92edo: Difference between revisions

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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).

== ~~Prime intervals~~ ==

== Theory ==

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{{c}} sharp. The alternate fifth 53\92 is a very flat fifth, flatter even than that of [[26edo]] and only 0.102{{c}} sharp of [[1/2-comma meantone]]; the 92bcccd val [[support]]s [[flattone]], while the 92bcccdd val supports [[Meantone_family#Flattertone|flattertone]]. 92edo is the highest in a series of four consecutive edos to temper out the [[quartisma]] (117440512/117406179).

[[~~Category:Equal divisions of the octave~~]]

=== Odd harmonics ===

[[~~Category~~:~~Quartismic~~]]

=== Subsets and supersets ===

Since 92 factors into 2<sup>2</sup> × 23, 92edo has subset edos {{EDOs| 2, 4, 23, and 46 }}.

== Intervals ==

== Instruments ==

A [[Lumatone mapping for 92edo]] is available.

== Music==

; [[Bryan Deister]]

* [https://www.youtube.com/shorts/5XFOALAzLiA ''microtonal improvisation in 92edo''] (2025)

* [https://www.youtube.com/watch?v=qWAinBYHwtE ''92edo waltz''] (2025)

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-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).
+{{Infobox ET}}
+{{ED intro}}
-== Prime intervals ==
+== Theory ==
-{{primes in edo|92|prec=2}}
+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{{c}} sharp. The alternate fifth 53\92 is a very flat fifth, flatter even than that of [[26edo]] and only 0.102{{c}} sharp of [[1/2-comma meantone]]; the 92bcccd val [[support]]s [[flattone]], while the 92bcccdd val supports [[Meantone_family#Flattertone|flattertone]]. 92edo is the highest in a series of four consecutive edos to temper out the [[quartisma]] (117440512/117406179).
-[[Category:Equal divisions of the octave]]
+=== Odd harmonics ===
-[[Category:Quartismic]]
+{{Harmonics in equal|92}}
+=== Subsets and supersets ===
+Since 92 factors into 2<sup>2</sup> × 23, 92edo has subset edos {{EDOs| 2, 4, 23, and 46 }}.
+== Intervals ==
+{{Interval table}}
+== Instruments ==
+A [[Lumatone mapping for 92edo]] is available.
+== Music==
+; [[Bryan Deister]]
+* [https://www.youtube.com/shorts/5XFOALAzLiA ''microtonal improvisation in 92edo''] (2025)
+* [https://www.youtube.com/watch?v=qWAinBYHwtE ''92edo waltz''] (2025)