Ratwolfsmic chords: Difference between revisions

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For triads, there are three pairs of chords in inverse relationship:

* 1-9/7-20/13 with steps of 9/7-6/5-13/10 and its inverse 1-6/5-20/13 with steps of 6/5-9/7-13/10; (→[[#Ratwolf triad|ratwolf triad]])

* 1-9/7-20/13 with steps of 9/7-6/5-13/10, and its inverse

* 1-7/6-13/10 with steps of 7/6-10/9-20/13 and its inverse 1-10/9-13/10 with steps of 10/9-7/6-20/13;

* 1-6/5-20/13 with steps of 6/5-9/7-13/10; (→[[#Ratwolf triad|ratwolf triad]])

* 1-10/9-6/5 with steps of 10/9-14/13-5/3 and its inverse 1-14/13-6/5 with steps of 14/13-10/9-5/3.

* 1-7/6-13/10 with steps of 7/6-10/9-20/13, and its inverse

* 1-10/9-13/10 with steps of 10/9-7/6-20/13;

* 1-10/9-6/5 with steps of 10/9-14/13-5/3, and its inverse

* 1-14/13-6/5 with steps of 14/13-10/9-5/3.

For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are:

For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are

* 1-6/5-13/10-14/7 ~~chord~~ with steps of 6/5-13/12-6/5-9/7;

* 1-6/5-13/10-14/7 with steps of 6/5-13/12-6/5-9/7;

* 1-7/6-13/10-9/5 ~~chord~~ with steps of 7/6-10/9-18/13-10/9;

* 1-7/6-13/10-9/5 with steps of 7/6-10/9-18/13-10/9;

* 1-3/2-5/3-9/5 ~~chord~~ with steps of 3/2-10/9-14/13-10/9.

* 1-3/2-5/3-9/5 with steps of 3/2-10/9-14/13-10/9.

The inversely related pairs of chords are:

The inversely related pairs of chords are

* 1-7/6-13/10-5/3 with steps of 7/6-10/9-9/7-6/5 and its inverse 1-7/6-7/5-9/5 with steps of 7/6-6/5-9/7-10/9;

* 1-7/6-13/10-5/3 with steps of 7/6-10/9-9/7-6/5, and its inverse

* 1-7/6-13/10-7/5 with steps of 7/6-10/9-14/13-10/7 and its inverse 1-7/6-5/3-9/5 with steps of 7/6-10/7-14/13-10/9;

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

* 1-13/10-5/3-13/7 with steps of 13/10-9/7-10/9-14/13 and its inverse 1-13/10-7/5-14/9 with steps of 13/10-14/13-10/9-9/7;

* 1-7/6-13/10-7/5 with steps of 7/6-10/9-14/13-10/7, and its inverse

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

* 1-7/6-5/3-9/5 with steps of 7/6-10/7-14/13-10/9;

* 1-9/7-5/3-13/7 with steps of 9/7-13/10-10/9-14/13 and its inverse 1-10/9-13/9-13/7 with steps of 10/9-13/10-9/7-14/13;

* 1-13/10-5/3-13/7 with steps of 13/10-9/7-10/9-14/13, and its inverse

* 1-13/12-7/6-13/10 with steps of 13/12-14/13-10/9-20/13 and its inverse 1-10/9-6/5-13/10 with steps of 10/9-14/13-13/12-20/13.

* 1-13/10-7/5-14/9 with steps of 13/10-14/13-10/9-9/7;

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

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

* 1-9/7-5/3-13/7 with steps of 9/7-13/10-10/9-14/13, and its inverse

* 1-10/9-13/9-13/7 with steps of 10/9-13/10-9/7-14/13;

* 1-13/12-7/6-13/10 with steps of 13/12-14/13-10/9-20/13, and its inverse

* 1-10/9-6/5-13/10 with steps of 10/9-14/13-13/12-20/13.

