Computational Creativity and Music - Computational Creativity Research: Towards Creative Machines - page 307

Fig. 15.3 First ( a ) and eleventh ( b ) sketches from Beethoven's Piano concerto in D (unfinished)
1815 from [ 3 ], pp. 346 and 352
evolves from simple origins to a quite chromatic (at least for its time) elegant form.
I have attempted on numerous occasions to fill in the missing sketches myself with-
out consulting the actual Beethoven ones, and found my own attempts difficult to
smoothly transition from (a) to (b). I invite readers to make this attempt themselves.
There is no better way to understand creativity than to produce examples yourself and
compare them with someone who has proven an expert in the field, like Beethoven.
The full set of sketches appears in CMMC ([ 4 ], p. 82) for reference.
Interestingly, Figs. 15.2 and 15.3 resemble the game situations of letter/words
and chess respectively. Figure 15.2 leaps from a smaller subset to a larger one like
letters to words, and Fig. 15.3 demonstrates a step-by-step approach to developing a
resolution to a problem like chess.
As an example of how a computer program might create new melodies following
the rules presented, imagine a group of pitches that contains, say, all the iterations
of the same pitch each including its previous and following pitches. For example,
the second-space A group in Fig. 15.3 would contain two instances (one from each
theme). The first instance would also have a record of fourth space E as preceding
pitch and fourth line D as following pitch, and the second instance of second-space A
would have fourth space E as preceding pitch (the same as in the previous instance),
and fifth line F-natural as following pitch. It would then not be difficult to imagine
similar groups of pitches representing all the pitches in the two themes.
The composing part of this simple program would first remove a beginning pitch
from the appropriate group (in this case either from the ledger line A above the staff
group) or the fifth line F-sharp group, the beginning pitches of the two examples.
For our example, let's choose the A above the staff from the first example. Then
the program would save that choice and select the next pitch's group based on the
following pitch of that choice (in this case G above the staff's group). The choices
now would be many since that G occurs six times—F-sharp, B, F-sharp, F-sharp,
A, and E being the following pitches—with F-sharp the most probable choice given
we choose randomly and there are three F-sharps present. The program continues in
like manner until it arrives at a pitch with no following pitch, which signals the end
of the melody. Note that at this point, previous pitches have had no impact on the
decision-making process, something I will soon describe.