Chords of superpyth: Difference between revisions
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Typing the chords requires consideration of the fact that superpyth conflates [[9/8]] with [[8/7]], and [[11/10]] with [[10/9]]. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. However, sometimes multiple such transversals exist, in which case the chord is a [[plurichord]], and the type is given for all possible interpretations. If the chord is essentially tempered, it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 8/7 or 10/9 above the root. | Typing the chords requires consideration of the fact that superpyth conflates [[9/8]] with [[8/7]], and [[11/10]] with [[10/9]]. If a transversal can be found which shows the chord to be essentially just, that transversal is listed along with a typing as otonal, utonal, or ambitonal. However, sometimes multiple such transversals exist, in which case the chord is a [[plurichord]], and the type is given for all possible interpretations. If the chord is essentially tempered, it is analyzed in terms of the transversal that requires the minimum amount of commas to be tempered out; if there is a tie between multiple transversals, it is analyzed in terms of the transversal which employs 8/7 or 10/9 above the root. | ||
Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.{{Overline|09}}[[{{c}}]]) and [[27edo|16\27]] (711.{{Overline|11}}{{c}}), and generates [[mos]] scales of the patterns [[2L 3s]] ( | Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.{{Overline|09}}[[{{c}}]]) and [[27edo|16\27]] (711.{{Overline|11}}{{c}}), and generates [[mos]] scales of the patterns [[2L 3s]] (pentic), [[5L 2s]] (diatonic), [[5L 7s]] (p-chromatic), [[5L 12s]], [[5L 17s]], and [[22L 5s]]. The pentic and diatonic scales contain some chords in the [[2.3.7 subgroup|2.3.7]] [[subgroup]], though the 12-note chromatic scale is needed to properly utilize intervals of [[5/1|5]], and intervals of [[11/1|11]] don't become common until the 17- and 22-note scales. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth has not been explored much either, so these mos scales would be a great place to start such explorations. | ||
== Triads == | == Triads == | ||
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| 1–5/4–10/7 | | 1–5/4–10/7 | ||
| Utonal | | Utonal | ||
| [[ | | [[28:35:40|1/(10:8:7)]] | ||
|- | |- | ||
| 22 | | 22 | ||
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| 1–9/7–3/2–12/7 | | 1–9/7–3/2–12/7 | ||
| Ambitonal | | Ambitonal | ||
| [[12:14:18:21]], [[14:18:21:24]]<br> 9-odd-limit [[ASS]] | | [[12:14:18:21]], [[14:18:21:24]]<br>[[9-odd-limit]] [[ASS]] | ||
|- | |- | ||
| 4 | | 4 | ||
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| 0–7–9–16 | | 0–7–9–16 | ||
| 1–10/9–5/4–11/8 | | 1–10/9–5/4–11/8 | ||
| Ptolemismic | | Ptolemismic/valinorsmic | ||
| | | | ||
|- | |- | ||