For pentads, there are three pairs of chords in inverse relationship:

* 1-10/9-13/10-13/9-13/7 with steps of 10/9-7/6-10/9-9/7-14/13 and its inverse 1-9/7-10/7-5/3-13/7 with steps of 9/7-10/9-7/6-10/9-14/13;

* 1-10/9-13/10-13/9-13/7 with steps of 10/9-7/6-10/9-9/7-14/13, and its inverse

* 1-13/12-13/10-5/3-13/7 with steps of 13/12-6/5-9/7-10/9-14/13 and its inverse 1-10/9-10/7-12/7-13/7 with steps of 10/9-9/7-6/5-13/12-14/13;

* 1-9/7-10/7-5/3-13/7 with steps of 9/7-10/9-7/6-10/9-14/13;

* 1-9/7-3/2-5/3-9/5 with steps of 9/7-7/6-10/9-14/13-10/9 and its inverse 1-7/6-3/2-5/3-9/5 with steps of 7/6-9/7-10/9-14/13-10/9.

* 1-13/12-13/10-5/3-13/7 with steps of 13/12-6/5-9/7-10/9-14/13, and its inverse

* 1-10/9-10/7-12/7-13/7 with steps of 10/9-9/7-6/5-13/12-14/13;

* 1-9/7-3/2-5/3-9/5 with steps of 9/7-7/6-10/9-14/13-10/9, and its inverse

* 1-7/6-3/2-5/3-9/5 with steps of 7/6-9/7-10/9-14/13-10/9.

Equal temperaments with ratwolfsmic chords include {{Optimal ET sequence| 5, 7, 8d, 12f, 19, 22, 26, 27, 31, 34d, 46, 53, 58, 72, 77, 84, 111 and 130 }}.

