Minismic chords: Difference between revisions

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m FloraC moved page Schisminic chords to Minismic chords: Name change followup
Name change followup
 
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'''Schisminic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the schismina, [[4096/4095]].  
'''Minismic chords''' are [[essentially tempered chord]]s tempered by the minisma, [[4096/4095]].  


There are two triads and three tetrads as 2.3.5.7.13 subgroup [[21-odd-limit]] essentially tempered chords.
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:  
The two minismic triads are in inverse relationship:  
* 1-16/13-21/16 with steps of 16/13-16/15-32/21, and its inverse  
* 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.
* 1-16/15-21/16 with steps of 16/15-16/13-32/21.
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* 1-16/15-21/16-7/5 with steps of 16/15-16/13-16/15-10/7.
* 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 minismic 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 }}.


[[Category:21-odd-limit]]
[[Category:21-odd-limit]]
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[[Category:Triads]]
[[Category:Triads]]
[[Category:Tetrads]]
[[Category:Tetrads]]
[[Category:Schisminic]]
[[Category:Minismic]]

Latest revision as of 09:25, 3 March 2026

Minismic chords are essentially tempered chords tempered by the minisma, 4096/4095.

There are two triads and three tetrads as 2.3.5.7.13 subgroup 21-odd-limit essentially tempered chords.

The two minismic 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 minismic chords include 53, 77, 87, 130, 140, 171, 217, 224, 270, 301, 311, 354, 441, 494, 571, 711, 795, 935, 1065, 1376 and 1506.