The famous results of Carey and Clampitt [N. Carey and D. Clampitt, Aspects of well-formed scales, Music Theory Spectr. 11 (1989), pp. 187-206] focus on scales generated by one interval and explain why some of these scales are preferable to others. Those preferable are called well-formed (WF). Their explanation is based on a theorem showing equivalence between âsymmetryâ and âclosureâ. In this paper, we propose and prove a generalization of this theorem. Instead of scales with a single generator, tone systems generated by two intervals are considered. In addition, various examples are given to illustrate the developed theoretical framework. Among them, the ancient Indian 22-Åruti system is interpreted as a WF two-dimensional tone system generated by the fifth and the Åruti. Finally, we draft open problems pertaining to the presented theory.View full textDownload full textKeywordsgenerated scale, closure condition, symmetry condition, generic Tonnetz , generated tone system, tight, loose, well-formedRelated var addthis_config = { ui_cobrand: "Taylor & Francis Online", services_compact: "citeulike,netvibes,twitter,technorati,delicious,linkedin,facebook,stumbleupon,digg,google,more", pubid: "ra-4dff56cd6bb1830b" }; Add to shortlist Link Permalink http://dx.doi.org/10.1080/17459737.2010.491975
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