2023edo: Difference between revisions
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→Rank-2 temperaments: since leaves true gen is just one period over reduced gen, this is easy to calculate |
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{{EDO intro|2023}} | {{EDO intro|2023}} | ||
== 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 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 | |||
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 === | |||
{{harmonics in equal|2023}} | |||
=== Subsets and supersets === | |||
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>. | ||
Revision as of 13:48, 26 March 2023
| ← 2022edo | 2023edo | 2024edo → |
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
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 |