dowling 1978 - scale and contour

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Psychological

R e v i e w

1978, V ol. 85, No. 4, 341-354

Scale and Contour: Two Components o f a Theory

of Memory fo r Melodies

W . Ja y Bowling

University of

Texas

at Dallas

This article

develops a two-component

model

of how melodies are stored in long-

and short-term

memory.

The first component is the overlearned perceptual-motor

schema

of the musical scale.

Evidence

is

presented

supporting the

l i fe t ime s ta-

bility of

scales

and the f a c t

that they

seem to

have

a

basically

logarithmic f o r m

cross-culturally. The second component, melodic contour, is

shown

to

funct ion

independently of

pitch interval

sequence in memory. A new experiment is re-

ported, using a recognition memory paradigm in whi ch tonal standard stimuli are

confused with s a me - c o n t o u r comparisons, whether they are exact transpositions

or tonal

answers,

but not

with

atonal comparison

stimuli.

This

result

is

con-

trasted with earlier work using atonal melodies and

shows

the

interdependence

o f the two components, scale and

contour.

Remembering melodies is a basic process in

the mus ic

be hav io r

o f

people

in a l l

cul tures.

This be hav io r

m ay

involve product ion,

a s

with

th e

singer performing

a

song

for an

audi -

ence or the part ic ipant in a s ignif icant socia l

event try ing

to

remember

th e appropriate

song. Or i t may involve recognit ion, as with

th e

l i s tener whose comprehension

of the

later

developm ents in a piece depends on mem o ry

f o r earlier parts. In this art ic le , I concentrate

on tw o components o f me mory

that

co nt ribute

to the

reproduct ion

and

recognit ion

o f

melo-

dies , nam ely, melodic contour a nd the music al

scale. I maintain tha t ac tual melodies , hea rd

Earlier

versions of this

article were

presented at

t he Mus i c Educa to r s Na t i ona l

Conference ,

Western

Divis ion,

San Franc i sco ,

1975,

and the

meeting

o f

N ew Amer i c an Music, Tangents III , Univers i ty of

W y o m i n g , 1977. Suppo r t for the experiment reported

here was provided in part by a Biomedical Sciences

Suppor t Grant to the University o f Texas a t Dallas

f rom th e Nat iona l Ins t i tutes o f Heal th .

I thank Dane Harwood, Dar lene Smith , James

Bartlett , Drew Hara re , Mark Goedecke , Cynthia

Nul l , Kelyn Rober ts , and Klaus Wachsmann for he lp-

ful discuss ions and co mm ents. And I especial ly wish

to t ha nk Mant l e Hoo d fo r b ring ing t he data o n

Indonesian tunings

t o my

at tent ion.

Requests

for reprints

s hou ld

be

sent

to W. Jay

Dowl ing ,

P r o g r a m in P s y c h o l o g y a nd H u ma n De-

velopment, Univers i ty of Texas at Dal las , Richardson,

Texas 75080.

or sung, are the product of two kinds of un-

derlying schemata. Firs t , there

is the

melodic

c o n to u r — th e pat tern

of ups and

downs—tha t

character izes a part icular melody. Second,

there is the overlearned music al scale to which

th e co ntour

is

a pplied

a nd

that underlies many

different

melodies.

It is as

though

th e

scale

constituted a ladder or

framework

on which

the ups and

downs

of the

contour

were

hung .

Two examples epi tom ize the behavio r th is

theory addresses. First ,

if

people

in our

West-

ern

European c ul ture hear a m elody

from

some non-Western culture using a non-West-

ern scale , the ir reproduct ions o f that melody

will

use

the ir

o wn

Western scale, preserving

the contour of the original melody. The scale

functions

a s a

classic example

o f a

sensori-

m o to r schema control l ing percept ion

and be-

hav ior . In this example, th e non-Western

melody is assimilated to the Western schema

(Frances , 19S8,

p.

4 9 ) . Part

of the

education

of ethnomusicologis t s is directed toward

free-

ing

them

from

the ir nat ive schemata

s o

that

they can hear accurate ly the pitches of non-

Western music .

Th e second example involves the use of

melodic

contour

in the

structure

o f

pieces

o f

music. One way a composer can tie a piece

together is to

repeat

th e

same contour

a t

dif-

ferent pitch levels, at different relative place-

Copyright 1978 by the Amer ican Psychological Association, Inc. 0033-295X/78/8504-0341$00.75

341



342

W. JAY

D O W L I N G

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1

Figure J. Sect ion A shows example s

from

Bee thoven 's P i ano Sona ta opus 14 no. 1, i l lu s t r a t ing

use of the

s ame me lod i c co n tour w ith different in terval s izes . (In tervals between notes

a re

s h o w n

be low the s t aves in semi tones . Excerp t s a re labeled with measure

number s . )

Sec t ion B i s an

Amer ican Indian example from Kol insk i (1970, p.

9 1 ) .

merits

on the sca le , o r even o n

different

scales.

Th e repet it i on p rov ides un i ty wi tho u t beco m-

ing

b o r i ng t h r ou g h b e i ng

to o

exac t . F i gure 1A

demonstra tes Beethoven ' s

use of

th i s device

in

h is

P i ano Sona ta opus

14 no . 1 .

Such

a

device relies on the listener's

ability

to recog-

n ize the melod i c con tour th r ough t r ansforma-

t ions

o f

p i t ch .

That

such processes

a re no t

confined

to

Western music

is

s hown

by Kol in-

ski's

(1970) example

from

the

Flathead

In-

d ian s (s ee F i gu r e I B ) . A d am s

( 1 9 7 6 )

h a s

provided

a

gu ide

to the

uses

o f

con tour con-

ceptual izat ions in e t hn om u s i c o l ogy .

In

w h a t

fol lows, I

will di scuss

(a)

scales

of pi tch

a nd

thei r character i s t i cs

and (b)

melod i c con tour s

a nd

their independence

in

m e m o r y . (Independence is

here used

in the

sense of referr ing to cases where one remem-

bers

one

th ing wi thou t r emember ing

a

related

th ing . ) I will also present a new exper iment

that

i l l u s t r a tes per fo rmance

in

m em or y

fo r

melo dies co nsistent with th e present two-

component theory .

Mus i ca l

Scales

Several aspects

o f

musica l sca les

a s

they

func t i on in var ious cu l tures are of par t i cu lar

interest

to the

psycho l og i s t . F i r s t ,

scales

con -

sist of d i screte s teps of p i tch , typ ica l ly f ive

o r seven

to the

oc t ave . This l imi t a t i on wou ld

seem

to

match qu i te wel l

th e

l imi t a t i ons

o f

people

a s

informat i on p rocesso r s . Second ,

musica l sca les of p i t ch a r e approx imate l y

l o g a r i t hm i c w i t h r e sp ec t to f requency , a fa c t

t ha t bear s d i r ec t l y

on the

prob lem

o f

pi tch

sca l ing

in

psychophys i c s . Th i rd , mus i ca l s ca l es

ca n be s l id co nt inuously up and do wn in p i tch

wi thou t d i s to r t ing the i r r e l a t i ve in terva l s i zes .

They serve a s h i gh l y s t ab l e

senso r imo to r

schemata wi th great f lex ib i l i ty of appl i cat ion.

Discrete Scale Steps

W i th fe w excep t i ons , th e cul tures of the

world use

d i sc re te changes

o f

p i t ch a l ong

a

mus i ca l s ca l e

in

creat ing thei r melodies . Since

th e s ing ing vo i ce a nd many ea r l y in s t ruments

a re capab le o f p roduc ing a con t inuous var i a -

t ion of p i tch , how i s i t

that

the mus i c o f t he

world

moves

by

di screte s teps? Helmh ol tz

( 1 9 5 4 )

ra i sed th i s quest ion ,

a nd

some

of the

answers

he

suggested

are

appeal ing even

to-

d ay .

Th e

u l t im ate b io l og i ca l func t ions

o f

dis-

crete steps

are as

ob s cu r e

a s the

func t ions

o f

melody or of music i t se l f . However , g iven that



M E M O R Y

FOR

MELODIES

343

we

have melody, discrete scale steps

can be

very useful. Helmhol tz argued

that

the di-

vision of the

pitch continuum into discrete

steps is desirable in order t h a t th e degree o f

melodic and rhy thmic movement migh t be

immediately apparent

to the

l istener.

