Otonality and utonality: Difference between revisions
Dummy index (talk | contribs) →Scales: fix |
+ an actual intro, more to come |
||
| Line 1: | Line 1: | ||
{{ | {{Interwiki | ||
| en = Otonality and utonality | |||
| de = | | de = | ||
| es = | | es = | ||
| ja = OtonalityとUtonality | | ja = OtonalityとUtonality | ||
}} | }} | ||
{{Wikipedia|Otonality and Utonality}} | {{Wikipedia|Otonality and Utonality}} | ||
'''Otonality''' and '''utonality''' are properties of [[chord]]s that describe if it is simpler to treat them as part of the [[harmonic series]] or [[subharmonic series]]. | |||
== Introduction == | == Introduction == | ||
Given a JI chord, how can we decide whether it is otonal or utonal? This might seem obvious at first, but it's actually surprisingly subtle. For example, the chord 10:12:15 is a 5-limit utonality (1/6:1/5:1/4), but it's also a 15-limit otonality, consisting of the 10th, 12th, and 15th harmonics of a fundamental. One reasonable definition is to say that a chord is otonal if its largest odd number is smaller than the largest odd number of its inverse, and utonal if the inverse has a smaller largest-odd-number. In other words, if inverting a chord increases its odd limit, it's otonal, and if it reduces it, it's utonal. That way 4:5:6 is otonal because it's simpler than its inverse, 10:12:15, and 10:12:15 is utonal because it is more simply expressed as 1/6:1/5:1/4. Because we're using odd limit and not integer limit, this definition is independent of the chord's voicing. Thus 4:5:6 is otonal even if voiced 3:4:5 or 2:3:5. | Given a JI chord, how can we decide whether it is otonal or utonal? This might seem obvious at first, but it's actually surprisingly subtle. For example, the chord 10:12:15 is a 5-limit utonality (1/6:1/5:1/4), but it's also a 15-limit otonality, consisting of the 10th, 12th, and 15th harmonics of a fundamental. One reasonable definition is to say that a chord is otonal if its largest odd number is smaller than the largest odd number of its inverse, and utonal if the inverse has a smaller largest-odd-number. In other words, if inverting a chord increases its odd limit, it's otonal, and if it reduces it, it's utonal. That way 4:5:6 is otonal because it's simpler than its inverse, 10:12:15, and 10:12:15 is utonal because it is more simply expressed as 1/6:1/5:1/4. Because we're using odd limit and not integer limit, this definition is independent of the chord's voicing. Thus 4:5:6 is otonal even if voiced 3:4:5 or 2:3:5. | ||
| Line 67: | Line 70: | ||
[[Category:Otonality and utonality| ]] <!-- main article --> | [[Category:Otonality and utonality| ]] <!-- main article --> | ||
{{Todo|improve synopsis}} | |||