Attractor tempos for metrical structures

作者：Gotham Mark^*

来源：Journal of Mathematics and Music, 2015, 9(1): 23-44.

DOI：10.1080/17459737.2014.980343

• modelling
• tempo
• timing
• metre
• pulse salience
• music
• mathematics
• 00A65
• 97M80

Through new mathematical modelling based on experimentally-substantiated principles of cognitive science, this article provides robust principles for identifying "attractor tempos" which optimise the salience of metrical structures. This sheds lights on core musical phenomena such as the inclination towards parti-cular tempos in given metrical contexts, the use of (non-optimal) tempos as a source of expressive tension in music, and even what it means for music to be "fast" or "slow" in the first place. The study does not purport to set out a comprehensive model of metrical listening, but simply to identify the core principles which are necessarily involved in establishing attractor tempos. The (limited) dependence of those principles on the initial modelling parameters is discussed. Furthermore, there is no prescription of "correct" tempos here, instead the attractors model a set of defaults against which musicians may select tempos for expressive effect. An Online Supplement to this article, providing a subsidiary data table and further mathematical details, may be accessed at http://dx.doi.org/10.1080/17459737.2014.980343.

• 出版日期2015-1-2