If

pitch

moved

con t inuous ly

in a

melody,

h e

argued,

i t would be

mu ch more difficult

to

decide

ex-

act ly h o w mu ch th e pitch h a d changed o r

what rhythmic , tempora l uni t s

h a d elapsed.

In fact ,

such

a

decision could

be

made only

o n

the basis of a fixed set of discrete

refer-

ence points anyway. That is , the l istener

would have

to

learn some

form o f

scale

a s a

cogni t ive framework

t h r ou gh w h i ch

to

deal

with

th e melo dies h e hears , cont inuous o r not.

Th e modern cogni t ive psychologis t ca n

eas i ly carry Helmhol tz ' s argument

o ne step

fur ther . Grant ing t h a t we need discrete scale

steps to

comprehend melodic movement ,

h o w

many should there be? Mil ler ' s

( 1 9 5 6 )

classic

ar t ic le suggested that human beings a re l im-

ited in their categorical judgment capabil i ty

to

using

7 ± 2

categories

on any one

dimen-

s ion. Most cu l tures

fall

with in th i s range, us-

ing f ive or seven dist inct scale step categories

wi th in

th e

octave.

A s

will

be

discussed below,

the system of categories repeats cycl ical ly

every octave. Thus , in Miller 's terms, a pitch

would be categor ized in terms of two dimen-

sions:

one for

pi tch level within

th e

octave

(of ten called

chroma)

and the

o ther

for oc-

tave level. Certain cultures t h a t would seem

at f irst

s i g h t

to

provide exceptions

to

this

pat tern turn

out on

closer inspect ion

not to.

For example, the mus ic of India typical ly

uses many very narrow intervals o f which 22

a re avai lab le with in

a n

oc tave. However,

melodies

are basical ly constructed out of

scales having seven

or so foca l

pitches,

and

the other neighboring tones

a re

used

a s

auxil-

iary tones around these focal pitches for the

purposes o f ornamenta t i on .

A t this point ,

I

need

to

in t roduce

a

con-

ceptual

scheme fo r

talking

about musica l

scales. This scheme h a s four levels o f abstrac-

t ion

from

the pitches of actual melodies and

shares cer ta in

features with th e

conceptual

schemes o f Hood

( 1 9 7 1 )

a nd Deutsch

( 1 9 7 7 ) .

I have discussed it in greater detai l in an-

other paper

(Bowl ing ,

No t e

1). The

mos t

abstract level is t h a t of the psychophys ica l

scale,

which

is the general

rule

system by

which

pi tch intervals

a re

related

to frequency

in tervals

o f

tones.

I will

a r gu e t h a t

the ap-

propr ia te form for the psych ophy s ica l sca le

is approx imate ly l oga r i t hmic , owing t o t he

fundamenta l

place o f octave judgments in hu-

man audi tory process ing. Th e second level is

that

of tonal mater ia l , which inc ludes the set

o f

pitch intervals in use by a part ic ula r cul-

ture

o r

wi th in

a

part icu lar genre.

In

Western

music , the tonal material would include the

set of

semitone intervals

of the

equal tem-

pered chromat ic sca le

but not

anchored

to any

part icu lar frequency.

Th e

third level

is

t h a t

o f

th e

tuning

sys tem, which cons is t s

of a se-

lect ion of a subset of the available pitch in-

tervals from the tonal mater ia l tha t are used

in

actua l melodies .

In

Western music ,

th e

tun-

ing

sys tem might cons is t

of the set of

intervals

represented by the white notes of the

p iano—

the set of

intervals with

th e

ascending cyc le

(in

semitones)

of [2, 2, 1, 2, 2, 2, 1]

repeat-

ing

every octave.

Th i s

set of intervals can

become the

bas is

of any of the

heptatonic

modes (that is , the modes with seven notes

per

o c t a v e ) : m ajo r , minor , or the m edieval

church modes.

The set of

intervals

of the

black notes on the p iano [2 , 3 , 2 , 2 ,

3 ]

c a n

also

funct ion a s a

tuning sys tem

for the

West-

ern pentatonic modes.

Th e most concrete level is mode. In going

from tuning sys tem to mode, two th ings hap-

pen.

Firs t ,

an anchor for the

frequencies

is

established,

a nd

what were pitch intervals

a t

th e m o re abst ract levels g et transla ted into

the pitches of notes. Second, a tonal

focus

in

th e

tuning sys tem

is

selected,

and a

tonal

h iera rchy

is

established

on the

tuning sys-

tem. (The tonal h i erarc hy determines which

notes

in the mod e a re more impor t an t a nd

dynamic tendencies of the notes as they

func-

t i on

in

melodies .) These

tw o

operat ions

a re

usual ly

combined in Western music under the

rubric

o f

selecting

a tonality, fo r

example,

tak ing the intervals of the whi te-note tuning

system

and

select ing

the key of

C-major ,

A -

minor , Eb-major ,

o r

C-dorian. Since

mode

in

m y

sys tem over laps cons iderably with

th e

term scale as used in the phrases

musical

scale

a nd diatonic scale, I

will

often use scale in



344

W .

JA Y DOWLING

w h a t follows as a synonym for mode . I want

to

caut ion

th e

reader, however,

that

scale

is

also used in ways that are not synonymous

with my use of mode, fo r example, in the

phrase chromatic scale, which i s more near ly

synonymous

with

m y term tonal material. M y

use of scale is informa l ; a s t r ic t ly

formal

sys-

tem would use only mode . I use the term

tonal

to

refer

to

melodies us ing

th e

notes

o f

well-known

modes. And I shou ld caut ion th e

reader

t h a t w h a t

I

h a v e

to s ay

here

is

most ly

i r re levant to the dispute among proponents

o f tempered, Py thag orean, and other natu-

ra l tuning systems wel l discussed by Ward

( 1 9 7 0 ) .

Logarithmic Scale

Th e musical sca les o f most cul tures repeat

themselves cycl ica l ly every octave.

Tones

an

oc t ave apa r t a re treated a s equivalent in some

sense and are

typica l ly

given the same name

(C, D, E; do, re , mi; or

B a r a n g ,

Sulu,

Data

[ I ndones i an ] ) . Tones t ha t a re psycho log i -

cal ly a nd mus ica l ly an oc t ave a p a r t have a

rat io between their fundamental frequencies

of approx imate ly 2/1. (The approxima te ly

will be discussed below.) Ward (1954) has

shown

that Westerners

a re

quite precise

in

lOOr

so

60

sett ing two pure tones (presented alternately)

to the

subjec t ive in te rva l

of an

oc tave .

This

is a ll

t h a t

is

required

to

produce

a

logar i thmic

psychophys ica l sca le

o f

p i tch :

Tones a t

equal

dis tances a long

th e

subjective pitch scale

(namely , an oc tave apar t ) shou ld be related

by equa l 'frequency rat ios .

Complicat ions ar ise because the subject ive

octave usual ly represents

a frequency rat io

j u s t s l igh t ly grea te r than

2/1.

Ward (1954 ;

replicated

by

Burns, 1974, us ing non-Western

subjects

and by

othe rs [Sundberg

&

Lind-

qvist , 1973] us ing Westerners) found that

t h rough

th e

midrange

of up to

frequencies

of

abou t

900 Hz, the

frequency rat io

o f a

subject ive, pure-tone octave wa s abou t

2.02/1 .

Th i s

ratio st i l l leads

to an

approximate ly

l oga r i t hmic

scale.

Ward's

results

a re

plot ted

in the

cu rve

o f

Figure

2 , which

shows

th e

tuning

of successive oc taves as cumulat ive de-

viat ions

from the 2/1 frequency

ratio

in

logar i thmic uni t s (hundredths o f a semitone,

o r

cents) . (A semitone represents a

frequency

rat io o f

2

1/12

/1).

Octaves having a 2/1 fre-

quency rat io would be represented in Figure

2

as a horizontal l ine . Stra ight segments o f

the curve with posit ive slope represent loga-

r i t hmic

pi tch scales with

a

greater than

2 /1

frequency

rat io

to the

octave.

3

40

2 0

o

-10

25

j 5

IOOO

2

F R E Q U E N C Y

OF

UPPER NO TE Hz)

Figure 2.

Cum ula t ive tuning devia t ions o f oc taves in cents (h undredths of a semi tone) as a

funct ion of the

fundamenta l f requency

of the

upper note

in the

octave

fo r

Burmese ha rp

(Xs;

Wil l i amson

&

Will iam so n, 1968)

and for

Indones ian gamelans us ing sUndro (circles)

and pilog

(tr iangles) tuning systems, (The Indonesian data are based on H o o d [1966; filled s ymbo l s ; = 2]

a nd Sur jodiningra t , Sudar jana , & Susanto [1969; open sym bols ; J V s =l l and 10 for sUndro a nd

ptlog, respect ive ly ] . The solid

line

is based o n Ward's [1954] data fo r pure- tone octave judgments . )



M E M O R Y FOR MELODIES

345

Figure

2

also shows some measurements

o f

non-Western instrument tunings: a se t

from

a Burmese h arp (Wil l iamson & Wil l iamson,

1968)

and several

sets

from

Indonesian

game-

l ans (Hood, 1966; Surjodiningra t , Sudarjana,

& Susanto, 1969) . Gamelan refers

to

both

th e

orchestra and the set of instruments , con-

sist ing

chief ly

o f gongs and mar imbas . Th e

correspondence of the tunings and Ward's

curve is very good, especial ly considering the

sorts o f systemat ic deviat ions within the oc-

tave in gamelan tunings discussed by Hood

(1966 ) . One reaso n t h a t th e fundamental f re-

quencies of gamelan tunings a re free to ap-

prox imate th e tunings o f s ubject ive octaves is

that there is not the same

a t t empt

a s

found

in th e

West

to

make fundamentals

o f

h i g h e r

tones match upper part ia ls (overtones)

o f

lower

tones. One reason fo r this is tha t acous-

t ica l ly gongs have very i rregular ser ies o f

upper part ials.

Western pianos

a re

tuned

to

octaves that

a re

s l ight ly greater than 2 /1 ratios, but the

deviation is smal ler than that fo r subjective

pure-tone oc taves (Mart in & Wa rd, 1961).

The reason for the deviation is that piano

strings are no t ideal, frict io nless , vibra ting

bodies

but

have

a

certa in amount

o f

stiffness.

This

stiffness

is most pronounced at the upper

and

lower extremes

of the

keyboard, where

th e rat io of the diameter to the length of the

string

is

re lat ive ly large .

The

stiffness

of the

strings leads

th e

frequencies

o f

upper part ia ls

to be

progress ive ly sharper than t rue har-

monics (which stand

in

integer ratios

to the

fundamenta l ) .

Hence, tuning upper funda-

mentals to partials o f lower notes will lead to

stretched octaves,

but

they

are not so

severely

stretched as those of the human ear. Our

Western emphasis o n consonance o f simul-

taneous

tones leads

us to prefer

this

piano

tuning over one in which melodic succession

would be g iven precedence. (See P l o m p &

Levelt, 1965, for a discussion of the contribu-

tion

o f

coincidence

o f

upper harmonics

to the

consonance o f complex tones.) These con-

siderations also

suggest

that

for the

same rea-

sons, a cappella choirs and string

quartets

will

tend

to use a 2 /1

octave, especial ly dur-

ing slow passages.

The precision of judgment of

Ward's

(1954) subjects is a very good reason fo r pre-

ferring a

quas i - l oga r i t hmic

scale to other can-

didates

for the

psychophys ica l sca le re l a t ing

pitch to frequency (Ward, 1970), Other rea-

sons inclu de the above cross-cul tural data and

th e

fact

t ha t one o f Ward's

(19S4)

subjec t s

who had absolute pi tch produced the same

scale by note label ing a s with th e oc tave

j udgment metho d. A noth er s t rand o f evidence

is

provided by Nul l

( 1 9 7 4 ) ,

who obta ined a

l oga r i thmic

scale using

a

s l ight ly

modif ied

magni tude es t imat ion method. One of the

cleverest

corroborat ions

of the log

scale

is

provided

by an

experiment

o f

At tneave

a nd

Olson

( 1 9 7 1 ) . They observed that musical ly

untra ined subjec t s

h a d

difficulty

in

p roduc ing

transposi t ions o f arbitrari ly selected pitch in-

tervals. Then, they

h i t

upon

th e

idea

that

cer t a in

interval sequences might

be

over-

learned

even by the unini t ia ted, fo r example,

th e Na ti ona l B roadca s t ing Company (NB C )

chimes. They

found

t h a t t he NBC ch imes had

always been presented at the same pitch level

— o n th e notes G-E-C in the middle register,

an ac ronym for the General Electric Corpora-

t ion.

They

asked subjects t o produce th e pat-

tern

at var ious pi tch levels above and below

the or iginal . The scal ing quest ion was, Would

transposit ions fol low a log scale , or a power

funct ion,

o r

something e lse? Subjects over-

whelmingly

responded with t ransposi t ions

a long a logar i thmic scale . Thus, g iven a mean-

ingful

task, untra ined subjects use a loga-

r i t h m i c scale fo r p i t ch .

Attneave

and

Olson's subjects demonstrate

ho w

stable the tonal sca le system is through-

o ut

life

once

it is

learned.

So do

Frances's

(1958) subjects, wh o

found

it easier to notice

changes

o n

rehearing tonal melodies than

atonal. Tonal scales constitute one of the most

durable families of perceptual-motor schemata

that have been observed

in

psycho logy , rank-

ing perhaps only

a f ter

th e schemata o f natu-

ral language in their stabil i ty and resistance

to change in adul t life. In fact , th e same kinds

of categorica l percept ion phenomena found

in the

phonetics

o f a

language seem

to

hold

f o r musical sca le pi tch judg ments (Burns,

1974) . It would probably surprise most

American psych o log i s ts h o w early in l ife these

perceptual-motor schemata a re acquired. Im -



346

W. JAY D O W LING

A =

+4

-2 +3 +2

B Jl»f

+4

-2 +3 +2

• T f M

3-1

3 2

3 -3

4-2 -2

-1 +3+3-1

Dow l l ng 8 Fuj l tani

Standard

Target

Tonal Answer

Atonal Contour

R a n d o m

H

I

+2 +

- 2 + 3

1 -2 3

S t a n d a r d

T a r g e t

o n t o u r

a n d o m

+ 1+2-3 -3

Figure

3. Sections A-E are examples o f s t imul i

f ro m

th e present experiment. (A i s the sample tonal stan-

dard s t imu lus ;

B i s the

target s t imulus ,

th e

exact

t ranspos i t ion of the s t andard; C i s the tonal a n-

swer lure, whi ch remains in the key of the s tandard

but at a

different

pi tch level ; D is the atonal lure

with th e s ame c o n t o u r as the s t andard; and E is the

r andomly different lure.) Sections

F-I a re

examples

o f

atonal s t imul i

from

Experiment

1 o f

Dowling

a nd Fuj i tani , 1971. (F is the sample s tandard s t imu-

lus ; G i s the target s t imulus , th e exact t ranspos i t ion

of th e s t a nda r d ; H i s t he s a m e - c o n t o u r l u r e ; and I

i s

th e r andomly different lu re . A ll staves a re notated

with a treble clef unders tood. Interval s in semi tones

a re

sh own under each stave.)

berty ( 1 9 69 ) found that 8 year olds a re able

to

not ice sh i f ts

o f

sca les wi th in

a

melody f rom

o ne key to

ano the r

a

semitone

or two

h igher .

They found sh i f t s

o f

mode

that

left

th e

under-

ly ing pa t tern

o f

interva l s unchanged

(as in the

tonal answer stimuli of the experiment re-

por ted below) much more difficult. Zenatt i

( 1 9 6 9 ) found that

8 year olds c a n recognize

three-note tona l melodies much better than

atonal. Five year olds find tona l a nd atonal

melodies equally

difficult

because

they

have

no t

y et

thorough ly interna l ized

th e scale.

