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the number of different chords in the sequence
the harmonic complexity of the chords series, mainly taking into account the
cadences and resolutions in the context of modern modal and tonal music, and
the modulations in the context of the latter.
11.3.4.3 Rhythmic Patterns
The rhythmic patterns are created by layering various iterative rhythmic patterns, all
synchronized to the same underlying pulse, each pattern being de
ned by an offset
from the common initial pulse and by a rhythmic density (number of pulses
between two onsets in the pattern). The superimposition is done by a logical OR
operation, considering the superimposed patterns to be bit vectors, a value of 1
representing an onset, and a value of 0 no onset.
Let
m
be the rhythmic patterns length,
q
the number of superimposed patterns,
of
i
the offset from the initial pulse of pattern number
i
, and
d
i
the rhythmic density
of pattern number
i
.
Let us consider that a bit vector is equivalent to a
finite set of integer numbers,
each number of the set representing a positive bit at the index corresponding to its
value in the vector, a rhythmic pattern
R
created by superimposition of patterns
P
i
can thus be de
ned by:
R ¼
[
i¼0
P
i
where P
i
¼
[
E
ðð
m
of
Þ=
d
Þ
n¼0
ð
11
:
2
Þ
ð
of
i
þ
d
i
m
Þ
s com-
plexity measure or other techniques of rhythmic complexity evaluation that assign
each pulsation a weight (see Fig.
11.5
).
As regards rhythmic complexity, we use a model based on Toussaint
'
11.3.4.4 Melody Generation
In order to generate melodies, MuZICO has a module taking as input the current
pitch scale and several rhythmic patterns generated using the techniques explained
in the previous section. Each note has a weight corresponding to its apparition order
in the process of building the current pitch scale. For each onset in the rhythmic
pattern, a note is chosen randomly using a Gaussian probability density varying
according to the corresponding rhythmic weight. An initial melodic pro
le is thus
obtained, which will be subsequently developed in a musical way by various
algorithms such as the Probabilistic Suf
ed
according to the modulation information sent by the grammar which generates the
chords, resulting in the
x Tree (PST). This pro
le is then modi
final melody to be plaid.
The complexity of such a melody can be evaluated and depends on the Gaussian
probability densities, as well as the PST con
guration parameters.
