cuddy, l. l. (1991). melodic patterns and tonal structure. psychomusicology- music, mind &...

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Psychomusicology, 7 0 , 107-126 ©1991 Psychomusicology MELODIC PATTERNS AND TONAL STRUCTURE: CONVERGING EVIDENCE Lola L. Cuddy Queen's University at Kingsto Perception of tonal st ruc tur e c onveyed by three-note melod ic patte rns 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 varian t o f t h e probe-tone technique in which lis- teners were asked to rate each note of t he chromatic scale as a key-note or tona l center fo r each pattern. T h e second exper imen t collected listener's judgments of structural goodness and of major/minor quality for each pattern. I n bot h experi- m ents, the great est amoun t of perceived st ruc tur e was associated with the majo r triad with ascending pitch contour. The data support the notion that the pitch relationships of the maj or t ri ad repre sen t a cog nitive prototy pe for the W est ern idiom. This article reports two investigations of the percep tion of tonal structure in short melo dic patterns. On this topic, ther e is a great deal of empirical evidence to support the notion that the perception of tonal structure is influenced by music know ledge [f or 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, i n the present experim ents, 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 hierarchy—the 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) w as that the major triad context conveyed a greater sen se of tonal structure than

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7/27/2019 Cuddy, l. l. (1991). Melodic Patterns and Tonal Structure. Psychomusicology- Music, Mind & Brain, 10(2), 107-126.

http://slidepdf.com/reader/full/cuddy-l-l-1991-melodic-patterns-and-tonal-structure-psychomusicology- 1/20

Psychomusicology, 70, 107-126©1991 Psychomusicology

MEL ODIC PATTERNS AND TONAL STRUCTURE:CONVERGING EVIDENCE

Lola L . CuddyQu een'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 apattern consisting of three notes in adjacent locations on the cycle of fifths. Pitchcontour 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 tonalcenter for each pattern. The second experiment collected listener's judgments ofstructural goodness and of major/minor quality for each pattern. In both experi-ments, the greatest amount of perceived structure was associated with the majortriad with ascending pitch contour. The data support the notion that the pitchrelationships of the major triad represent a cognitive prototype for the Westernidiom.

This article reports two investigations of the perception of tonal structure inshort melo dic patterns. On this topic, there is a great deal of em pirical evidenc e

to support the notion that the perception of tonal structure is influenced bymu sic knowledge [for reviews, see Dowling & Harwood (1986); Frances (195 8/198 8); Handel (19 89); Krumhansl (1990,1991)] . Descriptions of music know l-edge include abstract schematic representations of the hierarchical relationsam ong 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 interpretationof much of the empirical evidence, and has thereby questioned certain funda-

mental principles on which psycholog ical theories of tonal structure are based.The dispute is addressed, in the present experiments, by considering B utler's(1989, 1990) criticisms of a report by Cuddy and Badertscher (1987). Cuddyand Badertscher (1987) evaluated the tonal structure conveyed by three me-lod ic contexts by means of the probe-tone technique developed by Krumhansland colleagues (e.g ., Krumhansl & Kessler, 1982; Krumhansl & Shepard, 1979).The contexts in the Cuddy and Badertscher (1987) study were a major triadpattern, an ascending major scale , and a dim inished triad pattern, and listenerswere asked to rate how well each of the 12 tones of the chromatic scale com-

pleted the pattern. Tonal structure was a ssessed in terms of recovery of the tonalhierarchy—the extent to which probe-tone judgments reflected both a focaltone or tonic, and structural relations among other tones with respect to thetonic (Krumhansl, 1983; Krumhansl, 1990; Krumhansl & Kessler,1982; seealso Lerdahl, 1988 ). The evidence co llected by Cuddy and Badertscher (1987)was that the major triad context conveyed a greater sense of tonal structure thanthe other two contexts. It was su ggested that the major triad was prototypic oftonal structure.

