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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 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 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.


[[Category:13-odd-limit]]
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 chords]]
[[Category:Essentially tempered chords]]
[[Category:Essentially tempered chords]]
[[Category:Triad]]
[[Category:Triads]]
[[Category:Tetrad]]
[[Category:Tetrads]]
[[Category:Squbemic]]
[[Category:Squbemic]]
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