Huntmic chords: Difference between revisions

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'''Huntmic chords''' are ~~certain 13-limit~~ [[Dyadic chord|essentially tempered chords]] ~~which close at the octave~~ by ~~tempering out~~ the huntma, [[640/637]]. These include tetrads with [[step]]s of size ([[huntmic]] tempered) 5/4-16/13-8/7-8/7, 16/13-5/4-8/7-8/7 and 5/4-8/7-16/13-8/7, leading to the huntmic temperings of 1-5/4-20/13-7/4, 1-16/13-20/13-7/4 and 1-5/4-10/7-7/4. Note that the last chord can also be tempered by [[441/440]] to the [[werckismic chords|werckismic tetrad]]. Aside from tetrads, there are huntmic [[triad]]s, the huntmic tempered versions of 1-16/13-7/5 and 1-8/7-7/5.

'''Huntmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the huntma, [[640/637]].

The name huntmic comes from the fact that the [[optimal patent val]] for huntmic temperament is [[205edo]], the basis of the [[Hunt System]] of [[Aaron Andrew Hunt]]~~. Other [[EDO|equal temperaments]] with huntmic chords include {{EDOs| 22, 53, 68, 80, 94, 111, 121, 137, 205 and 215 }}~~.

Huntmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.5.7.13 subgroup [[13-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is

* 1-8/7-13/10 chord with steps of 8/7-8/7-20/13.

The inversely related pair of chords is

* 1-16/13-7/5 with steps of 16/13-8/7-10/7, and its inverse

* 1-8/7-7/5 with steps of 8/7-16/13-10/7.

For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are

* 1-16/13-7/5-7/4 chord with steps of 16/13-8/7-5/4-8/7;

* 1-8/7-16/13-7/5 chord with steps of 8/7-14/13-8/7-10/7.

The inversely related pairs of chords are

* 1-5/4-10/7-13/8 with steps of 5/4-8/7-8/7-16/13, and its inverse

* 1-8/7-13/10-13/8 with steps of 8/7-8/7-5/4-16/13;

* 1-8/7-13/10-13/7 with steps of 8/7-8/7-10/7-14/13, and its inverse

* 1-8/7-13/10-7/5 with steps of 8/7-8/7-14/13-10/7.

They can be extended to pentads:

* 1-8/7-10/7-13/8-7/4 with steps of 8/7-5/4-8/7-14/13-8/7, and its inverse

* 1-8/7-16/13-7/5-7/4 with steps of 8/7-14/13-8/7-5/4-8/7.

Equal temperaments with huntmic chords include {{Optimal ET sequence| 22, 53, 68, 80, 94, 111, 121, 137, 205 and 215 }}. The name huntmic comes from the fact that the [[optimal patent val]] for huntmic temperament is [[205edo]], the basis of the [[Hunt System]] of [[Aaron Andrew Hunt]].

[[Category:Essentially tempered chords]]

[[Category:Triads]]

[[Category:Tetrads]]

[[Category:Pentads]]

[[Category:Huntmic]]

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-'''Huntmic chords''' are certain 13-limit [[Dyadic chord|essentially tempered chords]] which close at the octave by tempering out the huntma, [[640/637]]. These include tetrads with [[step]]s of size ([[huntmic]] tempered) 5/4-16/13-8/7-8/7, 16/13-5/4-8/7-8/7 and 5/4-8/7-16/13-8/7, leading to the huntmic temperings of 1-5/4-20/13-7/4, 1-16/13-20/13-7/4 and 1-5/4-10/7-7/4. Note that the last chord can also be tempered by [[441/440]] to the [[werckismic chords|werckismic tetrad]]. Aside from tetrads, there are huntmic [[triad]]s, the huntmic tempered versions of 1-16/13-7/5 and 1-8/7-7/5.
+'''Huntmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the huntma, [[640/637]].
-The name huntmic comes from the fact that the [[optimal patent val]] for huntmic temperament is [[205edo]], the basis of the [[Hunt System]] of [[Aaron Andrew Hunt]]. Other [[EDO|equal temperaments]] with huntmic chords include {{EDOs| 22, 53, 68, 80, 94, 111, 121, 137, 205 and 215 }}.
+Huntmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.5.7.13 subgroup [[13-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
+For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is
+* 1-8/7-13/10 chord with steps of 8/7-8/7-20/13.
+The inversely related pair of chords is
+* 1-16/13-7/5 with steps of 16/13-8/7-10/7, and its inverse
+* 1-8/7-7/5 with steps of 8/7-16/13-10/7.
+For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are
+* 1-16/13-7/5-7/4 chord with steps of 16/13-8/7-5/4-8/7;
+* 1-8/7-16/13-7/5 chord with steps of 8/7-14/13-8/7-10/7.
+The inversely related pairs of chords are
+* 1-5/4-10/7-13/8 with steps of 5/4-8/7-8/7-16/13, and its inverse
+* 1-8/7-13/10-13/8 with steps of 8/7-8/7-5/4-16/13;
+* 1-8/7-13/10-13/7 with steps of 8/7-8/7-10/7-14/13, and its inverse
+* 1-8/7-13/10-7/5 with steps of 8/7-8/7-14/13-10/7.
+They can be extended to pentads:
+* 1-8/7-10/7-13/8-7/4 with steps of 8/7-5/4-8/7-14/13-8/7, and its inverse
+* 1-8/7-16/13-7/5-7/4 with steps of 8/7-14/13-8/7-5/4-8/7.
+Equal temperaments with huntmic chords include {{Optimal ET sequence| 22, 53, 68, 80, 94, 111, 121, 137, 205 and 215 }}. The name huntmic comes from the fact that the [[optimal patent val]] for huntmic temperament is [[205edo]], the basis of the [[Hunt System]] of [[Aaron Andrew Hunt]].
 [[Category:Essentially tempered chords]]
 [[Category:Triads]]
 [[Category:Tetrads]]
+[[Category:Pentads]]
 [[Category:Huntmic]]