368edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
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 | 368edo [[support]]s the 11-limit [[octoid]] temperament. The alternative 368f [[val]] supports the 13-limit octoid, and 368fff val supports the octopus temperament. | ||
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. | |||
== | === Odd harmonics === | ||
{{Harmonics in equal|368}} | |||
=== Subsets and supersets === | |||
Since 368 factors into {{factorization|368}}, 368edo has subset edos {{EDOs| 2, 4, 8, 16, 23, 46, 92, and 184 }}. | |||
Latest revision as of 22:35, 20 February 2025
| ← 367edo | 368edo | 369edo → |
368 equal divisions of the octave (abbreviated 368edo or 368ed2), also called 368-tone equal temperament (368tet) or 368 equal temperament (368et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 368 equal parts of about 3.26 ¢ each. Each step represents a frequency ratio of 21/368, or the 368th root of 2.
The equal temperament 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 octoid temperament. The alternative 368f val supports the 13-limit octoid, and 368fff val supports the octopus temperament.
368edo is very nearly the POTE tuning of 23-limit icositritonic temperament (46 & 161, named by Xenllium), which is supported by 46edo, 115edo, 161edo, 207edo, and the 368ci val.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.87 | -1.53 | -0.35 | +1.52 | -0.23 | +0.78 | +0.86 | -0.61 | -0.77 | -1.22 | +1.07 |
| Relative (%) | -26.6 | -47.0 | -10.7 | +46.8 | -7.1 | +23.8 | +26.4 | -18.6 | -23.7 | -37.3 | +32.9 | |
| Steps (reduced) |
583 (215) |
854 (118) |
1033 (297) |
1167 (63) |
1273 (169) |
1362 (258) |
1438 (334) |
1504 (32) |
1563 (91) |
1616 (144) |
1665 (193) | |
Subsets and supersets
Since 368 factors into 24 × 23, 368edo has subset edos 2, 4, 8, 16, 23, 46, 92, and 184.