Keenanismic chords: Difference between revisions

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A '''keenanismic chord''' is an ~~[[11-odd-limit]]~~ [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]]. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:

A '''keenanismic chord''' is an [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]].

Keenanismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.

There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:

* 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse

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* 1-6/5-11/8-3/2-12/7 with steps 6/5-8/7-12/11-8/7-7/6, and its inverse

* 1-12/11-5/4-3/2-7/4 with steps 12/11-8/7-6/5-7/6-8/7.

~~The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.~~

If we are willing to go as high as the [[15-odd-limit]], there are many more keenanismic chords, all of which have a step of size [[16/15]]. There are six additional keenanismic triads in the 15-odd-limit, 32 additional keenanismic tetrads and 44 additional pentads.

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-A '''keenanismic chord''' is an [[11-odd-limit]] [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]]. There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:
+A '''keenanismic chord''' is an [[essentially tempered chord]] which is tempered by the keenanisma, [[385/384]].
+Keenanismic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the [[11-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures.
+There are six keenanismic triads, consisting of three pairs of chords in inverse relationship:
 * 1-5/4-12/7 with steps 5/4-11/8-7/6, and its inverse
@@ Line 48: / Line 52: @@
 * 1-6/5-11/8-3/2-12/7 with steps 6/5-8/7-12/11-8/7-7/6, and its inverse
 * 1-12/11-5/4-3/2-7/4 with steps 12/11-8/7-6/5-7/6-8/7.
-The count of 11-limit chords is triads: 6, tetrads: 15, pentads: 6, for a total of 27.
 If we are willing to go as high as the [[15-odd-limit]], there are many more keenanismic chords, all of which have a step of size [[16/15]]. There are six additional keenanismic triads in the 15-odd-limit, 32 additional keenanismic tetrads and 44 additional pentads.