The distance geometry of deep rhythms and scales

Erik D. Demaine, Francisco Gomez-Martin, Henk Meijer, David Rappaport, Perouz Taslakian, Godfried T. Toussaint, Terry Winograd, David R. Wood

Research output: Chapter in Book/Report/Conference proceedingConference PaperResearchpeer-review

3 Citations (Scopus)

Abstract

We characterize which sets of k points chosen from n points spaced evenly around a circle have the property that, for each i = 1, 2, k-1, there is a nonzero distance along the circle that occurs as the distance between exactly i pairs from the set of k points. Such a set can be interpreted as the set of onsets in a rhythm of period n, or as the set of pitches in a scale of n tones, in which case the property states that, for each i = 1, 2, k -1, there is a nonzero time [tone] interval that appears as the temporal [pitch] distance between exactly i pairs of onsets [pitches]. Rhythms with this property are called Erdos-deep. The problem is a discrete, one-dimensional (circular) analog to an unsolved problem posed by Erdos in the plane.

Original languageEnglish
Title of host publicationProceedings of the 17th Canadian Conference on Computational Geometry, CCCG 2005
Subtitle of host publication17th Canadian Conference on Computational Geometry, CCCG 2005; University of Windsor, Canada; 10 August 2005 through 12 August 2005
Pages163-166
Number of pages4
Publication statusPublished - 1 Jan 2005
Externally publishedYes
EventCanadian Conference on Computational Geometry, CCCG 2005 - Windsor, Canada
Duration: 10 Aug 200512 Aug 2005
Conference number: 17th

Conference

ConferenceCanadian Conference on Computational Geometry, CCCG 2005
Abbreviated titleCCCG 2005
CountryCanada
CityWindsor
Period10/08/0512/08/05

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