2023edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == 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. | 2023edo is [[Enfactoring|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. | 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]]. | In the 2023e val, it supports the altierran rank-3 temperament tempering out the [[schisma]] and the [[quartisma]]. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{ | {{Harmonics in equal|2023}} | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 2023 factors as {{factorization|2023}}, 2023edo has subset edos {{EDOs| 7, 17, 119, and 289 }}. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
Note: 5-limit temperaments | Note: 5-limit temperaments supported by 289edo are not included. | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |- | ||
|17 | ! Periods<br />per 8ve | ||
|144\2023<br>(25\2023) | ! Generator* | ||
|85.417<br>(14.829) | ! Cents* | ||
|1024/975<br>(8192/8125) | ! Associated<br />ratio* | ||
|[[Leaves]] | ! Temperaments | ||
|- | |||
| 17 | |||
| 144\2023<br />(25\2023) | |||
| 85.417<br />(14.829) | |||
| 1024/975<br />(8192/8125) | |||
| [[Leaves]] | |||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
== Music == | == Music == | ||
; [[Eliora]] | |||
* [https://www.youtube.com/watch?v=8K2RYO_oCnM ''Bagatelle in 11/8♭ Leaves''] (2023) | |||
[[Category:Listen]] | |||
[[Category: | |||
Latest revision as of 23:06, 20 February 2025
| ← 2022edo | 2023edo | 2024edo → |
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 21/2023, 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 (%) | -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* |
Temperaments |
|---|---|---|---|---|
| 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 distinct
Music
- Bagatelle in 11/8♭ Leaves (2023)