Electronic Theses and Dissertations Theses, Dissertations, and Major Papers
1-1-1982
The pleasingness of sequential and simultaneous pairs of tones:
The pleasingness of sequential and simultaneous pairs of tones:
Effects of waveform, dissonance, and delay.
Effects of waveform, dissonance, and delay.
Robert W. Whissell
University of Windsor
Follow this and additional works at: https://scholar.uwindsor.ca/etd
Recommended Citation Recommended Citation
Whissell, Robert W., "The pleasingness of sequential and simultaneous pairs of tones: Effects of waveform, dissonance, and delay." (1982). Electronic Theses and Dissertations. 6775.
https://scholar.uwindsor.ca/etd/6775
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T w o e x p e r i m e n t s w e r e c o n d u c t e d to e x a m i n e the e f f e c t s of
d i s s o n a n c e , w a v e f o r m , d e l a y , m u s i c a l i n t e r v a l , a n d m u s i c a l
e x p e r i e n c e o n p l e a s i n g n e s s r a t i n g s f o r s i m u l t a n e o u s and c o n
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b y a c u r v e f i t t e d m o d e l a d a p t e d f r o m P l o m p a nd L e v e l t ' s
(1965) d i s s o n a n c e t h e o r y .
I n the s e q u e n t i a l t o n e s e x p e r i m e n t , 41 s u b j e c t s a s s i g n e d
r a t i n g s o f p l e a s i n g n e s s o f t o n e p a i r s a nd p r e f e r e n c e f or the
b e t t e r s o u n d i n g e l e m e n t of t o n e p a i r s . T w o h u n d r e d a nd ten
t a p e d t o n e p a i r s f r o m a f r e q u e n c y r a n g e of 300 t o 2 6 0 0 Hz
w e r e d e l i v e r e d in s i n e or s q u a r e w a v e f o r m , a t two d e l a y t i m e s
(100 a n d 500 m s ) , a t 70 d b S P L , b y h e a d p h o n e s to the s u b
j e c t s . S u b j e c t s w e r e r a n d o m l y a s s i g n e d to the w a v e f o r m and
d e l a y c o m b i n a t i o n s . D i s s o n a n c e w a s a v e r y w e a k p o s i t i v e f a c
t o r f o r p l e a s i n g n e s s r a t i n g s . A n e x p e c t a n c y m o d e l f or the
p l e a s i n g n e s s o f s e q u e n t i a l t o n e s w a s p r o p o s e d . I n d i v i d u a l
t o n e p r e f e r e n c e s w e r e s u p p o r t e d b y o t h e r r e s e a r c h f i n d i n g s
f o r th e i n v e r t e d "u" s h a p e d p r e f e r e n c e c u r v e .
In the s e c o n d e x p e r i m e n t , 23 s u b j e c t s r a t e d t he p l e a s
i n g n e s s o f t a p e d s i m u l t a n e o u s w a v e t o n e s for P y t h a g o r e a n
m u s i c a l i n t e r v a l s in a f r e q u e n c y r a n g e f r o m 50 t o 800 Hz.
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W i t h o u t the g i f t of hope, g r a n t e d t h r o u g h J e s u s Ch ri st ,
all m a n ' s e f f o r t s w o u l d be as h u m b l e as a w r i t e r ' s p e n w i t h
o u t ink.
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ral d r a f t s , and p r o v i d e d c a r e f u l i n s t r u c t i o n en r o u t e to a
m o r e r o b u s t e x p e r i m e n t a l p a r a d i g m . M y c o m m i t t e e h a s g i v e n
m a n y s u g g e s t i o n s w h i c h h a v e m a d e the w o r k m o r e c o n c i s e and
a u t h o r i t a t i v e .
Dr. R o b i n P a t c h e t t , in his c a p a c i t y as c o - a d v i s o r , a l s o
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p a r a t u s and p r o v i d e d d r a f t i n g s k i l l s for the f i gu r e s is a n
o t h e r to w h o m I e x t e n d m y thanks.
A fin al n o t e of t h a n k s g o e s to the s e c r e t a r y w h o typed
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P u r p o s e of the S t u d y 28
S t a t e m e n t of the P r o b l e m 29
II M e t h o d for E x p e r i m e n t O n e 31
S u b j e c t s 31
A p p a r a t u s and P r o c e d u r e 32
T a p e C o n s t r u c t i o n 33
A p p a r a t u s and P r o c e d u r e for T a p e 33 C o n s t r u c t i o n
T e s t i n g P r o c e d u r e 3 5
D e s i g n 36
III R e s u l t s 38
P l e a s i n g n e s s 38
S u b s i d i a r y A n a l y s i s for T a b l e 1 48
D i s s o n a n c e 52
T o n e P r e f e r e n c e s 5 4
IV D i s c u s s i o n 61
E x p e c t a n c y in C o n s e c u t i v e T o n e s 61 P a t t e r n s in P l e a s i n g n e s s R a t i n g s 64
D i s s o n a n c e 64
M u s i c a l E x p e r i e n c e , D e la y, W a v e f o r m , and 6 6
P l e a s i n g n e s s
T o n e P r e f e r e n c e s 67
A p p a r a t u s and P r o c e d u r e 70
T a pe C o n s t r u c t i o n 70
D e s i g n 71
VI R e s u l t s 74
T o n e P a i r s 74
D i s s o n a n c e and M u s i c a l E x p e r i e n c e 77
V I I D i s c u s s i o n 81
V I I I S u m m a r y and C o n c l u s i o n s 84
D i s s o n a n c e and P l e a s i n g n e s s 8 6
S i m p l i c i t y - C o m p l e x i t y 8 6
C o n s e c u t i v e T o n e s - A n E x p e c t a n c y M od e l 87
A P P E N D I X A A p p a r a t u s D i a g r a m 88
A P P E N D I X B C a l c u l a t i o n of D i s s o n a n c e 89
A P P E N D I X C S t a n d a r d I n s t r u c t i o n s to S u b j e c t s 93
A P P E N D I X D S a m p l e of D a t a F or m for E x p e r i m e n t O n e 94
A P P E N D I X E P l e a s i n g n e s s M e a n s for S q u a r e W a v e s by 95 D i s s o n a n c e C a t e g o r y and D e l a y
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T a b l e
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P a g e
A n a l y s i s of C o v a r i a n c e of P l e a s i n g n e s s r a t i n g s b y F r e q u e n c y S e p a r a t i o n b y W a v e
b y D e l a y by I n t e r v a l by M u s i c a l E x p e r i e n c e . 43
A n a l y s i s of V a r i a n c e of P l e a s i n g n e s s R a t i n g s
by D i s s o n a n c e C a t e g o r y and D e l a y ( Sq u a r e W a v e s ). 53
T - T e s t s for P l e a s i n g n e s s of S i n e W a v e D i s s o n
a nce and Dela y. 56
z - T e s t R e s u l t s for T o n e P r e f e r e n c e s . 60
F u n d a m e n t a l and H i g h e r T o n e C o m b i n a t i o n s . 72
R e p e a t e d A n a l y s i s of V a r i a n c e for T o n e pai rs . 75
A n a l y s i s of V a r i a n c e of P l e a s i n g n e s s R a t i n g s
b y D i s s o n a n c e G r o u p i n g by M u s i c a l E x p e r i e n c e . 78
F i g u r e
1 M e a n P l e a s i n g n e s s b y T o n e R a t i o for S i ne W a v e s
2 M e a n P l e a s i n g n e s s by T o n e R a t i o for S q u a r e W a v e s
3 M e a n P l e a s i n g n e s s b y I n t e r v a l
4 M e a n P l e a s i n g n e s s b y W a v e f o r m a nd D e l a y
5 E f f e c t of M u s i c a l E x p e r i e n c e and T o n e R a t i o o n P l e a s i n g n e s s
6 M e a n P l e a s i n g n e s s b y T o n e R a t i o b y W a v e f o r m and D e l a y
7 M e a n P l e a s i n g n e s s by M u s i c a l E x p e r i e n c e by W a v e f o r m and D e l a y
8 M e a n P l e a s i n g n e s s b y D i s s o n a n c e C a t e g o r y for S q u a r e W a v e s
9 M e a n P l e a s i n g n e s s H i s t o g r a m s b y D i s s o n a n c e for S i n e W a v e s
10 S t a n d a r d i z e d P r e f e r e n c e P r o p o r t i o n vs F r e q u e n c y in Hz
11 M e a n P l e a s i n g n e s s b y F u n d a m e n t a l b y M u s i c a l I n t e r v a l
12 E f f e c t of D i s s o n a n c e and M u s i c a l E x p e r i e n c e o n P l e a s i n g n e s s of T o n e p a i r s
13 C o m p a r i s o n of S i m u l t a n e o u s a nd C o n s e c u t i v e P l e a s i n g n e s s D a t a
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I N T R O D U C T I O N
O n e of the m a j o r i s s u e s a m o n g p h i l o s o p h e r s and t h e o r e t i
-c i a n s s i n -c e the time of P l a t o h a s b e e n the r e s o l u t i o n of the
m i n d - b o d y p r o b l e m : a c o n t e m p l a t i o n of the r e l a t i o n o r
d i c h o t o m y i n h e r e n t b e t w e e n t h at w h i c h e x i s t s and t h a t w h i c h
is p e r c e i v e d as e x i s t i n g . F e c h n e r , a G e r m a n p h y s i c i s t and
p i o n e e r p s y c h o l o g i s t , in h i s w o r k o n p s y c h o p h y s i c s and a e s
t h e t i c s e x a m i n e d f u n c t i o n a l o p e r a t i o n s l i n k i n g the p s y c h i c
a nd the p h y s i c a l (M ar x and H i l l i x , p. 37, 1973). I nd ee d,
m a n y p h e n o m e n a s u ch as p e r c e p t u a l i l l u s i o n s , t a s t e p r e f e r
e n c e , o r a c o u s t i c p r e f e r e n c e s a re r e a l l y i n v e s t i g a t i o n s into
the m i n d - b o d y p r o b l e m . In the c a s e of sound, m a n y ty pe s of
s o n i c s t i m u l i a re r e c e i v e d f r o m the e n v i r o n m e n t w h i c h s u r
r o u n d s us; b u t is w h a t we s e e m to "h ea r " in fact an a c c u r a t e
r e p r e s e n t a t i o n of the p h y s i c a l s e n s a t i o n t h a t w a s r e c e i v e d ?
