Pentacircle chords: Difference between revisions
Jump to navigation
Jump to search
m Improve readability; recategorize |
It's important to single ou the palindromic triad cuz it's the most fundamental form of these chords. The rest can be viewed as variations on it |
||
| Line 3: | Line 3: | ||
Pentacircle chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.9.7.11 [[subgroup]] [[11-odd-limit]], meaning that there are 3 [[triad]]s, 6 [[tetrad]]s and 2 [[pentad]]s, for a total of 11 distinct chord structures. | Pentacircle chords are of [[Dyadic chord/Pattern of essentially tempered chords|pattern 1b]] in the 2.9.7.11 [[subgroup]] [[11-odd-limit]], meaning that there are 3 [[triad]]s, 6 [[tetrad]]s and 2 [[pentad]]s, for a total of 11 distinct chord structures. | ||
The pentacircle triads | The three pentacircle triads include a palindrome since it identifies [[14/11]] by a stack of two [[9/8]]'s: | ||
* 1–9/ | * 1–9/8–14/11 with steps 9/8, 9/8, 11/7. | ||
* 1–9/ | |||
* | And an inversely related pair: | ||
* 1–9/8–16/11 with steps 9/8, 9/7, 11/8; | |||
* 1–9/8–14/9 with steps 9/8, 11/8, 9/7; | |||
The tetrads include the palindromic | The tetrads include the palindromic | ||
Latest revision as of 13:55, 11 October 2024
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.
Pentacircle chords are of pattern 1b in the 2.9.7.11 subgroup 11-odd-limit, meaning that there are 3 triads, 6 tetrads and 2 pentads, for a total of 11 distinct chord structures.
The three pentacircle triads include a palindrome since it identifies 14/11 by a stack of two 9/8's:
- 1–9/8–14/11 with steps 9/8, 9/8, 11/7.
And an inversely related pair:
- 1–9/8–16/11 with steps 9/8, 9/7, 11/8;
- 1–9/8–14/9 with steps 9/8, 11/8, 9/7;
The tetrads include the palindromic
- 1–9/8–14/9–7/4 with steps 9/8, 11/8, 9/8, 8/7;
- 1–9/8–11/8–14/9 with steps 9/8, 11/9, 9/8, 9/7.
And the inversely related pairs
- 1–11/8–11/7–16/9 with steps 11/8, 8/7, 9/8, 9/8, and its inverse
- 1–11/8–14/9–7/4 with steps 11/8, 9/8, 9/8, 8/7;
- 1–11/9–11/7–16/9 with steps 11/9, 9/7, 9/8, 9/8, and its inverse
- 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 its inverse
- 1–11/9–11/8–14/9–16/9 with steps 11/9, 9/8, 9/8, 8/7, 9/8.
Equal temperaments with pentacircle chords include 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, and 208, with 208edo giving the optimal patent val.