Augustmic chords: Difference between revisions
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There are 2 triads, 11 tetrads, 8 pentads and 1 hexad as 2.3.7.11.17 subgroup [[17-odd-limit]] essentially tempered chords. | There are 2 triads, 11 tetrads, 8 pentads and 1 hexad as 2.3.7.11.17 subgroup [[17-odd-limit]] essentially tempered chords. | ||
For triads, there is a pair of chords in inverse relationship: | For triads, there is a pair of chords in inverse relationship: | ||
* 1-12/11-7/6 with steps of 12/11-17/16-12/7 and its inverse 1-17/16-7/6 with steps of 17/16-12/11-12/7. | * 1-12/11-7/6 with steps of 12/11-17/16-12/7, and its inverse | ||
* 1-17/16-7/6 with steps of 17/16-12/11-12/7. | |||
For tetrads, there are one palindromic chord and five pairs of chords in inverse relationship. The palindromic chord is | For tetrads, there are one palindromic chord and five pairs of chords in inverse relationship. The palindromic chord is | ||
* 1-12/11-7/6-14/11 with steps of 12/11-17/16-12/11-11/7. | * 1-12/11-7/6-14/11 with steps of 12/11-17/16-12/11-11/7. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-17/16-3/2-11/6 with steps of 17/16-24/17-11/9-12/11 and its inverse 1-24/17-3/2-18/11 with steps of 24/17-17/16-12/11-11/9; | * 1-17/16-3/2-11/6 with steps of 17/16-24/17-11/9-12/11, and its inverse | ||
* 1-9/7-3/2-11/6 with steps of 9/7-7/6-11/9-12/11 and its inverse 1-7/6-3/2-18/11 with steps of 7/6-9/7-12/11-11/9; | * 1-24/17-3/2-18/11 with steps of 24/17-17/16-12/11-11/9; | ||
* 1-9/7-24/17-3/2 with steps of 9/7-12/11-17/16-4/3 and its inverse 1-17/16-7/6-3/2 with steps of 17/16-12/11-9/7-4/3; | * 1-9/7-3/2-11/6 with steps of 9/7-7/6-11/9-12/11, and its inverse | ||
* 1-9/7-11/8-3/2 with steps of 9/7-17/16-12/11-4/3 and its inverse 1-12/11-7/6-3/2 with steps of 12/11-17/16-9/7-4/3. | * 1-7/6-3/2-18/11 with steps of 7/6-9/7-12/11-11/9; | ||
* 1-3/2-12/7-11/6 with steps of 3/2-8/7-17/16-12/11 and its inverse 1-3/2-18/11-7/4 with steps of 3/2-12/11-17/16-8/7; | * 1-9/7-24/17-3/2 with steps of 9/7-12/11-17/16-4/3, and its inverse | ||
* 1-17/16-7/6-3/2 with steps of 17/16-12/11-9/7-4/3; | |||
* 1-9/7-11/8-3/2 with steps of 9/7-17/16-12/11-4/3, and its inverse | |||
* 1-12/11-7/6-3/2 with steps of 12/11-17/16-9/7-4/3. | |||
* 1-3/2-12/7-11/6 with steps of 3/2-8/7-17/16-12/11, and its inverse | |||
* 1-3/2-18/11-7/4 with steps of 3/2-12/11-17/16-8/7; | |||
For pentads, there are four pairs of chords in inverse relationship: | For pentads, there are four pairs of chords in inverse relationship: | ||
* 1-9/7-11/7-12/7-11/6 with steps of 9/7-11/9-12/11-17/16-12/11 and its inverse 1-11/9-11/7-12/7-11/6 with steps of 11/9-9/7-12/11-17/16-12/11; | * 1-9/7-11/7-12/7-11/6 with steps of 9/7-11/9-12/11-17/16-12/11, and its inverse | ||
* 1-9/7-11/8-3/2-11/6 with steps of 9/7-17/16-12/11-11/9-12/11 and its inverse 1-12/11-7/6-3/2-18/11 with steps of 12/11-17/16-9/7-12/11-11/9; | * 1-11/9-11/7-12/7-11/6 with steps of 11/9-9/7-12/11-17/16-12/11; | ||
* 1-9/7-3/2-12/7-11/6 with steps of 9/7-7/6-8/7-17/16-12/11 and its inverse 1-7/6-3/2-18/11-7/4 with steps of 7/6-9/7-12/11-17/16-8/7; | * 1-9/7-11/8-3/2-11/6 with steps of 9/7-17/16-12/11-11/9-12/11, and its inverse | ||
* 1-18/17-9/7-24/17-3/2 with steps of 18/17-11/9-12/11-17/16-4/3 and its inverse 1- | * 1-12/11-7/6-3/2-18/11 with steps of 12/11-17/16-9/7-12/11-11/9; | ||
* 1-9/7-3/2-12/7-11/6 with steps of 9/7-7/6-8/7-17/16-12/11, and its inverse | |||
* 1-7/6-3/2-18/11-7/4 with steps of 7/6-9/7-12/11-17/16-8/7; | |||
* 1-18/17-9/7-24/17-3/2 with steps of 18/17-11/9-12/11-17/16-4/3, and its inverse | |||
* 1-17/16-7/6-17/12-3/2 with steps of 17/16-12/11-11/9-18/17-4/3. | |||
Finally there is a palindromic hexad, | Finally there is a palindromic hexad, | ||
* 1-11/9-9/7-11/7-12/7-11/6 with steps of 11/9-18/17-11/9-12/11-17/16-12/11. | * 1-11/9-9/7-11/7-12/7-11/6 with steps of 11/9-18/17-11/9-12/11-17/16-12/11. | ||
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== Augustmic plurichords == | == Augustmic plurichords == | ||
The augustmic temperament has two inversely related pairs of triads and one palindromic tetrad as plurichords. | The augustmic temperament has two inversely related pairs of triads and one palindromic tetrad as plurichords. | ||
The palindromic tetrad is both otonal and utonal in the 17-odd-limit: | The palindromic tetrad is both otonal and utonal in the 17-odd-limit: | ||