User:TromboneBoi9/Approaches to weird EDOs: Difference between revisions

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+===A note on the 7/4===
+My favorite kinds of xenharmonic intervals are those that involve the factor of seven somehow, usually approximations of [[7/4]], [[7/6]], or [[8/7]].
+edo's approximation of the harmonic seventh 7/4 is 10\13 or 923&cent;, which, at a whopping '''45 cents flat''', is even more inaccurate than its approximation of [[3/2]]. Despite this, in practical use, 10\13 (to my ears, at least) appears to be a ''usable'' 7/4, at least when used sparingly among other passages that do 13edo "correctly".
+My hypotheses as to why:
+* I personally have more experience with [[24edo]] which has a pretty flat 7/4.
+* My ears might be confusing it for [[12/7]]: 10\13 is much closer to 12/7, which is roughly in the same quartertonal interval region (supermajor sixth/subminor seventh) and is also harmonically related to 7/4 (its [[3/1|tritave]] inversion).
+* My ears might be confusing it for [[55/32]]: The context in which I've used 10\13 the most often is in 0,4,6,10\13 or its subsets. In that chord, there are two 4\13 major thirds (approximating [[5/4]] well) separated by a 6\13 (approximating [[11/8]] well), so it could be said that 10\13 is acting as a 55/32 here. A just intonation chord 1/1, 5/4, 11/8 can reasonably be topped with either 7/4 ''or'' 55/32, and the two are only a [[56/55]] apart.
 ==8edo==