207edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
[[ | == Theory == | ||
207et [[tempering out|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit, [[6144/6125]] and [[19683/19600]] in the 7-limit, [[441/440]] and 43923/43904 in the 11-limit, and [[351/350]], [[676/675]], [[729/728]], [[847/845]], [[1716/1715]] in the 13-limit. It serves as a tuning in the 11- and 13-limit for the [[swetneus]] temperament. It is significantly more accurate on the 2.3.7.11.13 [[subgroup]], a favorite of many people, and one which contains both 729/728 and [[10648/10647]], which it tempers out. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|207}} | |||
=== Subsets and supersets === | |||
Since 207 factors into {{factorisation|207}}, 207edo has subset edos {{EDOs| 3, 9, 23, and 69 }}. | |||
== 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| -328 207 }} | |||
| {{mapping| 207 328 }} | |||
| +0.1595 | |||
| 0.1596 | |||
| 2.75 | |||
|- | |||
| 2.3.5 | |||
| 32805/32768, {{monzo| 2 31 -22 }} | |||
| {{mapping| 207 328 481 }} | |||
| −0.1942 | |||
| 0.5166 | |||
| 8.91 | |||
|- | |||
| 2.3.5.7 | |||
| 6144/6125, 19683/19600, 50421/50000 | |||
| {{mapping| 207 328 481 581 }} | |||
| −0.0825 | |||
| 0.4874 | |||
| 8.41 | |||
|- | |||
| 2.3.5.7.11 | |||
| 441/440, 3388/3375, 6144/6125, 19683/19600 | |||
| {{mapping| 207 328 481 581 716 }} | |||
| −0.0317 | |||
| 0.4477 | |||
| 7.72 | |||
|- | |||
| 2.3.5.7.11.13 | |||
| 351/350, 441/440, 676/675, 847/845, 3584/3575 | |||
| {{mapping| 207 328 481 581 716 766 }} | |||
| −0.0287 | |||
| 0.4087 | |||
| 7.05 | |||
|- | |||
| 2.3.5.7.11.13.17 | |||
| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088 | |||
| {{mapping| 207 328 481 581 716 766 846 }} | |||
| −0.0034 | |||
| 0.3834 | |||
| 6.61 | |||
|} | |||
=== 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 | |||
| 25\207 | |||
| 144.93 | |||
| 49/45 | |||
| [[Swetneus]] | |||
|- | |||
| 1 | |||
| 43\207 | |||
| 249.28 | |||
| 15/13 | |||
| [[Hemischis]] | |||
|- | |||
| 1 | |||
| 86\207 | |||
| 498.55 | |||
| 4/3 | |||
| [[Helmholtz (temperament)|Helmholtz]] | |||
|} | |||
<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 | |||