93edf

From Xenharmonic Wiki
Revision as of 13:59, 24 March 2025 by FloraC (talk | contribs) (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...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
← 92edf 93edf 94edf →
Prime factorization 3 × 31
Step size 7.5479 ¢ 
Octave 159\93edf (1200.12 ¢) (→ 53\31edf)
Twelfth 252\93edf (1902.07 ¢) (→ 84\31edf)
Consistency limit 18
Distinct consistency limit 18

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.

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

Approximation of harmonics in 93edf
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)
Approximation of harmonics in 93edf (continued)
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.