Minismic chords: Difference between revisions

Line 1:

'''Schisminic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the schismina, [[4096/4095]].

~~The~~ two ~~schisminic~~ triads ~~are in inverse relationship:~~

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

* 1-16/13-21~~/16 with steps 16/13~~-~~16/15~~-~~32/21 and its inverse 1-16/15-21/16 with steps 16/15-16/13-32/21~~.

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}}.

@@ Line 1: / Line 1: @@
 '''Schisminic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the schismina, [[4096/4095]].
-The two schisminic triads are in inverse relationship:
+There are two triads and three tetrads as 2.3.5.7.13 subgroup [[21-odd-limit]] essentially tempered chords.
-* 1-16/13-21/16 with steps 16/13-16/15-32/21 and its inverse 1-16/15-21/16 with steps 16/15-16/13-32/21.
-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}}.