Minismic chords: Difference between revisions
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Created page with "'''Schisminic chords''' are essentially tempered chords tempered by the schismina, 4096/4095. The two schisminic triads are in inverse relationship: * 1..." |
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'''Schisminic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the schismina, [[4096/4095]]. | '''Schisminic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the schismina, [[4096/4095]]. | ||
There are two triads and three tetrads as 2.3.5.7.13 subgroup [[21-odd-limit]] essentially tempered chords. | |||
They can be extended to following palindromic tetrads: | The two schisminic triads are in inverse relationship: | ||
* 1-15/13-16/13-15/8 with steps 15/13-16/15-32/21-16/15; | * 1-16/13-21/16 with steps of 16/13-16/15-32/21, and its inverse | ||
* 1-16/13-21/16-21/13 with steps 16/13-16/15-16/13-26/21; | * 1-16/15-21/16 with steps of 16/15-16/13-32/21. | ||
* 1-16/15-21/16-7/5 with steps 16/15-16/13-16/15-10/7. | |||
They can be extended to following palindromic tetrads: | |||
* 1-15/13-16/13-15/8 with steps of 15/13-16/15-32/21-16/15; | |||
* 1-16/13-21/16-21/13 with steps of 16/13-16/15-16/13-26/21; | |||
* 1-16/15-21/16-7/5 with steps of 16/15-16/13-16/15-10/7. | |||
Equal temperaments with schisminic chords include {{Optimal ET sequence|53, 77, 87, 130, 140, 171, 217, 224, 270, 301, 311, 354, 441, 494, 571, 711, 795, 935, 1065, 1376 and 1506}}. | Equal temperaments with schisminic chords include {{Optimal ET sequence|53, 77, 87, 130, 140, 171, 217, 224, 270, 301, 311, 354, 441, 494, 571, 711, 795, 935, 1065, 1376 and 1506}}. | ||
Revision as of 04:51, 26 November 2023
Schisminic chords are essentially tempered chords tempered by the schismina, 4096/4095.
There are two triads and three tetrads as 2.3.5.7.13 subgroup 21-odd-limit essentially tempered chords.
The two schisminic triads are in inverse relationship:
- 1-16/13-21/16 with steps of 16/13-16/15-32/21, and its inverse
- 1-16/15-21/16 with steps of 16/15-16/13-32/21.
They can be extended to following palindromic tetrads:
- 1-15/13-16/13-15/8 with steps of 15/13-16/15-32/21-16/15;
- 1-16/13-21/16-21/13 with steps of 16/13-16/15-16/13-26/21;
- 1-16/15-21/16-7/5 with steps of 16/15-16/13-16/15-10/7.
Equal temperaments with schisminic chords include 53, 77, 87, 130, 140, 171, 217, 224, 270, 301, 311, 354, 441, 494, 571, 711, 795, 935, 1065, 1376 and 1506.