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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|207}}
{{ED intro}}
==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.
== Theory ==
===Prime harmonics===
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}}
{{Harmonics in equal|207}}
===Subsets and supersets===
 
207 factors into 3<sup>2</sup> × 23, with subset edos {{EDOs|3, 9, 23, and 69}}.
=== Subsets and supersets ===
==Regular temperament properties==
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"
{| 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
! rowspan="2" | [[Subgroup]]
|{{monzo|-328 207}}
! rowspan="2" | [[Comma list]]
|{{val|207 328}}
! 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
| +0.1595
| 0.1596
| 0.1596
| 2.75
| 2.75
|-
|-
|2.3.5
| 2.3.5
|32805/32768, {{monzo|2 31 -22}}
| 32805/32768, {{monzo| 2 31 -22 }}
|{{val|207 328 481}}
| {{mapping| 207 328 481 }}
| -0.1942
| −0.1942
| 0.5166
| 0.5166
| 8.91
| 8.91
|-
|-
|2.3.5.7
| 2.3.5.7
|6144/6125, 19683/19600, 32805/32768
| 6144/6125, 19683/19600, 50421/50000
|{{val|207 328 481 581}}
| {{mapping| 207 328 481 581 }}
| -0.0825
| −0.0825
| 0.4874
| 0.4874
|8.41
| 8.41
|-
|-
|2.3.5.7.11
| 2.3.5.7.11
|441/440, 3388/3375, 3773/3750, 6144/6125
| 441/440, 3388/3375, 6144/6125, 19683/19600
|{{val|207 328 481 581 716}}
| {{mapping| 207 328 481 581 716 }}
| -0.0317
| −0.0317
| 0.4477
| 0.4477
| 7.72
| 7.72
|-
|-
|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
|{{val|207 328 481 581 716 766}}
| {{mapping| 207 328 481 581 716 766 }}
| -0.0287
| −0.0287
| 0.4087
| 0.4087
| 7.05
| 7.05
|-
|-
|2.3.5.7.11.13.17
| 2.3.5.7.11.13.17
|441/440, 561/560, 676/675, 936/935, 1632/1625, 8624/8619
| 351/350, 441/440, 561/560, 676/675, 847/845, 1089/1088
|{{val|207 328 481 581 716 766 846}}
| {{mapping| 207 328 481 581 716 766 846 }}
| -0.0034
| −0.0034
| 0.3834
| 0.3834
| 6.61
| 6.61
|}
|}
=== 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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! Associated<br />ratio*
! Temperaments
! Temperaments
|-
|-
|1
| 1
|25\207
| 25\207
|144.93
| 144.93
|49/45
| 49/45
|[[Swetneus]]
| [[Swetneus]]
|-
|-
|1
| 1
|43\207
| 43\207
|249.28
| 249.28
|15/13
| 15/13
|[[Hemischis]]
| [[Hemischis]]
|-
|-
|1
| 1
|86\207
| 86\207
|498.55
| 498.55
|4/3
| 4/3
|[[Helmholtz]]
| [[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
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
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