Superpyth: Difference between revisions

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Alternatively, for a sharper tuning, the 5th harmonic can be mapped to +14 generators, resulting in [[ultrapyth]]. For a tuning flat of 22edo, the 5th harmonic can be mapped to -13 generators to get [[quasisuper]].

If intervals of 11 are desired, the canonical way is to map 11/8 to +16 generators, or a doubly augmented second (C–D𝄪), tempering out 100/99. A simpler way to map it is to −6 generators, or a diminished fifth (C–G♭), by tempering out 99/98. The latter is called '''supra''' or '''suprapyth''', a name coined by [[Mike Battaglia]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96882.html#96895 Yahoo! Tuning Group | ''A few full 11-limit 896/891 temperaments'']</ref>. The two mappings unite on [[22edo]]. Note that the only reasonable tuning for suprapyth is 22edo, as sharper tunings swap the sizes of 11/10 and 12/11, and flatter tunings swap 11/10 and 10/9 as well as 7/5 and 10/7. However, by keeping the 2.3.7.11 mapping of suprapyth (simply called [[supra]]) and using the quasisuper mapping of 5, we get [[quasisupra]], which has a flexible tuning range.

If intervals of 11 are desired, the canonical way is to map [[11/8]] to +16 generators, or a doubly augmented second (C–D𝄪), tempering out [[100/99]]. A simpler way to map it is to −6 generators, or a diminished fifth (C–G♭), by tempering out [[99/98]]. The latter is called '''supra''' or '''suprapyth''', a name coined by [[Mike Battaglia]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96882.html#96895 Yahoo! Tuning Group | ''A few full 11-limit 896/891 temperaments'']</ref>. The two mappings unite on [[22edo]]. Note that the only reasonable tuning for suprapyth is 22edo, as sharper tunings swap the sizes of [[11/10]] and [[12/11]], and flatter tunings swap [[11/10]] and [[10/9]], as well as [[7/5]] and [[10/7]]. However, by keeping the 2.3.7.11 mapping of suprapyth (simply called [[supra]]) and using the quasisuper mapping of 5, we get [[quasisupra]], which has a flexible tuning range.

If intervals of 13 are desired, 13/8 is mapped to +13 generators, or a doubly augmented fourth (C–F𝄪), by tempering out [[31213/31104]].

If intervals of 13 are desired, 13/8 is mapped to +13 generators, or a doubly augmented fourth (C–F𝄪), by tempering out [[31213/31104]]. In practice, however, this mapping only works in [[27edo]], as flatter tunings swap the sizes of [[13/12]] and [[14/13]]. An alternative mapping is -14 generators, or a doubly diminished octave (C-C𝄫), by tempering out [[9604/9477]]. This has a more flexible range, but the only non-enfactored patent val supporting it which doesn't swap the sizes of 13/12 and 14/13 is that of 27edo. A more practical option is to split the sharp ~3/2 into two ~[[16/13]]'s, which results in [[beatles]], and has an alternative mapping of primes 5 and 11.

[[Mos scale]]s of superpyth have cardinalities of 5, 7, 12, 17, or 22.

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 Alternatively, for a sharper tuning, the 5th harmonic can be mapped to +14 generators, resulting in [[ultrapyth]]. For a tuning flat of 22edo, the 5th harmonic can be mapped to -13 generators to get [[quasisuper]].
-If intervals of 11 are desired, the canonical way is to map 11/8 to +16 generators, or a doubly augmented second (C–D𝄪), tempering out 100/99. A simpler way to map it is to −6 generators, or a diminished fifth (C–G♭), by tempering out 99/98. The latter is called '''supra''' or '''suprapyth''', a name coined by [[Mike Battaglia]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96882.html#96895 Yahoo! Tuning Group | ''A few full 11-limit 896/891 temperaments'']</ref>. The two mappings unite on [[22edo]]. Note that the only reasonable tuning for suprapyth is 22edo, as sharper tunings swap the sizes of 11/10 and 12/11, and flatter tunings swap 11/10 and 10/9 as well as 7/5 and 10/7. However, by keeping the 2.3.7.11 mapping of suprapyth (simply called [[supra]]) and using the quasisuper mapping of 5, we get [[quasisupra]], which has a flexible tuning range.
+If intervals of 11 are desired, the canonical way is to map [[11/8]] to +16 generators, or a doubly augmented second (C–D𝄪), tempering out [[100/99]]. A simpler way to map it is to −6 generators, or a diminished fifth (C–G♭), by tempering out [[99/98]]. The latter is called '''supra''' or '''suprapyth''', a name coined by [[Mike Battaglia]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96882.html#96895 Yahoo! Tuning Group | ''A few full 11-limit 896/891 temperaments'']</ref>. The two mappings unite on [[22edo]]. Note that the only reasonable tuning for suprapyth is 22edo, as sharper tunings swap the sizes of [[11/10]] and [[12/11]], and flatter tunings swap [[11/10]] and [[10/9]], as well as [[7/5]] and [[10/7]]. However, by keeping the 2.3.7.11 mapping of suprapyth (simply called [[supra]]) and using the quasisuper mapping of 5, we get [[quasisupra]], which has a flexible tuning range.
-If intervals of 13 are desired, 13/8 is mapped to +13 generators, or a doubly augmented fourth (C–F𝄪), by tempering out [[31213/31104]].
+If intervals of 13 are desired, 13/8 is mapped to +13 generators, or a doubly augmented fourth (C–F𝄪), by tempering out [[31213/31104]]. In practice, however, this mapping only works in [[27edo]], as flatter tunings swap the sizes of [[13/12]] and [[14/13]]. An alternative mapping is -14 generators, or a doubly diminished octave (C-C𝄫), by tempering out [[9604/9477]]. This has a more flexible range, but the only non-enfactored patent val supporting it which doesn't swap the sizes of 13/12 and 14/13 is that of 27edo. A more practical option is to split the sharp ~3/2 into two ~[[16/13]]'s, which results in [[beatles]], and has an alternative mapping of primes 5 and 11.
 [[Mos scale]]s of superpyth have cardinalities of 5, 7, 12, 17, or 22.