2814edo: Difference between revisions
Jump to navigation
Jump to search
→Theory: even 20% relative error doesn't guarantee consistency in the 17-odd-limit. 1/3 does |
clarify and add rank 2 temp |
||
| Line 9: | Line 9: | ||
In the 11-limit, it supports rank-3 [[odin]] temperament. | In the 11-limit, it supports rank-3 [[odin]] temperament. | ||
2814edo provides the [[optimal patent val]] for the rank-5 temperament tempering out the [[jacobin comma]], and as such it is also a tuning for the [[Double Bastille]] temperament in the 2.5.7.11.13 subgroup. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2814}} | {{Harmonics in equal|2814}} | ||
[[Category:Equal divisions of the octave|####]]<!-- 4-digit number --> | [[Category:Equal divisions of the octave|####]] | ||
== Regular temperament properties == | |||
=== Rank-2 temperaments === | |||
Note: 7-limit temperaments represented by [[1407edo]] are not included. | |||
{| class="wikitable center-all left-4" | |||
!Periods | |||
per 8ve | |||
!Generator | |||
(Reduced) | |||
!Cents | |||
(Reduced) | |||
!Associated | |||
Ratio | |||
!Temperament | |||
|- | |||
|1 | |||
|593\2814 | |||
|252.878 | |||
|53094899/45875200 | |||
|[[Double Bastille]] | |||
|}<!-- 4-digit number --> | |||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||
Revision as of 23:27, 16 December 2022
| ← 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 contorted, with the same commas tempered out as 1407edo.
In the 11-limit, it supports rank-3 odin temperament.
2814edo provides the optimal patent val for the rank-5 temperament tempering out the jacobin comma, and as such it is also a tuning for the Double Bastille temperament in the 2.5.7.11.13 subgroup.
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
(Reduced) |
Cents
(Reduced) |
Associated
Ratio |
Temperament |
|---|---|---|---|---|
| 1 | 593\2814 | 252.878 | 53094899/45875200 | Double Bastille |