# 2019edo

← 2018edo | 2019edo | 2020edo → |

**2019 equal divisions of the octave** (abbreviated **2019edo**), or **2019-tone equal temperament** (**2019tet**), **2019 equal temperament** (**2019et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2019 equal parts of about 0.594 ¢ each. Each step of 2019edo represents a frequency ratio of 2^{1/2019}, or the 2019th root of 2.

## Theory

2019edo is excellent in the 7-limit, and with such small errors it supports a noticeable amount of very high accuracy temperaments. While it is consistent in the 11-odd-limit, there is a large relative error on the representation of the 11th harmonic.

In higher limits, it tunes 23/16 and 59/32 with the comparable relative accuracy to the 2.3.5.7 subgroup (less than 7% error). A comma basis for the 2.3.5.7.23.59 subgroup is {14337/14336, 25921/25920, 250047/250000, 48234496/48234375, 843396867/843308032}.

### Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +0.000 | -0.023 | +0.016 | -0.029 | +0.242 | -0.112 | +0.245 | +0.258 | -0.043 | -0.157 | +0.284 |

relative (%) | +0 | -4 | +3 | -5 | +41 | -19 | +41 | +43 | -7 | -26 | +48 | |

Steps (reduced) |
2019 (0) |
3200 (1181) |
4688 (650) |
5668 (1630) |
6985 (928) |
7471 (1414) |
8253 (177) |
8577 (501) |
9133 (1057) |
9808 (1732) |
10003 (1927) |

### Subsets and supersets

Since 2019 factors into 3 × 673, 2019 contains 3edo and 673edo as subsets.

## Regular temperament properties

### Rank-2 temperaments

Periods per 8ve |
Generator* | Cents* | Associated Ratio* |
Temperaments |
---|---|---|---|---|

1 | 154\2019 | 91.530 | [46 -7 -15⟩ | Gross |

1 | 307\2019 | 182.467 | 10/9 | Minortone |

3 | 307\2019 | 182.467 | 10/9 | Domain |

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct