Horizmic chords: Difference between revisions
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'''Horizmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the horizma, [[833/832]]. | '''Horizmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the horizma, [[833/832]]. | ||
Horizmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.7.13.17 [[subgroup]] [[17-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. | |||
For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is | For triads, there are one palindromic chord and a pair of chords in inverse relationship. The palindromic chord is | ||
* 1-8/7-17/13 | * 1-8/7-17/13 with steps of 8/7-8/7-26/17. | ||
The inversely related pair of chords is | The inversely related pair of chords is | ||
* 1-14/13-8/7 with steps of 14/13-17/16-7/4 and its inverse 1-17/16-8/7 with steps of 17/16-14/13-7/4. | * 1-14/13-8/7 with steps of 14/13-17/16-7/4, and its inverse | ||
* 1-17/16-8/7 with steps of 17/16-14/13-7/4. | |||
For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | ||
* 1-14/13-8/7-16/13 | * 1-14/13-8/7-16/13 with steps of 14/13-17/16-14/13-13/8; | ||
* 1-17/16-8/7-17/14 | * 1-17/16-8/7-17/14 with steps of 17/16-14/13-17/16-28/17. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-8/7-16/13-17/13 with steps of 8/7-14/13-17/16-26/17 and its inverse 1-17/16-8/7-17/13 with steps of 17/16-14/13-8/7-26/17; | * 1-8/7-16/13-17/13 with steps of 8/7-14/13-17/16-26/17, and its inverse | ||
* 1-8/7-17/14-17/13 with steps of 8/7-17/16-14/13-26/17 and its inverse 1-14/13-8/7-17/13 with steps of 14/13-17/16-8/7-26/17. | * 1-17/16-8/7-17/13 with steps of 17/16-14/13-8/7-26/17; | ||
* 1-8/7-17/14-17/13 with steps of 8/7-17/16-14/13-26/17, and its inverse | |||
* 1-14/13-8/7-17/13 with steps of 14/13-17/16-8/7-26/17. | |||
They can be extended to pentads: | They can be extended to pentads: | ||
* 1-14/13-8/7-16/13-17/13 with steps of 14/13-17/16-14/13-17/16-26/17 and its inverse 1-17/16-8/7-17/14-17/13 with steps of 17/16-14/13-17/16-14/13-26/17. | * 1-14/13-8/7-16/13-17/13 with steps of 14/13-17/16-14/13-17/16-26/17, and its inverse | ||
* 1-17/16-8/7-17/14-17/13 with steps of 17/16-14/13-17/16-14/13-26/17. | |||
Equal temperaments with horizmic chords include {{Optimal ET sequence|10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150}}. | Equal temperaments with horizmic chords include {{Optimal ET sequence|10, 11, 21, 26, 31, 36, 46, 47, 57, 67, 83, 93, 103, 104 and 150}}. | ||