93edf: Difference between revisions
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Created page with "{{Infobox ET}} {{ED intro}} 93edf is closely related to 159edo, but with the perfect fifth instead of the octave tuned just. Like 159edo, 92edf is consi..." |
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== Theory == | |||
93edf is closely related to [[159edo]], but with the [[3/2|perfect fifth]] instead of the [[2/1|octave]] tuned just. Like 159edo, 92edf is [[consistent]] to the [[integer limit|18-integer-limit]]. | 93edf is closely related to [[159edo]], but with the [[3/2|perfect fifth]] instead of the [[2/1|octave]] tuned just. Like 159edo, 92edf is [[consistent]] to the [[integer limit|18-integer-limit]]. | ||
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 93 factors into primes as {{nowrap| 3 × 31 }}, 93edf contains [[3edf]] and [[31edf]] as subset edfs. | Since 93 factors into primes as {{nowrap| 3 × 31 }}, 93edf contains [[3edf]] and [[31edf]] as subset edfs. | ||
== See also == | |||
* [[159edo]] – relative edo | |||
* [[252edt]] – relative edt | |||
Revision as of 12:27, 9 April 2025
| ← 92edf | 93edf | 94edf → |
93 equal divisions of the perfect fifth (abbreviated 93edf or 93ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 93 equal parts of about 7.55 ¢ each. Each step represents a frequency ratio of (3/2)1/93, or the 93rd root of 3/2.
Theory
93edf is closely related to 159edo, but with the perfect fifth instead of the octave tuned just. Like 159edo, 92edf is consistent to the 18-integer-limit.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.12 | +0.12 | +0.23 | -1.14 | +0.23 | -2.46 | +0.35 | +0.23 | -1.02 | +0.03 | +0.35 |
| Relative (%) | +1.5 | +1.5 | +3.1 | -15.1 | +3.1 | -32.6 | +4.6 | +3.1 | -13.5 | +0.4 | +4.6 | |
| Steps (reduced) |
159 (66) |
252 (66) |
318 (39) |
369 (90) |
411 (39) |
446 (74) |
477 (12) |
504 (39) |
528 (63) |
550 (85) |
570 (12) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.36 | -2.34 | -1.02 | +0.47 | +1.18 | +0.35 | -2.68 | -0.90 | -2.34 | +0.15 | -1.33 | +0.47 |
| Relative (%) | -31.3 | -31.1 | -13.5 | +6.2 | +15.7 | +4.6 | -35.5 | -12.0 | -31.1 | +1.9 | -17.6 | +6.2 | |
| Steps (reduced) |
588 (30) |
605 (47) |
621 (63) |
636 (78) |
650 (92) |
663 (12) |
675 (24) |
687 (36) |
698 (47) |
709 (58) |
719 (68) |
729 (78) | |
Subsets and supersets
Since 93 factors into primes as 3 × 31, 93edf contains 3edf and 31edf as subset edfs.