Squbemic chords: Difference between revisions

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A ''squbemic chord'' is a 13-limit [[~~Dyadic_chord|~~essentially tempered ~~dyadic~~ chord]] which is defined via tempering out the squbema, 729/728. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.

A '''squbemic chord''' is a 13-limit [[essentially tempered chord]] which is defined via tempering out the squbema, [[729/728]].

Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.

There are two squbemic tetrads, the temperings of

* 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7, and

* 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13.

These contain two squbemic triads, the temperings of

* 1-9/8-13/9 with steps 9/8-9/7-18/13,

* 1-9/7-13/9 with steps 9/7-9/8-18/13.

Equal temperaments with squbemic chords include {{EDOs| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724 }}, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.

[[Category:13-odd-limit]]

[[Category:Essentially tempered chords]]

[[Category:Triad]]

[[Category:Tetrad]]

[[Category:Squbemic]]

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-A ''squbemic chord'' is a 13-limit [[Dyadic_chord|essentially tempered dyadic chord]] which is defined via tempering out the squbema, 729/728. There are two squbemic tetrads, the temperings of 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7 and 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13. These contain two squbemic triads, the temperings of 1-9/8-13/9 and 1-9/7-13/9.
+A '''squbemic chord''' is a 13-limit [[essentially tempered chord]] which is defined via tempering out the squbema, [[729/728]].
-Equal temperaments with squbemic chords include 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.
+There are two squbemic tetrads, the temperings of
+* 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7, and
+* 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13.
+These contain two squbemic triads, the temperings of
+* 1-9/8-13/9 with steps 9/8-9/7-18/13,
+* 1-9/7-13/9 with steps 9/7-9/8-18/13.
+Equal temperaments with squbemic chords include {{EDOs| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069, 1724 }}, with 1724edo giving the optimal patent val. Squebmic chords belong to a tempering of the 2.9.7.13 subgroup of the 13-limit.
+[[Category:13-odd-limit]]
+[[Category:Essentially tempered chords]]
+[[Category:Triad]]
+[[Category:Tetrad]]
+[[Category:Squbemic]]