Aureusmic chords: Difference between revisions
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'''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]]. | '''Aureusmic chords''' are [[essentially tempered dyadic chord]]s tempered by the aureusma, [[1445/1444]]. | ||
Aureusmic chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1a]] in the 2.5.17.19 [[subgroup]] [[19-odd-limit]], meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures. | |||
The most typical aureusmic triad is a palindrome since it identifies 5/4 by a stack of two 19/17's: | |||
* 1-19/17-5/4 chord with steps 19/17-19/17-8/5. | * 1-19/17-5/4 chord with steps 19/17-19/17-8/5. | ||
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* 1-20/19-19/17 with steps 20/19-17/16-34/19. | * 1-20/19-19/17 with steps 20/19-17/16-34/19. | ||
They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic | They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic tetrads are | ||
* 1-17/16-19/17-19/16 chord with steps 17/16-20/19-17/16-32/19; | * 1-17/16-19/17-19/16 chord with steps 17/16-20/19-17/16-32/19; | ||
* 1-20/19-19/17-20/17 chord with steps 20/19-17/16-20/19-17/10. | * 1-20/19-19/17-20/17 chord with steps 20/19-17/16-20/19-17/10. | ||
The inversely related pairs of | The inversely related pairs of tetrads are | ||
* 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse | * 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse | ||
* 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5; | * 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5; | ||
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* 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5. | * 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5. | ||
Then there | Then there is an inversely related pair of pentads: | ||
* 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse, | * 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse, | ||
* 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5. | * 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5. | ||
Latest revision as of 15:42, 26 July 2023
Aureusmic chords are essentially tempered dyadic chords tempered by the aureusma, 1445/1444.
Aureusmic chords are of pattern 1a in the 2.5.17.19 subgroup 19-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
The most typical aureusmic triad is a palindrome since it identifies 5/4 by a stack of two 19/17's:
- 1-19/17-5/4 chord with steps 19/17-19/17-8/5.
There is an inversely related pair which is even more squeezed:
- 1-17/16-19/17 with steps 17/16-20/19-34/19, and its inverse
- 1-20/19-19/17 with steps 20/19-17/16-34/19.
They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic tetrads are
- 1-17/16-19/17-19/16 chord with steps 17/16-20/19-17/16-32/19;
- 1-20/19-19/17-20/17 chord with steps 20/19-17/16-20/19-17/10.
The inversely related pairs of tetrads are
- 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse
- 1-20/19-19/17-5/4 with steps 20/19-17/16-19/17-8/5;
- 1-19/17-20/17-5/4 with steps 19/17-20/19-17/16-8/5, and its inverse
- 1-17/16-19/17-5/4 with steps 17/16-20/19-19/17-8/5.
Then there is an inversely related pair of pentads:
- 1-17/16-19/17-19/16-5/4 with steps 17/16-20/19-17/16-20/19-8/5 and its inverse,
- 1-20/19-19/17-20/17-5/4 with steps 20/19-17/16-20/19-17/16-8/5.
Equal temperaments with aureusmic chords include 12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286.