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Tuning continua and keyboard layouts

Milne, Andrew; Sethares, William and Plamondon, James (2008). Tuning continua and keyboard layouts. Journal of Mathematics and Music, 2(1) pp. 1–19.

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DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1080/17459730701828677
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Abstract

Previous work has demonstrated the existence of keyboard layouts capable of maintaining consistent fingerings across a parametrized family of tunings. This paper describes the general principles underlying layouts that are invariant in both transposition and tuning. Straightforward computational methods for determining appropriate bases for a regular temperament are given in terms of a row-reduced matrix for the temperament-mapping. A concrete description of the range over which consistent fingering can be maintained is described by the valid tuning range. Measures of the resulting keyboard layouts allow direct comparison of the ease with which various chordal and scalic patterns can be fingered as a function of the keyboard geometry. A number of concrete examples illustrate the generality of the methods and their applicability to a wide variety of commas and temperaments, tuning continua and keyboard layouts.

Item Type: Journal Article
Copyright Holders: 2008 Taylor & Francis
ISSN: 1745-9737
Keywords: temperament; comma; layout; button-lattice; swathe; isotone
Academic Unit/Department: Mathematics, Computing and Technology > Computing & Communications
Interdisciplinary Research Centre: Centre for Research in Computing (CRC)
Item ID: 21504
Depositing User: Andrew Milne
Date Deposited: 03 Jun 2010 11:37
Last Modified: 06 Dec 2010 15:31
URI: http://oro.open.ac.uk/id/eprint/21504
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