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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 exemp lars of the dom ain .... They are reference p oints to which

other category members are compared.. . . [Certain patterns] seem somehow'better'than others, because they are simpler, more regular, or more symm et-

r ic" (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 repre sentativ e of an ideal proto type. Jones (19 82) notes that the "tona l-

harm onic sch em e reflects a liste ne r's sense of the stable harm onic context and,

in particu lar, of the tonal center of a pie ce " (p. 2). The priority assigne d to the

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

1982; Ro berts & Shaw , 1984), with psych oaco ustical theories of sensory con -

sonance (following Helm holtz, 1863/1954), and with m usic 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 grou nds . 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 techniq ue w ith criticisms of current approaches to the study of the perc ep-

tion of tonal stru cture. In their place, Butler offers an alternative ac count based

on logical analysis of the interval content of music patte rns, the "recog nition of

critical intervallic relationships as they unfold throug hou t the mu sical perfor-

ma nce" (1989, p. 233).Butler (1989) cites, as comp atible with his own approach , Bro wn e's (1981)

analysis of the diatonic pitch set in terms of its interval-class con tent. B row ne

(1981) poin ts out that within the diatonic pitch set of seven pitch -classe s, 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 e ach interval class occurs in the diatonic set may be sum marized by

the vector <254361>.Next, Browne (1981) points out several properties of the vector, the most

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

contain s a full range of intervallic ubiquity. The six interval-classes occu r from

one to six tim es, 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 h ierarchization" (p . 6). Note that "rarity " and "common-ness" in this analysis

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

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occurrence in music. Frequency of occurrence in theiMerKalmecttoa®difteFrquency of occurrence of intervals in music are not in!e^efeie<^rjespoi»l^^!(Krumhansl, 1990). vitoaq^sq srfj moi

1!.

The psychological implication of Browne's (1981) analysisitstl^tscifeltona

intervals—the "rare" intervals—are much m ore informative thanj^terSirhf^tritablishing a sense o f tonality—a sense op po sit ion " in a diatonic 'f]$d&?!iFbw&aintervals aid position finding. Comm on intervals do not"(Browne, 198KfPP 8).If listeners are sen sitive to such information and rely on it for the determinate^ tof tonal structure, the diminished triad should yield a stronger sense of tonal *center than the major triad. The intervals contained in the diminished triadinclude the rare, i.e., infrequent, interval of a tritone; according to Brown andButler (198 1), three-note patterns including the tritone and one other m emberof the diatonic set "should provide an unambiguous indication o f tonal center"

(p . 48). The diminished triad B D F, for example, should implicate only thediatonic key of C major. On the other hand, intervals contained in a major triadlogically implicate three diatonic sets or keys. The rarest interval among thethree contained in the major triad is the major third, which occurs three tim es inthe diatonic set. Thus, for exam ple, the major triad C E G is a mem ber of threediatonic keys—C major, F major and G major—and may implicate each of

these keys.1

A third aspect of Butler's (1989, 1990) criticisms is concerned with the

order of the notes of the tritone interval contained in the diminished triad. Thediscovery of the tonal center of a diminished triad may be fac ilitated if the orderof the tones im plies a subdominant-to-leading-tone progression, or a subdomi-

nant-to-implied-dominant progression—for exam ple, the order D F B (Brown

& Butler, 1981). Accord ing to this notion, the temporal order used by Cuddyand Badertscher (1 987) for the dim inished triad context* B D B F, may not havebeen optimal for the identification of a tonal center.

The two experiments reported here deal with Butler's criticisms in threeways. The first involved a search for converging evidence for the difference

between major triad and diminished triad contexts reported by Cuddy and Badertscher(1987). The second involved the testing of additional patterns, and the thirdinvolved testing two different orders of notes w ithin patterns.

