207edo: Difference between revisions
→Regular temperament properties: review +1 |
m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== Theory == | == Theory == | ||
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=== 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" | {| 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 32: | Line 33: | ||
| 32805/32768, {{monzo| 2 31 -22 }} | | 32805/32768, {{monzo| 2 31 -22 }} | ||
| {{mapping| 207 328 481 }} | | {{mapping| 207 328 481 }} | ||
| | | −0.1942 | ||
| 0.5166 | | 0.5166 | ||
| 8.91 | | 8.91 | ||
| Line 39: | Line 40: | ||
| 6144/6125, 19683/19600, 50421/50000 | | 6144/6125, 19683/19600, 50421/50000 | ||
| {{mapping| 207 328 481 581 }} | | {{mapping| 207 328 481 581 }} | ||
| | | −0.0825 | ||
| 0.4874 | | 0.4874 | ||
| 8.41 | | 8.41 | ||
| Line 46: | Line 47: | ||
| 441/440, 3388/3375, 6144/6125, 19683/19600 | | 441/440, 3388/3375, 6144/6125, 19683/19600 | ||
| {{mapping| 207 328 481 581 716 }} | | {{mapping| 207 328 481 581 716 }} | ||
| | | −0.0317 | ||
| 0.4477 | | 0.4477 | ||
| 7.72 | | 7.72 | ||
| Line 53: | Line 54: | ||
| 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 }} | | {{mapping| 207 328 481 581 716 766 }} | ||
| | | −0.0287 | ||
| 0.4087 | | 0.4087 | ||
| 7.05 | | 7.05 | ||
| Line 60: | Line 61: | ||
| 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 }} | | {{mapping| 207 328 481 581 716 766 846 }} | ||
| | | −0.0034 | ||
| 0.3834 | | 0.3834 | ||
| 6.61 | | 6.61 | ||
| 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 90: | Line 92: | ||
| 498.55 | | 498.55 | ||
| 4/3 | | 4/3 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|} | |} | ||
<nowiki>* | <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 | ||