Sensamagic chords: Difference between revisions

Line 1:

A '''sensamagic chord''' is an [[essentially tempered dyadic chord]] tempered by the sensamagic comma, [[245/243]].

The sensamagic triad is a sensamagic chord with three notes when reduced to the octave.

The sensamagic triad is a sensamagic chord with three notes when reduced to the octave. One of the sensamagic triads in close position consists of two supermajor thirds, approximately [[9/7]], and a minor third, approximately [[6/5]], which closes at the octave because the sensamagic comma, 245/243, is tempered out:

One of the sensamagic triads in close position consists of two supermajor thirds, approximately [[9/7]], and a minor third, approximately [[6/5]], which closes at the octave because the sensamagic comma, 245/243, is tempered out:

* 1-9/7-5/3 with steps of 9/7-9/7-6/5.

Line 9:

Line 7:

The other sensamagic triads are

* 1-7/6-9/7, with steps of 7/6-10/9-14/9, and its inversion 1-7/6-9/5, with steps 7/6-14/9-10/9.

* 1-7/6-9/7, with steps 7/6-10/9-14/9, and its inversion

* 1-7/6-9/5, with steps 7/6-14/9-10/9.

For sensamagic tetrads there are

For sensamagic tetrads there are the following palindromes:

* 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3;

* 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5;

* 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5; and

* 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9.

And the following inversely related pairs:

* 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion

* 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5;

* 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion

* 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5.

For pentads there are

* 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion, 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9.

* 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion,

* 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9.

The [[9-odd-limit]] sensamagic chords ~~number is~~ triads~~: 3~~, tetrads~~: 6,~~ pentads~~: 2~~, for a total of 11.

The [[9-odd-limit]] sensamagic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.

Equal temperaments with sensamagic chords include {{EDOs| 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283 }}, with 283edo giving the [[optimal patent val]].

@@ Line 1: / Line 1: @@
 A '''sensamagic chord''' is an [[essentially tempered dyadic chord]] tempered by the sensamagic comma, [[245/243]].
-The sensamagic triad is a sensamagic chord with three notes when reduced to the octave.
+The sensamagic triad is a sensamagic chord with three notes when reduced to the octave. One of the sensamagic triads in close position consists of two supermajor thirds, approximately [[9/7]], and a minor third, approximately [[6/5]], which closes at the octave because the sensamagic comma, 245/243, is tempered out:
-One of the sensamagic triads in close position consists of two supermajor thirds, approximately [[9/7]], and a minor third, approximately [[6/5]], which closes at the octave because the sensamagic comma, 245/243, is tempered out:
 * 1-9/7-5/3 with steps of 9/7-9/7-6/5.
@@ Line 9: / Line 7: @@
 The other sensamagic triads are
-* 1-7/6-9/7, with steps of 7/6-10/9-14/9, and its inversion 1-7/6-9/5, with steps 7/6-14/9-10/9.
+* 1-7/6-9/7, with steps 7/6-10/9-14/9, and its inversion
+* 1-7/6-9/5, with steps 7/6-14/9-10/9.
-For sensamagic tetrads there are
+For sensamagic tetrads there are the following palindromes:
 * 1-7/6-9/7-3/2, with steps 7/6-10/9-7/6-4/3;
-* 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5;
-* 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5; and
 * 1-7/6-9/7-9/5 with steps 7/6-10/9-7/5-10/9.
+And the following inversely related pairs:
+* 1-7/6-3/2-9/5 with steps 7/6-9/7-6/5-10/9 and its inversion
+* 1-9/7-3/2-5/3 with steps 9/7-7/6-10/9-6/5;
+* 1-7/6-7/5-9/5 with steps 7/6-6/5-9/7-10/9 and its inversion
+* 1-7/6-9/7-5/3 with steps 7/6-10/9-9/7-6/5.
 For pentads there are
-* 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion, 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9.
+* 1-7/6-9/7-3/2-5/3 with steps 7/6-10/9-7/6-10/9-6/5 and its inversion,
+* 1-7/6-9/7-3/2-9/5 with steps 7/6-10/9-7/6-6/5-10/9.
-The [[9-odd-limit]] sensamagic chords number is triads: 3, tetrads: 6, pentads: 2, for a total of 11.
+The [[9-odd-limit]] sensamagic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
 Equal temperaments with sensamagic chords include {{EDOs| 19, 22, 27, 41, 46, 65, 68, 87, 128, 196, 283 }}, with 283edo giving the [[optimal patent val]].