2023edo

This page presents a novelty topic. It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks.

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 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

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

• Bagatelle in 11/8♭ Leaves, (Op. 2, No. 2) by Eliora