Biyatismic chords: Difference between revisions
Jump to navigation
Jump to search
mNo edit summary |
m -redundant category; +link |
||
| 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]]. | ||
The [[biyatismic]] temperament contains many possibilities for essentially tempered dyadic chords including 2 triads and 6 tetrads in the [[11-odd-limit]] of the 2.3.5.11 subgroup, but all of these become essentially just in the [[15-odd-limit]]. | The [[biyatismic]] temperament contains many possibilities for essentially tempered dyadic chords including 2 triads and 6 tetrads in the [[11-odd-limit]] of the 2.3.5.11 [[subgroup]], but all of these become essentially just in the [[15-odd-limit]]. | ||
The two biyatismic triads are in inverse relationship: | The two biyatismic triads are in inverse relationship: | ||
| Line 23: | Line 23: | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triad]] | [[Category:Triad]] | ||
[[Category:Tetrad]] | [[Category:Tetrad]] | ||
[[Category:Biyatismic]] | [[Category:Biyatismic]] | ||
Revision as of 06:51, 28 April 2023
Biyatismic chords are essentially tempered dyadic chords tempered by the biyatisma, 121/120.
The biyatismic temperament contains many possibilities for essentially tempered dyadic chords including 2 triads and 6 tetrads in the 11-odd-limit of the 2.3.5.11 subgroup, but all of these become essentially just in the 15-odd-limit.
The two biyatismic triads are in inverse relationship:
- 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 two palindromic chords and two 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
- 1-11/8-5/3-11/6 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 53.