92edo: Difference between revisions

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Rework, expand, -redundant categories ("category: quartismic" should only be added if it's a great tuning for it)
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{{Infobox ET}}
{{Infobox ET}}
The 92 divisions of '''92edo''' measure 13.0435 cents each. 92 is [[contorted]] through the 17-limit, with the same tuning and commas as [[46edo]], and hence attracts little interest, the [[patent fifth]] (54\92) is about 2.4 cents sharp. The alternate 53\92 generator is a very flat flattone fifth, flatter even than [[26edo]]. 92edo is the highest in a series of four consecutive EDOs to temper out the [[quartisma]] (117440512/117406179).
{{EDO intro|92}} The equal temperament is [[contorted]] through the 17-limit, with the same tuning and [[comma]]s as [[46edo]], and hence attracts little interest. That said, the approximation to the [[19/1|19th harmonic]] is much improved. Like 46, the [[patent fifth]] (54\92) is about 2.4 cents sharp. The alternate fifth 53\92 is a very flat fifth, flatter even than [[26edo]], and the 92bcccd val [[support]]s [[flattone]]. 92edo is the highest in a series of four consecutive edos to temper out the [[quartisma]] (117440512/117406179).


== Prime intervals ==
=== Odd harmonics ===
{{primes in edo|92}}
{{Harmonics in equal|92}}
 
[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
[[Category:Quartismic]]

Revision as of 13:53, 2 October 2023

← 91edo 92edo 93edo →
Prime factorization 22 × 23
Step size 13.0435 ¢ 
Fifth 54\92 (704.348 ¢) (→ 27\46)
Semitones (A1:m2) 10:6 (130.4 ¢ : 78.26 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro The equal temperament is contorted through the 17-limit, with the same tuning and commas as 46edo, and hence attracts little interest. That said, the approximation to the 19th harmonic is much improved. Like 46, the patent fifth (54\92) is about 2.4 cents sharp. The alternate fifth 53\92 is a very flat fifth, flatter even than 26edo, and the 92bcccd val supports flattone. 92edo is the highest in a series of four consecutive edos to temper out the quartisma (117440512/117406179).

Odd harmonics

Approximation of odd harmonics in 92edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +2.39 +4.99 -3.61 +4.79 -3.49 -5.75 -5.66 -0.61 +2.49 -1.22 -2.19
Relative (%) +18.3 +38.3 -27.7 +36.7 -26.8 -44.0 -43.4 -4.7 +19.1 -9.3 -16.8
Steps
(reduced)
146
(54)
214
(30)
258
(74)
292
(16)
318
(42)
340
(64)
359
(83)
376
(8)
391
(23)
404
(36)
416
(48)