# 13edt

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**13 equal divisions of the tritave** (**13edt**) is the nonoctave tuning system derived by dividing the tritave (3/1) into 13 equal steps of 146.3 cents each, or the thirteenth root of 3. It is best known as the equal-tempered version of the Bohlen-Pierce scale.

13edt can be described as approximately 8.202edo. This implies that each step of 13edt can be approximated by 5 steps of 41edo.

In the 7-limit, it tempers out 245/243 and 3125/3087, the same commas as bohpier temperament. It is less impressive in higher prime limits, but makes for excellent no-twos 7-limit harmony. For higher limits, the multiples of 13 (26edt, 39edt and 52edt) come to the fore.

## Theory

Prime interval | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | |
---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | -29.6 | 0.0 | -6.5 | -3.8 | -54.8 | -51.4 | +69.4 | +23.1 |

relative (%) | -20 | 0 | -4 | -3 | -37 | -35 | +47 | +16 | |

Patent val | 8 | 13 | 19 | 23 | 28 | 30 | 34 | 35 | |

Fifthspan | -1 | 0 | -4 | +2 | +3 | +6 | -1 | -6 |

## Intervals

*Main article: Intervals of BP*

Steps | Cents | Hekts | BP nonatonic degree | Corresponding JI intervals | Comments | Generator for... |
---|---|---|---|---|---|---|

1 | 146.3 | 100 | A1/m2 | 27/25~49/45 | ||

2 | 292.6 | 200 | M2/d3 | 25/21 | Sirius | |

3 | 438.9 | 300 | A2/P3/d4 | 9/7 | Linear BP | |

4 | 585.2 | 400 | A3/m4/d5 | 7/5 | Canopus | |

5 | 731.5 | 500 | M4/m5 | 75/49 | false 3/2 | false Father |

6 | 877.8 | 600 | A4/M5 | 5/3 | Arcturus | |

7 | 1024.1 | 700 | A5/m6/d7 | 9/5 | Arcturus | |

8 | 1170.4 | 800 | M6/m7 | 49/25 | false 2/1 | false Father |

9 | 1316.7 | 900 | A6/M7/d8 | 15/7 | Canopus | |

10 | 1463.0 | 1000 | P8/d9 | 7/3 | Linear BP | |

11 | 1609.3 | 1100 | A8/m9 | 63/25 | Sirius | |

12 | 1755.7 | 1200 | M9/d10 | 25/9~135/49 | ||

13 | 1902.0 | 1300 | A9/P10 | 3/1 | Tritave |

## JI approximation

## Regular temperament properties

*Main article: Bohlen-Pierce #Regular temperament properties*

## See also

- Bohlen-p_et
- Catalog of 3.5.7 subgroup rank two temperaments
- 19ED5: relative ED5
- 23ED7: relative ED7