Buzurgismic chords: Difference between revisions
Jump to navigation
Jump to search
Expand |
mNo edit summary |
||
| Line 1: | Line 1: | ||
'''Buzurgismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]]. | '''Buzurgismic chords''' are [[Dyadic chord|essentially tempered dyadic chords]] tempered by the buzurgisma, [[169/168]]. | ||
The [[buzurgismic]] temperament is very comparable to the [[biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]]. | The [[buzurgismic]] temperament is very comparable to the [[Biyatismic temperaments|biyatismic]] temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup [[13-odd-limit]]. | ||
The two buzurgismic triads are in inverse relationship: | The two buzurgismic triads are in inverse relationship: | ||
| Line 12: | Line 12: | ||
* 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3. | * 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse | * 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse | ||
* 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12; | * 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12; | ||
| Line 23: | Line 23: | ||
* 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13. | * 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13. | ||
The inversely related pairs of chords are | The inversely related pairs of chords are | ||
* 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse | * 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse | ||
* 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12; | * 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12; | ||
| Line 33: | Line 33: | ||
Finally, there is a palindromic hexad, | Finally, there is a palindromic hexad, | ||
* 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7. | * 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7. | ||
Equal temperaments with buzurgismic chords include {{Optimal ET sequence|7, 9, 10, 17, 19, 26, 27, 36, 46, 53, 63 and 72}}. | |||
[[Category:13-odd-limit]] | [[Category:13-odd-limit]] | ||
Revision as of 13:48, 1 November 2023
Buzurgismic chords are essentially tempered dyadic chords tempered by the buzurgisma, 169/168.
The buzurgismic temperament is very comparable to the biyatismic temperament. It has two triads, nine tetrads, seven pentads and one hexad in the 2.3.7.13 subgroup 13-odd-limit.
The two buzurgismic triads are in inverse relationship:
- 1-7/6-13/8 with steps 7/6-18/13-16/13;
- 1-18/13-13/8 with steps 18/13-7/6-16/13.
For tetrads, there are three palindromic chords and three pairs of chords in inverse relationship. The palindromic chords are
- 1-9/8-18/13-13/8 with steps 9/8-16/13-7/6-16/13;
- 1-3/2-13/8-13/7 with steps 3/2-13/12-8/7-13/12;
- 1-13/12-18/13-3/2 with steps 13/12-9/7-13/12-4/3.
The inversely related pairs of chords are
- 1-18/13-3/2-13/8 with steps 18/13-13/12-13/12-16/13, and its inverse
- 1-13/12-3/2-13/7 with steps 13/12-18/13-16/13-13/12;
- 1-13/12-3/2-7/4 with steps 13/12-18/13-7/6-8/7, and its inverse
- 1-18/13-3/2-12/7 with steps 18/13-13/12-8/7-7/6;
- 1-7/6-3/2-13/8 with steps 7/6-9/7-13/12-16/13, and its inverse
- 1-9/7-3/2-13/7 with steps 9/7-7/6-16/13-13/12.
For pentads, there are one palindromic chord and three pairs of chords in inverse relationship. The palindromic chord is
- 1-9/8-18/13-3/2-13/8 with steps 9/8-16/13-13/12-13/12-16/13.
The inversely related pairs of chords are
- 1-13/12-7/6-3/2-13/8 with steps 13/12-13/12-9/7-13/12-16/13, and its inverse
- 1-9/7-18/13-3/2-13/7 with steps 9/7-13/12-13/12-16/13-13/12;
- 1-13/12-7/6-3/2-7/4 with steps 13/12-13/12-9/7-7/6-8/7, and its inverse
- 1-9/7-18/13-3/2-12/7 with steps 9/7-13/12-13/12-8/7-7/6;
- 1-13/12-3/2-13/8-7/4 with steps 13/12-18/13-13/12-13/12-8/7, and its inverse
- 1-18/13-3/2-12/7-13/7 with steps 18/13-13/12-8/7-13/12-13/12;
Finally, there is a palindromic hexad,
- 1-13/12-7/6-3/2-13/8-7/4 with steps 13/12-13/12-9/7-13/12-13/12-8/7.
Equal temperaments with buzurgismic chords include 7, 9, 10, 17, 19, 26, 27, 36, 46, 53, 63 and 72.