To seek converging evidence forthe findings reported by Cuddy and Badertscher

(1987), the first experiment reported here used a probe-tone technique. The

instructions were changed, how ever, from the previous instructions to rate eachprobe-tone for pattern completion to instructions to rate each probe-tone as acandidate for the key n ote, or tonal center, of the pattern. The second experi-

ment collected direct judgments of structural quality and major/minor quality

conveye d by the patterns and these results were compared with results from theprobe-tone task.

The additional melodic patterns tested were the minor triad, and a patterncalled a "fifths" pattern. For the fifths pattern2, the three intervals contain ed inthe pattern were two perfect fifths (or fourths) and one major second, e.g.,

C F G . For both the minor triad and the fifths pattern, the logica l number ofkey s im plicated by the interval content is greater than for the diminished triad.

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The interval content of the minor triad logic ally implicates three diatonic keys;the interval content of the fifths pattern logic ally implicates five diatonic keys.From the perspective of logical analysis of interval content, neither patternshould 'elicit girtunambiguous sense of tonal center and accompanying struc-

tutalrKiera#ehymnd, therefore, neither should be as strong an indicator of tonalsff^iur&tothe diminished triad.

(o Ihdre is, how ever, evidence suggestive that the minor triad pattern and thefiflfc pattern might yield a reasonably strong sense of tonal structure. Withrespect to m inor triads, it has been shown w ith the probe-tone technique thatharmonic minor triads strongly instantiate the tonality of the root of the triad(Krumhansl & K essler, 1 982); minor triads suggested a single key to listenersto a greater extent than did diminished triads, which tended to be interpreted interms ofboth the major and minor keys in which the chord functioned harmoni-

cally . Cohen (1991) reported a study in which listeners were asked to listen toexcerpts from the Bach Preludes and to sing the scale of the key suggested bythe 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, Howe ll, and

W est (1985) reported experiments in w hich listeners heard three-note patterns,including fifths patterns (pitch-class sets of the type <5 , 0, 7>), and rated thegoodness-of-fit of a single tone following each pattern. The single tone waseither a mem ber of one of the scales lo gica lly implicated by the pattern or wasan out-of-scale note. For the fifths patterns, listeners readily rejected, as "wrong,"the note that did not fit within any o f the five scales implicated by the patterns.M oreover, the authors found that fifths patterns were more effec tive contextsfor producing rejections of n onscale no tes than were three-note patterns co n-taining the rare interval of the tritone (patterns implicative of only one dia tonic

scale). Cross, How ell, and W est (1985) conclud ed that "the lower the logicalscale specificity, the stronger the scalar schema" (p. 137). The authors arecareful to explain that scale identity may not be the same as key identity. H ow -

ever, to the extent that scale identity contributes to perceived tonal structure,the implications o f their conclusion appear to be opposite to Butler's (19 89 ,1990) proposals.

A final point deals with the order in which the notes of the pattern werepresented. In the present exper iments, all patterns were realized either as threenotes w ith 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 exemp lified an ordering that should, according to Butler (1 98 9) , beespecially 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 pred iction that tonal structure will b e m orereadily detected for patterns with a unidirectional pitch contour than for pat-terns with more com plex contours. Cuddy and Cohen (1976) found that majortriad patterns with unidirectional pitch contour were more easily recognizedunder transposition than w ere m ajor triad patterns with a contour that changed

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

General Method

ListenersListeners w ere volunteers from the university comm unity who had attainedat least Grade VIII Royal Conservatory level of performance in voice or aninstrument. This level is comparable to the practical com ponent of the Grade 12music curriculum in Ontario schools. A typical listener had received musictraining at the leve l of a junior in an undergraduate m usic program. No listenerwas a profession al m usician. Listeners ranged in age from 16 to 30; the ratio offemales to m ales was 2:1. They w ere paid $3 .00 per session for participation.

