Biyatismic chords: Difference between revisions
Jump to navigation
Jump to search
m Improve readability and +categories |
Corrections. 1-11/8-11/6 is clearly utonal; 1-9/8-11/8-11/6, 1-4/3-3/2-18/11, and 1-6/5-3/2-11/6 aren't 11-odd-limit concordances; all 15-odd-limit chords here are either essentially just or aren't concordances |
||
| Line 1: | Line 1: | ||
'''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]]. | ||
Biyatismic temperament contains many possibilities for essentially tempered dyadic chords including | Biyatismic temperament contains many possibilities for essentially tempered dyadic chords including 3 triads and 8 tetrads in the [[11-odd-limit]] of the 2.3.5.11 subgroup. | ||
The biyatismic triads | The 3 biyatismic triads are a palindromic chord and a pair of chords in inverse relationship. The palindromic chord is | ||
* 1-[[11/8]]-[[16/11]] chord with steps of 11/8-[[16/15]]-11/8. | * 1-[[11/8]]-[[16/11]] chord with steps of 11/8-[[16/15]]-11/8. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-11/8-[[5/3]] chord with steps of 11/8-[[11/9]]-[[6/5]]; | |||
* 1-11/8-[[5/3]] chord with steps of 11/8-[[11/9]]-[[6/5]] | * 1-6/5-16/11 chord with steps of 6/5-11/9-11/8. | ||
For tetrads, there are 2 palindromic chords and 3 pairs of chords in inverse relationship. The palindromic chords are | |||
* 1-9/8-11/8-18/11 chord with steps of 9/8-11/9-6/5-11/9 | * 1-9/8-11/8-18/11 chord with steps of 9/8-11/9-6/5-11/9; | ||
* 1-5/4-11/8-11/6 chord with steps of 5/4-11/10-4/3-11/10 | * 1-5/4-11/8-11/6 chord with steps of 5/4-11/10-4/3-11/10. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-11/9-11/8-18/11 chord with steps of 11/9-9/8-6/5-11/9, and 1-11/9-16/11-18/11 chord with steps of 11/9-6/5-9/8-11/9; | |||
* 1-11/9-11/8-18/11 chord with steps of 11/9-9/8-6/5-11/9 and 1-11/9-16/11-18/11 chord with steps of 11/9-6/5-9/8-11/9; | * 1-11/8-5/3-11/6 chord with steps of 11/8-11/9-11/10-11/10, and 1-11/10-6/5-16/11 chord with steps of 11/10-11/10-11/9-11/8; | ||
* 1-11/8-5/3-11/6 chord with steps of 11/8-11/9-11/10-11/10 and 1-11/10-6/5-16/11 chord with steps of 11/10-11/10-11/9-11/8 | * 1-5/4-3/2-11/6 chord with steps of 5/4-6/5-11/9-11/10, and 1-11/10-4/3-8/5 chord with steps of 11/10-11/9-6/5-5/4. | ||
* 1-5/4-3/2-11/6 chord with steps of 5/4-6/5-11/9-11/10 and 1-11/10-4/3-8/5 chord with steps of 11/10-11/9-6/5-5/4 | |||
Equal temperaments with biyatismic chords include {{Vals| 7-, 9-, 15-, 16-, 22-, 24-, 29-, 31-, 38-, 46-, and 53et }}. | Equal temperaments with biyatismic chords include {{Vals| 7-, 9-, 15-, 16-, 22-, 24-, 29-, 31-, 38-, 46-, and 53et }}. | ||
Revision as of 21:55, 6 January 2022
Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.
Biyatismic temperament contains many possibilities for essentially tempered dyadic chords including 3 triads and 8 tetrads in the 11-odd-limit of the 2.3.5.11 subgroup.
The 3 biyatismic triads are a palindromic chord and a pair of chords in inverse relationship. The palindromic chord is
The inversely related pairs of chords are
For tetrads, there are 2 palindromic chords and 3 pairs of chords in inverse relationship. The palindromic chords are
- 1-9/8-11/8-18/11 chord with steps of 9/8-11/9-6/5-11/9;
- 1-5/4-11/8-11/6 chord with steps of 5/4-11/10-4/3-11/10.
The inversely related pairs of chords are
- 1-11/9-11/8-18/11 chord with steps of 11/9-9/8-6/5-11/9, and 1-11/9-16/11-18/11 chord with steps of 11/9-6/5-9/8-11/9;
- 1-11/8-5/3-11/6 chord with steps of 11/8-11/9-11/10-11/10, and 1-11/10-6/5-16/11 chord with steps of 11/10-11/10-11/9-11/8;
- 1-5/4-3/2-11/6 chord with steps of 5/4-6/5-11/9-11/10, and 1-11/10-4/3-8/5 chord with steps of 11/10-11/9-6/5-5/4.
Equal temperaments with biyatismic chords include 7-, 9-, 15-, 16-, 22-, 24-, 29-, 31-, 38-, 46-, and 53et.