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 For triads, there are three pairs of chords in inverse relationship:
-* 1-9/7-20/13 with steps of 9/7-6/5-13/10 and its inverse 1-6/5-20/13 with steps of 6/5-9/7-13/10; (→[[#Ratwolf triad|ratwolf triad]])
+* 1-9/7-20/13 with steps of 9/7-6/5-13/10, and its inverse
-* 1-7/6-13/10 with steps of 7/6-10/9-20/13 and its inverse 1-10/9-13/10 with steps of 10/9-7/6-20/13;
+* 1-6/5-20/13 with steps of 6/5-9/7-13/10; (→[[#Ratwolf triad|ratwolf triad]])
-* 1-10/9-6/5 with steps of 10/9-14/13-5/3 and its inverse 1-14/13-6/5 with steps of 14/13-10/9-5/3.
+* 1-7/6-13/10 with steps of 7/6-10/9-20/13, and its inverse
+* 1-10/9-13/10 with steps of 10/9-7/6-20/13;
+* 1-10/9-6/5 with steps of 10/9-14/13-5/3, and its inverse
+* 1-14/13-6/5 with steps of 14/13-10/9-5/3.
-For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are:
+For tetrads, there are three palindromic chords and six pairs of chords in inverse relationship. The palindromic chords are
-* 1-6/5-13/10-14/7 chord with steps of 6/5-13/12-6/5-9/7;
+* 1-6/5-13/10-14/7 with steps of 6/5-13/12-6/5-9/7;
-* 1-7/6-13/10-9/5 chord with steps of 7/6-10/9-18/13-10/9;
+* 1-7/6-13/10-9/5 with steps of 7/6-10/9-18/13-10/9;
-* 1-3/2-5/3-9/5 chord with steps of 3/2-10/9-14/13-10/9.
+* 1-3/2-5/3-9/5 with steps of 3/2-10/9-14/13-10/9.
-The inversely related pairs of chords are:
+The inversely related pairs of chords are
-* 1-7/6-13/10-5/3 with steps of 7/6-10/9-9/7-6/5 and its inverse 1-7/6-7/5-9/5 with steps of 7/6-6/5-9/7-10/9;
+* 1-7/6-13/10-5/3 with steps of 7/6-10/9-9/7-6/5, and its inverse
-* 1-7/6-13/10-7/5 with steps of 7/6-10/9-14/13-10/7 and its inverse 1-7/6-5/3-9/5 with steps of 7/6-10/7-14/13-10/9;
+* 1-7/6-7/5-9/5 with steps of 7/6-6/5-9/7-10/9;
-* 1-13/10-5/3-13/7 with steps of 13/10-9/7-10/9-14/13 and its inverse 1-13/10-7/5-14/9 with steps of 13/10-14/13-10/9-9/7;
+* 1-7/6-13/10-7/5 with steps of 7/6-10/9-14/13-10/7, and its inverse
-* 1-9/7-3/2-5/3 with steps of 9/7-7/6-10/9-6/5 and its inverse 1-7/6-3/2-9/5 with steps of 7/6-9/7-6/5-10/9;
+* 1-7/6-5/3-9/5 with steps of 7/6-10/7-14/13-10/9;
-* 1-9/7-5/3-13/7 with steps of 9/7-13/10-10/9-14/13 and its inverse 1-10/9-13/9-13/7 with steps of 10/9-13/10-9/7-14/13;
+* 1-13/10-5/3-13/7 with steps of 13/10-9/7-10/9-14/13, and its inverse
-* 1-13/12-7/6-13/10 with steps of 13/12-14/13-10/9-20/13 and its inverse 1-10/9-6/5-13/10 with steps of 10/9-14/13-13/12-20/13.
+* 1-13/10-7/5-14/9 with steps of 13/10-14/13-10/9-9/7;
+* 1-9/7-3/2-5/3 with steps of 9/7-7/6-10/9-6/5, and its inverse
+* 1-7/6-3/2-9/5 with steps of 7/6-9/7-6/5-10/9;
+* 1-9/7-5/3-13/7 with steps of 9/7-13/10-10/9-14/13, and its inverse
+* 1-10/9-13/9-13/7 with steps of 10/9-13/10-9/7-14/13;
+* 1-13/12-7/6-13/10 with steps of 13/12-14/13-10/9-20/13, and its inverse
+* 1-10/9-6/5-13/10 with steps of 10/9-14/13-13/12-20/13.
 For pentads, there are three pairs of chords in inverse relationship:
-* 1-10/9-13/10-13/9-13/7 with steps of 10/9-7/6-10/9-9/7-14/13 and its inverse 1-9/7-10/7-5/3-13/7 with steps of 9/7-10/9-7/6-10/9-14/13;
+* 1-10/9-13/10-13/9-13/7 with steps of 10/9-7/6-10/9-9/7-14/13, and its inverse
-* 1-13/12-13/10-5/3-13/7 with steps of 13/12-6/5-9/7-10/9-14/13 and its inverse 1-10/9-10/7-12/7-13/7 with steps of 10/9-9/7-6/5-13/12-14/13;
+* 1-9/7-10/7-5/3-13/7 with steps of 9/7-10/9-7/6-10/9-14/13;
-* 1-9/7-3/2-5/3-9/5 with steps of 9/7-7/6-10/9-14/13-10/9 and its inverse 1-7/6-3/2-5/3-9/5 with steps of 7/6-9/7-10/9-14/13-10/9.
+* 1-13/12-13/10-5/3-13/7 with steps of 13/12-6/5-9/7-10/9-14/13, and its inverse
+* 1-10/9-10/7-12/7-13/7 with steps of 10/9-9/7-6/5-13/12-14/13;
+* 1-9/7-3/2-5/3-9/5 with steps of 9/7-7/6-10/9-14/13-10/9, and its inverse
+* 1-7/6-3/2-5/3-9/5 with steps of 7/6-9/7-10/9-14/13-10/9.
 Equal temperaments with ratwolfsmic chords include {{Optimal ET sequence| 5, 7, 8d, 12f, 19, 22, 26, 27, 31, 34d, 46, 53, 58, 72, 77, 84, 111 and 130 }}.