206edo: Difference between revisions

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'''206edo''' is the [[EDO|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 19-limit: <206 327 478 578 713 762 842 875| (patent val), <206 326 478 578 713 762 842 875| (206b), <206 326 478 578 712 762 842 875| (206be), and <206 327 479 579 713 763 842 875| (206cdf). Using the patent val, it tempers out the [[Sycamore family|sycamore comma]], 48828125/47775744 and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; 385/384, 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; 352/351, 1575/1573, 1625/1617, 2197/2178, and 4096/4095 in the 13-limit; 289/288, 375/374, 442/441, 715/714, and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit. Using the 206b val, it tempers out the [[Sensipent family|sensipent comma]], 78732/78125 and the [[Ampersand|Ampersand's comma]], 34171875/33554432 in the 5-limit; 225/224, 1029/1024, and 177147/175000 in the 7-limit; 4375/4356, 9801/9800, 15309/15125, and 73728/73205 in the 11-limit; 351/350, 364/363, 625/624, 1701/1690, and 31213/30976 in the 13-limit; 273/272, 833/832, 850/847, 1089/1088, 1225/1224, and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and 1445/1444 in the 19-limit. Using the 206be val, it tempers out 243/242, 385/384, 441/440, and 43923/43750 in the 11-limit; 351/350, 625/624, 847/845, 1001/1000, and 1573/1568 in the 13-limit; 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit; 363/361 and 729/722 in the 19-limit. Using the 206cdf val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and |4 -45 29> in the 5-limit; 4375/4374, 110592/109375, and 235298/234375 in the 7-limit; 176/175, 896/891, and 1331/1323 in the 11-limit; 640/637, 847/845, 1001/1000, and 2197/2187 in the 13-limit; 136/135, 256/255, 561/560, and 1275/1274 in the 17-limit; 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit.

'''206edo''' is the [[EDO|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19.

~~=Scales=~~

It is in[[consistent]] to the 5-limit and higher limit, with four mappings possible for the 19-limit:

[[~~skwares8|skwares8~~]]

* {{val| 206 327 478 578 713 762 842 875 }} ([[patent val]])

* {{val| 206 326 478 578 713 762 842 875 }} (206b)

* {{val| 206 326 478 578 712 762 842 875 }} (206be)

* {{val| 206 327 479 579 713 763 842 875 }} (206cdf)

[[~~skwares11|skwares11~~]]

Using the patent val, it tempers out

* 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit

* 4000/3969, 84035/82944, and 458752/455625 in the 7-limit

* [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit

* [[352/351]], 1575/1573, 1625/1617, 2197/2178, and 4096/4095 in the 13-limit

* 289/288, 375/374, 442/441, 715/714, and 2000/1989 in the 17-limit

* 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit

[[~~skwares14|skwares14~~]]

Using the 206b val, it tempers out

* 78732/78125 ([[sensipent]] comma) and 34171875/33554432 ([[ampersand]]) in the 5-limit

* 225/224, 1029/1024, and 177147/175000 in the 7-limit

* 4375/4356, 9801/9800, 15309/15125, and 73728/73205 in the 11-limit

* 351/350, 364/363, 625/624, 1701/1690, and 31213/30976 in the 13-limit

* 273/272, 833/832, 850/847, 1089/1088, 1225/1224, and 1458/1445 in the 17-limit

* 210/209, 495/494, 729/722, 1235/1232, and 1445/1444 in the 19-limit

Using the 206be val, it tempers out

* [[243/242]], 385/384, 441/440, and 43923/43750 in the 11-limit

* [[351/350]] (ratwolfsma), 625/624, 847/845, 1001/1000, and 1573/1568 in the 13-limit

* 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit

* 363/361 and 729/722 in the 19-limit

Using the 206cdf val, it tempers out

* 2048/2025 ([[diaschisma]]), and {{Monzo| 4 -45 29 }}; in the 5-limit

* 4375/4374, 110592/109375, and 235298/234375 in the 7-limit

* [[176/175]], 896/891, and 1331/1323 in the 11-limit

* 640/637, 847/845, 1001/1000, and 2197/2187 in the 13-limit

* 136/135, 256/255, 561/560, and 1275/1274 in the 17-limit

* 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit

== Scales ==

* [[skwares8]]

* [[skwares11]]

* [[skwares14]]

[[Category:Theory]]

[[Category:Edo]]

