Squbemic chords: Difference between revisions

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

'''Squbemic chords''' are [[Dyadic chord|essentially tempered chord]] tempered by the squbema, [[729/728]].

~~There are two squbemic tetrads, the temperings of~~

[[13-odd-limit]] squebmic chords belong to a tempering of the 2.9.7.13 subgroup, including two triads and three tetrads.

* 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~~

The two squbemic triads are in inverse relationship:

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

* 1-9/8-13/9 chord with steps of 9/8-9/7-18/13;

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

* 1-9/7-13/9 chord with steps of 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~~.

They can be extended to palindromic tetrads:

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

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

* 1-9/7-13/9-13/7 with steps of 9/7-9/8-9/7-14/13.

Equal temperaments with squbemic chords include {{Optimal ET sequence| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069 and 1724 }}, with 1724edo giving the optimal patent val.

[[Category:13-odd-limit]]

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-A '''squbemic chord''' is a 13-limit [[essentially tempered chord]] which is defined via tempering out the squbema, [[729/728]].
+'''Squbemic chords''' are [[Dyadic chord|essentially tempered chord]] tempered by the squbema, [[729/728]].
-There are two squbemic tetrads, the temperings of
+[[13-odd-limit]] squebmic chords belong to a tempering of the 2.9.7.13 subgroup, including two triads and three tetrads.
-* 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
+The two squbemic triads are in inverse relationship:
-* 1-9/8-13/9 with steps 9/8-9/7-18/13,
+* 1-9/8-13/9 chord with steps of 9/8-9/7-18/13;
-* 1-9/7-13/9 with steps 9/7-9/8-18/13.
+* 1-9/7-13/9 chord with steps of 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.
+They can be extended to palindromic tetrads:
+* 1-9/8-14/9-7/4 with steps of 9/8-18/13-9/8-8/7;
+* 1-9/8-13/9-13/8 with steps of 9/8-9/7-9/8-16/13;
+* 1-9/7-13/9-13/7 with steps of 9/7-9/8-9/7-14/13.
+Equal temperaments with squbemic chords include {{Optimal ET sequence| 24, 36, 41, 53, 58, 72, 111, 130, 183, 190, 224, 354, 373, 525, 597, 845, 1028, 1069 and 1724 }}, with 1724edo giving the optimal patent val.
 [[Category:13-odd-limit]]