## Abstract

The usual diatonic system is “dyadic,” for it privileges two intervals, the perfect octave and fifth; the usual harmonic system is “triadic,” for it privileges, in addition, the major and minor thirds (Sect. 9.1). The dyadic and triadic privileged intervals support, respectively, a dyadic/triadic notion of “consonance.” Every consonance other than the perfect prime has a unique “root,” such that, if the root is also the lower note, the consonance is “stable.” Section 9.2 studies the non-diatonic subset of the “cluster” (the set of all notes that may be received relative to the diatonic core, reduced to their register-zero representatives). It is shown that the subset consists of two length-five segments of the line of fifths, extending the seven-element core at either end to form a line-of-fifths segment totaling 17 elements exactly.

Original language | English |
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Title of host publication | Computational Music Science |

Publisher | Springer Nature |

Pages | 147-155 |

Number of pages | 9 |

DOIs | |

State | Published - 2013 |

### Publication series

Name | Computational Music Science |
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ISSN (Print) | 1868-0305 |

ISSN (Electronic) | 1868-0313 |

### Bibliographical note

Publisher Copyright:© 2013, Springer-Verlag Berlin Heidelberg.

## Keywords

- Consonant Triads
- Harmonic System
- Lowest Note
- Minor Thirds
- Perfect Octave