395edo: Difference between revisions
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m changed EDO intro to ED intro |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 395 factors into | Since 395 factors into {{factorisation|395}}, 395edo has [[5edo]] and [[79edo]] as its subset edos. | ||
== 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 | ! rowspan="2" | [[Comma list]] | ||
! rowspan="2" | [[Mapping]] | ! rowspan="2" | [[Mapping]] | ||
! rowspan="2" | Optimal<br>8ve | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning | ! colspan="2" | Tuning error | ||
|- | |- | ||
! [[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
! [[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
| Line 25: | Line 26: | ||
| {{monzo| -626 395 }} | | {{monzo| -626 395 }} | ||
| {{mapping| 395 626 }} | | {{mapping| 395 626 }} | ||
| 0.0577 | | +0.0577 | ||
| 0.0577 | | 0.0577 | ||
| 1.90 | | 1.90 | ||
| Line 32: | Line 33: | ||
| 32805/32768, {{monzo| -34 -43 44 }} | | 32805/32768, {{monzo| -34 -43 44 }} | ||
| {{mapping| 395 626 917 }} | | {{mapping| 395 626 917 }} | ||
| 0.1089 | | +0.1089 | ||
| 0.0864 | | 0.0864 | ||
| 2.84 | | 2.84 | ||
| Line 39: | Line 40: | ||
| 4375/4374, 32805/32768, 40500000/40353607 | | 4375/4374, 32805/32768, 40500000/40353607 | ||
| {{mapping| 395 626 917 1109 }} | | {{mapping| 395 626 917 1109 }} | ||
| 0.0560 | | +0.0560 | ||
| 0.1183 | | 0.1183 | ||
| 3.89 | | 3.89 | ||
| Line 46: | Line 47: | ||
| 1375/1372, 4375/4374, 32805/32768, 35937/35840 | | 1375/1372, 4375/4374, 32805/32768, 35937/35840 | ||
| {{mapping| 395 626 917 1109 1366 }} | | {{mapping| 395 626 917 1109 1366 }} | ||
| 0.1283 | | +0.1283 | ||
| 0.1792 | | 0.1792 | ||
| 5.90 | | 5.90 | ||
| 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> | ! Associated<br />ratio* | ||
! Temperaments | ! Temperaments | ||
|- | |- | ||
| Line 66: | Line 68: | ||
| [[Pontiac]] | | [[Pontiac]] | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
Latest revision as of 06:18, 21 February 2025
| ← 394edo | 395edo | 396edo → |
395 equal divisions of the octave (abbreviated 395edo or 395ed2), also called 395-tone equal temperament (395tet) or 395 equal temperament (395et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 395 equal parts of about 3.04 ¢ each. Each step represents a frequency ratio of 21/395, or the 395th root of 2.
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 distinct