207edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|207}} | |||
==Theory== | |||
It tempers out 32805/32768 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, 847/845, 676/675, 729/728, 1716/1715 in the 13-limit. It serves as the patent val in the 11- and 13-limits for [[Cataharry_temperaments#Swetneus|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=== | |||
207 factors into 3<sup>2</sup> × 23, with 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|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}} | |||
|{{val|207 328}} | |||
| +0.1595 | |||
| 0.1596 | |||
| 2.75 | |||
|- | |||
|2.3.5 | |||
|32805/32768, {{monzo|2 31 -22}} | |||
|{{val|207 328 481}} | |||
| -0.1942 | |||
| 0.5166 | |||
| 8.91 | |||
|- | |||
|2.3.5.7 | |||
|6144/6125, 19683/19600, 32805/32768 | |||
|{{val|207 328 481 581}} | |||
| -0.0825 | |||
| 0.4874 | |||
|8.41 | |||
|- | |||
|2.3.5.7.11 | |||
|441/440, 3388/3375, 3773/3750, 6144/6125 | |||
|{{val|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 | |||
|{{val|207 328 481 581 716 766}} | |||
| -0.0287 | |||
| 0.4087 | |||
| 7.05 | |||
|- | |||
|2.3.5.7.11.13.17 | |||
|441/440, 561/560, 676/675, 936/935, 1632/1625, 8624/8619 | |||
|{{val|207 328 481 581 716 766 846}} | |||
| -0.0034 | |||
| 0.3834 | |||
| 6.61 | |||
|} | |||
=== Rank-2 temperaments === | |||
{| class="wikitable center-all left-5" | |||
|+Table of rank-2 temperaments by generator | |||
! Periods<br>per 8ve | |||
! Generator<br>(reduced) | |||
! Cents<br>(reduced) | |||
! 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]] | |||
|} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||