S o u n d h a s long b e e n a m e s s a g e c a r r i e r : sou nd h a s c e r t a i n
p h y s i c a l p r o p e r t i e s , f r e q u e n c y ( v i b r a t i o n s p e r s ec o n d ) , in
t e n s i t y ( a m p l i t u d e o r d i s p l a c e m e n t of the v i b r a t i o n ) , t i m b r e
( q u a l i t y of s i m u l t a n e o u s l y b o r n f r e q u e n c i e s ) , and p u l s e ( t i m
ing b e t w e e n s u c c e s s i v e so und w a v e u n i t s ) . T h e s e d i m e n s i o n s
n o t e d h o w i n t i m a t e l y m a n ' s b e h a v i o u r h a s b e e n m o d i f i e d b y
sou nd . T h e e x p e r i m e n t s in this s t u d y f o c u s on f r e q u e n c y and
i n t e r v a l p r e f e r e n c e s for p a i r s of tones.
In 1929, L a i r d and C o y e l o o k e d a t the r e l a t i v e " a n n o y
i n g n e s s " of o n e t on e o r a n o t h e r in a t one c o m p a r i s o n task.
T h e y f ou n d f r e q u e n c i e s in the r an g e of 256 to 1024 Hz to be
l e s s a n n o y i n g t h a n 120 Hz and b e l o w o r 2048 Hz and above.
T h e i r a n n o y i n g n e s s c u r v e s e e m e d to be a s i m p l e i n v e r s i o n of
the t on al p r e f e r e n c e c u r v e s d i s c u s s e d b el ow .
De S o u z a et al. (1974) u se d the e q u a l l o u d n e s s c u r v e s as
m a p p e d b y F l e t c h e r and M u n s o n (1933) to e n s u r e t h at all to n al
s t i m u l i w e r e d e l i v e r e d at e q u a l s u b j e c t i v e l o u d n e s s l evels .
T h e e q u a l l o u d n e s s c u r v e s c o n t r o l l e d for p r e f e r e n c e s w h i c h
m i g h t h a v e b e e n a r e s u l t of l o u d n e s s r a t h e r t h a n the e x p e r i
m e n t a l v a r i a b l e , f r e q u e n c y . T h e D e S o u z a et al. d a t a s h o w e d
a p e a k in f r e q u e n c y p r e f e r e n c e at 400 Hz (and an i n v e r t e d "U"
s h a p e for the p r e f e r e n c e c u r v e ) .
In a s t u d y c o n d u c t e d for the N a t i o n a l B u r e a u of S t a n d
a r d s in W a s h i n g t o n ( D.C.), a r e - d e t e r m i n a t i o n of the e q u a l
l o u d n e s s c o n t o u r s w a s c a r r i e d o u t by M o l i n o (1973). M o l i n o
e s t a b l i s h e d e q u i v a l e n c e c u r v e s for the c o m p a r i s o n of tone
f r e q u e n c i e s of 125, 100 0, and 8 ,0 0 0 Hz at v a r i o u s d e c i b e l
l e v e l s of i n t e n s i t y 0, 10, 40, and 70 d b SPL. M o l i n o found
h i s d a t a to b e c o m p a r a b l e to t h a t of K i n g s b u r y (1927) f o r
ran ge ) . In c o m p a r i s o n w i t h the d a t a o£ F l e t c h e r and M u n s o n
( 19 3 3) , (the o t h e r e a r l y e x p e r i m e n t u si n g e a r p h o n e s ) , an u p
w a r d s h i f t of 10 d b for the M o l i n o and K i n g s b u r y d a t a m a d e
the c u r v e s m o r e c o m p a t i b l e w i t h tho se of F l e t c h e r and Mu ns on .
T h e d a t a of M o l i n o (1973), K i n g s b u r y (1927), and I n t e r n a t i o n
al O r g a n i z a t i o n for S t a n d a r d i z a t i o n (1959) f o r the m i d d l e
f r e q u e n c y r a n g e s, 200 to 4,0 00 Hz, a g r e e e x c e p t for a m i n o r
d i s c r e p a n c y in s h a p e a r o u n d the 2 ,0 00 Hz mark.
T h e R o b i n s o n and D a d s o n (1956) d a t a for free f i e l d e qu a l
l o u d n e s s c o n t o u r s , fall u n d e r c r i t i c i s m f r o m M o l i n o w h o n o t e s
t h a t in c o m p a r i s o n w i t h the e a r p h o n e d a t a s t u d i e s e v e n a l l o w
ing f or t h r e s h o l d a d j u s t m e n t s , c o r r e s p o n d e n c e w a s n o t c l o s e
( Mo l i n o , 1 9 7 3) . B e c a u s e of the g e n e r a l f l at c o n t o u r of the
70 p h o n e q u a l l o u d n e s s curve, as s h o w n in M o l i n o 1s and
o t h e r s ' d a t a , it w o u l d s e e m that this i n t e n s i t y w o u l d be u s e
ful as a n e q u a l l o u d n e s s c o n t r o l ; s u c h a c o n t r o l w as use d in
the B e r l y n e et al. (1967) e x p e r i m e n t s .
V i t z (1972) s t u d i e d b o t h f r e q u e n c y a nd l o u d n e s s p r e f e r
ence. F o r t hr e e l e v e l s of l o u d n e s s i n t e n s i t y , he f o u n d that
f r e q u e n c y p r e f e r e n c e p e a k e d in the r a n g e f rom 400 to 750 Hz,
w i t h s l o w d e c l i n e s on e i t h e r side.
A b r i e f c o m p a r i s o n b e t w e e n the f r e q u e n c y p r e f e r e n c e
c u r v e s of V i t z (1972) and De S o u z a et al. ( 1974) s h o w s the
v a l u e of the e q u a l l o u d n e s s c u r v e s in c l a r i f y i n g f r e q u e n c y
p r e f e r e n c e . T h e e q u a l l o u d n e s s c u r v e s of De S o u z a et al.
n o t use such a c o n t r o l , d i s p l a y a m o r e r o u n d e d p r e f e r e n c e
f un ction. S i n c e b o t h V i t z and De S o u z a et al. h a v e o n ly
s a m p l e d a small n u m b e r of f r e q u e n c i e s , the c o n t i n u i t y of d a t a
p o i n t s for a p r e f e r e n c e c u r v e is n ot co mplete.
U s i n g f o g h o r n s M o l i n o et al. (1974), e s t a b l i s h e d h i g h e r
p r e f e r e n c e s for p u r e tones of 300, 500, and 835 Hz or a c o m
p o s i t e tone c o m p o s e d of these f r e q u e n c i e s r a t h e r t han any
c o m p o s i t e tones h a v i n g a c o m p o n e n t of 120 Hz.
P a t c h e t t (1979) e x a m i n e d the m o s t p l e a s a n t a c o u s t i c s e t
ting m a d e by s u b j e c t s w h o used f r e q u e n c y as a free r e s p o n s e
v a r i a b l e . He found j u d g e m e n t s f o c u s i n g in a h a r r o w b a n d c e n
t e r i n g o n 399 Hz. T h e c o i n c i d e n c e b e t w e e n the f i nd i n g of
P a t c h e t t (whose s t i m u l i w e r e a d m i n i s t e r e d at c o n s t a n t i nt e n
sity) and the f i n d i n g s of De S o u z a ' s p r e f e r e n c e c u r v e w i t h
its p e a k at 400 Hz u si ng e qu a l l o u d n e s s s u g g e s t that an a b s o
l ute p r e f e r e n c e p o i n t o r band a r o u n d 400 Hz m i g h t exist. T he
f o l l o w i n g s e r i e s of a r t i c l e s e x p l o r e s the p r e f e r e n c e a s p e c t
in p a i r s of tones, o f t e n r e f e r r e d to as d y a d s o r intervals.
B ut first, a h i s t o r i c a l i n t r o d u c t i o n is in order.
T h e p e r c e p t i o n of c e r t a i n c o m b i n a t i o n s of tones as bei ng
m o r e p l e a s i n g o r a e s t h e t i c a l l y s t i m u l a t i n g m a y e x p l a i n the
type and a r r a n g e m e n t of m u s i c t ha t h as e n t e r t a i n e d m a n
t h r o u g h o u t the ages. F or P y t h a g o r a s , (as in H e l m h o l t z , 1954,
p. 1), the k e y f a c t o r for a e s t h e t i c e n j o y m e n t in m u s i c d e a l t
w i t h e s t a b l i s h i n g ideal r a t i o s of the f r e q u e n c i e s of the p a r
p h i l o s o p h i c a l in n a t u r e and b a s e d upon a s s u m p t i o n s of a r i t h
m e t i c p u r i t y and b e l i e f s of n u m b e r and h a r m o n y w h i c h w e r e in
v o g u e at the time and t o ok the f o rm of a k i nd of a r i t h m e t i c
m y s t i c i s m as in P o r t n o y (1954). T he f o l l o w e r s of P y t h a g o r a s
e x p a n d e d on the b e l i e f and b e c a m e m o r e r ad i c a l , e s p o u s i n g
t h a t n u m b e r s w e r e the b a s i s of na tu re , and t h a t m a n as a p a r t
of n a t ur e shou ld be e x p r e s s e d as s om e c o m b i n a t i o n of n u m b e r s
o r oth er . L o g i c a l l y , then, m a n ' s e n d e a v o u r s in the arts
o u g h t to r e f l e c t h is n u m e r i c a l b a s i s in n a t u r e and s in c e
n a t u r e was b e n e v o l e n t , then, m a n ' s e f f o r t s in the a r ts s h ou ld
h a v e some m o r a l value. By this c h a i n of r e a s o n i n g , the
P y t h a g o r e a n s had c o n c l u d e d that m u s i c itself (as an art) had
m o r a l value, w h i c h no d o u b t they had c h o s e n to p r o t e c t w i th
so me a r i t h m e t i c rule of p r e c i s i o n . A r i s t o t l e , as q u o t e d in
P o r t n o y (1954), is r e p o r t e d to h a ve s ai d of the P y t h a g o r e a n s :
" t h e y saw that m o d i f i c a t i o n s and the r a t i o s of m u s i c a l s c a le s
w e r e e x p r e s s i b l e in numbers; since, then, all o t h e r t hings
s e e m e d in t he i r w h o l e n a t u r e to be m o d e l l e d on n u m b e r s , and
n u m b e r s seemed to be the fir st t hi ng s in the w h o l e of na ture,
t h ey s u p p o s e d the e l e m e n t s of n u m b e r s to be the e l e m e n t s of
all things, and the w h o l e h e a v e n to be a m u s i c a l s c a l e and a
n um b er " (p. 6-7).
L a t e r P y t h a g o r e a n s a c t u a l l y c o n t e n d e d t ha t the s p e e d
ing h e a v e n l y b o d i e s did p r o d u c e m u s i c w h i c h u n f o r t u n a t e l y m a n
c ou l d not hear, b e c a u s e he w as so a c c u s t o m e d to it. For this
g r e a t i mp or ta n ce . L e g e n d has it that P y t h a g o r a s by m e a n s of
e x p e r i m e n t a t i o n w i t h s t r i n g e d i n s t r u m e n t s found the o p t i m a l
r a t i o s of p a r t s of the s t r in g to the w h o l e w h i c h p r o d u c e d
m o r e a e s t h e t i c sounds . T h e s e w e r e 2:1, 3:2, 4:3, and v a r i o u s
o t h e r r a t i o s of i n t e g e r numbe rs . H e r e w e re the oc ta v e, p e r
f e ct fifth, and p e r f e c t fourth. T h e two m u s i c a l i n s t r u m e n t s
of the time w e r e the lyre and the flute. T h e m u s i c of the
e ra w as m e l o d i c a l l y o r g a n i z e d and n ot h a r m o n i z e d . S t r i n g s
w e r e p l u c k e d or n o t e s w e r e p l a y e d s er ia ll y . F or the lyre e s
t a b l i s h i n g r a t i o s t h at w e r e a c c e p t a b l e , for s tr i n g s in e x c e s s
of th ree o r f ou r w o u l d be d i f f i c u l t , o w i n g to the c u l t u r a l
i n e r t i a of the time. T h e r o u t e t o w a r d s an a c c e p t a b l e m u s i c a l
s c a l e w o u l d be m a n y c e n t u r i e s in the m a k i n g . T o da y, the tun
ing s c a l e s are the P y t h a g o r e a n , N a t u r a l or (Just) I n t o n a t i o n ,
and the E qu a l T e m p e r e d w h i c h had t h e i r b a s i s in m a n y 3 and 4
tone su bs c al es . W o o d (1975) p r o v i d e s a b r i e f r e v i e w of these
d e v e l o p m e n t s (as d o m a n y t e x t b o o k s on m u s i c a l h i s t o r y or p h i
l o s o p h y , w i t h g r e a t e r e n l a r g e m e n t ) . T h e P y t h a g o r e a n s ca le
h as f o r m u l a e for o p t i m a l l y p l e a s i n g c o m b i n a t i o n s of tones,
h o w e v e r it has the d r a w b a c k of t h e r e b y c h e a t i n g m a n y h o r r i b l y
d i s s o n a n t (or u n p l e a s a n t sound in g) c o m b i n a t i o n s for the ca se s
w h e r e tonal i n t e r v a l s d o not c o m b i n e ideall y, and d u r i n g r e n
d i t i o n these n o t e s w o u l d be avoid ed . T h e c u r r e n t e q u a l t em
p e r e d a p p r o a c h h as d i v i d e d e a c h o c t a v e (2:1) i nt e r v a l into
t w e l v e s e m i t o n e s of e q u a l "size", w h e r e two s e m i t o n e s e qu a l
m i s n o m e r , si nc e e a c h s u c c e s s i v e tone is a p p r o x i m a t e l y 1.06
t im es the f r e q u e n c y of the n ote b elow. T he s t r u c t u r e of the
e q u a l t e m p e r e d a p p r o a c h w a s p r i m a r i l y g o v e r n e d b y the l i m i t e d
n u m b e r of d i s c r e t e n ot e s that c ou l d be fitted o n t o c e r t a i n
k e y e d i n s t r u m e n t s and a l s o by the e a s e of d e p a r t u r e or t r a n
s i t i o n of m e l o d y into d i f f e r e n t keys. N o t a b l y , some f r e q u e n
cy d i f f e r e n c e s b e t w e e n s h a r p s and f l a t s w e r e i gn ored and p r e
s u m e d to b e s o u n d e d as the same note, (for instance, C s h a r p
= D flat, F s h a r p = G flat, etc). In the equ al t e m p e r e d
s cal e, the P y t h a g o r e a n c o n s o n a n c i e s b e c a u s e of the "equal"
i n t e r v a l w i d t h are tune d s h a r p e r o r fl at te r as the s y s t e m
d i c t a t e s . T h e p i a n o is the p e r f e c t e x a m p l e of an e qu a l t e m
p e r e d in st ru m en t . A n o t h e r scale, the J u s t I n t o n a t i o n scale,
c a n be used by e i t h e r v i o l i n i s t s or s i n g e r s to p r o d u c e f re
q u e n c y i n t e r v a l s that are p e r c e i v e d to be b e t t e r than w h a t
the P y t h a g o r e a n s y s t e m or E qu a l t e m p e r e d scale has to offer,
p a r t i c u l a r l y for t hi rd s and sixths. A J u s t I n t o n a t i o n s i n g e r
m o d u l a t e s the f r e q u e n c y of the n o te sung to some ideal p e r
c e p t i o n of w h a t t ha t note shou ld be, g i v e n the c o n t e x t of the
m u s i c a l s i tu a t i o n . J u s t I n t o n a t i o n m e a n s s in gi ng of c l o s e
P y t h a g o r e a n c o n s o n a n c i e s or the s i n g i n g of s l i g h t l y s h a r p e r
o r f l a t t e r no te s t han in the m u s i c a l text.
T h e f o r e g o i n g d i s c u s s i o n s u g g e s t s that a m e a s u r e m e n t of
i n t e r v a l or s e q u e n c e p r e f e r e n c e s is h i g h l y r el a t e d to the
s t r u c t u r e of m u s i c a l s c a l e s or c o m p o s i t i o n s . S c a l e c o n
9
c o n s o n a n c i e s w h i l e trying to avoid d i s s o n a n t in tervals. But,
s u ch s c al es co ul d a l s o r e f l e c t s o c i a l p r e s s u r e s , or n a t u r al
p r e f e r e n c e s . T h e sta te of r e s e a r c h on w h o l e scal es is v e r y
m u c h at a b e g i n n i n g level, ho we v er , s in c e such i n v e s t i g a t i o n
is a n e w concept.
O ' K e e f f e (1975) e x a m i n e d p r e f e r e n c e s for pair e d m u s i c a l
e x c e r p t s p l a y i n g in e i t h e r the J u s t I n t o n a t i o n or E q u a l T e m
p e r e d scale for the c l a s s i c a l p i e c e s " S i l e n t N i g ht " and
" A m e r i c a the B e a u t i f u l " . T he song " S i l e n t N igh t" p r o d u c e d no
s i g n i f i c a n t d i f f e r e n c e s in scale p r e f e r e n c e s . H o w e v e r , the
r e n d i t i o n s of " A m e r i c a the B e a u t i f u l " w e r e s i g n i f i c a n t l y p r e
f e r r e d in the J u s t I n t o n a t i o n scale. T h e a u t h o r i nd ic a t e d the
s u b j e c t pool, c o m p o s e d of m o d e r a t e l y t r ai n e d and r e l a t i v e l y
u n t r a i n e d m u s i c i a n s , p r e f e r r e d J u s t I n t o n a t i o n . T he o b s e r v a
t i o n t en d s to s u b s t a n t i a t e the v i e w that s c a l e s y s t e m s could
be c h o s e n to c o m p l e m e n t the song c o n t e x t , t h e r e b y i n d i r e c t l y
a c c o u n t i n g for the s t u b b o r n e s s of som e m u s i c i a n s to a d o p t the
E q u a l T e m p e r e d scale. A v i e w n o t e d by M e n u h i n & Davis,
(1979) w a s that m o d i f i c a t i o n s of the Eq ua l T e m p e r e d S c a l e
( f l a t t e n i n g or s h a r p e n i n g of some notes) w e r e not a p p r o v e d by
m u s i c a l pur is ts . In a d d i t io n , O ' K e e f f e not ed that his fi nd
ings m i g h t be in c o n f l i c t w i t h t h o s e of W a r d and M a r t i n
(1961) w h o found the r e v e r s e s i t u a t i o n in scale p r e f e r e n c e s
for s e q u e n c e s of i n d i v i d u a l tones, r a t h e r than m u s i c a l e x
c erpts. M o r e r e s e a r c h is needed to c l a r i f y the f i n d i n g s of
T h e p r e f e r e n c e for c e r t a i n s o u n d s or c o m b i n a t i o n s of
s o u n d s in s e q u e n c e is a form of h a r m o n i c logic and is r el a te d
to the " t o n a l i t y " of m u s i c a l pieces. P a ul H i n d e m i t h , (1961,
p. 64) c l a i m e d that " T o n a l i t y d o u b t l e s s is a v e r y s u b t l e form
of g r a v i t a t i o n " . M u s i c that h as t o n a l i t y is s t r u c t u r e d
a r o u n d a k e y n o t e or "Tonic" a r o u n d w h i c h the o t h e r tones are
o r g a n i z e d . F r o m M a c h l i s (1961, p. 32) the f o l l o wi ng q u o t a
t ion a b o u t t o n a l i t y d e s c r i b e s its i mportanc e.
T h e s en s e of r e l a t e d n e s s to a c e n t r a l tone is k n o w n as
’t o n a l i t y ' . It has b e e n the f u n d a m e n t a l r e l a t i o n s h i p in
o u r m u s i c. As R o g e r S e s s i o n s h as writ te n , 'Tonality'
s h o u l d b e u n d e r s t o o d as the p r i n c i p a l m e a n s w h i c h c o m
p o s e r s of the s e v e n t e e n t h , e i g h t e e n t h , and n i n e t e e n t h
c e n t u r i e s e v o l v e d of o r g a n i z i n g m u s i c a l s o u n d s and g i v
ing t he m c o h e r e n t 'shape'.
A g r o u p of r e l a t e d tones w i t h a c o m m o n c e n t e r or
T o n i c is k n o w n as a 'key'. T h e tones of the ke y serve
as a b a s i c m a t e r i a l for a g i v e n c o m p o s i t i o n . The key,
t h a t is, m a r k s o ff an a r ea in m u s i c a l s pa ce w i t h i n w h i c h
m u s i c a l g r o w t h and d e v e l o p m e n t t ak e place.
C o m p o s e r s h e i g h t e n e d the ir m u s i c a l e f f e c t by m o v i n g or
" m o d u l a t i n g " f r o m the h o m e k ey to a n e w key, and r e t u rn i ng .
( M ac h li s, 1961). T w e n t i e t h c e n t u r y c o m p o s e r s s o m e t i m e s used
bi- and p o l y t o n a l i t y , that is, m u l t i p l e h o m e keys.
