2023edo: Difference between revisions
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== Theory == | == Theory == | ||
{{Harmonics in equal|2023}} | {{Harmonics in equal|2023}} | ||
2023edo is enfactored in the 5-limit, with the same mapping as [[289edo]]. | |||
In the patent val, it is good in the no-11s 17-limit, a property which it shares with [[323edo]]. As such, a 2.3.5.7.13.17 temperament can be created by merging 323 & 2023, which gives the comma basis {57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000}. It is also period-17, and maps the period to 25/24, which means [[septendecima]] is also tempered out. | In the patent val, it is good in the no-11s 17-limit, a property which it shares with [[323edo]]. As such, a 2.3.5.7.13.17 temperament can be created by merging 323 & 2023, which gives the comma basis {57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000}. It is also period-17, and maps the period to 25/24, which means [[septendecima]] is also tempered out. | ||
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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>. | ||
== Music == | |||
* [https://www.youtube.com/watch?v=8K2RYO_oCnM Bagatelle in 11/8♭, (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 20:21, 4 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 patent val, it is good in the no-11s 17-limit, a property which it shares with 323edo. As such, a 2.3.5.7.13.17 temperament can be created by merging 323 & 2023, which gives the comma basis {57375/57344, 111537/111475, 4860000/4857223, 340075827/340000000}. 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.