User:Hkm: Difference between revisions
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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 "intervallically 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. | 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 "intervallically 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 (usually) determinable the same way. The strength of a resolution tends to approximate the | 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 (usually) determinable the same way. The strength of a resolution tends to approximate the strength of the root of the last chord as a perceptual tonic of the chord of the resolution and those chords preceding it. | ||
Revision as of 19:48, 26 January 2026
The following equivalence forms a definition of the opposites "intervallically otonal" and "intervallically utonal." If any one of the following statements is true, then they are all true; if any one is false, they are all false.
- JI interval c between notes A and B, where A is below B, is intervallically otonal
- A is intervallically utonal to B
- B is intervallically 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 "intervallically 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 (usually) determinable the same way. The strength of a resolution tends to approximate the strength of the root of the last chord as a perceptual tonic of the chord of the resolution and those chords preceding it.
