Biyatismic chords: Difference between revisions
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Prefer voicing with the perfect fifth and sometimes other harmonics; one line each chord for readability |
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'''Biyatismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the biyatisma, [[121/120]]. | '''Biyatismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the biyatisma, [[121/120]]. | ||
There are two triads, nine tetrads, seven pentads and one hexad as 2.3.5.11 subgroup [[11-odd-limit]] essentially tempered chords. | There are two triads, nine tetrads, seven pentads and one hexad as 2.3.5.11 subgroup [[11-odd-limit]] essentially tempered chords. In this article, voicing with the [[perfect fifth]] is prioritized. | ||
The two biyatismic triads are in inverse relationship: | The two biyatismic triads are in inverse relationship: | ||
* 1-11/8-5/3 | * 1-11/8-5/3 with steps 11/8-11/9-6/5; | ||
* 1- | * 1-11/8-18/11 with steps 11/8-6/5-11/9. | ||
For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are | For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are | ||
* 1-9/8-11/8-18/11 | * 1-9/8-11/8-18/11 with steps 9/8-11/9-6/5-11/9; | ||
* 1- | * 1-11/10-11/8-3/2 with steps 11/10-5/4-11/10-4/3; | ||
* 1-3/2-18/11-11/6 | * 1-3/2-18/11-11/6 with steps 3/2-11/10-10/9-11/10. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-11/8- | * 1-11/8-3/2-18/11 with steps 11/8-11/10-11/10-11/9, and its inverse | ||
* 1-5/4-3/2-11/6 with steps | * 1-11/10-3/2-11/6 with steps 11/10-11/8-11/9-11/10; | ||
* 1-11/8- | * 1-5/4-3/2-11/6 with steps 5/4-6/5-11/9-11/10, and its inverse | ||
* 1-6/5-3/2-18/11 with steps 6/5-5/4-11/10-11/9; | |||
* 1-11/8-3/2-5/3 with steps 11/8-11/10-10/9-6/5, and its inverse | |||
* 1-11/10-3/2-9/5 with steps 11/10-11/8-6/5-10/9. | |||
For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is | For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is | ||
| Line 21: | Line 24: | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-11/8-3/2-5/3-11/6 with steps | * 1-11/8-3/2-5/3-11/6 with steps 11/8-11/10-10/9-11/10-11/10 and its inverse | ||
* 1-5/4-3/2-5/3-11/6 with steps | * 1-11/10-3/2-18/11-9/5 with steps 11/10-11/8-11/10-11/10-10/9; | ||
* 1-5/4-11/8-3/2-11/6 with steps | * 1-5/4-3/2-5/3-11/6 with steps 5/4-6/5-10/9-11/10-11/10 and its inverse | ||
* 1-6/5-3/2-11/8-11/6 with steps 6/5-5/4-11/10-11/10-10/9; | |||
* 1-5/4-11/8-3/2-11/6 with steps 5/4-11/10-11/10-11/9-11/10 and its inverse | |||
* 1-11/10-6/5-3/2-18/11 with steps 11/10-11/10-5/4-11/10-11/9. | |||
Finally there is a palindromic hexad, | Finally, there is a palindromic hexad, | ||
* 1-5/4-11/8-3/2-5/3-11/6 with steps | * 1-5/4-11/8-3/2-5/3-11/6 with steps 5/4-11/10-11/10-10/9-11/10-11/10. | ||
Equal temperaments with biyatismic chords include {{Optimal ET sequence| 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53 }}. | Equal temperaments with biyatismic chords include {{Optimal ET sequence| 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53 }}. | ||
Revision as of 12:24, 9 September 2023
Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.
There are two triads, nine tetrads, seven pentads and one hexad as 2.3.5.11 subgroup 11-odd-limit essentially tempered chords. In this article, voicing with the perfect fifth is prioritized.
The two biyatismic triads are in inverse relationship:
- 1-11/8-5/3 with steps 11/8-11/9-6/5;
- 1-11/8-18/11 with steps 11/8-6/5-11/9.
For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are
- 1-9/8-11/8-18/11 with steps 9/8-11/9-6/5-11/9;
- 1-11/10-11/8-3/2 with steps 11/10-5/4-11/10-4/3;
- 1-3/2-18/11-11/6 with steps 3/2-11/10-10/9-11/10.
The inversely related pairs of chords are
- 1-11/8-3/2-18/11 with steps 11/8-11/10-11/10-11/9, and its inverse
- 1-11/10-3/2-11/6 with steps 11/10-11/8-11/9-11/10;
- 1-5/4-3/2-11/6 with steps 5/4-6/5-11/9-11/10, and its inverse
- 1-6/5-3/2-18/11 with steps 6/5-5/4-11/10-11/9;
- 1-11/8-3/2-5/3 with steps 11/8-11/10-10/9-6/5, and its inverse
- 1-11/10-3/2-9/5 with steps 11/10-11/8-6/5-10/9.
For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
- 1-9/8-11/8-3/2-18/11 chord with steps of 9/8-11/9-11/10-11/10-11/9.
The inversely related pairs of chords are
- 1-11/8-3/2-5/3-11/6 with steps 11/8-11/10-10/9-11/10-11/10 and its inverse
- 1-11/10-3/2-18/11-9/5 with steps 11/10-11/8-11/10-11/10-10/9;
- 1-5/4-3/2-5/3-11/6 with steps 5/4-6/5-10/9-11/10-11/10 and its inverse
- 1-6/5-3/2-11/8-11/6 with steps 6/5-5/4-11/10-11/10-10/9;
- 1-5/4-11/8-3/2-11/6 with steps 5/4-11/10-11/10-11/9-11/10 and its inverse
- 1-11/10-6/5-3/2-18/11 with steps 11/10-11/10-5/4-11/10-11/9.
Finally, there is a palindromic hexad,
- 1-5/4-11/8-3/2-5/3-11/6 with steps 5/4-11/10-11/10-10/9-11/10-11/10.
Equal temperaments with biyatismic chords include 7, 9, 15, 16, 22, 24, 29, 31, 38, 46 and 53.