2023edo

← 2022edo

2023edo

2024edo →

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

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 (%)	-37.9	-26.1	-27.9	+24.2	-43.0	+1.0	+36.0	+6.3	+44.3	+34.2	-16.6
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 × 17², 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

Music

Eliora

• Bagatelle in 11/8♭ Leaves (2023)