Global Musical Tempo Transformations using Case Based ... - OFAI

From the resulting set of rules, the rules that have the highest percentage of
correct predictions are selected. In this way the obtained rule set consists of
a modest number of rules that all have a reasonable degree of generality.
The rules that are learned are conditional rules by PLCG, consisting of
a set of conditions (with and/or relations), that refer to the score, and an
action that is to be performed if the conditions are met. The actions refer
to the timing, dynamics and articulation of notes. They are not quantitative
but qualitative (actions can for example be ‘lengthen note’, or ‘play louder’).
An example of a rule that was discovered is:
lengthen IF
next dur ration < 1 &
metr strength ≤ 2
which should be read as “Lengthen a note if it is followed by a longer note
and if it is in a metrically weak position.”.
The models predicted in this way are partial models based on the note
level, so they leave opportunity for predicting regularities at higher structural
levels by other means. Widmer [120] used this opportunity by predicting
higher level regularities such as crescendo/decrescendo and
accelerando/ritardando using another machine learning approach, called Nearest
Neighbor Learning (NN). To achieve this, the performances that serve as
experience, are analyzed in terms of tempo and dynamics. Both tempo and
dynamics curves of the performances are fitted by quadratic functions iteratively
(in each round a function is fitted to the residual of the previous
round). These functions are stored for each performance. To predict the
tempo and dynamics of a new score, the tempo and dynamics functions of
the most similar ‘learned’ scores are taken. The similarity between scores is
taken as the Euclidean distance between a vector of musical attributes.
When the NN algorithm for predicting phrase level performance phenomena
is combined with the PLCG algorithm for predicting note level phenomena,
a composite and complete model emerges that predicts better than
either model alone.
ÖFAI’s machine learning approach to machine performance of music as
just described is currently one of the most advanced approaches in the field.
This is confirmed by the fact that there performance rendering system has
won the second prize at the 2002 RenCon Contest for machine rendering
of piano music. Nevertheless, Widmer notes some limitations and room for
improvement. The polynomial curve fitting seems to be more promising for
predicting dynamics than for tempo. The performance of the system could
also benefit from a richer representation language. Furthermore, possible
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