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

from the performance IOI’s. The first alternative shows mainly small time
scale timing deviations, and obscures trends, or larger time scale changes in
timing (such as rubato). The second alternative shows such global trends
more clearly. The second definition, ‘expression as deviation from the score’,
is realized as the deviations of IOI’s from the mean note or beat duration.
The results are equivalent to those of the first definition. Measurement of expressiveness
according to the third definition, ‘expression as deviation within
a performance’, is performed by relating the performed note IOI’s to the performed
bar IOI’s. This approach can clarify timing regularities that relate
to meter and rhythmical patterns.
2.1.2 Representation of Timing and Tempo
Related to the issue of interpreting different aspects of expressivity is the
argument for differentiation of tempo changes and timing [62, 13]. Although
both tempo changes and timing become manifest through temporal displacement
of musical events, they refer to different musical phenomena. Tempo
changes refer to the effect of speeding up or slowing down the performance
of the melody in a continuous manner, whereas timing refers to local displacements
of notes, chords or other musical events, with respect to the
tempo (in a manner of speaking, timing is on top of tempo changes). Honing
[62] notes that representations commonly used for describing musical performances
(like tempo-curves that map score times to instantaneous tempo,
or time-shift functions that map score times to deviations with respect to the
score) fail to capture both aspects separately. As a result, they cannot well
be used in systems for performance generation, since applying such functions
in composition (that is, apply one function on the result of another function)
yields undesired results. This is caused by the fact that the input of the
second function is not score-time but performance time. Time maps (TM’s)
are a better solution for such applications. A TM maps performance time
before transformation (pre-perturbed time) to performance time after transformation
(perturbed time), which allows for composition. Another practical
advantage of TM’s over tempo-curves or time-shift functions is that the former
provides performance time directly as output, whereas the latter two
require extra calculation to obtain performance time. However, TM’s also
have some limitations:
• Score times are lost in composition
• Support for concatenation is limited
• Access to score and performance durations in composition
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