2023edo: Difference between revisions
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added music |
now leaves is full 17-limit now that I composed the song and tried it out, writing it down in the table |
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2023edo is enfactored in the 5-limit, with the same mapping as [[289edo]]. | 2023edo is enfactored in the 5-limit, with the same mapping as [[289edo]]. | ||
In the patent val, it is | 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. | 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. | ||
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The divisors of 2023 are {{EDOs|1, 7, 17, 119, 289}}. It factors as 7 * 17<sup>2</sup>. | The divisors of 2023 are {{EDOs|1, 7, 17, 119, 289}}. It factors as 7 * 17<sup>2</sup>. | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
Note: 5-limit temperaments represented by 289edo are not included. | |||
{| class="wikitable center-all left-4" | |||
!Periods | |||
per 8ve | |||
!Generator | |||
(Reduced) | |||
!Cents | |||
(Reduced) | |||
!Associated | |||
Ratio | |||
!Temperament | |||
|- | |||
|17 | |||
|144\2023 | |||
(25\2023) | |||
|85.417 | |||
(14.829) | |||
|1024/975 | |||
(?) | |||
|[[Leaves]] | |||
|} | |||
== Music == | == Music == | ||
* [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭, (Op. 2, No. 2)] by [[Eliora]] | * [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭ Leaves, (Op. 2, No. 2)] by [[Eliora]] | ||
[[Category:Equal divisions of the octave|####]]<!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]]<!-- 4-digit number --> | ||
[[Category:Quartismic]] | [[Category:Quartismic]] | ||
Revision as of 18:46, 5 January 2023
| ← 2022edo | 2023edo | 2024edo → |
Theory
| 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) | |
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
(?) |
Leaves |