Information Technology Reference
In-Depth Information
Fig. 12.16
Sequence after inversion with fMRI_index = 5, giving a nearly neutral set of pitch
intervals
d ¼ 57
71
f
ð
Þ;
57
71
ð
Þ;
54
74
ð
Þ;
56
72
ð
Þ;
57
71
ð
Þ
g
d ¼
14
;
14
;
20
;
16
;
14
f
g
Then, the scaled modi
er values are calculated by multiplying the difference
values by the value of CS:
SMV¼
14
0
:
6
f
ð
Þ;
14
0
:
6
ð
Þ;
20
0
:
6
ð
Þ;
16
0
:
6
ð
Þ;
14
0
:
6
ð
Þ
g
SMV¼
8
:
4
;
8
:
4
;
12
;
9
:
6
;
8
:
4
f
g
Finally, the SMV values are summed with the original input to give a trans-
formed set of output values:
New pitches ¼ 71
8
:
4
f
ð
Þ;
71
8
:
4
ð
Þ;
74
12
ð
Þ;
72
9
:
6
ð
Þ;
71
8
:
4
ð
Þ
g
New pitches ¼ 62
:
6
;
62
:
6
;
62
;
62
;
62
:
6
f
g
Pitch values are rounded up to the nearest whole number as per the MIDI
standard, giving a transformed set of pitch values equal to {63, 63, 62, 62, 63},
which is rendered as {D#4, D#4, D4, D4, D#4}, as shown in Fig.
12.16
.
12.7.3.2 Pitch Scrambling Algorithm
In simple terms, the pitch scrambling algorithm orders the pitch values of the input
signal into a numerical list, which is then reordered randomly. This provides a
stochastic component to the transformation algorithm. Using the same measure as
for the previous example (Fig.
12.14
) as a starting point, let us examine the result of
applying this transformation. The process is as follows:
Input pitches: {71, 71, 74, 72, 71}
Order pitches in ascending order: {71, 71, 71, 72, 74}
Scramble the order of pitches randomly: {74, 72, 71, 71, 71}
Output pitches: {74, 72, 71, 71, 71}
In this case, the output would be rendered as {D5, C5, B4, B4, B4}. Rerunning
the transformation a further three times would give further variants, for example
{72, 74, 71, 71, 71}, {71, 74, 72, 71, 71} and {71, 74, 71, 72, 71}, rendered as {C5,
D5, B4, B4, B4}, {B4, D5, C5, B4, B4} and {B4, D5, B4, C5, B4}, respectively, as
illustrated in Fig.
12.17
.
As with the pitch inversion algorithm, the value of fMRI_index can be used to
create a control signal with which the amount of transformation can be varied. In
