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 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-G♭), by tempering out 99/98. The latter is called '''supra''', or '''suprapyth'''. The two mappings unite on [[22EDO~~|22edo~~]].

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-G♭), by tempering out 99/98. The latter is called '''supra''', or '''suprapyth'''. The two mappings unite on [[22edo|22EDO]].

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

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[[Category:Sensamagic clan]]

[[Category:Orwellismic temperaments]]

~~{{IoT}}~~

[[Category:Index of temperaments]]

[[Category:~~22edo~~]]

@@ Line 9: / Line 9: @@
 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 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-G♭), by tempering out 99/98. The latter is called '''supra''', or '''suprapyth'''. The two mappings unite on [[22EDO|22edo]].
+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-G♭), by tempering out 99/98. The latter is called '''supra''', or '''suprapyth'''. The two mappings unite on [[22edo|22EDO]].
 [[MOS scale]]s of superpyth have cardinalities of 5, 7, 12, 17, or 22.
@@ Line 299: / Line 299: @@
 [[Category:Sensamagic clan]]
 [[Category:Orwellismic temperaments]]
-{{IoT}}
+[[Category:Index of temperaments]]
-[[Category:22edo]]