Pentacircle chords: Difference between revisions
+pattern of chords |
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 |
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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: | ||
* | * 1–9/8–14/11 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 | 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 | 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: | 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 temperament]]s with pentacircle chords include {{EDOs| 22, 27, 41, 46, 58, 68, 80, 87, 121, 145, 167, and 208 }}, with 208edo giving the [[optimal patent val]]. | ||
[[Category:11-odd-limit]] | [[Category:11-odd-limit chords]] | ||
[[Category:Essentially tempered chords]] | [[Category:Essentially tempered chords]] | ||
[[Category:Triads]] | [[Category:Triads]] | ||