Résumés
Abstract
Classical meter theory, derived from European, notation-based musical practice, requires notionally absolute isochrony. This article proposes a more flexible concept of rhythmic frequencies (or periodicities) represented by continuous functions over time, and develops rhythmic theory from it that is more global in scope. A rhythm is a good fit to a given frequency if its onsets are close to peaks of one of these functions, without having to precisely coincide. This provides some useful tools for understanding properties of rhythms and how different rhythms interact, including the rhythmic spectrum which shows all the frequencies present in a rhythm. Maximally even rhythms like the African standard pattern and tamborim rhythm of samba, are those which maximize a given frequency for a given grid, and often function as basic rhythms (e.g. “timelines” or claves) in many musical traditions, as do other rhythms, like the “Bo Diddley” rhythm and Clave Son, with strong representation of a single frequency. When rhythms expressing nearby frequencies are combined, they interact to produce slow phase shifts over longer cycles, a feature of timeline rhythms, and also more complex isorhythmic designs in, for example, the late music of György Ligeti, and recent jazz compositions by Dave King and Miles Okazaki.
Keywords:
- clave,
- Fourier transform,
- György Ligeti,
- maximal evenness,
- meter theory,
- Miles Okazaki,
- polyrhythm,
- timeline rhythms
Résumé
La théorie métrique classique, issue de la pratique musicale européenne fondée sur la notation, implique la notion d’une isochronie absolue. Cet article propose une conception plus souple des fréquences rythmiques (ou périodicités), représentées par des fonctions continues dans le temps, de manière à développer une théorie rythmique plus large dans sa portée. Un rythme s’accorde bien avec une fréquence donnée si ses attaques se situent à proximité des pics de l’une de ces fonctions, sans devoir nécessairement coïncider de façon exacte. Cette approche offre des outils utiles pour comprendre les propriétés des rythmes ainsi que la manière dont différents rythmes interagissent, notamment le spectre rythmique, qui montre l’ensemble des fréquences présentes dans un rythme. Les rythmes optimalement répartis, tels que le « rythme africain standard » (African standard pattern) ou le rythme de tamborim dans la samba, sont ceux qui maximisent une fréquence donnée pour une grille donnée, et servent souvent de rythmes fondamentaux (par exemple, des « timelines » ou des claves) dans de nombreuses traditions musicales. Il en va de même pour d’autres rythmes, tels que le « rythme Bo Diddley » ou la clave son, caractérisés par une forte représentation d’une fréquence unique. Lorsque des rythmes exprimant des fréquences proches sont combinés, ils interagissent pour produire de lents déphasages sur des cycles plus longs – une caractéristique des rythmes timeline – ainsi que des conceptions isorythmiques plus complexes que l’on trouve, par exemple, dans les dernières oeuvres de György Ligeti et dans certaines compositions récentes de Dave King et Miles Okazaki.
Mots-clés :
- clave,
- György Ligeti,
- Miles Okazaki,
- polyrythmie,
- maximal evenness,
- rythmes timeline,
- théorie métrique,
- transformée de Fourier
Parties annexes
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