395edo: Difference between revisions
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Created page with "{{Infobox ET}} {{EDO intro|395}} == Theory == 395et is consistent to the 9-odd-limit. It tempers out 32805/32768 in the 5-limit; 283115520/282475249, 14348907/14336..." |
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== Theory == | == Theory == | ||
395edo is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[tempering out|tempers out]] [[32805/32768]] in the 5-limit; [[4375/4374]], [[65625/65536]], [[14348907/14336000]], and 40500000/40353607 in the 7-limit; [[support]]ing [[gold]] and [[pontiac]]. | |||
=== Prime harmonics === | === Prime harmonics === | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
395 factors into 5 × 79, | Since 395 factors into 5 × 79, 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|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 | ||
|- | |- | ||
![[TE error|Absolute]] (¢) | ! [[TE error|Absolute]] (¢) | ||
![[TE simple badness|Relative]] (%) | ! [[TE simple badness|Relative]] (%) | ||
|- | |- | ||
|2.3 | | 2.3 | ||
|{{monzo|-626 395}} | | {{monzo| -626 395 }} | ||
|{{mapping|395 626}} | | {{mapping| 395 626 }} | ||
| 0.0577 | | 0.0577 | ||
| 0.0577 | | 0.0577 | ||
| 1.90 | | 1.90 | ||
|- | |- | ||
|2.3.5 | | 2.3.5 | ||
|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 | ||
|- | |- | ||
|2.3.5.7 | | 2.3.5.7 | ||
|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 | ||
|- | |- | ||
|2.3.5.7.11 | | 2.3.5.7.11 | ||
|1375/1372, 4375/4374, | | 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 | ||
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! Temperaments | ! Temperaments | ||
|- | |- | ||
|1 | | 1 | ||
|164\395 | | 164\395 | ||
|498.23 | | 498.23 | ||
|4/3 | | 4/3 | ||
| | | [[Pontiac]] | ||
|} | |} | ||
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct | <nowiki>*</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 14:41, 16 January 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