Robotics Reference
In-Depth Information
occurrence of the notes, Pinkerton calculated the probability of occur-
rence for each:
.
Rest
=
0
297
.
C
=
0
163
.
D
=
0
112
E
0
.
132
=
F
0
.
066
=
G
0
.
149
=
A
0
.
045
=
B
0
.
036
=
The crudest form of music composition based on this data would simply
select each note based entirely on the frequencies, with no other con-
straints. But in composing music, the occurrence of a particular note
will normally exert a strong influence on the choice for the next note, for
example it is far more common to hear a series of notes going up or down
a scale in small steps, such as D, E, F or B, A, G, than it is to hear, for ex-
ample, D, A, E, B. So Pinkerton counted the number of times that each
note is paired with a particular successor note, and from these counts he
calculated the relative frequencies, shown in Figure 37.
19
Suppose for example that a particular note in a tune is an F. Pinker-
ton's data indicates that the probability of the next note being a rest is
0.15, the probability of it being a C is 0.00, the probability of it being a
D is 0.14, etc. In order to compose a tune using the data in this table,
Pinkerton simply chose the first note of the tune at random and then
chose each successive note (or rest) by reference to the frequency data in
the table.
Pinkerton discovered that snatches and phrases of his newly com-
posed sequences sounded quite tuneful, but that the random appearance
of rests, which would sometimes occur in the first note of a bar, would
create an unnatural effect. Since a rest can
never
occur at the beginning
of a bar, it proved necessary for Pinkerton to create tables with frequen-
cies for the rests that more closely resembled where they do occur in
a bar, with different tables catering for different rhythms. This tech-
nique improved the system's performance noticeably. Further possible
enhancements include using similar methods for composing harmony,
19
From page 80 of “Information Theory and Melody” by Richard Pinkerton,
Scientific American
,
vol. 194, no. 2, February 1956, pp. 77-86.
