Charismic chords: Difference between revisions
Jump to navigation
Jump to search
Created page with "'''Diasemismic chords''' are essentially tempered dyadic chords tempered by the diasemisma, 256/255. The diasemismic temperament contains many possib..." |
mNo edit summary |
||
| Line 7: | Line 7: | ||
* 1-9/8-24/17 with steps of 9/8-5/4-17/12. | * 1-9/8-24/17 with steps of 9/8-5/4-17/12. | ||
For tetrads, there are three palindromic | For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are | ||
* 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15; | * 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15; | ||
* 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12; | * 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12; | ||
| Line 17: | Line 17: | ||
* 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12 and its inverse 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12; | * 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12 and its inverse 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12; | ||
* 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12. | * 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12. | ||
Remarkable hexads include a palindromic chord: | |||
* 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15. | |||
Equal temperaments with diasemismic chords include {{Optimal ET sequence|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}. | Equal temperaments with diasemismic chords include {{Optimal ET sequence|7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111}}. | ||
| Line 24: | Line 27: | ||
[[Category:Triads]] | [[Category:Triads]] | ||
[[Category:Tetrads]] | [[Category:Tetrads]] | ||
[[Category:Hexads]] | |||
[[Category:Diasemismic]] | [[Category:Diasemismic]] | ||
Revision as of 01:45, 22 July 2023
Diasemismic chords are essentially tempered dyadic chords tempered by the diasemisma, 256/255.
The diasemismic temperament contains many possibilities for essentially tempered dyadic chords including two triads and eleven tetrads in the 17-odd-limit of the 2.3.5.17 subgroup.
The two diasemismic triads are in inverse relationship:
- 1-5/4-24/17 with steps of 5/4-9/8-17/12;
- 1-9/8-24/17 with steps of 9/8-5/4-17/12.
For tetrads, there are three palindromic chords and four pairs of chords in inverse relationship. The palindromic chords are
- 1-5/4-24/17-30/17 with steps of 5/4-9/8-5/4-17/15;
- 1-9/8-5/4-24/17 with steps of 9/8-10/9-9/8-17/12;
- 1-16/15-4/3-17/12 with steps of 16/15-5/4-16/15-24/17;
The inversely related pairs of chords are
- 1-5/4-24/17-15/8 with steps of 5/4-9/8-4/3-16/15 and its inverse 1-4/3-3/2-15/8 with steps of 4/3-9/8-5/4-16/15;
- 1-5/4-24/17-3/2 with steps of 5/4-9/8-16/15-4/3 and its inverse 1-16/15-6/5-3/2 with steps of 16/15-9/8-5/4-4/3;
- 1-5/4-4/3-24/17 with steps of 5/4-16/15-18/17-17/12 and its inverse 1-18/17-9/8-24/17 with steps of 18/17-16/15-5/4-17/12;
- 1-20/17-5/4-24/17 with steps 20/17-16/15-9/8-17/12 and its inverse 1-9/8-6/5-24/17 with steps of 9/8-16/15-20/17-17/12.
Remarkable hexads include a palindromic chord:
- 1-9/8-5/4-24/17-3/2-15/8 with steps of 9/8-10/9-9/8-16/15-5/4-16/15.
Equal temperaments with diasemismic chords include 7, 9, 10, 12, 15, 19, 22, 31, 34, 46, 53, 65, 77, 87, 99 and 111.