1147edo: Difference between revisions
mNo edit summary |
No edit summary |
||
| Line 4: | Line 4: | ||
1147edo can be defined as the unique ET in the [[2.3.7 subgroup]] that tempers out the [[Don Page comma]]s among the intervals [[9/8]], [[8/7]], and [[7/6]], and therefore contains [[28ed4/3]] and [[32ed9/7]] within it. This edo notably also tempers out the [[quartisma]], by virtue of 28ed4/3 mapping 7/6 to a number of steps divisible by 5. Therefore, the representation of [[33/32]] is accurate and the edo overall excels in the [[2.3.7.11 subgroup]], with an additional very good prime 43. | 1147edo can be defined as the unique ET in the [[2.3.7 subgroup]] that tempers out the [[Don Page comma]]s among the intervals [[9/8]], [[8/7]], and [[7/6]], and therefore contains [[28ed4/3]] and [[32ed9/7]] within it. This edo notably also tempers out the [[quartisma]], by virtue of 28ed4/3 mapping 7/6 to a number of steps divisible by 5. Therefore, the representation of [[33/32]] is accurate and the edo overall excels in the [[2.3.7.11 subgroup]], with an additional very good prime 43. | ||
In [[regular temperament]] terms, in addition to the quartisma, 1147edo also tempers out the [[elysia]] (117649/117612), and the comma {{monzo|18 -31 0 0 9}}, which sets [[44/27]] equal to [[9edt|4\9edt]], in the 2.3.7.11 subgroup. | In [[regular temperament]] terms, in addition to the quartisma, 1147edo also tempers out the [[elysia]] (117649/117612), and the comma {{monzo|18 -31 0 0 9}}, which sets [[44/27]] equal to [[9edt|4\9edt]] (alternatively the difference between the [[gothic comma]] and nine [[rastmas]]), in the 2.3.7.11 subgroup. | ||
=== Odd harmonics === | === Odd harmonics === | ||
Revision as of 03:32, 22 November 2024
| ← 1146edo | 1147edo | 1148edo → |
1147edo can be defined as the unique ET in the 2.3.7 subgroup that tempers out the Don Page commas among the intervals 9/8, 8/7, and 7/6, and therefore contains 28ed4/3 and 32ed9/7 within it. This edo notably also tempers out the quartisma, by virtue of 28ed4/3 mapping 7/6 to a number of steps divisible by 5. Therefore, the representation of 33/32 is accurate and the edo overall excels in the 2.3.7.11 subgroup, with an additional very good prime 43.
In regular temperament terms, in addition to the quartisma, 1147edo also tempers out the elysia (117649/117612), and the comma [18 -31 0 0 9⟩, which sets 44/27 equal to 4\9edt (alternatively the difference between the gothic comma and nine rastmas), in the 2.3.7.11 subgroup.
Odd harmonics
One should note that its prime 11 is inherited from 37edo, which is a strong convergent.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | +0.0502 | -0.2631 | -0.0378 | +0.0334 | -0.4230 | -0.3347 | -0.3901 | +0.4964 | -0.1090 | -0.4846 | -0.2542 | -0.1173 | +0.0778 | -0.1187 |
| Relative (%) | +0.0 | +4.8 | -25.2 | -3.6 | +3.2 | -40.4 | -32.0 | -37.3 | +47.4 | -10.4 | -46.3 | -24.3 | -11.2 | +7.4 | -11.3 | |
| Steps (reduced) |
1147 (0) |
1818 (671) |
2663 (369) |
3220 (926) |
3968 (527) |
4244 (803) |
4688 (100) |
4872 (284) |
5189 (601) |
5572 (984) |
5682 (1094) |
5975 (240) |
6145 (410) |
6224 (489) |
6371 (636) | |
Subsets and supersets
Since 1147 factors into 31 × 37, 1147edo has subset edos 31 and 37.
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |