Undecimal sensamagic chords: Difference between revisions
Created page with "'''Undecimal sensamagic chords''' are essentially tempered chords of undecimal (11-limit) sensamagic, with intervals in the 11-odd-limit tonality diamond. Sinc..." |
m Improve readability; recategorize |
||
| Line 1: | Line 1: | ||
'''Undecimal sensamagic chords''' are [[essentially tempered chord]]s of undecimal (11-limit) [[sensamagic]], with intervals in the [[11-odd-limit]] [[tonality diamond]]. Since [[245/243]] is tempered out in undecimal sensamagic, 9-odd-limit [[sensamagic chords]] are undecimal sensamagic chords. Since [[385/384]] is tempered out, [[keenanismic chords]] are also undecimal sensamagic chords. Finally, since [[896/891]] is tempered out, [[pentacircle chords]] are undecimal sensamagic chords. There are also undecimal sensamagic chords which are none of these, the essentially undecimal sensamagic chords. | '''Undecimal sensamagic chords''' are [[essentially tempered chord]]s of undecimal ([[11-limit]]) [[sensamagic]], with intervals in the [[11-odd-limit]] [[tonality diamond]]. Since [[245/243]] is tempered out in undecimal sensamagic, 9-odd-limit [[sensamagic chords]] are undecimal sensamagic chords. Since [[385/384]] is tempered out, [[keenanismic chords]] are also undecimal sensamagic chords. Finally, since [[896/891]] is tempered out, [[pentacircle chords]] are undecimal sensamagic chords. There are also undecimal sensamagic chords which are none of these, the essentially undecimal sensamagic chords. | ||
There are two pairs of inversely related tetrads: | There are two pairs of inversely related tetrads: | ||
* | * 1–9/8–16/11–7/4 with steps 9/8, 9/7, 6/5, 8/7 and its inversion, | ||
* | * 1–9/7–16/11–5/3 with steps 9/7, 9/8, 8/7, 6/5; | ||
* | * 1–9/8–5/4–16/11 with steps 9/8, 10/9, 7/6, 11/8 and its inversion, | ||
* | * 1–9/8–14/9–9/5 with steps 9/8, 11/8, 7/6, 10/9. | ||
There is one pair of inversely related pentads: | There is one pair of inversely related pentads: | ||
* | * 1–9/8–5/4–16/11–7/4 with steps 9/8, 10/9, 7/6, 6/5, 8/7 and its inversion | ||
* | * 1–7/6–9/7–16/11–5/3 with steps 7/6, 10/9, 9/8, 8/7, 6/5. | ||
And one in palindromic form: | And one in palindromic form: | ||
* | * 1–9/8–9/7–14/9–16/9 with steps 9/8, 8/7, 6/5, 8/7, 9/8. | ||
The number of chords is tetrad: 4 and pentad: 3, for a total of 7. | The number of chords is tetrad: 4 and pentad: 3, for a total of 7. | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Tetrads]] | [[Category:Tetrads]] | ||
[[Category:Pentads]] | [[Category:Pentads]] | ||
[[Category:Sensamagic]] | [[Category:Sensamagic]] | ||
Latest revision as of 14:02, 15 October 2024
Undecimal sensamagic chords are essentially tempered chords of undecimal (11-limit) sensamagic, with intervals in the 11-odd-limit tonality diamond. Since 245/243 is tempered out in undecimal sensamagic, 9-odd-limit sensamagic chords are undecimal sensamagic chords. Since 385/384 is tempered out, keenanismic chords are also undecimal sensamagic chords. Finally, since 896/891 is tempered out, pentacircle chords are undecimal sensamagic chords. There are also undecimal sensamagic chords which are none of these, the essentially undecimal sensamagic chords.
There are two pairs of inversely related tetrads:
- 1–9/8–16/11–7/4 with steps 9/8, 9/7, 6/5, 8/7 and its inversion,
- 1–9/7–16/11–5/3 with steps 9/7, 9/8, 8/7, 6/5;
- 1–9/8–5/4–16/11 with steps 9/8, 10/9, 7/6, 11/8 and its inversion,
- 1–9/8–14/9–9/5 with steps 9/8, 11/8, 7/6, 10/9.
There is one pair of inversely related pentads:
- 1–9/8–5/4–16/11–7/4 with steps 9/8, 10/9, 7/6, 6/5, 8/7 and its inversion
- 1–7/6–9/7–16/11–5/3 with steps 7/6, 10/9, 9/8, 8/7, 6/5.
And one in palindromic form:
- 1–9/8–9/7–14/9–16/9 with steps 9/8, 8/7, 6/5, 8/7, 9/8.
The number of chords is tetrad: 4 and pentad: 3, for a total of 7.