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| '''368edo''' is the [[EDO|equal division of the octave]] into 368 parts of 3.26087 [[cent]]s 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.
| | {{Infobox ET}} |
| | {{ED intro}} |
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| ==Related regular temperaments==
| | The equal temperament [[tempering out|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. |
| 368edo supports the 11-limit [[Ragismic microtemperaments|octoid temperament]]. Alternative 368f val supports the 13-limit octoid, and 368fff val supports the octopus temperament.
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| 368edo is very nearly the POTE tuning of [[23-limit]] 46&161 temperament (''Icositritonic'' temperament, named by [[User:Xenllium|Xenllium]]), which is supported by [[46edo]], [[115edo]], [[161edo]], [[207edo]], and the 368ci val. | | 368edo [[support]]s the 11-limit [[octoid]] temperament. The alternative 368f [[val]] supports the 13-limit octoid, and 368fff val supports the octopus temperament. |
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| ===Icositritonic temperament (46 & 161)===
| | 368edo is very nearly the POTE tuning of [[23-limit]] [[Porwell temperaments|icositritonic]] temperament ({{nowrap|46 & 161}}, named by [[User:Xenllium|Xenllium]]), which is supported by [[46edo]], [[115edo]], [[161edo]], [[207edo]], and the 368ci val. |
| '''<font style="font-size: 1.2em">7-limit</font>'''<br>
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| Commas: 6144/6125, 9920232/9765625<br><br>
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| POTE generator: ~64/63 = 29.3586<br><br>
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| Map: [<23 37 54 64|, <0 -1 -1 1|]<br><br>
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| EDOs: 23, 46, 69, 115, 161, 207<br><br>
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| Badness: 0.1966<br><br>
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| '''<font style="font-size: 1.2em">11-limit</font>'''<br>
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| Commas: 441/440, 6144/6125, 35937/35840<br><br>
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| POTE generator: ~64/63 = 29.3980<br><br>
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| Map: [<23 37 54 64 79|, <0 -1 -1 1 1|]<br><br>
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| EDOs: 23, 46, 69, 115, 161, 207<br><br>
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| Badness: 0.06461<br><br>
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| '''<font style="font-size: 1.2em">13-limit</font>'''<br>
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| Commas: 351/350, 441/440, 847/845, 3584/3575<br><br>
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| POTE generator: ~64/63 = 29.2830<br><br>
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| Map: [<23 37 54 64 79 84|, <0 -1 -1 1 1 2|]<br><br>
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| EDOs: 46, 115, 161, 207<br><br>
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| Badness: 0.04048<br><br>
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| '''<font style="font-size: 1.2em">17-limit</font>'''<br>
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| Commas: 351/350, 441/440, 561/560, 847/845, 1089/1088<br><br>
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| POTE generator: ~64/63 = 29.2800<br><br>
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| Map: [<23 37 54 64 79 84 94|, <0 -1 -1 1 1 2 0|]<br><br>
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| EDOs: 46, 115, 161, 207<br><br>
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| Badness: 0.02468<br><br>
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| '''<font style="font-size: 1.2em">19-limit</font>'''<br>
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| Commas: 351/350, 441/440, 456/455, 476/475, 513/512, 847/845<br><br>
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| POTE generator: ~64/63 = 29.3760<br><br>
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| Map: [<23 37 54 64 79 84 94 96|, <0 -1 -1 1 1 2 0 3|]<br><br>
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| EDOs: 46, 115, 161, 207<br><br>
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| Badness: 0.02158<br><br>
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| '''<font style="font-size: 1.2em">23-limit</font>'''<br>
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| Commas: 276/275, 351/350, 391/390, 441/440, 456/455, 476/475, 847/845<br><br>
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| POTE generator: ~64/63 = 29.3471<br><br>
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| Map: [<23 37 54 64 79 84 94 96 104|, <0 -1 -1 1 1 2 0 3 0|]<br><br>
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| EDOs: 46, 115, 161, 207<br><br>
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| Badness: 0.01774
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| ==Related scales== | | === Odd harmonics === |
| Icositritonic scales
| | {{Harmonics in equal|368}} |
| *[[Icositritonic69]]
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| *[[Icositritonic115]]
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| *[[Icositritonic161]]
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| *[[Icositritonic207]]
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| [[Category:Equal divisions of the octave]]
| | === Subsets and supersets === |
| | Since 368 factors into {{factorization|368}}, 368edo has subset edos {{EDOs| 2, 4, 8, 16, 23, 46, 92, and 184 }}. |