Aureusmic chords: Difference between revisions
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There is an inversely related pair which is even more squeezed: | 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. | * 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 chords are | They can be extended to the following tetrads, with two palindromic chords and two pairs of chords in inverse relationship. The palindromic chords are | ||
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The inversely related pairs of chords are | The inversely related pairs of chords 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; | * 1-19/17-19/16-5/4 with steps 19/17-17/16-20/19-8/5, and its inverse | ||
* 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. | * 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 are two inversely related pentads: | Then there are two inversely related 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. | * 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 {{Optimal ET sequence|12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286}}. | Equal temperaments with aureusmic chords include {{Optimal ET sequence| 12, 13, 25, 31, 37, 43, 56, 68, 81, 93, 124, 137, 149, 205, 230 and 286 }}. | ||
[[Category:19-odd-limit]] | [[Category:19-odd-limit]] | ||
Revision as of 06:35, 21 July 2023
Aureusmic chords are essentially tempered dyadic chords tempered by the aureusma, 1445/1444.
The most typical aureusmic triad is a palindrome in the 2.5.17.19 subgroup 19-odd-limit 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 chords 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 chords 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 are two inversely related 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.