M e n u h i n & D a v i s (1979), p r o v i d e a s u m m a r y of the a t on a l
s t r e s s e s the e q u a l i t y of all the keys. M e n u h i n & D av i s noted
that S c h o e n b e r g b a s e d his s y s t e m on the 'tone r o w 1 , the a r
r a n g e m e n t of the t w e l v e s e m i t o n e s of the o ctave, in a g i v e n
order. For S c h o e n b e r g , the c o m p o s e r c o u l d not r e p e a t a ny
tones until the e n t i r e s e q u e n c e had b e e n used. B o t h m e l o d i e s
and h a r m o n i e s had to use the tone row. H ow e v e r , the a ut h o r s
no te d t hat S c h o e n b e r g i a n m u s i c d e s p i t e a d e m a n d i n g n o v e l t y
b e c a m e a c c e p t e d in o p e r a s b e f o r e the turn of the t w e n t i e t h
ce nt u ry . M y e r s (1968) o b s e r v e d the a b a n d o n i n g of t o n a l i t y in
f a v o ur of t w e l v e - t o n e c o m p o s i t i o n or in g e n e r a l , a t on al m u s i c
w as the m o s t c l e a r tren d in t w e n t i e t h c e n t u r y music. H o w e v e r ,
he n ot e d that s e v e r a l " m a s t e r p i e c e s " of the t w e n t i e t h c e n t u r y
s t il l used the p r i n c i p l e of t o na li ty . Also, a g r e a t a m o u n t
of t w e n t i e t h c e n t u r y m u s i c r e m a i n s at l e a s t b i t o n a l or po ly
-t onal r a -t h e r -than a-tonal. As a g e n e r a l i t y M y e r s o f f e r e d that
" Thus we see a g r a d u a l g r o w i n g of tonal e m a n c i p a t i o n . . . " and
p r o v i d e d s e v e r a l e x a m p l e s . T h e s t u d y of p r e f e r e n c e s of
s e q u e n t i a l t on e s r e p r e s e n t s a v e r y b a s i c i n v e s t i g a t i o n of
tonalit y: the s h i f t i n g of p r e f e r e n c e p a t t e r n s from n ote to
n o t e .
T h e b u l k of the r e s e a r c h on tone p r e f e r e n c e see ms to
h a v e b e e n d o n e w i t h tone p a i r s o r i n t er va ls , and is c l o s e l y
i n v o l v e d w i t h the n o t i o n of c o n s o n a n c e and d i s s o n a n c e . M o s t
of the s t u d i e s a t t e m p t e d to use r a t i n g s o r r a n k i n g s of tonal
p a i r s a c c o r d i n g to d i f f e r e n t a e s t h e t i c c r it er ia . H i s t o r i c a l
b l e i n to t wo b r o a d c a t e g o r i e s , m u s i c i a n s and n o n - m u s i c i a n s .
In 1918, M a l m b e r g r e q u i r e d a g r o u p of m u s i c i a n s and p s y
c h o l o g i s t s to r a n k t w o - t o n e c o m b i n a t i o n s for " s m o o t h n e s s ,
p u r i t y , and b l e n d i n g " . T h e o r d e r i n g s w e r e h i g h l y c o r r e l a t e d
a nd y i e l d e d a c o n s o n a n c y - d i s s o n a n c y s e r i e s h e a d e d by o ct a v e ,
p e r f e c t fifth, and m a j o r sixth.
In 1928, G u e r n s e y p r o d u c e d a s i m i l a r r a n k i n g w i t h r e
s p e c t to c o n s o n a n c e u s i n g m u s i c i a n s . H o w e v e r , w h e n j u d g e
m e n t s w e r e r e q u i r e d u n d e r the c a t e g o r y of p l e a s a n t n e s s , the
o r d e r w a s d i f f e r e n t . T h e j u d g e m e n t s w e r e o r d e r e d s ix th s ,
t h i r d s , p e r f e c t f o ur t h , and m i n o r s e v e n t h .
In 1914, V a l e n t i n e d e v e l o p e d a p r e f e r e n c e r a t i n g s c a l e
t h a t w a s s i m i l a r to t h a t of G u e r n s e y in 1928 w h o used a s e v
e n - p o i n t p l e a s i n g - d i s p l e a s i n g c o n t i n u u m . T h e l i s t w a s h e a d e d
b y m i n o r third, o c t a v e , m a j o r sixt h, and m i n o r sixth.
F r o m the a b o v e e v i d e n c e , f o r the s a m p l e p o p u l a t i o n s ,
(the m u s i c i a n s ) , the c o n c e p t s of c o n s o n a n c e and d i s s o n a n c e
c l e a r l y d i f f e r f r om i m p r e s s i o n s of p l e a s i n g n e s s or d i s p l e a s
i n g n e s s .
V a n de G ee r, L e v e l t , and P l o m p (1962) a sk e d n o n - s p e c i a l
ists in m u s i c to r a t e tone p a i r s o n s e v e n - p o i n t s c a l e s of
c o n s o n a n t d i s s o n a n t , b e a u t i f u l u g l y , and e u p h o n i u s n o n e u p h o
-nius. U n d e r f a c t o r a n a l y s i s , V a n d e G e e r et al. f ou nd the
s c a l e s to be r e p r e s e n t a t i v e of a c o m m o n d i m e n s i o n for tone
r a ti n g . H i g h e s t l o c a t i o n s w e r e a w a r d e d to s ix th s, t hi rd s,
T o c l a r i f y the d i c h o t o m y b e t w e e n l a y m e n and m u s i c i a n s ,
F r a n c e s (1958) f o u n d that l a y m e n a w a r d e d the h i g h e r r a t i n g s
to the o c t a v e and f i f t h as c o m p a r e d to the m u s i c i a n s .
F r a n c e s a l s o c o m p a r e d two s e r i e s of f i v e - t o n e c ho r d s , o n e
m a r k e d l y d i s s o n a n t and the o t h e r c o n s o n a n t , he f ou nd the p r o
f e s s i o n a l m u s i c i a n s r e j e c t e d the c o n s o n a n t c ho rd s.
A c c o r d i n g to the l i t e r a t u r e , m u s i c i a n s and l a y m e n h a v e
d i f f e r e n t p r e f e r e n c e c r i t e r i a w h i c h t h e y use to e v a l u a t e to n
al d y a d s ( i n t e r v a l s ) . Al so , t h e r e are a n u m b e r of s c a l e s of
a e s t h e t i c p r e f e r e n c e a s s o c i a t e d w i t h tone p a i r c o m p a r i s o n s .
S p e c i f i c a l l y , c o n s o n a n c e and d i s s o n a n c e c o u l d m e a n d i f f e r e n t
t h i n g s to d i f f e r e n t g r o u p s , and c o n s o n a n c e is n o t n e c e s s a r i l y
the s o l e c r i t e r i o n f or p l e a s i n g n e s s .
M a n y t h e o r i e s a t t e m p t to e x p l a i n the f a c t o r s u n d e r l y i n g
d i s s o n a n c e . H e r m a n H e l m h o l t z ( f r o m 1877 t r a n s l a t e d in 1954)
d e f i n e d c o n s o n a n c e as a n a b s e n c e of b e a t s b e t w e e n s i m u l t a n e
o u s l y s o u n d e d tones. A b e a t (or be at s ) is the r e g u l a r i n t e r
r u p t i o n of a p e r c e i v e d m u s i c a l n o t e (or notes) by s h o r t p u l s e
(or p u l s e s ) of h i g h e r i n t e n s i t y nois e. T h e b e a t is the p r o
d u c t of p e r i o d i c w a v e s u m m a t i o n and c a n c e l l a t i o n . W h e n w a v e
t r a i n s of c o m p o n e n t f r e q u e n c i e s for a n o te are in p h a s e at
r e l a t i v e m a x i m u m a m p l i t u d e s , a b e a t w i l l o c cu r. T o c o n t i n u e ,
then, for H e l m h o l t z , c o n s o n a n c e for c o m p l e x tones, t h a t is,
t o n e s c a r r y i n g u p p e r o v e r t o n e s w o u l d m e a n that the o v e r t o n e s
w o u l d tend to h a r m o n i z e (with the f u n d a m e n t a l ) and be w i t h o u t
w o u l d p r o d u c e bea ts . (The b e a t s m a y n o t be a b l e to be h e a r d ,
b u t add to the p s y c h o l o g i c a l r o u g h n e s s of the i m p r e s s i o n g i v
en b y the n o t e s b e i n g p l a y e d ) .
