Catadictmic chords: Difference between revisions

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For triads, there are three pairs of chords in inverse relationship:  
For triads, there are three pairs of chords in inverse relationship:  
* 1-16/13-11/8 with steps of 16/13-10/9-16/11 and its inverse 1-16/11-13/8 with steps of 16/11-10/9-16/13;
* 1-16/13-11/8 with steps of 16/13-10/9-16/11, and its inverse  
* 1-13/10-16/11 with steps of 13/10-9/8-11/8 and its inverse 1-11/8-20/13 with steps of 11/8-9/8-13/10;
* 1-16/11-13/8 with steps of 16/11-10/9-16/13;
* 1-11/10-16/13 with steps of 11/10-9/8-13/8 and its inverse 1-9/8-16/13 with steps of 9/8-11/10-13/8.
* 1-13/10-16/11 with steps of 13/10-9/8-11/8, and its inverse  
* 1-11/8-20/13 with steps of 11/8-9/8-13/10;
* 1-11/10-16/13 with steps of 11/10-9/8-13/8, and its inverse  
* 1-9/8-16/13 with steps of 9/8-11/10-13/8.


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  
* 1-16/13-16/11-9/5 chord with steps of 16/13-13/11-16/13-10/9;
* 1-16/13-16/11-9/5 with steps of 16/13-13/11-16/13-10/9;
* 1-9/8-11/8-20/13 chord with steps of 9/8-11/9-9/8-13/10;
* 1-9/8-11/8-20/13 with steps of 9/8-11/9-9/8-13/10;
* 1-9/8-16/13-18/13 chord with steps of 9/8-11/10-9/8-13/9.
* 1-9/8-16/13-18/13 with steps of 9/8-11/10-9/8-13/9.


The inversely related pairs of chords are:
The inversely related pairs of chords are  
* 1-13/10-16/11-9/5 with steps of 13/10-9/8-16/13-10/9 and its inverse 1-16/13-18/13-9/5 with steps of 16/13-9/8-13/10-10/9;
* 1-13/10-16/11-9/5 with steps of 13/10-9/8-16/13-10/9, and its inverse  
* 1-9/8-16/11-9/5 with steps of 9/8-13/10-16/13-10/9 and its inverse 1-16/13-8/5-9/5 with steps of 16/13-13/10-9/8-10/9;
* 1-16/13-18/13-9/5 with steps of 16/13-9/8-13/10-10/9;
* 1-13/11-13/10-16/11 with steps of 13/11-11/10-9/8-11/8 and its inverse 1-9/8-16/13-16/11 with steps of 9/8-11/10-13/11-11/8;
* 1-9/8-16/11-9/5 with steps of 9/8-13/10-16/13-10/9, and its inverse  
* 1-13/10-16/11-8/5 with steps of 13/10-9/8-11/10-5/4 and its inverse 1-11/10-16/13-8/5 with steps of 11/10-9/8-13/10-5/4;
* 1-16/13-8/5-9/5 with steps of 16/13-13/10-9/8-10/9;
* 1-11/10-16/13-11/8 with steps of 11/10-9/8-10/9-16/11 and its inverse 1-10/9-5/4-11/8 with steps of 10/9-9/8-11/10-16/11;
* 1-13/11-13/10-16/11 with steps of 13/11-11/10-9/8-11/8, and its inverse  
* 1-11/10-16/13-9/5 with steps of 11/10-9/8-16/11-10/9 and its inverse 1-16/11-18/11-9/5 with steps of 16/11-9/8-11/10-10/9.
* 1-9/8-16/13-16/11 with steps of 9/8-11/10-13/11-11/8;
* 1-13/10-16/11-8/5 with steps of 13/10-9/8-11/10-5/4, and its inverse  
* 1-11/10-16/13-8/5 with steps of 11/10-9/8-13/10-5/4;
* 1-11/10-16/13-11/8 with steps of 11/10-9/8-10/9-16/11, and its inverse  
* 1-10/9-5/4-11/8 with steps of 10/9-9/8-11/10-16/11;
* 1-11/10-16/13-9/5 with steps of 11/10-9/8-16/11-10/9, and its inverse  
* 1-16/11-18/11-9/5 with steps of 16/11-9/8-11/10-10/9.


For pentads, there are three pairs of chords in inverse relationship:
For pentads, there are three pairs of chords in inverse relationship:  
* 1-16/13-16/11-8/5-9/5 with steps of 16/13-13/11-11/10-9/8-10/9 and its inverse 1-9/8-16/13-16/11-9/5 with steps of 9/8-11/10-13/11-16/13-10/9;
* 1-16/13-16/11-8/5-9/5 with steps of 16/13-13/11-11/10-9/8-10/9, and its inverse  
* 1-9/8-16/11-18/11-9/5 with steps of 9/8-13/10-9/8-11/10-10/9 and its inverse 1-11/10-16/13-8/5-9/5 with steps of 11/10-9/8-13/10-9/8-10/9;
* 1-9/8-16/13-16/11-9/5 with steps of 9/8-11/10-13/11-16/13-10/9;
* 1-13/10-16/11-8/5-9/5 with steps of 13/10-9/8-11/10-9/8-10/9 and its inverse 1-9/8-16/13-18/13-9/5 with steps of 9/8-11/10-9/8-13/10-10/9.
* 1-9/8-16/11-18/11-9/5 with steps of 9/8-13/10-9/8-11/10-10/9, and its inverse  
* 1-11/10-16/13-8/5-9/5 with steps of 11/10-9/8-13/10-9/8-10/9;
* 1-13/10-16/11-8/5-9/5 with steps of 13/10-9/8-11/10-9/8-10/9, and its inverse  
* 1-9/8-16/13-18/13-9/5 with steps of 9/8-11/10-9/8-13/10-10/9.


Equal temperaments with catadictmic chords include {{Optimal ET sequence| 7, 12, 19, 22, 24, 26, 29, 31, 43, 46, 50, 53, 72 and 96 }}.
Equal temperaments with catadictmic chords include {{Optimal ET sequence| 7, 12, 19, 22, 24, 26, 29, 31, 43, 46, 50, 53, 72 and 96 }}.