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In this last category, the corpus can be considered as a
training environment to create generative models (among
them C. Chuan and E. Chew [11], Microsoft MysongSongsmith software [20]) and/or as a musical memory in
which fragments are retrieved and combined to create the
new material (G. Ramalho's jazz bass player ImPact [18]).
The definition of the segmentation unit in the corpus
processing is one of the key differences: the grain can
be key notes of a reduced melody in C. Chuan and E.
Chew's system, a single chord in Songsmith and the software Band in a Box (PG Music), or particular chord chunks
in G. Ramalho's ImPact. The idea is to find the right balance between long enough slices to provide plausibility
and coherence in the returned accompaniment, and fine
enough slices to avoid recopying too long and identifiable segments from the corpus. In the case of Improtek,
the chosen unit is the beat. Indeed, the oracle structure
prevents from choosing between musical smoothness and
innovation by providing continuity by construction, and
enables to work with such a fine grain.
2.2. Oracle and pattern recognition
The oracle was initially conceived for optimal string matching, and was extended for computing repeated factors in
a word and for data compression. This acyclic automaton
represents at least all the factors in a word, and the incremental construction algorithm is time and space linear in
its length (for the details of the construction algorithm, see
[1]).
The formal properties of the oracle structure are detailed in the founding articles, and fully applied to the issue of stylistic reinjection [4] in several OMax papers. We
briefly summarize here the tools providing the continuity
and coherence of the sequences generated through an oracle: the forward transitions and the suffix links.
The forward transitions (forward links, plain lines)
enable to reach every sub-pattern in the original sequence
starting from the initial state. In this way, every progression between consecutive states of the original sequence
can be generated.
dashed lines). They point at the final state of the previously encountered occurrences of a pattern.
Figure 2. Oracle for the sequence abcadbcd: repeated
sub-pattern.
In the example of fig. 2, a suffix link connects the
states 7 and 3. 3 is indeed the leftmost position where a
longest repeated suffix of the sequence ending in 7 (abcadbc) is recognized: bc.
The oracle structure can be used as a tool to create
new sequences by a non-linear navigation following the
previously introduced links thanks to its understanding of
the logic in the progressions present in the strings. In a
musical application, its ability to preserve the discourse
of the original material enables to develop an aesthetics
close to that of the musicians in interaction.
3. IMPROVISING WITHIN A METRIC AND
HARMONIC FRAMEWORK
3.1. The beat hypothesis
The philosophy of the current version of OMax is to turn
every single musical event into a state in an oracle object.
The free real-time navigation [2] through a thus structured
memory makes it an interactive instrument dedicated to
improvisation in a free musical context. The approach
of the ImproteK project differs by the integration of two
paradigms. First, its improvisations take place in an underlying harmonic structure represented by a chord progression we will refer to as grid. In this way, it makes
the system able to expand its modeling on harmonization
and arrangement. Then, it takes a metric framework into
account by setting the beat as the elementary unit in its
acquisitions, restitutions, and generations.
The only musical hypothesis is therefore the existence
of a regular beat in the material listened and produced by
ImproteK. The tendancy to the synchronization with a periodic beat being a deep universal of the human music perception [17], this sole assumption does not make the system oriented towards a restricted musical field. Starting
from this point, we add a notion of labels making some
musical slices separated by beats, making them equivalent (see section 5.1.2). This process enriches the set of
possible combinations, but does not carry any harmonic
hypothesis. Indeed, as discussed in the last section, the
references to the jazz idiom through this article come from
the context in which ImproteK has been used so far.
Figure 1. Oracle for the sequence abcadbcd: generation
of a sub-pattern starting from the initial state.
Fig. 1 shows the oracle for the sequence abcadbcd and
illustrates this point by displaying a path using forward
transitions to generate the sub-sequence bcd (0, 2, 3, 8),
originally occurring between the states 5 and 8.
The oracle also locates the repeated sub-pattern in the
original sequence with the suffix links (backward links,
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