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The | {{Infobox ET}} | ||
{{ED intro}} | |||
== Theory == | |||
The equal temperament [[tempering out|tempers out]] the [[parakleisma]], {{monzo| 8 14 -13 }}, and the [[septendecima]], {{monzo| -52 -17 34 }}, in the [[5-limit]]. In the [[7-limit]] it tempers out 19683/19600 ([[cataharry comma]]), 16875/16807 ([[canopic comma]]), and 65625/65536 ([[horwell comma]]) so that it [[support]]s the [[mirkat]] temperament, and in fact provides the [[optimal patent val]]. It also gives the optimal patent val for mirkat in the [[11-limit]], tempering out [[540/539]], [[1375/1372]], [[3025/3024]] and [[8019/8000]]. In the [[13-limit]] it tempers out [[847/845]], [[625/624]], [[1575/1573]] and [[1716/1715]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|255}} | |||
=== Subsets and supersets === | |||
Since 255 factors into {{nowrap| 3 × 5 × 17 }}, 255edo has subset edos {{EDOs| 3, 5, 15, 17, 51, and 85 }}. | |||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{Monzo| -404 255 }} | |||
| {{Mapping| 255 404 }} | |||
| +0.246 | |||
| 0.246 | |||
| 5.22 | |||
|- | |||
| 2.3.5 | |||
| {{Monzo| 8 14 -13 }}, {{monzo| -36 11 8 }} | |||
| {{Mapping| 255 404 592 }} | |||
| +0.226 | |||
| 0.203 | |||
| 4.30 | |||
|- | |||
| 2.3.5.7 | |||
| 16875/16807, 19683/19600, 65625/65536 | |||
| {{Mapping| 255 404 592 716 }} | |||
| +0.117 | |||
| 0.257 | |||
| 5.46 | |||
|- | |||
| 2.3.5.7.11 | |||
| 540/539, 1375/1372, 8019/8000, 65625/65536 | |||
| {{Mapping| 255 404 592 716 882 }} | |||
| +0.136 | |||
| 0.233 | |||
| 4.95 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator | |||
|- | |||
! Periods<br>per 8ve | |||
! Generator* | |||
! Cents* | |||
! Associated<br>ratio* | |||
! Temperaments | |||
|- | |||
| 1 | |||
| 52\255 | |||
| 244.71 | |||
| 15/13 | |||
| [[Subsemifourth]] (255) | |||
|- | |||
| 1 | |||
| 67\255 | |||
| 315.29 | |||
| 6/5 | |||
| [[Counterpara]] | |||
|- | |||
| 1 | |||
| 74\255 | |||
| 348.24 | |||
| 11/9 | |||
| [[Eris]] (255) | |||
|- | |||
| 3 | |||
| 39\255 | |||
| 183.53 | |||
| 10/9 | |||
| [[Mirkat]] (255f) | |||
|- | |||
| 3 | |||
| 3\255 | |||
| 14.12 | |||
| 126/125 | |||
| [[Mutt]] (7-limit) | |||
|- | |||
| 5 | |||
| 2\255 | |||
| 9.41 | |||
| 176/175 | |||
| [[Hemiquintile]] / hemiquint (255) / hemiquintilis (255f) | |||
|- | |||
| 5 | |||
| 4\255 | |||
| 18.82 | |||
| 81/80 | |||
| [[Quintile]] | |||
|- | |||
| 17 | |||
| 7\255 | |||
| 32.94 | |||
| 1990656/1953125 | |||
| [[Chlorine]] (5-limit) | |||
|} | |||
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | |||
[[Category:Mirkat]] | |||