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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
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342
W. JAY
D O W L I N G
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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
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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
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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 . )
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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 -
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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
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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
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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
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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 .
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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
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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
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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
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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.
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Essays in honor of
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M anusc r ip t in prepa r a t i o n .
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•
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