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-'''206edo''' is the [[EDO|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19. It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 19-limit: &lt;206 327 478 578 713 762 842 875| (patent val), &lt;206 326 478 578 713 762 842 875| (206b), &lt;206 326 478 578 712 762 842 875| (206be), and &lt;206 327 479 579 713 763 842 875| (206cdf). Using the patent val, it tempers out the [[Sycamore family|sycamore comma]], 48828125/47775744 and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; 385/384, 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; 352/351, 1575/1573, 1625/1617, 2197/2178, and 4096/4095 in the 13-limit; 289/288, 375/374, 442/441, 715/714, and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit. Using the 206b val, it tempers out the [[Sensipent family|sensipent comma]], 78732/78125 and the [[Ampersand|Ampersand's comma]], 34171875/33554432 in the 5-limit; 225/224, 1029/1024, and 177147/175000 in the 7-limit; 4375/4356, 9801/9800, 15309/15125, and 73728/73205 in the 11-limit; 351/350, 364/363, 625/624, 1701/1690, and 31213/30976 in the 13-limit; 273/272, 833/832, 850/847, 1089/1088, 1225/1224, and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and 1445/1444 in the 19-limit. Using the 206be val, it tempers out 243/242, 385/384, 441/440, and 43923/43750 in the 11-limit; 351/350, 625/624, 847/845, 1001/1000, and 1573/1568 in the 13-limit; 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit; 363/361 and 729/722 in the 19-limit. Using the 206cdf val, it tempers out the [[Diaschismic family|diaschisma]], 2048/2025 and |4 -45 29&gt; in the 5-limit; 4375/4374, 110592/109375, and 235298/234375 in the 7-limit; 176/175, 896/891, and 1331/1323 in the 11-limit; 640/637, 847/845, 1001/1000, and 2197/2187 in the 13-limit; 136/135, 256/255, 561/560, and 1275/1274 in the 17-limit; 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit.
+'''206edo''' is the [[EDO|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19.
-=Scales=
+It is in[[consistent]] to the 5-limit and higher limit, with four mappings possible for the 19-limit:
-[[skwares8|skwares8]]
+* {{val| 206 327 478 578 713 762 842 875 }} ([[patent val]])
+* {{val| 206 326 478 578 713 762 842 875 }} (206b)
+* {{val| 206 326 478 578 712 762 842 875 }} (206be)
+* {{val| 206 327 479 579 713 763 842 875 }} (206cdf)
-[[skwares11|skwares11]]
+Using the patent val, it tempers out
+* 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit
+* 4000/3969, 84035/82944, and 458752/455625 in the 7-limit
+* [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit
+* [[352/351]], 1575/1573, 1625/1617, 2197/2178, and 4096/4095 in the 13-limit
+* 289/288, 375/374, 442/441, 715/714, and 2000/1989 in the 17-limit
+* 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit
-[[skwares14|skwares14]]
+Using the 206b val, it tempers out
+* 78732/78125 ([[sensipent]] comma) and 34171875/33554432 ([[ampersand]]) in the 5-limit
+* 225/224, 1029/1024, and 177147/175000 in the 7-limit
+* 4375/4356, 9801/9800, 15309/15125, and 73728/73205 in the 11-limit
+* 351/350, 364/363, 625/624, 1701/1690, and 31213/30976 in the 13-limit
+* 273/272, 833/832, 850/847, 1089/1088, 1225/1224, and 1458/1445 in the 17-limit
+* 210/209, 495/494, 729/722, 1235/1232, and 1445/1444 in the 19-limit
+Using the 206be val, it tempers out
+* [[243/242]], 385/384, 441/440, and 43923/43750 in the 11-limit
+* [[351/350]] (ratwolfsma), 625/624, 847/845, 1001/1000, and 1573/1568 in the 13-limit
+* 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit
+* 363/361 and 729/722 in the 19-limit
+Using the 206cdf val, it tempers out
+* 2048/2025 ([[diaschisma]]),  and {{Monzo| 4 -45 29 }}; in the 5-limit
+* 4375/4374, 110592/109375, and 235298/234375 in the 7-limit
+* [[176/175]], 896/891, and 1331/1323 in the 11-limit
+* 640/637, 847/845, 1001/1000, and 2197/2187 in the 13-limit
+* 136/135, 256/255, 561/560, and 1275/1274 in the 17-limit
+* 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit
+== Scales ==
+* [[skwares8]]
+* [[skwares11]]
+* [[skwares14]]
+[[Category:Theory]]
 [[Category:Edo]]