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'''[[Ed11|Division of the 11th harmonic]] into 42 equal parts''' ( | {{Infobox ET}} | ||
'''[[Ed11|Division of the 11th harmonic]] into 42 equal parts''' (42ED11) is related to [[12edo|12 EDO]], but with the 11/1 rather than the 2/1 being just. The octave is about 13.9092 cents compressed and the step size is about 98.8409 cents. It is consistent to the 11-[[integer-limit]], but not to the 12-integer-limit. In comparison, 12EDO is only consistent up to the 10-integer-limit. | |||
{| class="wikitable" | {| class="wikitable" | ||
| Line 15: | Line 16: | ||
| | 1 | | | 1 | ||
| | 98.8409 | | | 98.8409 | ||
| | | | | 18/17 | ||
| | | | | | ||
|- | |- | ||
| Line 25: | Line 26: | ||
| | 3 | | | 3 | ||
| | 296.5227 | | | 296.5227 | ||
| | | | | 19/16 | ||
| | | | | | ||
|- | |- | ||
| Line 40: | Line 41: | ||
| | 6 | | | 6 | ||
| | 593.0454 | | | 593.0454 | ||
| | | | | 45/32 | ||
| | | | | | ||
|- | |- | ||
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| | 8 | | | 8 | ||
| | 790.7272 | | | 790.7272 | ||
| | | | | 30/19 | ||
| | | | | | ||
|- | |- | ||
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| | 10 | | | 10 | ||
| | 988.4090 | | | 988.4090 | ||
| | | | | 16/9 | ||
| | | | | | ||
|- | |- | ||
| Line 85: | Line 86: | ||
| | 15 | | | 15 | ||
| | 1482.6136 | | | 1482.6136 | ||
| | | | | 33/14 | ||
| | | | | | ||
|- | |- | ||
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| | 27 | | | 27 | ||
| | 2668.7044 | | | 2668.7044 | ||
| | | | | 14/3 | ||
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==See also== | == Regular temperaments == | ||
* [[12edo|12EDO]] | {{See also| Quintaleap family }} | ||
* [[19ed3| | |||
* [[28ed5|28ED5]] | 42ED11 can also be thought of as a [[generator]] of the 11-limit temperament which tempers out 100/99, 225/224, and 85184/84035, which is a cluster temperament with 12 clusters of notes in an octave (''[[Quintaleap family #Quintapole|quintapole]]'' temperament, 12&85). Alternative 12&97 temperament can also be used, which tempers out 100/99, 245/242, and 458752/455625 in the 11-limit. | ||
* [[31ed6|31ED6]] | |||
* [[34ed7|34ED7]] | == See also == | ||
* [[40ed10|40ED10]] | * [[12edo|12EDO]] - relative EDO | ||
* [[19ed3|19ED3]] - relative EDT | |||
* [[28ed5|28ED5]] - relative ED5 | |||
* [[31ed6|31ED6]] - relative ED6 | |||
* [[34ed7|34ED7]] - relative ED7 | |||
* [[40ed10|40ED10]] - relative ED10 | |||
{{todo|expand}} | |||
Latest revision as of 19:22, 1 August 2025
| ← 41ed11 | 42ed11 | 43ed11 → |
Division of the 11th harmonic into 42 equal parts (42ED11) is related to 12 EDO, but with the 11/1 rather than the 2/1 being just. The octave is about 13.9092 cents compressed and the step size is about 98.8409 cents. It is consistent to the 11-integer-limit, but not to the 12-integer-limit. In comparison, 12EDO is only consistent up to the 10-integer-limit.
| degree | cents value | corresponding JI intervals |
comments |
|---|---|---|---|
| 0 | 0.0000 | exact 1/1 | |
| 1 | 98.8409 | 18/17 | |
| 2 | 197.6818 | ||
| 3 | 296.5227 | 19/16 | |
| 4 | 395.3636 | ||
| 5 | 494.2045 | 4/3 | |
| 6 | 593.0454 | 45/32 | |
| 7 | 691.8863 | ||
| 8 | 790.7272 | 30/19 | |
| 9 | 889.5681 | ||
| 10 | 988.4090 | 16/9 | |
| 11 | 1087.2499 | 15/8 | |
| 12 | 1186.0908 | ||
| 13 | 1284.9317 | 21/10 | |
| 14 | 1383.7726 | ||
| 15 | 1482.6136 | 33/14 | |
| 16 | 1581.4545 | 5/2 | |
| 17 | 1680.2954 | ||
| 18 | 1779.1363 | ||
| 19 | 1877.9772 | ||
| 20 | 1976.8181 | 22/7 | |
| 21 | 2075.6590 | ||
| 22 | 2174.4999 | 7/2 | |
| 23 | 2273.3408 | ||
| 24 | 2372.1817 | ||
| 25 | 2471.0226 | ||
| 26 | 2569.8635 | 22/5 | |
| 27 | 2668.7044 | 14/3 | |
| 28 | 2767.5453 | ||
| 29 | 2866.3862 | 110/21 | |
| 30 | 2965.2271 | ||
| 31 | 3064.0680 | ||
| 32 | 3162.9089 | ||
| 33 | 3261.7498 | ||
| 34 | 3360.5907 | ||
| 35 | 3459.4316 | ||
| 36 | 3558.2725 | ||
| 37 | 3657.1134 | 33/4 | |
| 38 | 3755.9543 | ||
| 39 | 3854.7952 | ||
| 40 | 3953.6361 | ||
| 41 | 4052.4770 | ||
| 42 | 4151.3179 | exact 11/1 | paramajor fourth plus three octaves |
Regular temperaments
42ED11 can also be thought of as a generator of the 11-limit temperament which tempers out 100/99, 225/224, and 85184/84035, which is a cluster temperament with 12 clusters of notes in an octave (quintapole temperament, 12&85). Alternative 12&97 temperament can also be used, which tempers out 100/99, 245/242, and 458752/455625 in the 11-limit.