The Cognitive Neuroscience of Music

(A)^2 (B)

(C) (D)

(E) (F)

103

102

∆F

101

102 103 104

7 6 5 4 3 2

(^110125102251032)
5
5
2
2255
2
1.0
0.8
0.6
0.4
0.2
0
0 0.2 0.4
x critical bandwidth
0.6 0.8 1.0 1.0
0.8
0.6
0.4
0.2
0
Dissonance
Consonance
Consonance
10
o(Semitones) .5 1 2 34 6 8 10 12
8
6
4
2
0
0 2 5 10 20 50 100
(%)
Frequency deviation 100(f 2 -f 1 )/f 1
EXP. IB 11 .IB 12
22 Subjects
f 1
f 1 =440Hz
57 dB
(SPL)
f 2
Consonance scale value
Frequency of higher tone
440 494
Roughness
(dyad of
pure tones).
Consonance
(dyad of
pure tones)
Consonance
(dyad of harmonic
complex tones)
Lower
tone
440Hz
(A 4 )
Higher
tone
1 554 622 698 784 Hz 880
0.8
0.6
0.4
0.2
Evaluation (arbitrary units)
0
A 4 B 4 C 5 FD 5 5 G 5 A 5
Higher note
65
80
100
120
140
160
180
Unison
Minor second
1st only
1:1 1:2
Absolute dissonance (AD)
200
220
240
260
285
01 23 456789101112
0
20
40
60
80
100
120
Relative dissonance (RD)
140
160
180
1,2,3,4,5,6th 200
440 Hz (^528586550660) 733.3 Hz 880220
Interval width in semitones (n)
Dynamic
domain Staticdomain
Lower frequency ∆F
Figure 9.6(A) Just-noticeable roughness (line) as a function of the frequency difference between two pure tones (F)
and the lower frequency of the tones. Tones were presented monaurally at 60 phons. The barsshow the interquartile range
of 20 subjects (musical background not given). (Adapted from Ref. 67 Figure 9.1, p. 883.) (B) Plomp and Levelt’s data on
consonance ratings as a function ofFfor simultaneous pure tones with a mean frequency of 1000 Hz. Tones were pre-
sented in free field at 65 dB SPL. The solid lineshows the mean consonance ratings of 10 subjects (musical background
not given).Dashed linesshow the interquartile range. (Adapted from Ref. 51 Figure 9.6, p. 554.) (C) Plomp and Levelt’s
idealized plot of the relationship between consonance and critical bandwidth. The yaxis is in units of consonance (left)
and dissonance (right). (From Plomp and Levelt^51 [Figure 9.10, p. 556]. Reproduced by permission.) (D) Terhardt’s idea-
lized plot showing the relationship of consonance and roughness to interval width (root at A 4 , 440 Hz). The solid line
shows consonance vs Fwhen the interval is composed of two pure tones. The dotted lineshows consonance vs F 0 when
the interval is composed of two complex tones, each containing several lower harmonics. The dashed lineshows the
roughness of two pure tones as a function ofF. (From Terhardt^13 [Figure 9.1, p. 281]. Reproduced by permission.)
(E) Kameoka and Kuriyagawa’s data on consonance as a function ofFfor simultaneous pure tones with the root at A 4
and intensities of 57 dB SPL. The dashed lineis the mean performance of 22 audio engineers who performed the task
twice (solid lineswith blackand white triangles). (From Kameoka and Kuriyagawa^72 [Figure 9.1, p. 1452]. Reproduced by
permission.) (F) Kameoka and Kuriyzgawa’s plot of dissonance as a function of interval width. The dashed lineat the top
shows the function when the interval is composed of two pure tones. The solid lineat the bottomgives the calculated dis-
sonance of an interval composed of two complex tones, each containing the first six harmonics at 57 dB SPL. (Adapted
from Kameoka and Kuriyagawa,^35 Figure 9.8, p. 1465.)