PatternsTest 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 patterns—the majortriad, a pattern of fifths (as described above), the minor triad, and the dimin-

ished triad. The patterns w ith ascending contour are exemplified byC4E

4G

4, C 4

F4G

4, D 4F 4 A4, and B 3D 4F 4 , respectively . The patterns with reversing contour

are exemplified by E4G 4C 4, G4C

4F4,A 4D 4F 4, and D 4F 4B 3, respectively.3 In the

experiments, the patterns were transposed to d ifferent, randomly selec ted, fre-quency locations w ithin the overall range B3 to D 5.

Fourteen practice patterns were also constructed. They w ere three-note

diatonic patterns within the range of an octa ve, and all were different from thetest 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 19.3kHz. 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 thesystem of equal temperament, with A 4 = 44 0 H z. The amplitude of each tone

was set according to the Fletcher-Munson loudness contou rs. The overall levelwas 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 sing le block. T he order of

trials, and the frequency location of the pattern presented on each trial, were

random ized independently for each listener. The patterns were delivered throughSennheiser HD-424 headphones to the listener seated in a sound-proof booth.

Respo nses were entered on a Zenith Z19 conso le located in the booth and storedin the host com puter for analysis. Trials w ere 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

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"feelings or imp ressio ns." Therefore, no feedback was provided on either prac-

tice or test trials .

Experiment I

In the first expe rimen t, listeners were asked to jud ge the suitability of eac hof the 12 note s of the chromatic sca le as a tonic or key cen ter 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 w as tested once for each pa ttern.Th e tim bre 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

heigh t. Listen ers w ere asked to rate the suitability of the key-probe as a tonic or

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

good " and " 6 " represented "very po or." They w ere told that the timb re 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 com pletion but

as an abstra ct key-ce nter for the pattern.

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

lected key-p rob es. 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 w as paired with each of

12 key -pro bes. In the test trials, two patterns and their pairings w ith 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 DiscussionFor each test pattern, a set of mean ratings across the 13 listeners was

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

be called the key -probe profile for the pa ttern.

The eig ht panels of Figure 1 show the set of me an ratings obtained for each

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

of each pattern have been c ollapsed to a single frequency location—the note-

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C4

E4

G4

Major Triad Ascending

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

5 -

C F G4

•y\.5

<

Fifth Patterns Ascending.

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

4 -

5"

C Eb4

G4

kA^.Minor Triad A scending

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

4 -

5 "

e E b 4 G b 4

WW-Diminshed Triad Ascending

I I I I I I I I I I I IDbAbEbBb 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 IDbAb EbBb F C G D A E B F #

Q4 C4 F4

Fifth Patterns Reversing6

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 -

G4CEb

4

Minor Triad Reversing

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

E b4G b

4C

4

4 - 1

Diminshed Triad Reversing

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

KEY-PROBE ORDERED BY CYCLE OF FIFTHSFigure 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-han d colum n is reve rsing pitch conto ur. The note nam es for the key

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

each pattern given within each panel.

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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/? <.001).

Th e entries in Table 1 show significant differences am ong key-prob e rat-

ings for all test patterns except the diminished triad patterns . Inspec tion of thetable from the top to the bottom row reveals a gradual decrease in 9

2. The

systematic differences among key-probe ratings were greatest for the major

triad pattern with ascending pitch contour. The results for this pattern were

followed, in order, by the major triad pattern with reversing contour and the

fifths patte rns, then followed by the minor and dim inished triad patterns.4 These

Table 1

Summary statistics for key-probe profiles for eight stimulus patterns (Experi-

ment 1). The upper entry in each cell is the F-ratio for the profile data. Themiddle entry is 9

2, an estimate of variance among the mean ratings. The lower

entry is the MS error

Pitch contour

Pattern

Major triad

Fifths

Minor triad

Diminished triad

Ascending

6.57****, 6.54

.82, .82

1.91, 1.92

479****

.45

1.54

3.30***

.28

1.67

1.37

.05

1.71

Reversing

5 g7****

.55

1.47

5 44**** 5.89****

.50, .57

1.45,1.51

2.64**

.20

1.58

1.01

.002

1.77

Note: **** p < .0001, *** p < .001, ** p < .005

de cre ase s in systematic differences were not accompanied by a systematic in-cr ea se in error variance (the listener x key-probe interaction).

