292edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
[[Category: | == Theory == | ||
292edo is closely related to [[146edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 3 -18 11 }} ([[quartonic comma]]) and {{monzo| 38 -2 -15 }} ([[luna comma|luna/hemithirds comma]]) in the [[5-limit]]; 5120/5103 ([[5120/5103|hemifamity]]), 390625/388962 ([[dimcomp comma|dimcomp]]), 420175/419904 ([[wizma]]), and 4802000/4782969 ([[canousma]]) in the [[7-limit]]; 1375/1372, [[5632/5625]], [[6250/6237]], [[9801/9800]] and [[14641/14580]] in the [[11-limit]]; [[352/351]], [[625/624]], [[847/845]], [[1716/1715]], and [[2080/2079]] in the [[13-limit]]. | |||
It provides the [[optimal patent val]] for the [[undim]] temperament in the 7-, 11-, and 13-limit, and notably [[support]]s [[hemifamity temperaments #Semiseptiquarter|semiseptiquarter]] and [[semiluna]]. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|292}} | |||
=== Subsets and supersets === | |||
Since 292 factors into 2<sup>2</sup> × 73, 292edo has subset edos {{EDOs| 2, 4, 73, and 146 }}. | |||
== 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| 463 -292 }} | |||
| {{mapping| 292 463 }} | |||
| −0.2476 | |||
| 0.2475 | |||
| 6.02 | |||
|- | |||
| 2.3.5 | |||
| {{monzo| 3 -18 11 }}, {{monzo| 38 -2 -15 }} | |||
| {{mapping| 292 463 678 }} | |||
| −0.1633 | |||
| 0.2346 | |||
| 5.71 | |||
|- | |||
| 2.3.5.7 | |||
| 5120/5103, 390625/388962, 420175/419904 | |||
| {{mapping| 292 463 678 820 }} | |||
| −0.2148 | |||
| 0.2219 | |||
| 5.40 | |||
|- | |||
| 2.3.5.7.11 | |||
| 1375/1372, 5120/5103, 5632/5625, 14641/14580 | |||
| {{mapping| 292 463 678 820 1010 }} | |||
| −0.1353 | |||
| 0.2544 | |||
| 6.19 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 352/351, 625/624, 847/845, 1716/1715, 14641/14580 | |||
| {{mapping| 292 463 678 820 1010 1081 }} | |||
| −0.3480 | |||
| 0.2736 | |||
| 6.66 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 352/351, 625/624, 715/714, 847/845, 1225/1224, 2025/2023 | |||
| {{mapping| 292 463 678 820 1010 1081 1194 }} | |||
| −0.2376 | |||
| 0.2696 | |||
| 6.56 | |||
|} | |||
=== 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 | |||
| 11\292 | |||
| 45.21 | |||
| 250/243 | |||
| [[Quartonic]] (5-limit) | |||
|- | |||
| 1 | |||
| 47\292 | |||
| 193.15 | |||
| 262144/234375 | |||
| [[Luna]] | |||
|- | |||
| 1 | |||
| 59\292 | |||
| 242.47 | |||
| 147/128 | |||
| [[Septiquarter]] | |||
|- | |||
| 1 | |||
| 111\292 | |||
| 456.16 | |||
| 125/96 | |||
| [[Qak]] | |||
|- | |||
| 2 | |||
| 47\292 | |||
| 193.15 | |||
| 121/108 | |||
| [[Semiluna]] | |||
|- | |||
| 2 | |||
| 59\292 | |||
| 242.47 | |||
| 121/105 | |||
| [[Semiseptiquarter]] | |||
|- | |||
| 4 | |||
| 121\292 | |||
| 497.26 | |||
| 4/3 | |||
| [[Undim]] | |||
|} | |||
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | |||
[[Category:Aberschismic]] | |||
[[Category:Septiquarter]] | |||
[[Category:Semiluna]] | |||
[[Category:Undim]] | |||