%0 Journal Article %1 3340148620080101 %A Milne, Andrew %A Sethares, William %A Plamondon, James %D 2008 %J Journal of Mathematics & Music %K Keyboard Musik Mutabor Klaviatur Musiktheorie Tonsysteme %N 1 %P 1 - 19 %R 10.1080/17459730701828677 %T Tuning continua and keyboard layouts. %U http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=33401486&site=ehost-live %V 2 %X 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. ABSTRACT FROM AUTHOR

@article{3340148620080101, 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. [ABSTRACT FROM AUTHOR]}, added-at = {2013-02-02T14:43:14.000+0100}, author = {Milne, Andrew and Sethares, William and Plamondon, James}, bdsk-file-1 = {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}, bdsk-url-1 = {http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=33401486&site=ehost-live}, bdsk-url-2 = {http://www.zentralblatt-math.org/zmath/en/search/?format=complete&q=an:1160.00310}, biburl = {https://www.bibsonomy.org/bibtex/297661136f89ea35ad905fac625ef1fd9/ks-plugin-devel}, date-added = {2009-10-24 19:55:20 +0200}, date-modified = {2010-03-17 13:50:14 +0100}, doi = {10.1080/17459730701828677}, groups = {public}, interhash = {cfd823a6f0ad042abb89e5764fb41d45}, intrahash = {f5a954d837d34b3f082db9c28aa17806}, issn = {17459737}, journal = {Journal of Mathematics \& Music}, keywords = {Keyboard Musik Mutabor Klaviatur Musiktheorie Tonsysteme}, number = 1, pages = {1 - 19}, timestamp = {2013-02-02T14:43:14.000+0100}, title = {Tuning continua and keyboard layouts.}, url = {http://search.ebscohost.com/login.aspx?direct=true&db=a9h&AN=33401486&site=ehost-live}, username = {keinstein}, volume = 2, year = 2008 }