Augustmic chords: Difference between revisions
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'''Augustmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the augustma, [[154/153]]. | '''Augustmic chords''' are [[Dyadic chord|essentially tempered chords]] tempered by the augustma, [[154/153]]. | ||
There are 2 triads, | 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 | 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 | ||
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* 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; | * 1-3/2-12/7-11/6 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 | 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 1-11/9-11/7-12/7-11/6 with steps of 11/9-9/7-12/11-17/16-12/11; | ||
* 1-9/7-11/8-3/2-11/6 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; | * 1-9/7-11/8-3/2-11/6 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; | ||
* 1-9/7-3/2-12/7-11/6 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; | * 1-9/7-3/2-12/7-11/6 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 1-4/3-17/12-17/11-17/9 with steps of 4/3-17/16-12/11-11/9-18/17. | * 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 1-4/3-17/12-17/11-17/9 with steps of 4/3-17/16-12/11-11/9-18/17. | ||
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== Augustmic plurichords == | == Augustmic plurichords == | ||
The augustmic temperament has two inversely related pairs of triads as plurichords: | The augustmic temperament has two inversely related pairs of triads and one palindromic tetrad as plurichords. | ||
* 7:9:11 triad which has steps of 22/17-17/14-14/11 and its inverse 14:17:22 triad which has steps of 11/9-9/7-14/11 | |||
The palindromic tetrad is both otonal and utonal in the 17-odd-limit: | |||
* 14:17:18:22 tetrad which has steps of 11/9-18/17-11/9-14/11 or 17/14-18/17-17/14-14/11. | |||
The inversely related pairs of triads are any three of the components of the tetrad: | |||
* 7:9:11 triad which has steps of 22/17-17/14-14/11 and its inverse 14:17:22 triad which has steps of 11/9-9/7-14/11; | |||
* 14:17:18 triad which has steps of 11/9-18/17-17/11 and its inverse 17:18:22 triad which has steps of 18/17-17/14-14/9. | * 14:17:18 triad which has steps of 11/9-18/17-17/11 and its inverse 17:18:22 triad which has steps of 18/17-17/14-14/9. | ||