Superpyth: Difference between revisions

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If the 5th harmonic is used at all, it is mapped to -9 generators, so C-D# is 5/4. So superpyth is "the opposite" of septimal meantone in several different ways: meantone has 4/3 tempered wide so that intervals of 5 are simple and intervals of 7 are complex, while superpyth has 4/3 tempered narrow so that intervals of 7 are simple while intervals of 5 are complex.

If intervals of 11 are desired, the ~~simplest reasonable~~ way is to map 11/8 to 6 generators (so 11/8 is a "diminished fifth"), by tempering out 99/98. ~~This temperament~~ is called "'''supra'''", or "'''suprapyth'''".

If intervals of 11 are desired, the canonical way is to map 11/8 to -16 generators, so 11/8 is a double augmented second (C-Dx), tempering out 100/99. Yet a simpler but reasonable way is to map it to +6 generators, so 11/8 is a diminished fifth (C-Gb), by tempering out 99/98. The latter is called '''supra''', or '''suprapyth'''. The two mappings unite on [[22edo]].

~~MOSes include~~ 5, 7, 12, 17, ~~and~~ 22.

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

== Temperament data ==

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 If the 5th harmonic is used at all, it is mapped to -9 generators, so C-D# is 5/4. So superpyth is "the opposite" of septimal meantone in several different ways: meantone has 4/3 tempered wide so that intervals of 5 are simple and intervals of 7 are complex, while superpyth has 4/3 tempered narrow so that intervals of 7 are simple while intervals of 5 are complex.
-If intervals of 11 are desired, the simplest reasonable way is to map 11/8 to 6 generators (so 11/8 is a "diminished fifth"), by tempering out 99/98. This temperament is called "'''supra'''", or "'''suprapyth'''".
+If intervals of 11 are desired, the canonical way is to map 11/8 to -16 generators, so 11/8 is a double augmented second (C-Dx), tempering out 100/99. Yet a simpler but reasonable way is to map it to +6 generators, so 11/8 is a diminished fifth (C-Gb), by tempering out 99/98. The latter is called '''supra''', or '''suprapyth'''. The two mappings unite on [[22edo]].
-MOSes include 5, 7, 12, 17, and 22.
+[[MOS scale]]s of superpyth have cardinalities of 5, 7, 12, 17, or 22.
 == Temperament data ==