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Open Access item Aesthetics, dynamics, and musical scales: A golden connection.

Authors:Cartwright, Julyan H. E.
González, Diego L.
Piro, Oreste
Stanzial, Domenico
Keywords:Music and drama, Music technology, Theory of music
Issue Date:14-Nov-2002
Publisher:Taylor & Francis
Citation:Journal of New Music Research 31(1): 51-58 (2002)
Abstract:Number theory has recently found a quantity of applications in the natural and applied sciences, and in particular in the study of nonlinear dynamical systems. As our sensory systems are highly nonlinear, it is natural to suppose that number theory also plays an important rôle in the description of perception, including aesthetics. Here we present a mathematical construction, based on number-theoretical properties of the golden mean, that generates meaningful musical scales of different numbers of notes. We demonstrate that these numbers coincide with the number of notes that an equal-tempered scale must have in order to optimize its approximation to the currently used harmonic musical intervals. Scales with particular harmonic properties and with more notes than the twelve-note scale now used in Western music can be generated. These scales offer interesting new possibilities for artists in the emerging musical world of microtonality and may be rooted in objective phenomena taking place in the nonlinearities of our perceptual and nervous systems.
Description:12 pages, 5 figures, 4 tables.-- Pre-print archive.
Publisher version (URL):http://dx.doi.org/10.1076/jnmr.31.1.51.8099
URI:http://hdl.handle.net/10261/18003
ISSN:0929-8215 (Print)
1744-5027 (Online)
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