Superpyth: Difference between revisions

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| Comma basis = [[64/63]] (2.3.7); <br> [[64/63]], [[245/243]] (7-limit); <br>[[64/63]], [[100/99]], [[245/243]] (11-limit)

| Mapping = 1; 1 9 -2 16

| Edo join 1 = 5e | Edo join 2 = 22

| Edo join 1 = 22 | Edo join 2 = 27e

| Generator = 3/2

| Generator tuning = 710.1

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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]]. 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 13 tends to be tuned very sharp except in 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. Alternatively, one can keep the superpyth mappings of 5 and 11 to get [[~~Archytas~~ clan#Thomas|thomas]].

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 13 tends to be tuned very sharp except in 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. Alternatively, one can keep the superpyth mappings of 5 and 11 to get [[archytas clan #Thomas|thomas]].

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

@@ Line 10: / Line 10: @@
 | Comma basis = [[64/63]] (2.3.7); <br> [[64/63]], [[245/243]] (7-limit); <br>[[64/63]], [[100/99]], [[245/243]] (11-limit)
 | Mapping = 1; 1 9 -2 16
-| Edo join 1 = 5e | Edo join 2 = 22
+| Edo join 1 = 22 | Edo join 2 = 27e
 | Generator = 3/2
 | Generator tuning = 710.1
@@ Line 30: / Line 30: @@
 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]]. 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 13 tends to be tuned very sharp except in 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. Alternatively, one can keep the superpyth mappings of 5 and 11 to get [[Archytas clan#Thomas|thomas]].
+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 13 tends to be tuned very sharp except in 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. Alternatively, one can keep the superpyth mappings of 5 and 11 to get [[archytas clan #Thomas|thomas]].
 [[Mos scale]]s of superpyth have cardinalities of 5, 7, 12, 17, or 22.