207edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
| Line 9: | Line 9: | ||
=== Subsets and supersets === | === Subsets and supersets === | ||
Since 207 factors into | Since 207 factors into {{factorisation|207}}, 207edo has subset edos {{EDOs| 3, 9, 23, and 69 }}. | ||
== Regular temperament properties == | == 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 | | 2.3 | ||
| {{ | | {{Monzo| -328 207 }} | ||
| {{ | | {{Mapping| 207 328 }} | ||
| +0.1595 | | +0.1595 | ||
| 0.1596 | | 0.1596 | ||
| Line 23: | Line 32: | ||
| 2.3.5 | | 2.3.5 | ||
| 32805/32768, {{monzo| 2 31 -22 }} | | 32805/32768, {{monzo| 2 31 -22 }} | ||
| {{ | | {{Mapping| 207 328 481 }} | ||
| | | −0.1942 | ||
| 0.5166 | | 0.5166 | ||
| 8.91 | | 8.91 | ||
| Line 30: | Line 39: | ||
| 2.3.5.7 | | 2.3.5.7 | ||
| 6144/6125, 19683/19600, 50421/50000 | | 6144/6125, 19683/19600, 50421/50000 | ||
| {{ | | {{Mapping| 207 328 481 581 }} | ||
| | | −0.0825 | ||
| 0.4874 | | 0.4874 | ||
| 8.41 | | 8.41 | ||
| Line 37: | Line 46: | ||
| 2.3.5.7.11 | | 2.3.5.7.11 | ||
| 441/440, 3388/3375, 6144/6125, 19683/19600 | | 441/440, 3388/3375, 6144/6125, 19683/19600 | ||
| {{ | | {{Mapping| 207 328 481 581 716 }} | ||
| | | −0.0317 | ||
| 0.4477 | | 0.4477 | ||
| 7.72 | | 7.72 | ||
| Line 44: | Line 53: | ||
| 2.3.5.7.11.13 | | 2.3.5.7.11.13 | ||
| 351/350, 441/440, 676/675, 847/845, 3584/3575 | | 351/350, 441/440, 676/675, 847/845, 3584/3575 | ||
| {{ | | {{Mapping| 207 328 481 581 716 766 }} | ||
| | | −0.0287 | ||
| 0.4087 | | 0.4087 | ||
| 7.05 | | 7.05 | ||
| Line 51: | Line 60: | ||
| 2.3.5.7.11.13.17 | | 2.3.5.7.11.13.17 | ||
| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088 | | 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088 | ||
| {{ | | {{Mapping| 207 328 481 581 716 766 846 }} | ||
| | | −0.0034 | ||
| 0.3834 | | 0.3834 | ||
| 6.61 | | 6.61 | ||
|} | |||
=== Rank-2 temperaments === | === 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 | |||
| 20\207 | |||
| 115.94 | |||
| 77/72 | |||
| [[Countermiracle]] / counterbenediction | |||
|- | |- | ||
| 1 | | 1 | ||
| Line 76: | Line 98: | ||
| 498.55 | | 498.55 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|} | |||
<nowiki/>* In [[normal forms #Minimal-generator form|minimal-generator form]] | |||