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]]
[[Category:13-odd-limit]]

Revision as of 23:36, 2 November 2023

Squbemic chords are essentially tempered chord tempered by the squbema, 729/728.

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

The two squbemic triads are in inverse relationship:

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

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 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.

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