key to other keys. Such an interpretation does

not imply an "all-or-nothing" approach to tonality. Although the major triad C

E G most strongly instantiates C as a tonal center, it also implicates the two

other diatonic keys to which the triad belongsF next, and then G (Figure 1).

Cuddy 123

The point here, however, is that not all keys are implicated to the same degree.

Rather, the implication of key relationships involves a hierarchical structure.

Multiple tonalities or key-centers may exist simultaneously, but with percep-

tual priority assigned according to hierarchical principles of organization.

A number of issues remain to be addressed. Questions remain concerning

the cues used to detect tonal centers for patterns deviating from the prototype,

and the role of music experience in the implementation of these cues. Listeners

may have multiple strategies availablefor example, strategies to listen for

specific interval distributions, interval sequences, or implied harmonic pro-

gressions. It is promising to note, in answer to Butler's (19S9,1990) criticism

that strategies to rate probe tones are unreliable, that listeners in our experi-

ments produced reliable responses to a given test pattern. Thus, although listen-

ers may flexibly adapt strategies in order to deal with a specific pattern,fhey do

so consistently.

Questions remain concerning the effects of serial order of the tones ^f

melodic patterns. The data suggest that patterns with ascending pitch contour

are perceived as more structurally coherent than patterns with reversing con-

tour (with the possible exception of fifths patterns). This finding may reflect a

general perceptual process described by the Gestalt principle of "good continu-

ation," but given that a limited number of serial orders was tested, no firtn

conclusion can be made.

Further questions concern the role of larger contexts. According to the

present evidence, the rare interval of a tritone is not a reliable cue to tonal

structure. This finding, of course, leaves open the possibility that the tritone

may serve to consolidate or to disambiguate tonal information conveyed by

longer melodic patterns (Cuddy et al., 1981) or folk-melodies (Boltz, 198$).

However, other "predictable, prototypical aspects of a tonality" may be of greater

importance in establishing the tonal strength of a melody (Dowling, 1991, p.

307).

The present work was addressed to Butler's criticisms of Cuddy and Badertscher

(1987). It provides no support for the notton that the results obtained by Cuddy

and Badertscher (1987) were simply Artifacts of a flawed methodology. In-

stead, the theoretical interpretation of these results in terms of the representa-

tion of the tonal hierarchy (Krumhansl, 1990) or the stability conditions of the

basic pitch space (Lerdahl, 1988) is further strengthened by the converging

evidence of the present experiments.

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Footnotes 1 The above description of logical implications of intervallic patterns is simplified

by referring only to the diatonic system, and this simplification will be retained in the present discussion. It is acknowledged that patterns may also implicate other systems, such as the minor modes (Butler, 1989, Footnote 13). Minor systems, however, intro-duce additional complexities, such as the presence of several variants, and the loss of the unique-multiplicity principle for all but the variant known as the natural or pure minor. Including the logical implications of minor keys for the patterns studied in the present experiments does not change their relative ordering in terms of the total number of keys implicated. Therefore the complexities of the minor systems with respect to the analysis of logical implication need not be introduced further here.

2 The arrangment of notes in the fifths patterns was determined by a constraint to keep the pitch range of all test patterns similar. Had the notes been arranged to form two successive intervals of a fifth, the span would be greater than an octave and consider-ably greater than the span of any other test pattern. For both arrangements, however, the frequency of occurrence of the intervals in the interval vector, and the number of keys logically specified, is the same.

3 Because the present experiments were not intended to provide a systematic ac-count of order effects, the direction of the reversal was selected arbitrarily with two constraints. The first constraint was that there be fwo instances where the contour ascended and then descended, and two instances where the contour descended and then ascended. The second was that the reversing contour for the diminished triad could be interpreted as a subdominant-to-dominant progression.

4 Fourier analysis of the profiles (Cuddy & Badertschef, 1987; Krumhansl, 1990) produced analogous results. The total amount of variance attributable to the harmonic partials (total variability about the mean) was calculated for each profile. The ordering of patterns from greatest to least amount of variance was major triad patterns, fifths patterns, minor triad patterns, and finally, diminished triad patterns.

5 Because of the unreliable nature of the ratings for diminished triad patterns (Table 1), the overall hierarchical regression was also conducted excluding the diminished triad patterns. The result was similar to that reported in the text above, with a gain of 7% in total variance accounted for.

Author Notes This research was supported by the Natural Sciences and Engineering Research

Council of Canada and the Advisory Research Committee of Queen's University. Karen Smith and Alan Marr provided excellent technical assistance. Valuable comments on an earlier draft were provided by A.J. Cohen, C.L. Krumhansl, and M.G. Wiebe. Edito-rial comments of M.R. Jones and four anonymous reviewers are also gratefully ac-knowledged. Requests for reprints should be sent to L.L. Cuddy, Department of Psy-chology, Queen's University, Kingston, Ontario, Canada, K7L 3N6.

126 Psychomusicology Fall 1991