112edo: Difference between revisions

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== Theory ==

112edo has two great perfect ~~fifths~~, the lower of which approximates ~~1/4~~-comma meantone (just a tad lower), and the upper of ~~which- the~~ [[patent fifth]]~~- is~~ identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/~~27|28:~~27]] while -8 fifths gives a near-just [[39/32~~|32:39~~]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17~~|17:21~~]].

112edo has two great [[3/2|perfect fifth]]s, the lower of which approximates [[quarter-comma meantone]] (just a tad lower), and the upper of which—the [[patent fifth]]—is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27]] while −8 fifths gives a near-just [[39/32]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17]].

One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.

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=== Odd harmonics ===

=== Subsets and supersets ===

Since 112 factors into {{factorization|112}}, 112edo has subset edos {{EDOs| 2, 4, 7, 8, 14, 16, 28, and 56 }}. [[224edo]], which doubles it, is a strong 13-limit system.

== Intervals ==

== Music ==

; [[Cam Taylor]]

* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv ''Circulating 2.3.7.11.13 Floaty Piano Improv'']

* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv Circulating 2.3.7.11.13 Floaty Piano Improv] by [[Cam Taylor]]

== See also ==

[[Skip fretting system 112 9 11]]

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

[[Category:Listen]]

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 {{Infobox ET}}
-{{EDO intro|112}}
+{{ED intro}}
 == Theory ==
-edo has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which- the [[patent fifth]]- is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27|28:27]] while -8 fifths gives a near-just [[39/32|32:39]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17|17:21]].
+edo has two great [[3/2|perfect fifth]]s, the lower of which approximates [[quarter-comma meantone]] (just a tad lower), and the upper of which—the [[patent fifth]]—is identical to the perfect fifth of [[56edo]], a great inverse gentle fifth where +5 fifths gives a near-just [[28/27]] while −8 fifths gives a near-just [[39/32]] (identical to 2 degrees of [[7edo]]) and +9 fifths gives a close approximation to [[21/17]].
 One can form a 17-tone circle by taking 15 large fifths and 2 small fifths, as above, which gives some nice interval shadings a wee bit different from [[17edo]], but sharing a similar structure.
@@ Line 8: / Line 9: @@
 === Odd harmonics ===
 {{Harmonics in equal|112|intervals=odd}}
+=== Subsets and supersets ===
+Since 112 factors into {{factorization|112}}, 112edo has subset edos {{EDOs| 2, 4, 7, 8, 14, 16, 28, and 56 }}. [[224edo]], which doubles it, is a strong 13-limit system.
+== Intervals ==
+{{Interval table}}
 == Music ==
+; [[Cam Taylor]]
+* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv ''Circulating 2.3.7.11.13 Floaty Piano Improv'']
-* [https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv Circulating 2.3.7.11.13 Floaty Piano Improv] by [[Cam Taylor]]
+== See also ==
+[[Skip fretting system 112 9 11]]
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Listen]]