88edo: Difference between revisions
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|88}} | |||
== Theory == | |||
Using two different approximations to the perfect fifth (one of 51 steps and one of 52 steps), it is compatible with both [[Meantone|meantone temperament]] and the particular variety of [[superpyth]] temperament(s) supported by [[22edo|22 equal temperament]], respectively. The meantone fifth is 0.0384 cents flatter than that of [[Lucy Tuning]] and, thus, audibly indistinguishable from it. It also gives the [[optimal patent val]] for the 11-limit [[Meantone_family|mothra]] and [[Didymus_rank_three_family|euterpe]] temperaments. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|88}} | {{Harmonics in equal|88}} | ||
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[[Category:Meantone]] | [[Category:Meantone]] | ||
[[Category:Mothra]] | [[Category:Mothra]] | ||
[[Category:Dual-fifth]] | |||
Revision as of 22:33, 28 November 2022
| ← 87edo | 88edo | 89edo → |
Theory
Using two different approximations to the perfect fifth (one of 51 steps and one of 52 steps), it is compatible with both meantone temperament and the particular variety of superpyth temperament(s) supported by 22 equal temperament, respectively. The meantone fifth is 0.0384 cents flatter than that of Lucy Tuning and, thus, audibly indistinguishable from it. It also gives the optimal patent val for the 11-limit mothra and euterpe temperaments.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -6.50 | -4.50 | -0.64 | +0.64 | -5.86 | +4.93 | +2.64 | +4.14 | +2.49 | +6.49 | -1.00 |
| Relative (%) | -47.7 | -33.0 | -4.7 | +4.7 | -43.0 | +36.1 | +19.4 | +30.3 | +18.2 | +47.6 | -7.3 | |
| Steps (reduced) |
139 (51) |
204 (28) |
247 (71) |
279 (15) |
304 (40) |
326 (62) |
344 (80) |
360 (8) |
374 (22) |
387 (35) |
398 (46) | |