Eleven year olds

find

both types equal ly easy.

But with

four -

and six-note melodies, even

adults find the atonal m o r e difficult, in agree-

ment with Frances

( 1 9 5 8 ) .

In

th i s di scuss ion

of

musical scales ,

I

have

not tried

to

inco rpo ra te Shepard ' s (196 4)

hel ica l theory o f pi tch scales. I wish to note,

however , that I bel ieve th e present theory

com p a t i b l e with h i s . It only requires that th e

hel ix be sprung somewhat to a l low for Ward's

enlarged subjective octaves.

I

believe Shep-

ard's demonstra t ion

of the

audi tory barber

po le could

be

repl icated using Ward's

quasi-

l oga r i thmic scale. Th e issue of the

acceptance

of

th e hel ica l model a s a pitch scale h a s n o t

been settled, however. Fo r example , Deutsch

( 1 9 7 2 ) h a s demonstra ted that in the recog-

ni t ion of fami l i a r

tunes , chroma ( the qua l i ty

of

C -ness, D-ness , or E-ness; do-ness, re-ness,

or mi-ness) does no t

suffice

as a cue t o tune

ident i ty .

M e m o r y fo r Melodi c Co ntour

Fo r everyone except th e small percentage

of the popula t ion having abso lute pi tch , wel l -

known

melodies must

be

s tored

a s

sequences

of

pitch intervals between successive notes

(Deuts ch , 1969) .

In

this section,

I

have

as-

sembled evidence that memory for the con-

t ou r

(the ups and downs of the melodic

interva l s ) c a n funct ion separa te ly f rom mem-

ory fo r

exact interval s izes.

That

is , the

con-

t ou r

i s an abs trac t ion from the ac tua l melody

that can be remembered independently of

pi tches or interva l s izes .

This

is true for mel-

odies in both shor t- term and long- term

m e m o r y .

Retrieval from Short-term Mem ory

The c ontour s o f

brief,

novel atonal mel-

odies

can be

retr ieved

f rom

shor t- term mem-

o ry even when

th e

sequence

o f

exac t intervals

canno t .

This

po in t

is illustrated by an ex-

per iment

by

Dowl ing

a nd

Fuj i tani

( 1 9 7 1 , Ex-

per iment 1) . They used a shor t- term recogni-

t ion memory paradigm in wh ich th e standard



MEMORY

FO R MELODIES

347

s t imulus o n

each trial

was a

randomly gen-

erated

five-note

melody having smal l p i tch

intervals between successive notes. Th e com-

parison stimulus followed th e standard after

a

brief

pause. Three types of comparison mel-

odies were the same as the standard in both

contour and pitch intervals, or had the same

contour

but different

intervals ,

o r

were dif-

ferent in

bo th con tour

a nd

intervals ( i .e. ,

were

novel random sequences). These are i l-

lus t ra ted

in

Figure

3,

Sections

F-I.

Different

groups

o f

subjects

had the task o f

distinguish-

ing amon g th e

following

types o f comparison

melody: exactly the same versus random , ex-

actly th e same versus same contour, and same

contour versus random. Half the subjects were

given

comparisons start ing

on the

same pitch

as the s tandard; th e o ther ha l f h a d com-

parisons wh os e start ing note was transposed

to

another pitch level.

Th e results

showed

that

when

th e

compar i son s ta r t s

on the

same pitch

level a s the standard, exact-same comparisons

a re easily distinguished from either random

comparisons

o r

same-contour ,

different-inter-

va l comparisons . In other words, it was easy

to reject a ny comparison s t imulus

t h a t

di d

no t conta in exact ly th e same pitches as the

standard. When th e comparison melodies were

transposed, ho wever, exact-same targets a nd

sam e-contour co mparisons were easi ly dis-

tinguished from random ones

but

almost

im -

possible to tell apart. Listeners responded o n

th e

basis

of the

presence

o r

absence

of the

contour

and

were unable

to

recognize

th e

sameness o f intervals when these were added

to th e contour .

Thus,

when

th e listener is t ry ing to retrieve

an

exact

set of

intervals from memory ,

th e

best

he can do

under

the

above conditions

is

retrieve th e con tour . It is cr it ical to this re -

sult t h a t

th e

target melodies

be

atonal ,

that

is , not

using

th e pitches o f a

musical scale

famil ia r

to the subjects. Frances (1958 ) found

a l tera t ions

in

tonal melodies easier

to

detect

than a l tera t ions

in

atonal melodies.

A

ma j o r

theme in the present article is t h a t there a re

two

components

a t

work

in the

normal

process

o f

melody recogni t ion: contour and scale.

Bowling

and Fujitani (1971 , Experiment 1)

explored th e extreme case where th e role o f

th e scale h ad been all but eliminated. They

found contour recogni t ion

to be

completely

dominant over pitch interval recognit ion.

However,

o ne

would

no t

expect

th e

same

re -

sult

with tonal melodies. The

overlearned

scale

framework

shou ld make recogn i t i on

o f

th e difference between a tonal target melody

and an

atonal

lure having the same contour

much

easier. (These st imuli are i l lustrated in

Figures 3B and 3D.)

Dis t inguish ing

between a tonal melody a nd

a tonal lure having th e same contour as the

first melody but starting o n a

different

note

of th e same modal sca le should be very d i f -

ficult . The

rela t ionship

'between

this l a s t pair

of

melodies is the same a s

that

o f a

fugue

sub-

ject and its

tonal answer.

Such a pair is i l-

lustrated

by

Figures

3A and 3C.

There

a re

two ways

to

th ink

of the

tonal answer

in

terms

of the conceptual scheme o f tuning sys-

tem and

mode.

1. We might th ink of the tonal answer as

consisting of the same set of diatonic inter-

vals

translated

into a new mo de. The

interval

pa t te rn

of the

tuning sys tem

(i n

Figure

3, the

whi te notes of the piano) remains f ixed at the

same pitch level, while

th e

tonality

of the

melody in the sense of its starting pitch level

is

moved to a new place in the tuning system.

T hus ,

both

th e

s tandard

and the

tonal answer

in Figure 3 (A and C ) h ave the d ia tonic in-

tervals

[ +

2 ,

-1, + 2, +1] , but the first is

in C-major and the second is in A-minor.

2. The tonal answer mig ht be tho ugh t of

a s

remaining in the same mode a s the stan-

dard, which is exact ly the way a tonal answer

is

treated

in a fugue. In that case, th e

pitches

of

the mode remain fixed while the

starting

pitch of the melody is

shifted

to a

different

degree

of the scale.

Both melodies

in

Figure

3 (A and C) would remain in C-major, and

th e

difference

between them would be that th e

standard begins

on the first

degree

and the

tonal answer on the sixth degree of the modal

scale.

I

prefer

th e second o f these ch aracteriza-

tions

fo r

describing

th e

cognitive processing

involved

in the

experiment

presented

below.

This

is

because

th e

t ime interval between

th e

presentat ion

of the

standard

and the

tonal

an-

swer is short . Th e standard is coded a s being

in a part icu lar major mode. When th e listener



348

W. JAY B O W LING

hears the tonal answer immediately following

th e

standard, nothing

in

that comparison pat-

tern demands that he change mode. There-

fore,

he hears the tonal answer in the same

mode

a s the

standard. Diatonic interval pat-

tern (contour in a restricted sense) and mode

c an function a s features of the standard.

Tonal answers would then be difficult to dis-

t inguish

from sta ndard st imuli because they

sha re these two features . Exact t ransposi t ions

force

th e listener to change mode in midtr ia l .

Exact t ransposi t ions share

th e

feature

o f

hav ing th e same intervals a s t h e standards

when measured in semitones ( that i s , a t the

level of tonal

ma te r i a l ) .

The experiment thus

brings these sets o f feature s imilar i t ies into

confl ict wi th each o the r .

Lest too persuasive an argument here make

th e results of the experiment seem a foregone

conclusion, let me introduce a plausible the-

o ry that makes a

different

predict ion

from

th e two-component

scale-contour

theory. It

could

be, according to th is theory, that con-

tours are not stored in memory independently

of interval sizes. Dowling and Fuj i t an i g o t

the ir resul t because they used unnatural

atonal melodies. Atona l intervals

a re

difficult

to

remember, both because l i s teners have

no t

had much prac t i ce wi th them and because

they

do not

occu r

a s part of an

overlearned

scale schema. However,

if we

replicate Dowl-

ing a nd Fuj i tani us ing tonal materia ls , we

will get a very different result . The interval

sequences o f tonal standard melodies will be

easily learned because they fall

o n a

well-

known

scale.

Thus ,

changes in those intervals

will

be easily noticed whether the change is

to an

atonal melody

or to a

tonal melody

in

another mode. Th e listeners should a t least

do better than chance

in

discr iminat ing

ex-

a c t transposit ions from tonal answers. (T o

give this theory

i ts

due,

I

should note t h a t

pilo t work with a few professio nal music ians

convinces me

t h a t

they can perform in the

wa y

just descr ibed).

Th e two-component theory, on the other

hand, claims t h a t even with

tonal

melodies,

contour

(in the

sense

of ups and

downs mea-

sured in diatonic intervals) a nd interval sizes

(measured

in

semitones

at the

level

o f tonal

materia l) a re stored independently, th e latter

s imply a s a

mode label .

Tonal i ty c an

func-

t ion

as a cue to

dist inguish

a

tonal melody

from a n atonal one. But changes in interval

size that leave tonal i ty intact will

be

difficult

to notice.

Experiment

o n

Tonal Melodies

Thi s experiment

is

based

on the

paradigm

o f Dowl ing a nd Fuj i tani (197 1, Experiment

1 ) . It copies the condit ions of

t h a t

experi-

ment in which compar i son me lodie s were

transposed (i.e. , began on a different pi tch

from th e standard melodies) and in which th e

subject 's task was to reco gnize only exact

t ranspos i t ions of the standards. Th e most im -

por t an t difference between

the two

experi-

ments i s that in Dowling and Fuj i tani , a l l

melodies were atonal ; whi le in the present

experiment, al l but one type o f compar i son

melody were tonal . Other differences

in

method

derived

from differences in the avai lable

equipment, subject populations, and the de-

s i rab i l i ty o f

equalizing expected interval size

between tonal and atonal melodies used in

th e present experiment. Since th e most com-

parable condit ions in the tw o

experiments—

those

o f dist inguishing targets from randomly

different

comp a r i s on s— gav e rough l y compara -

ble results

( 8 1 %

a nd

8 4%

vs . 89 ), the ef-

fects o f changes in these other variables a re

apparent ly negl ig ible fo r purposes o f estab-

l i sh ing the qual i ta t ive resul ts toward which

this study is directed.

Using tonal melodies

in

this paradigm

makes possible th e in t roduct ion of one more

type of comparison melody: the tonal answer.

In this type, th e compar i son beg ins o n a d i f -

ferent pitch from

th e

standard

but

stays

with in th e same diato nic scale. T h u s , th e pitch

intervals between tones will generally be

changed,

but the

melody will st i l l

be

tonal .

Figure 3 shows examples of th is and the other

types of comparison st imuli used in the pres-

ent

experiment and t ha t o f Dowling a nd

Fuji tani .

Method

Subjects.

Twenty-o ne students

a t the

Univers i ty

o f Texas

a t

Dal la s served

in

four separa te

g r o u p



M E M O R Y F O R M E L O D I E S

349

sess ions , mos t

o f

t h e m

receiv ing

ext ra credi t

in

upper level psychology courses

fo r

their participa-

t ion . Subject s were d ivided into g roups on the bas i s

o f a pos texper iment ques t ionnaire . Subject s in the

exper ienced g r o u p had 2 o r m o r e y e a r s o f m u s i c a l

t r a in ing ( inc lud ing s t udy ing a n in s t rument o r vo i ce

or p lay ing a n ins t rum ent in an ensemb le but ex-

c lud ing t ak ing mus i c co ur se s o r s ing ing in c h o i r ) .

In the inexper ienced g roup, subject s h a d less t h a n

2

y ea r s t r a in ing . M eans

for the two

g ro ups were

5.0

and .14 years t ra i n ing , re spect ive ly . The mea n

age o f subject s was 30.4 years and was comparable

in

t h e t wo g ro ups .

There

were three males and seven

fema les

in the

exper ienced g roup

a nd

seven males

a nd f o u r females in the inexper ienced g roup (a d i f -

ference t h a t p r o b a b l y reflects

a

tendency

to

g ive

females

mus ic le s sons in our

c u l t u r e ) .

P e r f o r m a n c e

o f

ma le s and

fema les

in t h e t wo g ro ups was r o ug h ly

co m parab le , w i t h a s l i g h t supe r io r i t y o f expe rienced

males.

Procedure. Subjec t s were ins t ruc ted that t h i s

wa s

a n expe r imen t in m e m o r y fo r melodies . O n e ach trial,

t h ey h e a rd a pa i r o f br ief m elodies , and th e ir t a sk

was t o s ay wh e t h e r t h e t wo were t h e s ame o r d i f -

ferent.

Fo r th is purpose , t hey responded us ing a

f o u r - c a t e g o r y

sca le with responses

o f sure

same,

same, different,

and sure different . There were

48

t r ia l s in the exper iment and they wro te the ir re -

sponses on a shee t o f paper provided. The exper i -

menter expla ined tha t a l l compar ison s t imul i , even

those th a t were the sam e, would s t a r t on a

different

note

f rom th e

s t a n d a r d . W h a t

wa s

i m p o r t a n t

in de-

t e rmining sameness w a s t h a t no t o n ly t he ups and

downs

bu t

a l s o

th e

dis t ances among

th e

notes

be

t he same.

Th e

exper imenter

referred t o t he

poss i -

bi l i t y o f s ing ing Happy B i r t h da y s t a r t ing o n d i f -

ferent

notes a s a n

illustration

of how the

same mel-

o dy co u ld o ccur a t different pi t ch leve ls as long as

th e

d i s t ance s amo ng

th e

notes remained

th e

s ame .

Th e exper imenter presented o ne example o f e ach o f

th e

types

o f s t imulus pa i r s . Af t e r responding to ques-

t ions , th e exper imenter t hen presented the 48 tr i a l s .

Stimuli. St imul i were play ed o n a fre sh ly tuned

Ste inway piano

a nd

recorded

o n

t ape .

They

were

presented to subject s over loudspeakers a t c o m f o r t a -

ble

l i s tening leve ls v ia h ig h -q ua l i t y reproduct ion

equipment . The t iming o f s t imul i was cont ro l led by

a Da vis t imer produc ing c l icks every .67 sec , wh i ch

were bare ly audible on the t ape . In a l l s t imul i , t he

ra te

of presenta t ion o f t he quar te r-no te va lues ( J )

of F igure

3 was 3 tones per sec . Thus , each s t imulus

was 2 sec in dura t io n. There wa s a 2-sec blank in-

te rva l be tween s t andard

a nd

co mpar i s o n s t imul i

o n

each tr i a l and a 5-sec response interval fo l lowing

th e

co mpar i s o n s t imulus .

A

warn ing , co ns i s t ing

o f

th e

exper imenter ' s vo ice announcing

th e

t r i a l num-

ber, preceded

th e

onse t

o f

each t r ia l

by 2

sec.

A ll s t andard s t imul i began o n midd le C ( f u nda -

menta l

f requency of 262

Hz) . Th e re

are 16

poss ib le

co n t o ur s

for f ive-note

sequences , provid ing unisons

are exc luded. The contours o f t he standard s t i m u l i

on each o f t he 48 tr i a l s of the experiment were se-

lec ted by us ing th ree success ive random permutat ions

o f th e

o rde r

of the 16

c o n t o u r s .

T h u s ,

e a c h c o n t o u r

appeared as a standard

exact ly

three times in the

exper imen t .

Th e interva l s izes be tween no tes o f t he

t ona l s t imul i were chosen with the

fo l lowing

p r o b a -

bi l i t ies o f

d i a t o n i c s c a l e s t eps :

P (±\

s tep)

=.67;

P

(±2

s teps)

=

.33.

