395edo: Difference between revisions
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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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== 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 | 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" | ||
|- | |- | ||
|2.3 | ! rowspan="2" | [[Subgroup]] | ||
|{{monzo|-626 395}} | ! rowspan="2" | [[Comma list]] | ||
|{{mapping|395 626}} | ! rowspan="2" | [[Mapping]] | ||
| 0.0577 | ! rowspan="2" | Optimal<br />8ve stretch (¢) | ||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| -626 395 }} | |||
| {{mapping| 395 626 }} | |||
| +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 | ||
| 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 | ||
|- | |- | ||
|1 | | 1 | ||
|164\395 | | 164\395 | ||
|498.23 | | 498.23 | ||
|4/3 | | 4/3 | ||
| | | [[Pontiac]] | ||
|} | |} | ||
<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | |||
<nowiki>* | |||