88edo: Difference between revisions
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In music, '''88 equal temperament''' is the scale derived by dividing the octave into 88 equally large steps, 13.6363 [[cent|cent]]s in size. 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|superpyth]] temperament(s) supported by [[22edo|22 equal temperament]], respectively. The meantone fifth is 0.0384 cents flatter than that of [[Lucy_Tuning|Lucy Tuning]] and, thus, audibly indistinguishable from it. It also gives the [[Optimal_patent_val|optimal patent val]] for the 11-limit [[Meantone_family|mothra]] and [[Didymus_rank_three_family|euterpe]] temperaments. | In music, '''88 equal temperament''' is the scale derived by dividing the octave into 88 equally large steps, 13.6363 [[cent|cent]]s in size. 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|superpyth]] temperament(s) supported by [[22edo|22 equal temperament]], respectively. The meantone fifth is 0.0384 cents flatter than that of [[Lucy_Tuning|Lucy Tuning]] and, thus, audibly indistinguishable from it. It also gives the [[Optimal_patent_val|optimal patent val]] for the 11-limit [[Meantone_family|mothra]] and [[Didymus_rank_three_family|euterpe]] temperaments. | ||
{{harmonics in equal|88}} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category:Euterpe]] | [[Category:Euterpe]] | ||
Revision as of 23:05, 20 January 2022
In music, 88 equal temperament is the scale derived by dividing the octave into 88 equally large steps, 13.6363 cents in size. 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.
| 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) | |