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

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)

2023edo is enfactored in the 5-limit, with the same mapping as 289edo.

In the 17-limit on the patent val, it is a tuning for the leaves temperament. It is also period-17, and maps the period to 25/24, which means septendecima is also tempered out.

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.

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