F o r s i m u l t a n e o u s s o u n d i n g of p u r e ton es , H e l m h o l t z a d v o
c a t e d t h a t d i s s o n a n c e is d u e to b e a t s b e t w e e n the to n es d e
p e n d i n g o n the i n t e r v a l ( f r e q u e n c y d i f f e r e n c e ) b e t w e e n the
n o t e s , ( k n o w n as the b e a t f r e q u e n c y ) .
A c c o r d i n g to B e r l y n e (1971), S t u m p f in 1893 c o u n t e r e d
H e l m h o l t z ' s c o n c e p t i o n of d i s s o n a n c e b y s t a t i n g t h at d i s s o n
a n c e c o u l d o c c u r w i t h o u t b eats. F r o m h i s e x p e r i m e n t a t i o n ,
S t u m p f c o n c l u d e d t h a t c o n s o n a n t t o n e p a i r s w e r e h a r d e r to
d i s c r i m i n a t e and he p r o p o s e d the n o t i o n of " f u s i o n " . T h i s
w a s the t e n d e n c y of c o m p o n e n t t o n e s to be h e a r d as a unit or
w h o l e u n d e r c o n d i t i o n s of c o n s o n a n c e . T h e ide a w a s that in
c o n s o n a n c e , t on e s w e r e fused into a k i n d of i r r e d u c i b l e G e s t
-a l t i s t w h o l e t h -at w -a s n ot -a n -a l y z -a b l e i n to s u b p -a r t s . H e nc e,
the ideal or c o n s o n a n t t w o - t o n e c l a n g c o u l d n o t be p e r c e i v e d
as two, b u t i n s t e a d as one tone. H o w e v e r , a f a c t o r a n a l y t i c
s t u d y by V a n de G e e r , L e ve l t , and P l o m p (1962) d i s c l o s e d the
f u s i o n d i m e n s i o n ( c o m p o s e d of the a d j e c t i v e s ; s i m p l e - m u l t i
ple, r o u g h - s m o o t h , and a c t i v e - p a s s i v e ) w a s i n d e p e n d e n t of the
f a c t o r " c o n s o n a n t - d i s s o n a n t " : f u r t h e r , the i n v e s t i g a t o r s
fou nd the d e g r e e of f u s i o n i n c r e a s e d w i t h f r e q u e n c y d i s p a r i t y
b e t w e e n the tones. A ls o, a c c o r d i n g to P l o m p a nd L e v e l t
( 19 65 ), S t u m p f s u b s e q u e n t l y fo und w e a k n e s s in the theory.
sim-i l a r sim-i t y to that of H e l m h o l t z . H o w e v e r , K r u e g e r e m p h a s i z e d
the i m p o r t a n c e of the b e a t i n g of d i f f e r e n c e tones a g a i n s t
e a c h o t h e r: (A d i f f e r e n c e tone is s i m i l a r to a b e a t f r e q u e n
cy b e t w e e n m e m b e r s of a tone p a i r , but, it r e f e r s to the
b e a t s t h a t are a r e s u l t of d i s h a r m o n y b e t w e e n c o n f l i c t i n g
r a t i o s of p a r t i a l s to t h e m s e l v e s o r to f u n d a m e n t a l s ) . Fo r
K r u e g e r c o n s o n a n c e w a s a c h i e v e d b y d u p l i c a t i o n o r s i m i l a r i t y
of the d i f f e r e n c e tones. M o r e c o n s o n a n t i n t e r v a l s w o u l d h a v e
m o r e s u c c e s s i v e d i f f e r e n c e t on es o s c i l l a t i n g at the s am e f r e
q u e n c y . T h i s w o u l d in t u r n g i v e r i s e to the o v e r a l l s e n s a
t i o n of f e w e r c o m p o n e n t s and h e n ce , d e v e l o p a s i m p l e r and
m o r e a e s t h e t i c i m p r e s s i o n .
T h e i n t e r f e r e n c e m o d e l s of H e l m h o l t z and K r u e g e r h a v e
f ou n d s o me r e c e n t s u p p o r t . In e x p e r i m e n t s of d i c h o t i c tonal
p r e s e n t a t i o n (two tones, o n e to e a c h e a r b y e a r p h o n e s ) , as in
S a n d i g (1939), i n t e r v a l s of d i s s o n a n t f r e q u e n c y d i f f e r e n c e
s u ch as the m a j o r s e c o n d and the m a j o r s e v e n t h w e r e found to
be m o r e c o n s o n a n t in the d i c h o t i c task. T o s i m p l i f y , if
t o n e s a re s i m u l t a n e o u s l y s e n t to the s a m e ear, i n t e r f e r e n c e
m a y r e s u l t at the p o i n t of r e c e p t i o n , g i v i n g r i s e to the p e r
c e p t i o n of d i s s o n a n c e . If the t o n e s a re s e p a r a t e d , (one p e r
e a r ) , t h e n e a c h e a r c o u l d p r o c e s s the s i g n a l c a r r i e d by tha t
t o n e w i t h o u t i n t e r f e r e n c e and t h e r e f o r e w i t h p e r c e p t i o n of
c o n s o n a n c e . T h e s t u d i e s i m p o r t a n t l y s u g g e s t the l oc u s of the
p s y c h o l o g i c a l i m p r e s s i o n of c o n s o n a n c e o r d i s s o n a n c e as o r i g
and m o r e i n t e g r a t i v e c o g n i t i v e l e vels.
L i p p s in 1885 , p o s t u l a t e d t h a t a c o u s t i c v i b r a t i o n s w e r e
u n c o n s c i o u s l y c o u n t e d and t h a t in the c a s e of c o n s o n a n c y m a n y
a c o u s t i c v i b r a t i o n s c o i n c i d e , l e a d i n g a g a i n to a p a r s i m o n i o u s
s t r u c t u r e for a e s t h e t i c c o n s o n a n c e . L i p p s m u s t c o n t e n d w i t h
the o b j e c t i o n that the r e l a t i o n s of c o n s o n a n c y are no t e l i m
i n a t e d w h e n n o t e s a r e s l i g h t l y m i s t u n e d (e.g., 2 0 1 : 3 0 0 in
s t e a d of the f if t h 2 0 0 : 3 0 0 , see P e t e r s o n and S m i th , ( 19 30)).
T h e m a j o r fla w in the t h e o r y is the a s s u m p t i o n that the e ar
is a b l e to u n c o n s c i o u s l y r e s o l v e o r c o u n t all c o m p o n e n t f r e
q u e n c i e s for c o m p l e x i nt e r v a l s .
O t h e r s h a v e p r o p o s e d c u l t u r a l t h e o r i e s for c o n s o n a n c e
and d i s s o n a n c e . T h e f o r m u l a t i o n by L u n d i n (1947, 1968) of a
t h e o r y for c u l t u r a l e x p l a n a t i o n of c o n s o n a n c e and d i s s o n a n c e
w a s g r e a t l y i n f l u e n c e d b y a n o t h e r p i o n e e r in the f i e l d of
m u s i c a l m e a s u r e m e n t , C. E. S e a s h o r e . A f t e r s h o w i n g the
d i c h o t o m y b e t w e e n f r e q u e n c y and p i t c h , t h a t is, t hat p i t c h is
the p s y c h o l o g i c a l c o r r e l a t e of f r e q u e n c y and is s u b j e c t i v e in
n a t u r e , L u n d i n q u o t e s S e a s h o r e (p. 25):
P i t c h d i s c r i m i n a t i o n is n ot a m a t t e r of l o g i c a l th ou gh t.
It is r a t h e r an i m m e d i a t e i m p r e s s i o n , f ar m o r e p r i m i t i v e
t h a n r e f l e c t i v e t h o u g h t , and d e p e n d e n t u p o n the p r e s e n c e
o r a b s e n c e in v a r i o u s d e g r e e s of the s e n s i t i v e m e c h a n i s m
of the inn er ear.
