385edo: Difference between revisions
m Skip disambiguation |
m changed EDO intro to ED intro |
||
(3 intermediate revisions by one other user not shown) | |||
Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]] and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit. | 385edo has a reasonable approximation to the 11-limit, and perhaps beyond. The equal temperament [[tempering out|tempers out]] [[19683/19600]], [[589824/588245]], and [[703125/702464]] in the 7-limit; [[540/539]], [[8019/8000]], 43923/43904, 151263/151250, 160083/160000, 166698/166375, and 172032/171875 in the 11-limit. It [[support]]s [[hemipental]] and provides the [[optimal patent val]] for the 7-limit version thereof. Using the [[patent val]], it tempers out [[1575/1573]], [[1716/1715]], [[2200/2197]], [[4096/4095]], [[6656/6655]], and [[10648/10647]] in the 13-limit; and [[936/935]], [[1275/1274]], 1377/1375, and [[2601/2600]] in the 17-limit. | ||
=== Prime harmonics === | === Prime harmonics === | ||
Line 13: | Line 13: | ||
== 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 53: | Line 54: | ||
| 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000 | | 540/539, 1575/1573, 2200/2197, 4096/4095, 8019/8000 | ||
| {{mapping| 385 610 894 1081 1332 1425 }} | | {{mapping| 385 610 894 1081 1332 1425 }} | ||
| | | −0.0394 | ||
| 0.2207 | | 0.2207 | ||
| 7.08 | | 7.08 | ||
Line 60: | Line 61: | ||
| 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095 | | 540/539, 936/935, 1377/1375, 1575/1573, 2200/2197, 4096/4095 | ||
| {{mapping| 385 610 894 1081 1332 1425 1574 }} | | {{mapping| 385 610 894 1081 1332 1425 1574 }} | ||
| | | −0.0693 | ||
| 0.2171 | | 0.2171 | ||
| 6.97 | | 6.97 | ||
Line 67: | Line 68: | ||
=== 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 87: | Line 89: | ||
|- | |- | ||
| 5 | | 5 | ||
| 80\385<br>(3\385) | | 80\385<br />(3\385) | ||
| 249.35<br>(9.35) | | 249.35<br />(9.35) | ||
| 81/70<br>(176/175) | | 81/70<br />(176/175) | ||
| [[Hemipental]] | | [[Hemipental]] | ||
|- | |- | ||
| 5 | | 5 | ||
| 160\385<br>(6\385) | | 160\385<br />(6\385) | ||
| 498.70<br>(18.70) | | 498.70<br />(18.70) | ||
| 4/3<br>(81/80) | | 4/3<br />(81/80) | ||
| [[Pental (temperament)|Pental]] (5-limit) | | [[Pental (temperament)|Pental]] (5-limit) | ||
|} | |} | ||
<nowiki>* | <nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct | ||
[[Category:Hemipental]] | [[Category:Hemipental]] |