112edo: Difference between revisions

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

~~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|17edo~~]]~~, but sharing a similar structure~~.

== Theory ==

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]].

~~=Music in 112EDO=~~

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.

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

=== Odd harmonics ===

~~[[Category:31edo]]~~

[[~~Category:what_is~~]]

[[Category:~~wiki~~]]

=== 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'']

== See also ==

[[Skip fretting system 112 9 11]]

[[Category:Listen]]

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-EDO has two great perfect fifths, the lower of which approximates 1/4-comma meantone (just a tad lower), and the upper of which is identical to the perfect fifth of [[56edo|56edo]], a great inverse gentle fifth where +5 fifths gives a near-just 27:28 while -8 fifths gives a near-just 32:39 (identical to 2 degrees of [[7edo|7edo]]) and +9 fifths gives a close approximation to 17:21.
+{{Infobox ET}}
+{{ED intro}}
-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|17edo]], but sharing a similar structure.
+== Theory ==
+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]].
-=Music in 112EDO=
+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.
-[https://soundcloud.com/camtaylor-1/17_112edo-circulating-2371113-floaty-piano-improv Circulating 2.3.7.11.13 Floaty Piano Improv] by Cam Taylor
+=== Odd harmonics ===
-[[Category:31edo]]
+{{Harmonics in equal|112|intervals=odd}}
-[[Category:what_is]]
-[[Category:wiki]]
+=== 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'']
+== See also ==
+[[Skip fretting system 112 9 11]]
+[[Category:Listen]]