Abstract
This paper describes the temporal model of a scheduler geared towards show control and live music applications. This model relies on multiple inter-related temporal axes, called timescales. Timescales allow scheduling computations using abstract dates and delays, much like a score uses symbolic positions and durations (e.g. bars, beats, and note values) to describe musical time. Abstract time is ultimately mapped onto wall-clock time through the use of time transformations, specified as tempo curves, for which we provide a formalism in terms of differential equations on symbolic position. In particular, our model allows specifying tempo both as a function of time or as a function of symbolic position, and allows piecewise tempo curves to be built from parametric curves.
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Notes
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We deliberately avoid the term beats here. We think it would bring some confusion by conflating the notion of time unit with the notion of meter, and by suggesting that all beats are of equal conceptual length. This is, in fact, rather a Western exception than a universal norm.
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One difference, however, is that we use the word tempo here to refer to the ratio of internal symbolic time units over source symbolic time units, rather than the number of beats per minutes, since the latter could depend on the musical meter of the timescale.
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Textbooks usually choose the letter \(t\) to denote the parameter of parametric curves. We instead choose the letter \(s\) to disambiguate it from time.
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Note that here we can find an equation in \(s\). This is beneficial as it allows our numerical solver to find the parameter \(s\) once, and then evaluate the Bézier curve and its derivatives using only polynomials in \(s\). The same change of variable is done in Eq. 13. It is unfortunately useless with Eq. 10 and Eq. 14, since \(s\) can’t be computed directly from the independant variable.
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The word context here is left intentionally broad. It could encompass the threading model, the data lifetime, the nature of the execution environment (e.g. native code scheduling interpreted code and vice versa), or even the machine on which the code is executed.
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The notions of fiber, coroutine, or green thread are very closely related, and the distinction between them, if any, is amenable to debate. One could argue that green thread is more appropriate in the context of a virtual machine or runtime environment, while coroutine originates from programming language design. The term fiber may capture a more general view of the concept, but more importantly it happens to be shorter to type.
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Although the use of shared or ‘smart’ pointers bears its share of problems and, in our opinion, usually warrants a reassessment of the architecture, handles to long-lived, reference-counted objects living behind an API boundary are usually fine: in this scenario, there can be no cycles across the boundary, objects memory can’t be directly accessed by user code, and performance problems can be alleviated by the use of centralized memory management.
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Fouilleul, M., Bresson, J., Giavitto, JL. (2023). A Polytemporal Model for Musical Scheduling. In: Aramaki, M., Hirata, K., Kitahara, T., Kronland-Martinet, R., Ystad, S. (eds) Music in the AI Era. CMMR 2021. Lecture Notes in Computer Science, vol 13770 . Springer, Cham. https://doi.org/10.1007/978-3-031-35382-6_12
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