Pentacircle chords: Difference between revisions
Jump to navigation
Jump to search
m Added links (as requested by the to:do notice) |
m Removing from Category:Chords using Cat-a-lot |
||
| Line 24: | Line 24: | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Pentacircle]] | [[Category:Pentacircle]] | ||
[[Category:Tetrad]] | [[Category:Tetrad]] | ||
Revision as of 03:51, 28 April 2023
A pentacircle chord is an essentially tempered dyadic chord in the 2.9.7.11 subgroup in the 11-odd-limit, tempering out the pentacircle comma, 896/891.
The pentacircle triads are three in number:
- 1-9/7-16/9 with steps 9/7-11/8-9/8
- 1-9/7-16/11 with steps 9/7-9/8-11/8
- 1-11/7-16/9 with steps 11/7-9/8-9/8.
There are six pentacircle tetrads:
- the palindromic 1-9/8-14/9-7/4 with steps 9/8-11/8-9/8-8/7
- the palindromic 1-9/8-11/8-14/9 with steps 9/8-11/9-9/8-9/7
- the inverse pair 1-11/8-11/7-16/9 with steps 11/8-8/7-9/8-9/8 and 1-11/8-14/9-7/4 with steps 11/8-9/8-9/8-8/7
- the inverse pair 1-11/9-11/7-16/9 with steps 11/9-9/7-9/8-9/8 and 1-11/9-11/8-14/9 with steps 11/9-9/8-9/8-9/7
Finally, there are two pentacircle pentads, inversely related:
- 1-11/9-11/8-11/7-16/9 with steps 11/9-9/8-8/7-9/8-9/8
- 1-11/9-11/8-14/9-16/9 with steps 11/9-9/8-9/8-8/7-9/8
The count of chords is triads: 3, tetrads: 6, pentads: 2, for a total of 11.
Equal divisions of the octave with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, 208, 266e and 433bce.