( L a t e r in 1 9 3 8 ) . . . T r a i n i n g , l ik e m a t u r a t i o n r e s u l t s in
ing, and the d e v e l o p m e n t of h a b i t s of use in m u s i c a l
o p e r a t i o n s . T r a i n i n g p r o b a b l y d o e s n ot m o d i f y the c a p a c
ity of the s e n s e o r g a n a ny m o r e than the p l a y i n g of the
g o o d v i o l i n m a y i m p r o v e the q u a l i t y of its tone.
F o r L u n d i n , "the c o n s o n a n c e o r d i s s o n a n c e of a m u s i c a l i n t e r
v a l is m e r e l y an i n d i v i d u a l j u d g e m e n t t hat is c u l t u r a l l y d e
t e r m i n e d r a t h e r than c a u s e d b y s o m e a b s o l u t e p r o p e r t y of the
s t i m u l i " (p. 98). He s u p p o r t e d h i s a r g u m e n t s b y p r o o f s f r o m
o t h e r r e s e a r c h e r s . L u n d i n not ed , f i r s t l y , that the c r i t e r i a
used b y i n d i v i d u a l s for t h e i r j u d g e m e n t s is a f u n c t i o n of
c u l t u r a l infl ue nc e . A c c o r d i n g to B u gg (1933), u n t r a i n e d p e r
s o n s tend to be m o r e i n f l u e n c e d b y a f f e c t i v e f a c t o r s in t he i r
j u d g e m e n t . C o n s o n a n c e and d i s s o n a n c e is m o r e a p r o d u c t of
l ik e o r d i s l i k e of a m u s i c a l i n t e r v a l . V a l e n t i n e (1914)
f o u n d c h i l d r e n ' s p r e f e r e n c e s to v a r y a c r o s s s c h o o l g r o u p s ,
and t h a t as a c h i l d g r o w s o l d e r t h e r e w a s a d e v e l o p m e n of
c e r t a i n k i n d s of c o n s o n a n c e p r e f e r e n c e . C o l l m a n (1972) foun d
a s i g n i f i c a n t r e l a t i o n s h i p b e t w e e n the a b i l i t y to d i s t i n g u i s h
p i t c h and the c a p a c i t y to d i s c e r n c o n s o n a n c e (as a d u l t s
d e f i n e d it to be) f or e l e m e n t a r y s c h o o l c h i l d r e n . A s w e l l ,
he n o t e d that a e s t h e t i c j u d g e m e n t w a s m o r e h i g h l y r e l a t e d to
m e n t a l age th an is v i s u a l d i s c r i m i n a t i v e j u d g e m e n t . C o l l m a n
p r o p o s e d that e a r l y i n s t r u c t i o n in m u s i c w o u l d f a c i l i t a t e the
d e v e l o p m e n t of p i t c h d i s c r i m i n a t i o n and c o n s o n a n c e p r e f e r
e n c e .
be m o d i f i e d by r e p e t i t i o n (of d i s s o n a n t i n t e r v a l s ) , as in
M o o r e (1914). M e y e r (1903) f o u n d s u b j e c t s w i t h an i n i t ia l
d i s l i k e for q u a r t e r - t o n e A s i a t i c m u s i c d e v e l o p e d g r e a t e r p r e
f e r e n c e for it w i t h r e p e t i t i o n . F i n a l l y , L u n d i n p o s t u l a t e d
t h a t j u d g e m e n t s of c o n s o n a n c y a r e c o n t e x t u a l l y b o u n d , and
c o m p a r a t i v e in v a l ue y the m u s i c a l s e t t i n g d e t e r m i n e s the c o n
s o n a n c y for i n d i v i d u a l t one i n t e r v a l s . T o f i n i s h w i t h a
f i n a l a p p r a i s a l f r o m L u n d i n (p. 10 0) , " T h e j u d g e m e n t w h i c h we
w i l l m a k e will be a f u n c t i o n of m a n y c o n d i t i o n s . S o m e of
t h e s e we h a v e m e n t i o n e d : the p a r t i c u l a r c r i t e r i o n w h i c h on e
s e l e c t s as a s t a n d a r d for h i s j u d g e m e n t , p r e v i o u s e x p e r i e n c e
w i t h the in te rv al , the c o n t e x t in w h i c h the i n t e r v a l a p p e a r s ,
and g e n e r a l and s p e c i f i c c u l t u r a l b a c k g r o u n d so far as m u s i c
is c o n c e r n e d , and m o r e p a r t i c u l a r l y so far as c o n s o n a n c e and
d i s s o n a n c e are c o n c e r n e d . " P e r h a p s , c o n c e r n i n g the P y t h a g o r
e a n s , and in f a v o u r of h i s c u l t u r a l v i e w s , L u n d i n (1967, p.
69) n o t e d that the G r e e k s m i g h t h a v e p r e f e r r e d a s ca le
s m a l l e r than o ur o c t a v e and that m a n y d i f f e r e n t s c a l e s h a v e
a p p e a r e d in a v a r i e t y of c u l t u r e s .
P l o m p and L e v e l t (1965) t o o k a p h y s i o l o g i c a l s t a n d on
c o n s o n a n c e and d i s s o n a n c e and f o u n d s o m e s u p p o r t for
H e l m h o l t z ' s i n t e r f e r e n c e t h e o r y from an a p p r o a c h d e p e n d e n t on
b e a t s v i a a c r i t i c a l b a n d w i d t h . T h e a s s u m p t i o n of the c r i t i
c al b a n d w i d t h is that the E r e q u e n c y s e p a r a t i o n of t on e s in a
tone i n t e r v a l c o u l d a f f e c t the c o n s o n a n c y o r d i s s o n a n c y of
in 1965, for a tone p a i r w i t h a m e a n f r e q u e n c y of 500 Hz, the
c r i t i c a l b a n d w i d t h was r o u g h l y in the r a n g e of 10 to 75 Hz.
T h e i r a n a l y s i s a l s o c o n t i n u e d to s h o w t h at the c r i t i c a l b a n d
w i d t h is g r e a t e r for tone p a i r s w i t h h i g h e r m e a n f r e q u e n c i e s ,
and l e s s e r for lower. M a x i m a l d i s s o n a n c e as H e l m h o l t z (1877
t r a n s l a t e d 1954) had t h o u g h t of it w a s a r o u n d 33 c y c l e s p er
s e c o n d d i f f e r e n c e b e t w e e n the ton es , but, P l o m p and L e v e l t
had s h o w n it to be r o u g h l y 25% of a c r i t i c a l b a n d w i d t h w h i c h
i n c r e a s e d in size w i t h the m e a n f r e q u e n c y . T h e idea of d i s
s o n a n c e as b ei n g m a i n t a i n e d by r o u g h n e s s b e a t s w a s upheld.
P l o m p and L e v e l t p e r f o r m e d s o me s t a t i s t i c a l a p p l i c a t i o n s of
the c r i t i c a l b a n d w i d t h to B a c h ' s T r i o S o n a t a for O r g a n No. 3
in C m i n o r and D v o r a k ' s S t r i n g Q u a r t e t Op. 51 in E flat
m a j o r . T h e y n o t e d that d i f f e r e n c e t o n e s fell q u i t e o f t e n
w i t h i n the c r i t i c a l b a n d w i d t h b u t a l m o s t a l w a y s tended to e x
c ee d the v e r y d i s s o n a n t 25% m a r k of the c r i t i c a l b a n d w i d t h .
It is i m p o r t a n t to n o t e t ha t not all b e a t i n g is n e c e s s a r i l y
u n p l e a s a n t in nature.
