395edo: Difference between revisions
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== Regular temperament properties == | == Regular temperament properties == | ||
{| class="wikitable center-4 center-5 center-6" | {| class="wikitable center-4 center-5 center-6" | ||
|- | |||
! rowspan="2" | [[Subgroup]] | ! rowspan="2" | [[Subgroup]] | ||
! rowspan="2" | [[Comma list|Comma List]] | ! rowspan="2" | [[Comma list|Comma List]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve Stretch (¢) | ! rowspan="2" | Optimal<br />8ve Stretch (¢) | ||
! colspan="2" | Tuning Error | ! colspan="2" | Tuning Error | ||
|- | |- | ||
| Line 53: | Line 54: | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
{| class="wikitable center-all left-5" | {| class="wikitable center-all left-5" | ||
|+Table of rank-2 temperaments by generator | |+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | ||
! Periods<br>per 8ve | |- | ||
! Periods<br />per 8ve | |||
! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio* | ! Associated<br />Ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 66: | Line 68: | ||
| [[Pontiac]] | | [[Pontiac]] | ||
|} | |} | ||
{{orf}} | |||
Revision as of 00:58, 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 |