There were

f o u r

t y pe s

o f

co mpar i s o n me lo dy . Each

o f t h e se f o u r types o c c u r r ed equal ly of ten

in the

th r ee

b lo cks

of 16

t r i a l s ( r ando mly de t e rm ined) .

A ll

co m par i s o n me lo d ie s beg an o n e i t h e r t h e E abo ve

or the A

be low middle

C

( r ando mly de t e rmined) .

Th e se t r an spo s i t i o n s we re ch o sen a s be ing mo de ra t e ly

d i s t an t f r om

C

b o t h

in

pi t ch leve l

(+4 and — 3

semitones ) and in sh a red p i t ch e s ( t h r e e a nd f o u r ,

r e s pec t ive l y ) . (F rance s , 1958, h a s s h o w n

r e mo t e

t r an spo s i t i o n s

in the

la t te r sense harder

to

r e c o g -

nize t h a n

near

t ranspos i t ions . ) Target co mpar i s o n

s t imu l i

(see F igure

3B )

were exact t ranspos i t ions

to

the s t anda rds to t he key o f E o r A. They re t a ined

exact ly t he in terva l s izes o f t he s t anda rds . Tona l

an s wer

co mpar i s o n s t imul i ( s ee

F igure

3C) were lures

t h a t

s t ar ted

on E or A but that

rema ined

in C, the

s a m e key a s t he s t anda rd , and had the s ame co n-

t o u r

a nd

d ia t o n i c in t e rva l s . Th us ,

th e

interva l s izes

in semitones d id no t remain the same as in the s t an-

dard , wh i le t he tona l sca le remained the same.

A t o n a l

s ame-co n t o ur co mpar i s o n s t imul i ( s ee F ig -

ure 3D )

were lures t ha t re t a ined

th e

c o n t o u r

o f t h e

s t a n d a r d

but

tha t used interva ls randomly se lec ted

wi t h o u t r e g a rd fo r tona l sca le s . Th e pro bab i l i t i e s o f

in te rva l s izes o f t he a tona l lures were P (±1 semi-

t o n e )

= .17,

P (±2

semi t o ne s ) =.33, and

P

(±3

semi-

t on es ) — .50. (These probabi l i t ie s were c hosen s o

t h a t t h e expec t ed in t e rva l

size

of a t one sequence

w o u l d be 2 .33 semitones . Th is i s co mpa rable to t he

expected interval s ize

o f

2 . 2 7 s e m it o ne s

for the

tonal

sequences. The

latter

figure was

calculated

as a

weigh ted average o f t he d ia tonic in te rva l s izes , with-

o ut reg a rd fo r s t a r t ing p i t ch . Th e f a c t that a l l stan-

dard s t imul i began o n C , imm edia te ly next to a

1-semitone

in t e rva l , wo u ld l o wer t h i s e s t ima t e s l i g h t l y

in the

present case . )

Th e

rando m different s t imul i

(see F ig ure 3E ) were lu res h av ing different c o n -

t o u r s

f r om

t h e s t anda rds ( r ando m ly s e le c ted) a nd

different dia tonic sca le in te rva ls se lec ted jus t as with

th e s t anda rds .

Data

analysis. Th e fo ur - c a t eg o ry co nf idence judg -

ments were used

to

genera te individua l memory

o p-

era t ing charac te r i s t ics (MOC)

fo r

e ach sub je c t

fo r

each o f t he th ree types o f s t imulus compar isons . Hi t

ra tes were g iven by responses t o t he t arge t s t imul i .

These

h i t

ra tes were plo t ted separa te ly ag a ins t t h ree

sets

o f

fa lse a l a rm r a t e s g iven

by

responses

to

t o na l

answer , atonal

contour,

and random lures to

give

t h ree areas under

the M OC fo r

e ach sub je c t . Areas

under the MOC can be in terpre ted as an es t imate o f

w h a t

th e

pro po r t i o n co r re c t wo u ld

be in the

ca se

w h e r e c h a n c e p e r f o r m a n c e is .50 (Swets , 1973) .

Area s under the M OC were eva luated us ing an un-

weig h t ed-means ana ly s i s o f v a r i a n c e fo r unequal ce l l

s izes due to the unequal numbers o f exper ienced

and inexper ienced sub ject s .



350

W.

JA Y

BOWLING

Table

1

Areas Under

th e

Mem ory Operating

Characteristic of the

Experiment

Compared

with Similar Conditions of Dowling and

Fujitani's

(1971}

Experiment 1

G r o u p

Target

Target

vs. vs. Target

t o n a l

a t ona l v s .

answer

c o n tou r r a ndom

Experienced

Inexperienced

Dowling a nd

Fuj i t an i

.48

.49

—

.79

.59

.53

.84

.81

.89

Results

Table

1 shows th e mean areas under th e

M O C

for the two

g roups

and the

three s t imulus

compar i sons . The main effect of s t imulus

compar i son type was s ignif icant ,

F(2,

38 ) =

77.35, p <

.001. Distinguishing between tar-

gets

a nd

tona l answer lures

wa s

very difficult,

with c hance perform anc e in bo th g roups . Dis-

t inguish ing targets

from

atonal same-contour

lures

wa s

somewhat eas ier ,

a nd

d i s t ingu i sh ing

targets from random lures was eas ies t of a l l .

The Exper ience X St imulus

Type

in te r a c t i on

was s ignif icant , F(2, 38) = 8.01, p < .001,

ma in ly

reflecting

a difference o f abi l i ty in

dis t inguish ing ta rgets from atonal same-con-

t ou r lures . Th e m a i n effect o f experience ap-

proached s ignif icance

at the .05

level.

This

modest

effect

i s consonant wi th the modest

corre la t ions found by D owl ing and Fuj i t an i

between

per fo rmance on the i r task and ex-

perience.

Genera l Discuss ion o f

Short - term

Recogni t ion

of

Melodies

Th e present results i l lustrate th e impor tance

of

scale as

well

as contour in shor t- term rec-

ogni t ion memory for melodies . This po int i s

b r o ug h t

out by

com par ison wi th

th e

results

of

D owling and Fuj i tani (see Table 1) . Both

studies

found

that

the two

melodies

a re

rela-

t ive ly easy to dis t inguish in

that

they have

different contours, with performance in the

.80s. Dowl ing a nd Fuj i tani ' s subjects found it

difficult to dis t inguish between tw o

atonal

melodies wi th the same contour but different

interval

sizes,

performing at around the

chance level of .50. In the present experiment,

subjec ts found

it

easier

to

re jec t

a n atonal

compar i son me lody when it was preceded by

a

tona l s t anda rd me lody .

This

wa s

especially

true o f experienced subjects wh o presumably

h a v e a f i rmly interna l ized modal sys tem.

What subjec ts in the present experiment

found

extremely difficult, performing a t

chance ,

was

dis t inguish ing between exac t

transpos i t ions

o f

comparison melodies

to new

tona l keys and

sh i f t s

o f the contour a l ong the

same dia tonic sca le as the standard. Both ex-

perienced

a nd

inexperienced subjects

h a d

t rouble

wi th th i s

task. Phenomeno log i ca l l y ,

th e

compar i son s t imul i

in

Pairs

A-B and

A-C o f F igure 3 sound

natural,

while th e

compar i son

in

P a i r

A-D

sounds strange.

This resul t i l lus tra tes

th e

separateness

o f

th e func t ions o f

c o n to u r

a nd

mode.

Th e

func-

t ion of mode is not to fix a set of intervals

in semitones

a s

belong ing

to a

melody.

If it

were, tona l answers would not be confused

with exac t t ranspos i t ions . Th e mode is simply

a f r amework o n which th e contour m a y b e

h u n g .

Fo r

brief

melodies heard only once,

th e

po in t on the modal sca le where th e melody

beg ins

i s no t

taken into account. What sub-

jects seem

to

a c c o un t

for is

that both

th e

mode and the contour are the s ame in the

tw o melodies.

This resul t should not be taken to mean

that

diatonic scale intervals a re somehow psy-

cho log ica l ly equa l .

Th e

concept

o f

subjec t ive

equa l i ty applies best

to the

level

of the

psy-

chophys i c a l

scale.

Th e

aes thet ic purpose

o f

using differently sized pitch intervals

in mo-

da l scales would be lost if al l the intervals

in the mode were subjec t ive ly the same. Dif-

ferent

intervals a re used because they pro-

vide melodic interest. Melodies a re translated

into

different

modes because that i s more in-

teresting than rei terating them in the same

mode.

M us i c i ans find tuning sys tems

that

use

only subjectively equal intervals dul l because

they deny

a

ma jo r s ource

o f

melodic

variety.

This is the principal cr i t ic ism of the whole-

tone scale with which

Debussy and

others

experimented around

th e

turn

of the

century.

Moreover ,

Frances

(1958, Exper iment

2 )

found evidence that makes

th e

subjective



M E M O R Y FO R M E L O DI E S

351

equa l i t y

o f modal intervals difficult to believe

in.

Frances

mistuned certain notes

o n a

piano

and then placed these notes in various melodic

contexts. He

found

t h a t

when the mis tuning

was in the

d i rec t i on

of the

dynamic tendency

o f

the tone in i t s modal context , the a l tera-

t ion was much less l ikely to be not iced than

when the

mi s t u n in g

was in the

oppos i te

di-

rec t ion. Th i s means t h a t the subject ive inter-

va l s ize changes with modal context . Such

changes

would

be consonant

with

th e

theory

t h a t dia tonic intervals tend

to be

subject ively

equal provided that the changes due to con-

text make large intervals

(in the

sense

of the

psychophys r c a l

sca le and tonal mater ia l

levels)

smal ler and smal l in tervals larger .

However ,

Frances go t t he oppos i te resul t . In

al l of his cases, i t was small intervals t h a t

became

sm a l le r.

Th e confus ion o f

target melodies

a nd

tona l

answers does

no t

occur wi th

well-known

mel-

odies s tored in long-term memory. At tneave

a nd Olson

( 1 9 7 1 )

have shown that with fa -

mi l i a r melodies, exact interval s izes

a re

pre-

c ise ly remembered. In

fac t ,

famil iar melodies

can be

used

a s

mnemonic s

fo r

ret r ieving sca le

intervals ,

a s

when

a

m usic s tudent uses

th e

song Over

There to

remember descending

m ajo r

s ixths

( — 9

semitones)

or the

song

There's

a Place for Us for asc ending mino r

sevenths ( + 10 sem ito nes). But even for fa-

mi l i a r melodies , the contour and mode can

funct ion

independently, as when Frere

Jacques

o r

Twinkle, Twinkle

a re

sung

in

a mi nor key o r when their co ntours are recog-

nized in

spite

o f

distorted interval s izes

(Bowling & Hol lombe,

1 9 7 7 ) .

That

memory

fo r

exact interval s izes

of fa-

mi l i a r

m elodies is so goo d raises the quest ion

o f

how such melodies are s tored. They cannot

be s tored s imply as contour p lus sca le , s ince

that would leave the skips unspecif ied. Twin-

kle, Twinkle

and the Andante

theme

from

Haydn's

Surprise Symphony

wo uld be stored

near ly iden t i ca l l y : th e co n tou r [ 0 , +,0,

+,0,

— ±, 0,

—

0, — 0, — ] (where 0 = unison,

+ = up, and —

=

dow n) beginning

on the

tonic and in the major mode. What is needed

i s a way of

spec ify ing

skips along the diatonic

sca le . What I

will

suggest is a three-valued

dimens ion of quas i - l inguis t ic marking. Inter-

vals

of one

dia tonic s tep

will be

u n mark ed ;

two-step intervals wi ll be ma rked

s

for sk ip ;

and

larger leaps wi l l be marked

be,

where

x gives th e n u m b e r o f steps. In th i s sy s tem,

Twinkle, Twinkle becom es

[0 ,

+

]4

,

0, + ,

0,

-, -, 0, -, 0, -, 0, -],

whi le Haydn ' s

Andante becomes

[0, +

s

, 0, +

s

, 0, -„, +,

0, — „ 0,

—

s

, 0,

—

8

] . T h i s

sys tem takes

ad-

vantage of the f ac t tha t re l a t ive ly nar row in-

terva ls predominate in the mus ic of the world

(Bowling, 1968). Of the 26 intervals in the

first two

phrases

of the two

songs jus t c i ted,

12 a re un i sons (0

s t e p s ) ,

7 are one s tep (un-

m a r k e d ) ,

6 are two s teps (ma rked s ) , and

1 i s

four

steps (marked

14 ) .

In order to document th i s predominance

o f sma l l d i a t on ic in terva l s more ful ly

and to

s h o w

tha t us ing the present sys tem of mark-

ing would put

cons iderably less load

o n

mem-

o ry

t h an would remem bering l i tera l ly every

interval s ize,

1

counted

a l l t he

intervals

in

the co l lect ion of 80 Appalachian songs by

Sha rp a nd

Rarpe le s

( 1 9 68 ) . I chose th i s co l -

lec t ion because

it was

compi led

by

careful

s cho l a r s from

a n

almost exclus ively voca l t ra-

di t ion

tha t does no t u se ha rmoniz ing accom-

paniments . Th e col lect ion is jus t abou t th e

r ight s ize to produce s tab le da t a , and the

songs in i t

were selected with o ut

a ny

obvious

biases regarding the phenomenon under in-

vest igat ion. I first categorized the 80 songs

into those us ing heptatonic modes ( seven

notes

to the

o c t av e ;

46

songs )

a nd

those

us -

ing

pentatonic modes

(five

notes to the oc-

tave;

34 songs) . For

convenience,

and be-

cause

th e

existence

o f a

system

o f

hexa ton ic

modes

i s no t

indisputable,

I

treated

the 21

songs that used only six notes of the scale a s

heptatonic (an example of such a song is

Twinkle, Twinkle ).

This

decision would

if

any th ing b i a s

th e

interval count aga inst smal l

d ia tonic intervals , s ince

a

hexatonic step

across

th e note

omitted from

the hepta tonic

mode

wa s

counted

a s a

skip.

(It is

interest ing

t h a t the note omit ted from the heptatonic

mode was

a lways

one of the

pair

o f

notes

in

th e underly ing tuning sys tem

that

stands

in

th e

unique 6-semitone interval

to

each other

— B

or F in the

white-note tuning

sys tem—

a nd

t h a t

th e

6-semitone interval

did not

occur

in any of the heptatonic songs .) A subsequent



35 2

W .

JAY BOWLING

Table

2

Percentages of Diatonic

Intervals

of

Different

Sizes

in the 80 Songs of Sharp

and

Karpeles (1968}, with Unisons

Omitted

Mode

type

Interval s ize

in

diatonic steps

2

3 4 >4

Heptatonic

(46

songs,

1,544 intervals)

Pentatonic

(34 songs,

1,334 intervals)

56

30 8 3 2

81 15 2 1 1

check

on the

da ta showed

that

separa t ing

th e

hexatonic songs from

th e

hep ta ton ic

h a s a

negligible effect on the

frequency

dis t r ibu-

tion of interval sizes.

Th e

songs were strophic. That

is ,

m o r e

o r

less the same melody was repeated for the

several verses. Fo r present purposes, each in-

terval

in one

st rophe

o f

each song

wa s

co unted

once. Where th e r h y t h m differed from strophe

to s t rophe (because o f

different

words ) ,

I

used the rhythm of the f irst strophe.

Unisons accounted fo r 23 and 2 5% of

th e

intervals

in the

heptatonic

and pentatonic

modes, respect ively. Taking unisons

and un-

marked diatonic steps together accounted for

66 and 86% of al l the

hep ta ton ic

a nd

pentatonic intervals . Omit t ing unisons

from

cons iderat ion

al lows us to see what percent-

ages of + and — intervals need to be marked

s

o r

1.

Table

2

shows these

da t a .

Fo r

both mode types ,

th e

unmarked intervals

a c -

cou n t

fo r

over ha l f

th e

cases. Only 13%

o f

hep ta ton ic and 4% of the pentatonic intervals

need to be coded as leaps.

