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 language | English (US) |
|---|---|
| Pages | 163-166 |
| Number of pages | 4 |
| State | Published - Jan 1 2005 |
| Event | 17th Canadian Conference on Computational Geometry, CCCG 2005 - Windsor, Canada Duration: Aug 10 2005 → Aug 12 2005 |
Conference
| Conference | 17th Canadian Conference on Computational Geometry, CCCG 2005 |
|---|---|
| Country | Canada |
| City | Windsor |
| Period | 8/10/05 → 8/12/05 |
Fingerprint
ASJC Scopus subject areas
- Geometry and Topology
- Computational Mathematics
Cite this
Demaine, E. D., Gomez-Martin, F., Meijer, H., Rappaport, D., Taslakian, P., Toussaint, G. T., Winograd, T., & Wood, D. R. (2005). The distance geometry of deep rhythms and scales. 163-166. Paper presented at 17th Canadian Conference on Computational Geometry, CCCG 2005, Windsor, Canada.