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{{Infobox ET}}
{{Infobox ET}}
'''107edo''' is the [[EDO|equal division of the octave]] into 107 parts of 11.214953271 cents each. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 7-limit: {{val|107 170 248 300}} (patent val), {{val|107 169 248 300}} (107b), {{val|107 170 249 300}} (107c), and {{val|107 170 249 301}} (107cd). Using the patent val, it tempers out the [[Magic family|small diesis]], [[3125/3072]] and 33554432000/31381059609 in the 5-limit; [[1029/1024]], 2240/2187, and 3125/3087 in the 7-limit; [[100/99]], 1232/1215, and 1331/1323 in the 11-limit. Using the 107b val, it tempers out the [[syntonic comma]], [[81/80]] and {{monzo|-61 -1 27}}; in the 5-limit; [[2401/2400]], [[2430/2401]], and 234375/229376 in the 7-limit; [[385/384]], 1350/1331, 1375/1372, and 1944/1925 in the 11-limit. Using the 107c val, it tempers out the immunity comma, 1638400/1594323 and the valentine comma, 1990656/1953125 in the 5-limit; [[126/125]], [[1029/1024]], and 307328/295245 in the 7-limit; [[121/120]], [[176/175]], [[441/440]], and 184877/177147 in the 11-limit. Using the 107cd val, it tempers out [[1728/1715]], 4000/3969, and 28672/28125 in the 7-limit; 121/120, [[896/891]], 1375/1372, and 3168/3125 in the 11-limit.
{{EDO intro|107}}


It is the 28th [[prime edo]].
== Theory ==
107edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four [[mapping]]s possible for the 7-limit: {{val| 107 170 248 300 }} ([[patent val]]), {{val| 107 '''169''' 248 300 }} (107b), {{val| 107 170 '''249''' 300 }} (107c), and {{val| 107 170 '''249''' '''301''' }} (107cd).  


==Theory==
Using the patent val, it tempers out [[3125/3072]] (magic comma) and 33554432000/31381059609 in the 5-limit; [[1029/1024]], 2240/2187, and 3125/3087 in the 7-limit; [[100/99]], 1232/1215, and 1331/1323 in the 11-limit.
Since 107edo has a step of 11.214953271 cents, it also allows one to use its MOS scales as circulating temperaments.  
 
{| class="wikitable"
Using the 107b val, it tempers out [[81/80]] (syntonic comma) and {{monzo| -61 -1 27 }}; in the 5-limit; [[2401/2400]], [[2430/2401]], and 234375/229376 in the 7-limit; [[385/384]], 1350/1331, 1375/1372, and 1944/1925 in the 11-limit.
|+Circulating temperaments in 107edo
 
Using the 107c val, it tempers out 1638400/1594323 (immunity comma) and 1990656/1953125 (valentine comma) in the 5-limit; [[126/125]], [[1029/1024]], and 307328/295245 in the 7-limit; [[121/120]], [[176/175]], [[441/440]], and 184877/177147 in the 11-limit.
 
Using the 107cd val, it tempers out [[1728/1715]], 4000/3969, and 28672/28125 in the 7-limit; 121/120, [[896/891]], 1375/1372, and 3168/3125 in the 11-limit.
 
=== Subsets and supersets ===
107edo is the 28th [[prime edo]].
 
=== Odd harmonics ===
{{Harmonics in equal|107}}
 
== 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|170 -107}}
| {{val|107 170}}
| -1.4471
| 1.4453
| 12.89
|-
| 2.3.5
| 3125/3072, {{monzo|18 -23 8}}
| {{val|107 170 248}}
| -0.2497
| 2.0685
| 18.44
|-
| 2.3.5.7
| 2240/2187, 1029/1024, 3125/3072
| {{val|107 170 248 300}}
| +0.1987
| 1.9529
| 17.41
|-
| 2.3.5.7.11
| 100/99, 1232/1215, 1375/1372, 1029/1024
| {{val|107 170 248 300 370}}
| +0.2622
| 1.7513
| 15.62
|-
| 2.3.5.7.11.13
| 100/99, 196/195, 275/273, 1232/1215, 1029/1024
| {{val|107 170 248 300 370 396}}
| +0.1917
| 1.6065
| 14.32
|-
| 2.3.5.7.11.13.17
| 100/99, 196/195, 136/135, 275/273, 1232/1215, 1547/1536
| {{val|107 170 248 300 370 396}}
| +0.3048
| 1.5129
| 13.49
|}
 
== Scales ==
Since 107edo has a step of 11.214953271 cents, it also allows one to use its [[mos scale]]s as [[circulating temperament]]s{{clarify}}.  
{| class="wikitable mw-collapsible mw-collapsed"
|+ style=white-space:nowrap | Circulating temperaments in 107edo
!Tones
!Tones
!Pattern
!Pattern
Line 270: Line 339:
|22L 63s
|22L 63s
|}
|}
{{Harmonics in equal|107}}
==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|170 -107}}
|{{val|107 170}}
| -1.4471
| 1.4453
| 12.89
|-
|2.3.5
|3125/3072, {{monzo|18 -23 8}}
|{{val|107 170 248}}
| -0.2497
| 2.0685
| 18.44
|-
|2.3.5.7
|2240/2187, 1029/1024, 3125/3072
|{{val|107 170 248 300}}
| +0.1987
| 1.9529
| 17.41
|-
|2.3.5.7.11
|100/99, 1232/1215, 1375/1372, 1029/1024
|{{val|107 170 248 300 370}}
| +0.2622
| 1.7513
| 15.62
|-
|2.3.5.7.11.13
|100/99, 196/195, 275/273, 1232/1215, 1029/1024
|{{val|107 170 248 300 370 396}}
| +0.1917
| 1.6065
| 14.32
|-
|2.3.5.7.11.13.17
|100/99, 196/195, 136/135, 275/273, 1232/1215, 1547/1536
|{{val|107 170 248 300 370 396}}
| +0.3048
| 1.5129
| 13.49
|}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Prime EDO]]
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