2814edo: Difference between revisions
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Cleanup; clarify the title row of the rank-2 temp table |
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== Theory == | == Theory == | ||
2814edo has all the | 2814edo has all the [[harmonic]]s from 3 to 17 approximated below 1/3 relative error and it is as a corollary [[consistent]] in the [[17-odd-limit]]. | ||
In the 7-limit, it is | In the 7-limit, it is [[Enfactoring|enfactored]], with the same [[comma]]s [[Tempering out|tempered out]] as [[1407edo]]. In the 11-limit, it supports rank-3 [[odin]] temperament. In the 13-limit it tempers out [[6656/6655]] and supports the 2.5.7.11.13 [[subgroup]] [[double bastille]] temperament. | ||
In the 11-limit, it supports rank-3 [[odin]] temperament. | |||
In the 13-limit it tempers out [[6656/6655]] and supports the 2.5.7.11.13 subgroup [[ | |||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 19: | Line 15: | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
! Periods<br>per 8ve | ! Periods<br>per 8ve | ||
! Generator | ! Generator* | ||
! Cents | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio | ||
! Temperament | ! Temperament | ||
| Line 28: | Line 24: | ||
| 252.878 | | 252.878 | ||
| 53094899/45875200 | | 53094899/45875200 | ||
| [[Double | | [[Double bastille]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||
Revision as of 11:49, 15 October 2023
| ← 2813edo | 2814edo | 2815edo → |
Theory
2814edo has all the harmonics from 3 to 17 approximated below 1/3 relative error and it is as a corollary consistent in the 17-odd-limit.
In the 7-limit, it is enfactored, with the same commas tempered out as 1407edo. In the 11-limit, it supports rank-3 odin temperament. In the 13-limit it tempers out 6656/6655 and supports the 2.5.7.11.13 subgroup double bastille temperament.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.036 | +0.040 | +0.044 | +0.068 | -0.016 | -0.051 | +0.142 | -0.129 | -0.153 | -0.046 |
| Relative (%) | +0.0 | -8.4 | +9.4 | +10.3 | +15.9 | -3.7 | -12.0 | +33.2 | -30.3 | -35.9 | -10.8 | |
| Steps (reduced) |
2814 (0) |
4460 (1646) |
6534 (906) |
7900 (2272) |
9735 (1293) |
10413 (1971) |
11502 (246) |
11954 (698) |
12729 (1473) |
13670 (2414) |
13941 (2685) | |
Regular temperament properties
Rank-2 temperaments
Note: 7-limit temperaments represented by 1407edo are not included.
| Periods per 8ve |
Generator* | Cents* | Associated Ratio |
Temperament |
|---|---|---|---|---|
| 1 | 593\2814 | 252.878 | 53094899/45875200 | Double bastille |
* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct