117edo: Difference between revisions

Line 1:

'''117edo''' is the [[EDO|equal division of the octave]] into 117 parts of 10.2564102564 ~~cents~~ each.

'''117edo''' is the [[EDO|equal division of the octave]] into 117 parts of 10.2564102564 [[cent]]s each.

It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 11-limit: <117 185 272 328 405| (patent val), <117 186 272 329 405| (117bd), <117 185 271 328 404| (117ce), and <117 185 272 329 405| (117d).

Using the patent val, it tempers out the [[syntonic comma]], 81/80 and |69 -1 -29> in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, supporting the 7-limit [[~~Meantone family|mohajira temperament~~]]; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the [[Didymus rank three family|terpsichore rank-3 temperament]]; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit.

Using the patent val, it tempers out the [[syntonic comma]] (81/80) and |69 -1 -29> in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, supporting the 7-limit [[Mohajira]] temperament; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the [[Didymus rank three family|terpsichore rank-3 temperament]]; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit.

Using the 117bd val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and 17179869184/16142520375 in the 5-limit; 245/243, 3136/3125, and 51200/50421 in the 7-limit; 176/175, 1232/1215, 1375/1372, and 2560/2541 in the 11-limit; 169/168, 364/363, 640/637, 832/825, and 3200/3159 in the 13-limit.

Line 9:

Using the 117ce val, it tempers out the [[Magic family|small diesis]], 3125/3072 and 282429536481/268435456000 in the 5-limit; 2401/2400, 3645/3584, and 4375/4374 in the 7-limit; 243/242, 441/440, and 1815/1792 in the 11-limit; 105/104, 275/273, 1287/1280, and 2025/2002 in the 13-limit.

Using the 117d val, it tempers out 126/125, 225/224, and 14495514624/13841287201 in the 7-limit; 99/98, 176/175, 441/440, and 12582912/12400927 in the 11-limit; 144/143, 640/637, 648/637, 1001/1000, and 43940/43923 in the 13-limit, supporting the 13-limit [[~~Meantone family|grosstone temperament~~]].

Using the 117d val, it tempers out 126/125, 225/224, and 14495514624/13841287201 in the 7-limit; 99/98, 176/175, 441/440, and 12582912/12400927 in the 11-limit; 144/143, 640/637, 648/637, 1001/1000, and 43940/43923 in the 13-limit, supporting the 13-limit [[Grosstone]] temperament.

[[Category:Edo]]

@@ Line 1: / Line 1: @@
-'''117edo''' is the [[EDO|equal division of the octave]] into 117 parts of 10.2564102564 cents each.
+'''117edo''' is the [[EDO|equal division of the octave]] into 117 parts of 10.2564102564 [[cent]]s each.
 It is inconsistent to the 5-limit and higher limit, with four mappings possible for the 11-limit: &lt;117 185 272 328 405| (patent val), &lt;117 186 272 329 405| (117bd), &lt;117 185 271 328 404| (117ce), and &lt;117 185 272 329 405| (117d).
-Using the patent val, it tempers out the [[syntonic comma]], 81/80 and |69 -1 -29&gt; in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, supporting the 7-limit [[Meantone family|mohajira temperament]]; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the [[Didymus rank three family|terpsichore rank-3 temperament]]; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit.
+Using the patent val, it tempers out the [[syntonic comma]] (81/80) and |69 -1 -29&gt; in the 5-limit; 6144/6125, 31104/30625, and 403368/390625 in the 7-limit, supporting the 7-limit [[Mohajira]] temperament; 540/539, 1344/1331, 1617/1600, and 3168/3125 in the 11-limit, supporting the [[Didymus rank three family|terpsichore rank-3 temperament]]; 144/143, 196/195, 364/363, 729/715, and 3146/3125 in the 13-limit.
 Using the 117bd val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and 17179869184/16142520375 in the 5-limit; 245/243, 3136/3125, and 51200/50421 in the 7-limit; 176/175, 1232/1215, 1375/1372, and 2560/2541 in the 11-limit; 169/168, 364/363, 640/637, 832/825, and 3200/3159 in the 13-limit.
@@ Line 9: / Line 9: @@
 Using the 117ce val, it tempers out the [[Magic family|small diesis]], 3125/3072 and 282429536481/268435456000 in the 5-limit; 2401/2400, 3645/3584, and 4375/4374 in the 7-limit; 243/242, 441/440, and 1815/1792 in the 11-limit; 105/104, 275/273, 1287/1280, and 2025/2002 in the 13-limit.
-Using the 117d val, it tempers out 126/125, 225/224, and 14495514624/13841287201 in the 7-limit; 99/98, 176/175, 441/440, and 12582912/12400927 in the 11-limit; 144/143, 640/637, 648/637, 1001/1000, and 43940/43923 in the 13-limit, supporting the 13-limit [[Meantone family|grosstone temperament]].
+Using the 117d val, it tempers out 126/125, 225/224, and 14495514624/13841287201 in the 7-limit; 99/98, 176/175, 441/440, and 12582912/12400927 in the 11-limit; 144/143, 640/637, 648/637, 1001/1000, and 43940/43923 in the 13-limit, supporting the 13-limit [[Grosstone]] temperament.
 [[Category:Edo]]