# Superparticular number

**Superparticular numbers**, also called

**epimoric ratios**, are improper rational fractions of the form

Examples:

Ratio | Name | Related musical interval |
---|---|---|

2:1 | duplex | diapason (P8) |

3:2 | sesquialterum | diapente (P5) |

4:3 | sesquitertium | diatessaron (P4) |

5:4 | sesquiquartum | ditonus (M3) |

6:5 | sesquiquintum | semiditonus (m3) |

9:8 | sesquioctavum | tonus (M2) |

18:17 | (super)sesquiseptimus decimus | semitonium (m2) |

## See also

## External links

- The new Arithmonic Mean — Preliminaries by D. Gómez.
- An Arithmetical Rubric by Siemen Terpstra, about the application of superparticular numbers to harmony.
- Superparticular numbers applied to construct pentatonic scales by David Canright.