Moreover ,

th e

leaps

a re

used

in

generally

predictable ways in the songs. Of 202 leaps

o f three or more steps in the heptatonic songs ,

106 ( 5 2 % ) occur red in one of the

following

tw o contexts : (a ) pick-up notes a t the

start

o f

a

phra se

o r

leaps

to the

s t a r t

of a new

phrase

(a s

between

th e

second

a nd

th i rd

phrases o f

Twinkle,

Twinkle ; 75 instances)

and (b) passages in which th e same interval

a nd rhy thmic pa t t e rn inc lud ing th e leap wa s

repeated

in the

same song

(as in the first and

penul t im a te phrases of Twinkle, Twinkle ;

31 ins t ances ) . Th e occur rence o f leaps is also

redundant with mo de. A mo ng the pentatonic

modes, for example, th e mode whose ascend-

ing intervals in semitones are [2, 3, 2, 2, 3]

had only

1%

leaps

in its

songs versus

4%

for

th e

other modes.

A nd each

mode

has i t s

own

pattern of more and less probable leaps.

Fo r example, no leaps were observed between

th e seventh a nd

four th

degrees of the m a j o r

mode ( the

6-semitone

in t e rv a l ) .

The scarc i ty of leaps and their redundant

usage when they do occur reduces cons idera-

bly the load on memory. Therefore, i t seems

plaus ib le to charac ter ize th e memory s t o rage

of

the p i tch mater ia l of an actua l melody as

a co mbinat ion of mo de and co ntour , inc lud-

ing

a

spec i f i c a t i on

of the

start ing pitch level

in

th e

mod e

and the

mark ing

o f

skips

and

leaps. It is impor t an t to note that th i s ana l -

ysis

is

restricted

to the

pi tch mater ia l . With

rea l melodies , rhythm must p lay a n imp o r t an t

par t in memory . Ko l insk i (196 9 ) in h is anal-

ysis

o f var iants of the song

Barbara Allen

provides num ero us ins tances in which the

very same contour and mode, with a change

in rhy t hm, b ecome a

different

song , often in

ano ther cu l tu re . Fo r example, a change in

r h y t h m turns

one of the

var iants into

th e

sextet

from Lucia

di

Lammermoor. In fact ,

it is

ar t i f i c i a l

even to think of rhy thmles s

melodies.

In the

state

of our

knowledge, this

is a necessary ar t i f ic ia l i ty , s ince th e problem

becomes enormo us ly complex when rhy thm

is

added.

Thinking

Rather than jus t ho ld ing

a

melodic phrase

in short - term memory, subjects in

Bowl ing ' s

( 1 9 7 2 )

s tudy

o n

melodic t ransformat ions

h a d

to turn it upside down, backwards , o r b o t h .

Recogn i t i on

fol lows

that order o f increas ing

difficulty. Of interes t here i s the fact t h a t

subjects

were able only to recognize the mel-

odic contour when so t ransformed and not

th e exact interva l s izes .

Long-term Memory

In addit ion to being preserved in short-

term memo ry, melodic co ntours a l so seem to



M E M O R Y

FOR

MELODIES

353

be

retr ievable f rom long- te rm mem ory inde-

pendently

o f

interval s izes. W h ite (1960) dis-

torted familiar melodies such

a s

Yankee

Doo dle and On Top of Old Smokey by

chang ing the pi tch intervals between notes

by

doubl ing them, adding

a

semitone,

a nd

so on .

Whi l e

th e

undistorted melodies were

recognized

94 of the t ime, melodies sub-

jected

to

these contour-prese rv ing t ransforma-

t ions were

recognized

a t

abou t

the 80%

level.

Other c o ntour-preserving t ransform at io ns such

a s

sett ing

a ll

in te rva l s

to 1

semito ne produced

a greater decrement in performance ( to

around th e 65

level).

However, contour-

dest roying

t ransformat ions produced even

g reater decrements. For example, rando mizi ng

th e

intervals

o r

subt rac t ing

2

semitones from

them

even when this changed the ir s ign pro-

duced performance

in the

45-50 range.

(I t

is

difficult because

o f

sampl ing prob lems

to

s a y

w h a t

th e

chance level

in

White 's task was,

though i t was undoubtedly in the 10-20%

range. The

rhy t hmic pa t te rn s

of the

tunes

presented alone

on one

pi tch were recog nized

with 33% accuracy . )

Bowling and Fuj i tani

(1971 ,

Experiment

2) refined som ewhat Wh i te' s approach us ing

five f ami l i a r tunes whose first two phrases

could be s ty l ized in to the same rhythmic pa t -

tern.

They

used three kinds o f distortion:

preservat ion o f con tour ,

preservat ion

o f

con-

tour plus relat ive interval size (i .e. , the

grea ter - than/ les s - than

re lat ionships

o f

succes-

sive intervals were preserved), and preserva-

tion of the underlying harmonic structure of

th e

melody whi le des t roy ing contour . The

contour-preserving

distort ion produced a dec-

rement

in

performance from

99%

(undis-

torted) dow n to 5 9% . Preserving th e re lative

interval sizes only boosted this a

little

(to

66%). Des t roy ing contour led to a

perform-

ance

o f

28%. (Chance level

was

probably

between

20% and 3 0 % ) .

Melodic contours o f fami l i ar tunes can be

recognized even though th e distortion of in-

terval sizes is very great . Deutsch

( 1 9 7 2 )

showed

that dis tort ing a tune by adding or

subtra ct ing o ne or two

oc taves from each pitch

made it very difficult to recognize . But i f th e

octave distortion is carried out with a preser-

va t ion o f con tou r , per fo rmance is remarkably

improved (Dowling

& Ho l lombe, 1 9 7 7 ) .

One final consideration is that long-term

memory

has t he

func t ion

in

musical ly non-

l i tera te

societies

o f

preserving

th e

musical cul-

ture , inc luding

th e

melodies . Wh at

we

would

expect from the present theory is that var i-

ants

o f a

tu ne would sha re certa in s imilar i t ies ,

namely, those that ar i se from very s imilar

con tours be ing hung on the under ly ing sca le

f ramework

in

var ious ways . This variat ion

m i g h t occu r

fo r

three principal reasons: for-

get t ing

of the

o r i g ina l intervals ,

th e

desire

to

create interesting innovations

by

manipulating

in terval relat ionships (as sho wn in Figure

1) , and changes o f ins t ruments and scale sys-

tems that necess i tate t ransformat ions

o f

mel-

odies (as in the

case

o f

adapt ing

a

non-West-

ern melody to a Western scale). A l l o f these

processes a re probab ly opera t ing , fo r example,

in th e

var i a t ions

of the

tune Barbara Allen

studied

by Seeger (1966) and Kol inski

( 1 9 6 9 ) . Th e

most s t r iking resul t

o f

Seeger's

s tudy of 76 variants o f Barba ra Al len in

the U.S. Library of Congress i s that they

fall

into famil ies

based

on the

shar ing

o f

close ly re lated contours . These contours

fall

onto the ir sca les

in

var ious ways , produc ing

a

profus ion

o f

s im i l a r

but

interest ingly var ied

melodies.

Reference

Note

1.

Do wl ing , W. J. Musical scales and p s y c h o p h y s i c a l

sca le s :

Their

psy ch o lo g i c a l real i ty. In T. Rice &

R . Falck

(Eds . ) , Cross-cultural approaches

to

music:

Essays in honor of

Mieczyslaw

Kolinski.

M anusc r ip t in prepa r a t i o n .

References

A d a m s , C . R . M e lo d i c co n t o ur t y po lo g y .

Ethno-

musicology, 1976 ,

20 ,

179-215.

A ttneave, F, , & Olson, R.

K . Pitch

a s med ium: A

ne w

appro ach to psy ch o ph y s i c a l s c a l ing . American

Journal

of

Psychology, 1971,

84 ,

147-166.

Burn s , E . M.

Octave adjus tment

by

non-Western

mus ic ians . Journal of the Acoustical Society of

America, 1974 , 56, S25 . (Abs t r a c t )

Deut sch ,

D .

Music recogni t ion. Psychological

Re-

view,

1969,

76 ,

300-307.

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•

dowling 1978 - scale and contour

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