Information Technology Reference
In-Depth Information
Below are examples of three of the transformation algorithms, which illustrate the
effect of varying the fMRI_index: pitch inversion, pitch scrambling and pitch delta.
12.7.3.1 Pitch Inversion Algorithm
Given an input musical sequence, the pitch inversion algorithm creates a new
sequence, which is effectively the input sequence turned upside down. For instance,
a sequence rising in pitch would descend in pitch after being passed through this
transformation. In order to illustrate this, let us consider the measure produced in
generation phase example, as shown in Fig.
12.14
. Incidentally, this measure will
be used as the starting point for the following two transformation examples as well.
The melody interval musicode for this measure is {0, 0, 3, 2, 1}, and the note
pitch musicode is {B4, B4, D5, C5, B4}. In this case, the MIDI values are 71, 71,
74, 72 and 71, respectively; MIDI uses a range of 128 pitch values. There are a
variety of ways to accomplish a pitch inversion, including diatonic and chromatic
options, or inversions around a speci
c sounding pitch. MusEng processes pitch
inversion simply by subtracting the current MIDI pitch value from 128, and
substituting in the resulting natural number as the new pitch value. For instance, the
transformed pitch values for our example created using this technique would be as
follows: (128
71 = 57), (128
71 = 57), (128
74 = 54), (128
72 = 56) and
−
−
−
−
(128
−
71 = 57).
The resulting MIDI values are 57, 57, 54, 56 and 57, yielding the following pitch
sequence {A3, A3, F#3, G#3, A3}. Note that the inverted sequence maintains the
original melody interval musicode of {0, 0, 3, 2, 1}, while giving an upside down
melody, as shown in Fig.
12.15
.
The example above assumed a maximal fMRI index value of 9, which once
scaled to create a CS gives 1.0. However, as mentioned in the introduction to this
section, varied degrees of transformations are also possible by scaling the amount of
transformation according to the value of the fMRI_index. The difference between
the input and the transformed pitches is multiplied by the CS, before being summed
with the input to create the
final transformed output value (Eq.
12.3
).
New pitch ¼ Input pitch
þðð
Input pitch
transf pitch
Þ
f
ð
12
:
3
Þ
½
ð
fMRI index
þ
1
Þ
0
:
1
Þg
Let us examine what happens if we assume an fMRI_index equal to 5, which
yields a CS equal to 0.6. In this case, we would expect an output approximately
halfway between the original pitch and the inversion, in other words an almost
neutral set of intervals. First, the difference
d
between the maximal inversion and
the input signal for each of the musicode values needs to be calculated as follows:
Fig. 12.15
Newly inverted sequence, after transformation of measure in Fig.
12.14
