Seminaiadmic chords: Difference between revisions
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'''Seminaiadmic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the seminaiadma, [[442/441]]. | '''Seminaiadmic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the seminaiadma, [[442/441]]. | ||
Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures. | Seminaiadmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 2]] in the 2.3.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 6 triads, 15 tetrads and 6 pentads, for a total of 27 distinct chord structures. | ||
For triads, there are three pairs of chords in inverse relationship: | For triads, there are three pairs of chords in inverse relationship: | ||
* 1-17/14-7/4 with steps of 17/14-13/9-8/7 and its inverse 1-13/9-7/4 with steps of 13/9-17/14-8/7; | * 1-17/14-7/4 with steps of 17/14-13/9-8/7, and its inverse | ||
* 1-9/8-17/14 with steps of 9/8-14/13-28/17 and its inverse 1-14/13-17/14 with steps of 14/13-9/8-28/17; | * 1-13/9-7/4 with steps of 13/9-17/14-8/7; | ||
* 1-14/13-8/7 with steps of 14/13-18/17-7/4 and its inverse 1-18/17-8/7 with steps of 18/17-14/13-7/4. | * 1-9/8-17/14 with steps of 9/8-14/13-28/17, and its inverse | ||
* 1-14/13-17/14 with steps of 14/13-9/8-28/17; | |||
* 1-14/13-8/7 with steps of 14/13-18/17-7/4, and its inverse | |||
* 1-18/17-8/7 with steps of 18/17-14/13-7/4. | |||
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 | ||
* 1-17/16-17/14-7/4 with steps of 17/16-8/7-13/9-8/7; | * 1-17/16-17/14-7/4 with steps of 17/16-8/7-13/9-8/7; | ||
* 1-14/13-17/14-17/13 with steps of 14/13-9/8-14/13-26/17; | * 1-14/13-17/14-17/13 with steps of 14/13-9/8-14/13-26/17; | ||
* 1-14/13-8/7-16/13 with steps of 14/13-18/17-14/13-13/8. | * 1-14/13-8/7-16/13 with steps of 14/13-18/17-14/13-13/8. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-9/8-17/14-7/4 with steps of 9/8-14/13-13/9-8/7 and its inverse 1-13/9-14/9-7/4 with steps of 13/9-14/13-9/8-8/7; | * 1-9/8-17/14-7/4 with steps of 9/8-14/13-13/9-8/7, and its inverse | ||
* 1-9/8-17/14-18/13 with steps of 9/8-14/13-8/7-13/9 and its inverse 1-8/7-16/13-18/13 with steps of 8/7-14/13-9/8-13/9; | * 1-13/9-14/9-7/4 with steps of 13/9-14/13-9/8-8/7; | ||
* 1-9/8-17/14-9/7 with steps of 9/8-14/13-18/17-14/9 and its inverse 1-18/17-8/7-9/7 with steps of 18/17-14/13-9/8-14/9; | * 1-9/8-17/14-18/13 with steps of 9/8-14/13-8/7-13/9, and its inverse | ||
* 1-17/16-9/8-17/14 with steps of 17/16-18/17-14/13-28/17 and its inverse 1-14/13-8/7-17/14 with steps of 14/13-18/17-17/16-28/17; | * 1-8/7-16/13-18/13 with steps of 8/7-14/13-9/8-13/9; | ||
* 1-14/13-8/7-18/13 with steps of 14/13-18/17-17/14-13/9 and its inverse 1-17/14-9/7-18/13 with steps of 17/14-18/17-14/13-13/9; | * 1-9/8-17/14-9/7 with steps of 9/8-14/13-18/17-14/9, and its inverse | ||
* 1-14/13-8/7-28/17 with steps of 14/13-18/17-13/9-17/14 and its inverse 1-13/9-26/17-28/17 with steps of 13/9-18/17-14/13-17/14. | * 1-18/17-8/7-9/7 with steps of 18/17-14/13-9/8-14/9; | ||
* 1-17/16-9/8-17/14 with steps of 17/16-18/17-14/13-28/17, and its inverse | |||
* 1-14/13-8/7-17/14 with steps of 14/13-18/17-17/16-28/17; | |||
* 1-14/13-8/7-18/13 with steps of 14/13-18/17-17/14-13/9, and its inverse | |||
* 1-17/14-9/7-18/13 with steps of 17/14-18/17-14/13-13/9; | |||
* 1-14/13-8/7-28/17 with steps of 14/13-18/17-13/9-17/14, and its inverse | |||
* 1-13/9-26/17-28/17 with steps of 13/9-18/17-14/13-17/14. | |||
For pentads, there are three pairs of chords in inverse relationship: | For pentads, there are three pairs of chords in inverse relationship: | ||
* 1-17/16-9/8-17/14-7/4 with steps of 17/16-18/17-14/13-13/9-8/7 and its inverse 1-17/16-17/14-7/4-17/9 with steps of 17/16-8/7-13/9-14/13-18/17; | * 1-17/16-9/8-17/14-7/4 with steps of 17/16-18/17-14/13-13/9-8/7, and its inverse | ||
* 1-14/13-17/14-17/13-17/9 with steps of 14/13-9/8-14/13-13/9-18/17 and its inverse 1-14/13-17/14-17/13-18/13 with steps of 14/13-9/8-14/13-18/17-13/9; | * 1-17/16-17/14-7/4-17/9 with steps of 17/16-8/7-13/9-14/13-18/17; | ||
* 1-9/8-17/14-9/7-18/13 with steps of 9/8-14/13-18/17-14/13-13/9 and its inverse 1-14/13-8/7-16/13-18/13 with steps of 14/13-18/17-14/13-9/8-13/9. | * 1-14/13-17/14-17/13-17/9 with steps of 14/13-9/8-14/13-13/9-18/17, and its inverse | ||
* 1-14/13-17/14-17/13-18/13 with steps of 14/13-9/8-14/13-18/17-13/9; | |||
* 1-9/8-17/14-9/7-18/13 with steps of 9/8-14/13-18/17-14/13-13/9, and its inverse | |||
* 1-14/13-8/7-16/13-18/13 with steps of 14/13-18/17-14/13-9/8-13/9. | |||
Equal temperaments with seminaiadmic chords include {{Optimal ET sequence|10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}. | Equal temperaments with seminaiadmic chords include {{Optimal ET sequence|10, 17g, 19g, 22f, 26, 36, 46, 53, 58, 94, 104, 130 and 140 }}. | ||