The resu lts of Tab le 1 indicate that the key -probe rating s were most clea rly

differentiated for the major triad pattern with ascending contour, and most

weakly differentiated for the diminished triad patterns. The differences be-

tween patterns cannot be attributed to differences in the consistency of the

response strategies across listene rs. Rathe r, for a given pattern, listeners were

in agreement as to the degree of differentiation among key-probes.

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T a b l e 2

Correlations between key-probe profiles and standardized profiles around the

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

E4

G4

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 profileDb 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: E 4 G 4 C 4

.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

: C4F

4G

4

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

Eb4

G4Pattern: Minor triad ascending

Standardized minor key profiledb ab eb bb f c g d

-.08 .07 -.21 .06 .49 J% .03 -.30Pattern: 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 .08Exemplar:

A E

.69 -.53

Exemplar:

a e

.06 -.08

Exemplar:

A E

.27 -.26

b f#

-.30 -.53G4C4Eb4

B F#

-.29 -.06

C4Eb

4Gb

4

b f#

.03 -.02

E b 4 G b 4 C 4

B F#

.02 -.25

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A further correlational analysis was conducted to examine an alternative

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

count w as that ratings simply reflected the tones contained in the pattern . Tw o

sets of predictors w ere derived and w ill be referred to as the unweigh ted version

and the weighted version, respectively, of a pattern-content model. For theunweighted version, it was assumed that key-probes were rated according to

wh ether or not the pitch-class of the key-probe m atched 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 assum ed, in addition

Table 3

Correlations between key-probe profiles and predictors based on unwe ightedversion (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 pa tte rn ," 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.

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

the correlation obtained betwe en key-prob e ratings and the unw eighted p red ic-

tor values.The low er entry in each cell is the correlation obtained betw een key -

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

line for the major triad pattern w ith ascending con tour and fifths pattern with

reversing contou r are the results for the replication of the pattern repres ented by

the cell.

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Ta ble 3 reveals a slight advantage of the weighted version of the pa ttern-

conten t mo del 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 acc ount based on the standardizedprofiles. 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

we re significant be yond the .005 level.

A com parison be tween the underlined correlation s in Table 2 and the cor-

relatio ns in Ta ble 3 suggests that tonal hierarchy predicto rs usually acc ounted

for a greate r amou nt of the variability in key-p robe ratings than did predictors

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

hierarc hical regression on the entire set of key -prob e profiles (10 pattern s 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 inform ation about tonal structure.5

The results of the first e xperiment suggest that the major triad pattern w ithascending contour occupied a privileged position among the patterns tested.

This pattern w as associated with the greatest amount of differentiation am ong

the key-p robe rating s. It was followed, in amount of differentiation amo ng ke y-

probe ra ting s, by the major triad with reversing contou r, and the fifths patte rns.

M uch wea ker differentiation amon g key-pro be ratings occurred for mino r and

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

the number of keys logically implicated by the patterns.

Experiment IIIn the first expe rimen t, it was found that key-p robe ratings for major triad

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

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

ticularly effective context in that it yielded the strongest differentiation amo ng

key -prob es and the clearest indication of tonal structu re. In the second exp eri-

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

structu re through the analysis of key-p robe rating s, the second experime nt co l-

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

(Cuddy, C ohen, & Mewhort, 1981; Garner, 1974), and judgm ents 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 experim ent. In the

first pa rt, listeners were asked to rate the perceived structural goodn ess of each

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pattern on a 6-point sca le. It was suggested to listeners that structural goo dne ss

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-

siven ess, or good form ." In the second part, listeners w ere asked to rate eachpattern on a 6-point scale for "major/minor quality" where " 1 " represented

"very strong major qua lity" and "6 " represented "very strong mino r qu ality."

