# 2023edo

← 2022edo | 2023edo | 2024edo → |

^{2}**2023 equal divisions of the octave** (abbreviated **2023edo** or **2023ed2**), also called **2023-tone equal temperament** (**2023tet**) or **2023 equal temperament** (**2023et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 2023 equal parts of about 0.593 ¢ each. Each step represents a frequency ratio of 2^{1/2023}, or the 2023rd root of 2.

## Theory

2023edo is enfactored in the 5-limit, with the same mapping as 289edo. As such it maps the period to 25/24, which means septendecima is also tempered out. In the 17-limit on the patent val, it is a tuning for the leaves temperament.

If we impose a stricter harmonic approach, and require all errors to be below 25%, the subgroup consisting of first 7 such harmonics for 2023edo is 2.13.17.23.47.61.71.

In the 2023e val, it supports the altierran rank-3 temperament tempering out the schisma and the quartisma.

### Prime harmonics

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | -0.225 | -0.155 | -0.166 | +0.143 | -0.255 | +0.006 | +0.214 | +0.037 | +0.263 | +0.203 | -0.098 |

relative (%) | -38 | -26 | -28 | +24 | -43 | +1 | +36 | +6 | +44 | +34 | -17 | |

Steps (reduced) |
3206 (1183) |
4697 (651) |
5679 (1633) |
6413 (344) |
6998 (929) |
7486 (1417) |
7904 (1835) |
8269 (177) |
8594 (502) |
8886 (794) |
9151 (1059) |

### Subsets and supersets

Since 2023 factors as 7 × 17^{2}, 2023edo has subset edos 7, 17, 119, and 289.

## Regular temperament properties

### Rank-2 temperaments

Note: 5-limit temperaments supported by 289edo are not included.

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

17 | 144\2023 (25\2023) |
85.417 (14.829) |
1024/975 (8192/8125) |
Leaves |

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

## Music

*Bagatelle in 11/8♭ Leaves*(2023)