110edo: Difference between revisions

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-'''110edo''' is the [[EDO|equal division of the octave]] into 110 parts of 10.9090909091 cents each. It tempers out 15625/15552 and 3486784401/3355443200 in the 5-limit. Using the patent val, it tempers out 1728/1715, 3125/3087, and 3645/3584 in the 7-limit.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Edo]]
+== Theory ==
+The equal temperament [[tempering out|tempers out]] 15625/15552 ([[15625/15552|kleisma]]) and 3486784401/3355443200 in the 5-limit. Using the [[patent val]], it tempers out [[1728/1715]], [[3125/3087]], and 3645/3584 in the 7-limit.
-{{PAGENAME}} has a step size of {{#expr: 1200/110}} cents. It reinforces [[55edo]] with the same 3, but a flat 5 instead of sharp 5 (in patent val), it also gains a new 7, 11 and especially 13, now quite accurate. But if you want the meantone system back you can still use every other note, experiencing the wonders of generic meantone with non-standard 7, or the new 7, or whatever you choose. It's wonderful either way.
+=== Odd harmonics ===
+{{Harmonics in equal|110}}
-[[Category:Stub]]
+=== Subsets and supersets ===
+Since 110 factors into {{factorization|110}}, 110edo has subset edos {{EDOs| 2, 5, 10, 11, 22, and 55 }}.
+ed8, built by taking every third step of 110edo, is a system where primes 3, 5, 7, 11, 17, 23, 29 are mapped exactly as in 110edo.
+== Intervals ==
+{{Interval table}}
+== Instruments ==
+* [[Lumatone mapping for 110edo]]
+{{stub}}