368edo: Difference between revisions
Created page with "'''368edo''' is the equal division of the octave into 368 parts of 3.26087 cents each. It tempers out 1220703125/1207959552 (ditonma) and 205891132094649/204800000..." Tags: Mobile edit Mobile web edit |
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==Related regular tempemraments== | ==Related regular tempemraments== | ||
368edo supports the 11-limit [[Ragismic microtemperaments|octoid tempemrament]]. Alternative 368f val supports the 13-limit octoid, 368fff val supports the octopus tempemrament. | 368edo supports the 11-limit [[Ragismic microtemperaments|octoid tempemrament]]. Alternative 368f val supports the 13-limit octoid, and 368fff val supports the octopus tempemrament. | ||
368edo is very nearly the POTE tuning of [[23-limit]] 46&161 tempemrament (''Icositritonic'' tempemrament, named by [[User:Xenllium|Xenllium]]), which is supported by [[46edo]], [[115edo]], [[161edo]], [[207edo]], and the 368ci val. | 368edo is very nearly the POTE tuning of [[23-limit]] 46&161 tempemrament (''Icositritonic'' tempemrament, named by [[User:Xenllium|Xenllium]]), which is supported by [[46edo]], [[115edo]], [[161edo]], [[207edo]], and the 368ci val. | ||
===Icositritonic tempemrament (46 & 161)=== | |||
'''<font style="font-size: 1.2em">7-limit</font>'''<br> | |||
Commas: 6144/6125, 9920232/9765625<br><br> | |||
POTE generator: ~64/63 = 29.3586<br><br> | |||
Map: [<23 37 54 64|, <0 -1 -1 1|]<br><br> | |||
EDOs: 23, 46, 69, 115, 161, 207<br><br> | |||
Badness: 0.1966<br><br> | |||
'''<font style="font-size: 1.2em">11-limit</font>'''<br> | |||
Commas: 441/440, 6144/6125, 35937/35840<br><br> | |||
POTE generator: ~64/63 = 29.3980<br><br> | |||
Map: [<23 37 54 64 79|, <0 -1 -1 1 1|]<br><br> | |||
EDOs: 23, 46, 69, 115, 161, 207<br><br> | |||
Badness: 0.06461<br><br> | |||
'''<font style="font-size: 1.2em">13-limit</font>'''<br> | |||
Commas: 351/350, 441/440, 847/845, 3584/3575<br><br> | |||
POTE generator: ~64/63 = 29.2830<br><br> | |||
Map: [<23 37 54 64 79 84|, <0 -1 -1 1 1 2|]<br><br> | |||
EDOs: 46, 115, 161, 207<br><br> | |||
Badness: 0.04048<br><br> | |||
'''<font style="font-size: 1.2em">17-limit</font>'''<br> | |||
Commas: 351/350, 441/440, 561/560, 847/845, 1089/1088<br><br> | |||
POTE generator: ~64/63 = 29.2800<br><br> | |||
Map: [<23 37 54 64 79 84 94|, <0 -1 -1 1 1 2 0|]<br><br> | |||
EDOs: 46, 115, 161, 207<br><br> | |||
Badness: 0.02468<br><br> | |||
'''<font style="font-size: 1.2em">19-limit</font>'''<br> | |||
Commas: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845<br><br> | |||
POTE generator: ~64/63 = 29.3760<br><br> | |||
Map: [<23 37 54 64 79 84 94 96|, <0 -1 -1 1 1 2 0 3|]<br><br> | |||
EDOs: 46, 115, 161, 207<br><br> | |||
Badness: 0.02158<br><br> | |||
'''<font style="font-size: 1.2em">23-limit</font>'''<br> | |||
Commas: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845<br><br> | |||
POTE generator: ~64/63 = 29.3471<br><br> | |||
Map: [<23 37 54 64 79 84 94 96 104|, <0 -1 -1 1 1 2 0 3 0|]<br><br> | |||
EDOs: 46, 115, 161, 207<br><br> | |||
Badness: 0.01774 | |||
==Related scale== | |||
*[[Icositritonic115]] | |||
*[[Icositritonic161]] | |||
*[[Icositritonic207]] | |||
[[Category:Edo]] | [[Category:Edo]] | ||
Revision as of 23:29, 17 March 2019
368edo is the equal division of the octave into 368 parts of 3.26087 cents each. It tempers out 1220703125/1207959552 (ditonma) and 205891132094649/204800000000000 in the 5-limit; 4375/4374, 16875/16807, and 33756345/33554432 in the 7-limit. Using the patent val, it tempers out 540/539, 1375/1372, and 4000/3993 in the 11-limit; 2205/2197, 4225/4224, and 10648/10647 in the 13-limit.
Related regular tempemraments
368edo supports the 11-limit octoid tempemrament. Alternative 368f val supports the 13-limit octoid, and 368fff val supports the octopus tempemrament.
368edo is very nearly the POTE tuning of 23-limit 46&161 tempemrament (Icositritonic tempemrament, named by Xenllium), which is supported by 46edo, 115edo, 161edo, 207edo, and the 368ci val.
Icositritonic tempemrament (46 & 161)
7-limit
Commas: 6144/6125, 9920232/9765625
POTE generator: ~64/63 = 29.3586
Map: [<23 37 54 64|, <0 -1 -1 1|]
EDOs: 23, 46, 69, 115, 161, 207
Badness: 0.1966
11-limit
Commas: 441/440, 6144/6125, 35937/35840
POTE generator: ~64/63 = 29.3980
Map: [<23 37 54 64 79|, <0 -1 -1 1 1|]
EDOs: 23, 46, 69, 115, 161, 207
Badness: 0.06461
13-limit
Commas: 351/350, 441/440, 847/845, 3584/3575
POTE generator: ~64/63 = 29.2830
Map: [<23 37 54 64 79 84|, <0 -1 -1 1 1 2|]
EDOs: 46, 115, 161, 207
Badness: 0.04048
17-limit
Commas: 351/350, 441/440, 561/560, 847/845, 1089/1088
POTE generator: ~64/63 = 29.2800
Map: [<23 37 54 64 79 84 94|, <0 -1 -1 1 1 2 0|]
EDOs: 46, 115, 161, 207
Badness: 0.02468
19-limit
Commas: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845
POTE generator: ~64/63 = 29.3760
Map: [<23 37 54 64 79 84 94 96|, <0 -1 -1 1 1 2 0 3|]
EDOs: 46, 115, 161, 207
Badness: 0.02158
23-limit
Commas: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845
POTE generator: ~64/63 = 29.3471
Map: [<23 37 54 64 79 84 94 96 104|, <0 -1 -1 1 1 2 0 3 0|]
EDOs: 46, 115, 161, 207
Badness: 0.01774