Pentacircle chords: Difference between revisions
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A '''pentacircle chord''' is an [[ | 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; and 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; and 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 and 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. | The count of chords is triads: 3, tetrads: 6, pentads: 2, for a total of 11. | ||
Equal divisions with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, 208, 266e and 433bce. | Equal divisions with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, 208, 266e and 433bce. | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category:Chords]] | [[Category:Chords]] | ||
[[Category:Essentially tempered chords]] | |||
[[Category:Pentacircle]] | [[Category:Pentacircle]] | ||
[[Category:Tetrad]] | [[Category:Tetrad]] | ||
[[Category:Todo:add links]] | [[Category:Todo:add links]] | ||
Revision as of 07:12, 20 May 2021
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; and 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; and 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 and 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 with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, 208, 266e and 433bce.