Catadictmic chords: Difference between revisions
Created page with "'''Catadictmic chords''' are essentially tempered dyadic chords tempered by the catadictma, 1287/1280. Catadictmic chords are of Dyadic chord/Pattern o..." |
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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 | * 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 | * 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 | * 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 | * 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 }}. | ||