395edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{ | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br />8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |- | ||
| 2.3 | | 2.3 | ||
| Line 41: | Line 50: | ||
| 0.1792 | | 0.1792 | ||
| 5.90 | | 5.90 | ||
|} | |||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{ | {| class="wikitable center-all left-5" | ||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br />per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br />ratio* | |||
! Temperaments | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 51: | Line 67: | ||
| 4/3 | | 4/3 | ||
| [[Pontiac]] | | [[Pontiac]] | ||
|} | |||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | |||
Revision as of 13:18, 16 November 2024
| ← 394edo | 395edo | 396edo → |
Theory
395edo is consistent to the 9-odd-limit. The equal temperament tempers out 32805/32768 in the 5-limit; 4375/4374, 65625/65536, 14348907/14336000, and 40500000/40353607 in the 7-limit; supporting gold and pontiac.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00 | -0.18 | -0.49 | +0.29 | -1.44 | +0.99 | +1.37 | +0.21 | +0.59 | +0.30 | +0.28 |
| Relative (%) | +0.0 | -6.0 | -16.2 | +9.5 | -47.5 | +32.6 | +45.2 | +6.9 | +19.3 | +9.8 | +9.2 | |
| Steps (reduced) |
395 (0) |
626 (231) |
917 (127) |
1109 (319) |
1366 (181) |
1462 (277) |
1615 (35) |
1678 (98) |
1787 (207) |
1919 (339) |
1957 (377) | |
Subsets and supersets
Since 395 factors into 5 × 79, 395edo has 5edo and 79edo as its subset edos.
Regular temperament properties
| Subgroup | Comma list | Mapping | Optimal 8ve stretch (¢) |
Tuning error | |
|---|---|---|---|---|---|
| Absolute (¢) | Relative (%) | ||||
| 2.3 | [-626 395⟩ | [⟨395 626]] | 0.0577 | 0.0577 | 1.90 |
| 2.3.5 | 32805/32768, [-34 -43 44⟩ | [⟨395 626 917]] | 0.1089 | 0.0864 | 2.84 |
| 2.3.5.7 | 4375/4374, 32805/32768, 40500000/40353607 | [⟨395 626 917 1109]] | 0.0560 | 0.1183 | 3.89 |
| 2.3.5.7.11 | 1375/1372, 4375/4374, 32805/32768, 35937/35840 | [⟨395 626 917 1109 1366]] | 0.1283 | 0.1792 | 5.90 |
Rank-2 temperaments
| Periods per 8ve |
Generator* | Cents* | Associated ratio* |
Temperaments |
|---|---|---|---|---|
| 1 | 164\395 | 498.23 | 4/3 | Pontiac |
* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct