## 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 |
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Title of host publication | Proceedings of the 17th Canadian Conference on Computational Geometry, CCCG 2005 |

Subtitle of host publication | 17th Canadian Conference on Computational Geometry, CCCG 2005; University of Windsor, Canada; 10 August 2005 through 12 August 2005 |

Pages | 163-166 |

Number of pages | 4 |

Publication status | Published - 1 Jan 2005 |

Externally published | Yes |

Event | Canadian Conference on Computational Geometry, CCCG 2005 - Windsor, Canada Duration: 10 Aug 2005 → 12 Aug 2005 Conference number: 17th |

### Conference

Conference | Canadian Conference on Computational Geometry, CCCG 2005 |
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Abbreviated title | CCCG 2005 |

Country | Canada |

City | Windsor |

Period | 10/08/05 → 12/08/05 |