2023edo

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← 2022edo2023edo2024edo →
Prime factorization 7 × 172
Step size 0.593178¢
Fifth 1183\2023 (701.73¢) (→169\289)
Semitones (A1:m2) 189:154 (112.1¢ : 91.35¢)
Dual sharp fifth 1184\2023 (702.323¢)
Dual flat fifth 1183\2023 (701.73¢) (→169\289)
Dual major 2nd 344\2023 (204.053¢)
Consistency limit 7
Distinct consistency limit 7

2023 equal divisions of the octave (2023edo), or 2023-tone equal temperament (2023tet), 2023 equal temperament (2023et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 2023 equal parts of about 0.593 ¢ each.

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

Approximation of odd harmonics in 2023edo
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

The divisors of 2023 are 1, 7, 17, 119, 289. It factors as 7 * 172.

Regular temperament properties

Rank-2 temperaments

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

Periods

per 8ve

Generator

(Reduced)

Cents

(Reduced)

Associated

Ratio

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

Music