Bo th par ts of the expe rimen t 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 pattern s, and the frequency location w ithin the range, were both indepen-

dently random ized 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

prac tice phas e and 15 trials in the test phase for ratings of major/m inor qua lity.

The entir e 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 patte rns (upper entry in each cell) and the standard error of the mea n (low er

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

tion of Ta ble 4 yield s the following obse rvation s, supported by tests of orthog o-

nal contrasts within the ANOVA.

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Major triad patterns and fifths patte rns received higher ratings of struc tural

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 re ceived higher ratings than the fifths patte rn, F(1 , 17) = 6.54, p < .02; for reversing contours, the means were reversed, but

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

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

terns appe ar to favor higher ratings for minor triads than for diminish ed triad s,

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 Iminor quality for eight stimulus patterns (Experiment 2). The

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

dim inished triad patterns, patterns w ith ascending pitch contour received higher

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

two m eans collected for each replicated pattern w ere similar (for the major triad

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

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-

m at 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

A N O V A .

Major triad patterns and fifths patterns w ere jud ged to conve y a strong

sense of major key; min or and diminished triad patterns w ere jud ged to convey

a strong sense of min or key. The difference in ratings wa s highly sig nificant, F

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

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terns were sim ilar in direction to those found for ratings of structural g ood ness .

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; fo r

reversin g conto urs, the mea ns were rever sed, but we re not significantly differ-

ent, F (1,17) = 1.78,/? > .15).The slight differences b etween m eans for mino r and diminished triad p at-

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

for each replicated pattern w ere 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 patternwas associated with the highest deg ree of structural quality in the first p art of

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

(both over all, and in comparison to other major and fifths pattern s).

Differences betwee n the two parts of the experime nt may also be noted. In

particu lar, the perceptu al structure of m inor and dim inished triad patterns was

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

judged to be clear and strong.

Th e reliability of the replicatio ns; and the stability of the standard erro rs 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 structuresconv eyed by the major and the diminished triad (Cuddy & Badertsch er, 1987).

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

mo re effective in recove ring the tonal hierarchy than a diminished triad pa ttern.

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

patter ns revealed a clear sense of key center, and contain ed information about

the tonal hierarchy of the key . Ke y-pro be profiles for the dimin ished triad p at-

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

expe rimen t, both structural quality and the sense of major mo dality were ra ted

significantly higher for the major triad patterns than for the diminished triadpatterns. These differences between the major triad and diminished triad pat-

terns are convergent with the differences reported by Cuddy and Badertscher

(198 7). Altering the order of the notes in the triads, in the present exp erimen ts,

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

ences.

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Supplem entary eviden ce was provided by the testing of fifths patterns and

m inor triad p atterns. Findin gs for the fifths pattern—the most ambiguous of all

patterns tested in terms of number of keys implicated—yielded data that re-

sem bled the data for major triad patterns. Key-probe profiles yielded evidenc e

of a strong tonal center. Ratings of structural quality and major m odality 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, comp ared to key-p robe profiles for major triad pa tterns, the distinc-

tion betw een key-pro bes was much w eaker. Minor triad patterns were judg ed to

be of moderate to weak structural qua lity, but to yield a strong sense of m inor

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

quality (also found for diminished triads) is worth pursuin g; it may bea r on the

affective charac ter of m inor triads and mode s. Major triads are associated w ithpositive affect, m inor with negative affect (Crow der, 1984, 1985; Crow der &

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

m ore ambigu ous and less stable than the major m od e" (p. 226). The association

of the minor m ode w ith negative affect (i.e., angu ish and suffering) he attributes

to the "deviant, unstable cha racter" (p. 228) of the mod e; it is "qu asi-chro m atic

and chan geab le" (p.224).

Exa min ation of the results for all four patterns tested yielded no support for

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

number of diatonic keys logically implicated. Moreover, there was no supportfor the possibility that key-probe rating s for all four patterns me rely reflected

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

terns also contained evid ence of sensitivity to tonal structure convey ed by the

patterns.

Ov erall, 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 ma pped on a stable, abstract, internally consisten t representation

of the hierarchical p itch relationships of W estern tonal m usic. A pattern such as

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

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

represen tation. 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 m ore readily than did the rem ain-

ing patterns.

The p resent data (Experiment 1), Cuddy and Badertscher (1987), andKrumhansl

and Kess ler (1982) all conv erge on the finding that the major triad m ost stronglyinstantiates 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 othe r keys. Such an interpretation do es

not imply an "all-o r-not hing " 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 key s to which the triad belongs—F next, and then G (Figure 1).

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Butler, D. (1989). Describing the perception of tonality in music: A critique of thetonal hierarchy theory and a proposal for a theory of interval lie rivalry. MusicPerception, 6,219-242.

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distinction in young children. Proceedings of the First International Conferenceon Music Perception and Cognition (pp. 389-3 94). Kyo to, Japan.Cuddy, L.L., & Badertscher, B. (1987). Recovery of the tonal hierarchy: Some com-

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delays. Perception and Psychophysics, 50 ,305-313.Do wling , W.J., & Harwood, D. (1986). Music cognition. New York: Academic Press.Frances, R. (1988). The perception of music. (W.J. Dowling, Trans.). Hillsdale, NJ:

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Footnotes1 The abov e description of logical imp lications of intervallic patte rns is simp lified

by referring only to the diaton ic system , and this simplification will be retained in thepresent discussion. It is acknow ledged that patterns may also implicate other systems,such as the minor mod es (Butler, 1989, Footno te 13). Minor sy stems, however, intro-duce additional complexities, such as the presence of several variants, and the loss ofthe unique-multiplicity principle for all but the variant known as the natural or pureminor. Including the logical implications of minor keys for the patterns studied in thepresen t experim ents do es not chan ge their relative orderin g in terms of the total num berof key s imp licated. Therefore the com plex ities of the min or systems with respect to theanalysis of logical implication need not be introduced further here.

2 The arrangment of notes in the fifths pattern s was determ ined by a con straint to

keep the pitch rang e of all test pattern s similar. Had the notes been arrang ed to form twosucce ssive intervals of a fifth, the span would be greater than an octave and cons ider-ably greater than the span of any other test pattern . For both arran gem ents, how ever, thefrequency of occurrence of the intervals in the interval vector, and the num ber of keyslogically 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 twoconstraints. The first constraint was that there be fwo instances where the contourascended and then descended, and two instances where the contour descended and thenascended. 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)produ ced an alogous results. The total amount of variance attributable to the harmon icpartia ls (total variability ab out the mean ) was calculated for each profile. The ord eringof patterns from greatest to least amount of variance was major triad patterns, fifthspatterns, minor triad patterns, and finally, dim inished triad patterns.

5Beca use of the unreliable nature of the ratings for diminished triad pattern s (Tab le

1), the overall hierarchical regression was also conducted excluding the diminishedtriad patterns. The result w as similar to that reported in the text abo ve, with a gain of 7%in total variance accounted for.

Author NotesThis research was supported by the Natural Sciences and Engineering Research

Council of Canada and the Advisory Research Com mittee of Quee n's U niversity. KarenSmith and Alan Marr provided excellent technical assistance. Valuable comments onan earlier draft were provided by A .J. Coh en, C.L. Krumhan sl, and M.G. Wiebe. Ed ito-rial comments of M.R. Jones and four anonymous reviewers are also gratefully ac-know ledged. R equests for reprints should be sent to L.L. Cud dy, Department of Psy-chology, Queen's University, Kingston, Ontario, Canada, K7L 3N6.