User:Hkm: Difference between revisions

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-The following equivalent statements form a definition of the opposites "intervalically otonal" and "intervalically utonal":
-- JI interval c between notes A and B, where A is below B, is intervalically otonal
-- A is intervalically utonal to B
-- B is intervalically otonal to A
-- c tends to have higher prime factors in the numerator and more prime factors in the denominator
-If the JI interpretations of a cent value (from which that cent value draws its perceptual properties) tend to be otonal, then the cent value is called "roughly otonal." Even JI ratios that are "intervalically utonal" can be "roughly otonal": 32/25, which is quite close to 7/6 and is perceived as a tempered version of such, is an example. Simpler intervals tend to have more prominent effects and larger capture regions for rough otonality.
-HKM finds that the perceptual root of a chord is the interval which tends to be the most roughly utonal and consonant to the other notes of the chord, and the perceptual tonic of a progression is (somewhat) determinable the same way. The strength of a resolution tends to approximate the strengths of notes of the last chord as perceptual tonics of the chord of the resolution and those chords preceding it.

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