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 and 10/9 above the root.

Superpyth [[~~generate~~]]s [[~~MOS~~]] scales of 5, 7, 12, 17, 22, and ~~27 notes~~. The highest complexity of any chord on this list is 18 generators, and would thus require the 22-note MOS. ~~That being said, even~~ the 5- and 7-note MOSes contain some chords in the [[2.3.7 subgroup|2.3.7-]][[subgroup]], though the 12- and 17-note MOSes are needed to ~~explore~~ full 7- and 11-limit harmonies. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth hasn't been explored much either, so these MOS scales ~~are~~ a great place to start such explorations.

Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.09[[{{c}}]]) and [[27edo|16\27]] (711.11{{c}}), and generates scales of the [[MOS]] patterns [[2L 3s]] (pentatonic), [[5L 2s]] (diatonic), [[5L 7s]] (chromatic), [[5L 12s]], [[5L 17s]], and [[22L 5s]]. The highest complexity of any chord on this list is 18 generators, and would thus require the 22-note 5L 17s MOS, though there are many chords of much lower complexity. Even the 5-note (pentatonic) and 7-note (diatonic) MOSes contain some chords in the [[2.3.7 subgroup|2.3.7-]][[subgroup]], though the 12- and 17-note MOSes are needed to properly utilize full 7- and 11-limit harmonies. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth hasn't been explored much either, so these MOS scales would be a great place to start such explorations.

== Triads ==

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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 and 10/9 above the root.
-Superpyth [[generate]]s [[MOS]] scales of 5, 7, 12, 17, 22, and 27 notes. The highest complexity of any chord on this list is 18 generators, and would thus require the 22-note MOS. That being said, even the 5- and 7-note MOSes contain some chords in the [[2.3.7 subgroup|2.3.7-]][[subgroup]], though the 12- and 17-note MOSes are needed to explore full 7- and 11-limit harmonies. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth hasn't been explored much either, so these MOS scales are a great place to start such explorations.
+Superpyth is generated by a sharp [[~]][[3/2]] between [[22edo|13\22]] (709.09[[{{c}}]]) and [[27edo|16\27]] (711.11{{c}}), and generates scales of the [[MOS]] patterns [[2L&nbsp;3s]] (pentatonic), [[5L&nbsp;2s]] (diatonic), [[5L&nbsp;7s]] (chromatic), [[5L&nbsp;12s]], [[5L&nbsp;17s]], and [[22L&nbsp;5s]]. The highest complexity of any chord on this list is 18 generators, and would thus require the 22-note 5L&nbsp;17s MOS, though there are many chords of much lower complexity. Even the 5-note (pentatonic) and 7-note (diatonic) MOSes contain some chords in the [[2.3.7 subgroup|2.3.7-]][[subgroup]], though the 12- and 17-note MOSes are needed to properly utilize full 7- and 11-limit harmonies. Superpyth has hardly been explored in the 11-limit, and full 7-limit superpyth hasn't been explored much either, so these MOS scales would be a great place to start such explorations.
 == Triads ==