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for augmented chords). More scales can be added easily (to deal with rarer chords
like altered, or minor diminished 5th), but adding more scales or training sequence
does not improve substantially the quality of the generation.
It turns out that
playing out
can be easily integrated in our framework. As we
have seen, playing out or side-slips may be considered as an excursion from the
tonality to another one, followed by a smooth landing to the right tonality. More
generally, we can consider side-slips as specific
formal transforms
, operating on,
e.g., the last generated phrase. Formally, side-slips can be introduced as yet another
case in the
GenerateBeat()
method introduced in Sect.
5.4.2
:
GenerateBeatAsTransform(context, H, i):
// context represents the last generated output
return Transform(context, N)
where Transform is defined for each possible transform, e.g.:
Transform (phrase, N)
return Transpose (phrase, N, 1) ;
The particular side-slip consisting in transposing the last phrase one semitone
up, can simply be represented by a transform operation, taking a phrase as input and
producing its transposition. Other reasonable bebop transforms include:
•
Transposing a semitone, a minor third, a tritone or an octave up or down;
•
Reversing then transposing a semitone up or down, as illustrated in Fig.
5.22
(4th
case).
Transforms can also be used to implement many
tricks
invented by bebop improvis-
ers, such as transposing diatonically the phrase, by taking into account the harmony
of the next beat (see the Coltrane or Di Meola examples in Sect.
5.2.4
).
A most important aspect of formal transforms is the landing strategy: How to
come back seamlessly to the original tonality? Our Markov framework provides
the landing strategy for free: transforms may produce notes which are out-of-key,
but the various strategies we proposed for negotiating chord changes can be used
readily to ensure a smooth return to the key. As an example, Fig.
5.22
shows a
phrase generated on chord sequence composed only of
A minor
chords.
The decision to use a formal transform, again, belongs to the intentional score,
i.e. is taken at the beat level. In the case of a purely automatic improvisation system,
this decision can be determined by musical heuristics, such as the following:
•
When a chord is used for a long time, e.g. more than 1 measure (the original
reason for the introduction of side-slips in the first place);
•
When a NSF case is encountered (thereby avoiding the use of a repair mecha-
nism);
•
When a
direction
is imposed (e.g., go up pitch wise) but no easy way to satisfy it
is found (see Sect.
5.5.2
on control below).
It is important to stress out that transforms are grammatical constructs, and as such
cannot be learned effectively using any Markov mechanism. Using phrases such
