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7 5 5
3
3
3
r
r
5
3
3 r
r
r
7 5
3
r
r 5
7
5 5
3
r
7
3
3
3
-1
-2
1 1
-2
1
1 -1
1
1 -1 2
1
-1 -2 1
d 7
m d 4
m 6
d
m 6
d 6
m 6
2
4
5
Fig. 15.10 The same-sounding diminished seventh chord resolving four different but correct ways
In this new phrase, the chromatic F-sharp in measure one creates an 'associa-
tion of two ideas heretofore not considered related but now revealed as logically
connected.' An average student in a music theory class would never think of turning
in an assignment like Fig. 15.9 . A highly creative student, however, would, since it
follows the rules the models follow. One might argue that the new output in Fig. 15.9
was created by a machine program having no idea what it was doing. I would argue
that it was I who created Fig. 15.9 first, knowing full well what I was doing, and
then I programmed my computer following exactly the process just described to imi-
tate the process. Since my computer program had only the information I had when
composing its output and we both followed the same rules, are we not both creative?
For those interested, the second chord in Fig. 15.9 is called a secondary dominant
of the dominant chord in C-major, a simple kind of chromatic motion that was most
likely one of the first to invade diatonic harmony in the late Renaissance or early
Baroque periods of music history. Whether such chords occurred by the method
just described or not, no one knows. But I contend that it's certainly one reasonable
hypothesis.
Figure 15.10 presents something more advanced than secondary dominants, a
diminished seventh chord which by virtue of its symmetrical nature and voice leading
allows the root to exist as any of the pitches present in the chord.
Without going into details here, each of the four examples sounds the same but are
differently spelled and thus allow the voice leading from a database of examples to
provide it with several options for resolution. Figure 15.11 shows how this is possible.
In the case of the output in Fig. 15.11 b, the final example of the diminished seventh
chord reaffirms the second measure chord excepting the latter B-natural is respelled
as a C-flat. The respelling allows for the modulation to E-flat.
Again, I must emphasize here that I created this output first, and then used the
program to output the same thing based on the data in the database.
As a final example of machine musical creativity, I here present an even more
complex example involving chromatic pitches in both the database and in the out-
put, but with the output involving a different and creative result. In Fig. 15.12 ,the
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