T h e m e c h a n i c s of the c r i t i c a l b a n d w i d t h e f f e c t c om e
f r o m i n t e r f e r e n c e p a t t e r n s in the i n n e r ear. T h e c o c h l e a of
the ear, w h i c h r e c e i v e s its a c o u s t i c input from a c o l l e c t i o n
of s ma l l b o n e s that b e a t o n a s k i n m e m b r a n e , is o p t i m a l l y
s e n s i t i v e to s u c c e s s i v e l y l o w e r p i t c h e s a l o n g its l e n g t h (as
d i s t a n c e f ro m the s t a p e s i n c r e a s e s as in K l i n g and Rig gs,
1972). T o be h e a r d as a c e r t a i n p i t c h , a f r e q u e n c y of v i b r a
of the cochl ea . O n the b a s i l a r m e m b r a n e , the p r o x i m i t y of
tw o s t i m u l a t i o n area s, (one for e a c h of two tones) d e t e r m i n e s
the e x t e n t of m u t u a l or h a r m o n i c b e n e f i t . D i s s o n a n c e then,
is e q u a t e d w i t h p a r t i a l and d e s t r u c t i v e o v e r l a p of s t i m u l a
t i o n a reas , that is, b ei n g i n side a c r i t i c a l b a n d w i d t h . C o n
s o n a n c e is r e l a t e d to c o m p l e t e o v e r l a p of s t i m u l a t i o n a r ea
( u n i s o n ) , or c o m p l e t e s e p a r a t i o n of s t i m u l a t i o n areas. A
q u o t e f r o m G a l i l e o G a l i l e i in 1638 , as in C r e w and S a l v i o
(1963) g i v e s an e a r l y v i e w of d i s s o n a n c e .
A g r e e a b l e c o n s o n a n c e s are p a i r s of to ne s w h i c h s t r i k e
the e ar w i t h a c e r t a i n r e g u l a r i t y ; this r e g u l a r i t y c o n
s i s t s in the f a ct tha t the p u l s e s d e l i v e r e d b y the two
tones, in the s am e i n t e r v a l of time, shall be c o m m e n s u r
a b l e in nu mb er , so as not to k e e p the e a r d r u m in p e r
p e t u a l t orm en t, b e n d i n g in two d i f f e r e n t d i r e c t i o n s in
o r d e r to y i e l d to the e v e r - d i s c o r d a n t i m p u l s e s
(p. 100).
T h e n o t i o n of the e a r d r u m as e x p e r i e n c i n g d i s s o n a n c e as a
p a i n f u l v i b r a t i o n p a t t e r n r e p r e s e n t e d an e a r l i e r v i e w of the
m e c h a n i c s of d i s s o n a n c e . It r e m a i n e d l a r g e l y to V o n B ek e s y ,
c e n t u r i e s later, w h o w o n the N o b e l P r i z e for his r e s e a r c h in
a u d i t i o n , to a s s i s t in the d i s c o v e r y of the locus of d i s s o n
a n c e p e r c e p t i o n . V o n B e k e s y s h o w e d that n e i t h e r h a r m o n i c s
n o r d i f f e r e n c e tones w e r e the r e s u l t of e a r d r u m v i b r a t i o n
p a t t e r n , nor w e r e h a r m o n i c s the r e s u l t of m i d d l e e a r d i s t o r
a b l e to b e g e n e r a t e d in the m i d d l e e a r ( Kl in g and R i g g s ,
(1972). M o r e r e c e n t l y , the t h e o r y of the o r i g i n of h a r m o n i c s
h a s b e e n s p e c u l a t e d to be in f lu id e d d i e s of the i n n e r e a r or
as b e i n g in the p r o x i m i t y of n e u r a l a u d i t o r y f i b e r s u n d e r the
b a s i l a r m e m b r a n e (Kli ng & R i g g s , 1 9 72 ).
O d d l y , w i t h o u t s u ch i n t e r f e r e n c e m e c h a n i s m s , p a t t e r n s of
c o n s o n a n c e and d i s s o n a n c e w o u l d p r o b a b l y n o t e x i s t for the
h u m a n l i s t e n e r , s i n c e o t h e r w i s e t o l e r a n c e for m a n y p a i r s of
s o u n d s m i g h t be e q u a l , and w i t h o u t the i n t e r f e r e n c e p a t t e r n s
for c o n s o n a n c e and d i s s o n a n c e ; the c a l i b r a t i o n of m u s i c a l
s c a l e s int o d i s c r e t e s t e p s (for h a r m o n y ) w o u l d n ot h a v e a ny
m e a n i n g .
T o s u m m a r i z e , the d e g r e e of f r e q u e n c y s e p a r a t i o n for the
c o m p o n e n t s of a t w o - t o n e i n t e r v a l is the c r u c i a l v a r i a b l e in
d e t e r m i n i n g the r e l a t i v e c o n s o n a n c y of the p e r c e i v e d n o t e or
n otes. If the d e g r e e of s e p a r a t i o n is w i t h i n a c e r t a i n span
( w h ic h m i g h t be a m e c h a n i c a l l y c r i t i c a l d i s t a n c e o n the b a s
ilar m e m b r a n e ) t h e n the p e r c e p t i o n m i g h t be o ne of d i s s o n
a n c e .
A n a r t i c l e by S o d e r q u i s t (1970) c o n c e r n e d i t s e l f w i t h
" f r e q u e n c y a n a l y s i s and the c r i t i c a l b a n d " ; it i n v e s t i g a t e d
s u b j e c t ' s a b i l i t y to d i s c r i m i n a t e (as a f o r c e d c h o i c e task)
a l t e r n a t i v e f r e q u e n c i e s t ha t w e r e o r w e r e n o t c o m p o n e n t s of
the c o m p l e x tone. T h e s u b j e c t s i n d i c a t e d w h i c h of the two
c o m p a r i s o n t on e s c o i n c i d e d w i t h s o m e f r e q u e n c y c o m p o n e n t of
m o n i c o v e r t o n e s , to a v o i d h a r m o n i c c ues). T h e e x p e r i m e n t
f ou n d tha t m u s i c i a n s o u t - p e r f o r m e d n a i v e s u b j e c t s in the
a b i l i t y to d i s c e r n g r e a t e r n u m b e r s of the e n h a r m o n i o u s t one
c o m p o n e n t s .
A s a final c o n c l u s i o n to h i s a r t i c l e , S o d e r q u i s t h y p o
t h e s i z e d that m u s i c i a n s w e r e a b le to s e p a r a t e o u t m o r e c o m
p o n e n t s b e c a u s e t h e y h ad a n a r r o w e r and m o r e r e c t a n g u l a r
c r i t i c a l band. T h e r e f o r e , m u s i c i a n s h ad m o r e d i s c r i m i n a t i o n
p o w e r and g r e a t e r a c c u r a c y t h a n " n a i v e " i n d i v i d u a l s .
T e r h a r d t (1973) c o u n t e r e d the a d e q u a c y of the m o s t w i d e
ly a c c e p t e d v i e w on c o n s o n a n c e - d i s s o n a n c e (that of the c r i t i
cal ba nd, P l o m p and L e v e l t , 1965) b y s t a t i n g t hat f i r s t l y ,
r o u g h n e s s ( d i s s o n a n c e ) c a n be p e r c e i v e d by s u b j e c t s for n o t e s
s e p a r a t e d by an i n t e r v a l t h a t is w i d e r t ha n c r i t i c a l an d s e c
o n d l y , t h a t d i c h o t i c o r s u c c e s s i v e t o n a l s t i m u l i p r o d u c e no
r o u g h n e s s , (this is c o n t r a r y to M a h e r , 1 9 7 5 ), and t h i rd ly ,
t h a t c o m p l e x t o n e s as e l e m e n t s of m u s i c are n e v e r d i s s o n a n t .
T e r h a r d t se em s to i n d i c a t e t h a t c o m p l e x to ne s are n o t d i s s o n
ant in t h e m s e l v e s , b u t r a t h e r t h a t m u s i c a l c o n t e x t b r i n g s
a b o u t the p e r c e p t i o n of d i s s o n a n c e for the c o m p l e x tone.
T h e m o d e l w h i c h T e r h a r d t d e v e l o p s f or m u s i c a l p e r c e p
t i on is b a s e d o n p i t c h a s s o c i a t i o n s t h a t a r e a d a p t e d f r o m e x
p e r i e n c e w i t h f r e q u e n c y a s s o c i a t i o n s in s p e e c h f o r m a n ts . He
p r o p o s e d two t y p e s of t o n a l e v a l u a t i o n . T h e s e are: the c a t
a b o l i c , o r a n a l y t i c m o d e , w h i c h p e r m i t s the l i s t e n e r to b r e a k
