2814edo: Difference between revisions
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clarify and add rank 2 temp |
This isn't the OPV for jacobin. The OPV is 3395. Note to editors: plz learn about the concept before making such claims |
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In the 11-limit, it supports rank-3 [[odin]] 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 [[Double Bastille]] temperament. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|2814}} | {{Harmonics in equal|2814}} | ||
== Regular temperament properties == | == Regular temperament properties == | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
Note: 7-limit temperaments represented by [[1407edo]] are not included. | Note: 7-limit temperaments represented by [[1407edo]] are not included. | ||
{| class="wikitable center-all left-4" | {| class="wikitable center-all left-4" | ||
!Periods | ! Periods<br>per 8ve | ||
per 8ve | ! Generator<br>(Reduced) | ||
!Generator | ! Cents<br>(Reduced) | ||
(Reduced) | ! Associated<br>Ratio | ||
!Cents | ! Temperament | ||
(Reduced) | |||
!Associated | |||
Ratio | |||
!Temperament | |||
|- | |- | ||
|1 | | 1 | ||
|593\2814 | | 593\2814 | ||
|252.878 | | 252.878 | ||
|53094899/45875200 | | 53094899/45875200 | ||
|[[Double Bastille]] | | [[Double Bastille]] | ||
|}<!-- 4-digit number --> | |} | ||
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number --> | |||
[[Category:Jacobin]] | [[Category:Jacobin]] | ||
Revision as of 09:03, 17 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.
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 (Reduced) |
Cents (Reduced) |
Associated Ratio |
Temperament |
|---|---|---|---|---|
| 1 | 593\2814 | 252.878 | 53094899/45875200 | Double Bastille |