Superpyth: Difference between revisions

Line 5:

| ja =

}}

'''Superpyth''' is a [[regular temperament|temperament]] where [[~]][[3/2]] is a [[generator]], and the septimal comma ([[64/63]]) is [[tempering out|tempered out]], so that a stack of two perfect fifths [[octave reduction|octave-reduced]] gives a major whole tone that represents both [[9/8]] and [[8/7]] (likewise, two perfect fourths give a minor seventh that represents both [[7/4]] and [[16/9]], so intervals such as A–G and C–B♭ are harmonic sevenths). ~~Since the generator is~~ a ~~perfect fifth, superpyth can be notated using the same standard [[chain-of-fifths notation]]~~ that ~~is also used for~~ [[~~meantone~~]], ~~with the understanding~~ that ~~sharps are sharper than flats (for example, A♯ is sharper than B♭) just like in~~ [[~~Pythagorean tuning]], in contrast to meantone where sharps are flatter than or equal to the corresponding flats. [[17edo|10\17]], [[22edo|13\22]], and [[27edo|16\27~~]] ~~are typical tunings of the generator~~.

'''Superpyth''' is a [[regular temperament|temperament]] where [[~]][[3/2]] is a [[generator]], and the septimal comma ([[64/63]]) is [[tempering out|tempered out]], so that a stack of two perfect fifths [[octave reduction|octave-reduced]] gives a major whole tone that represents both [[9/8]] and [[8/7]], and likewise, two perfect fourths give a minor seventh that represents both [[7/4]] and [[16/9]], so intervals such as A–G and C–B♭ are harmonic sevenths. Moreover, three fourths reach a subminor third that approximates [[7/6]], while four fifths reach a supermajor third that approximates [[9/7]].

As a ~~consequence of the~~ fifth ~~being tuned sharp~~, ~~three fourths reach a subminor third~~ that ~~approximates 7/6 instead of 6/5~~, ~~while four fifths reach a supermajor third~~ that ~~approximates 9/7~~.

Since the generator is a perfect fifth, superpyth can be notated using the same standard [[chain-of-fifths notation]] that is also used for [[meantone]], with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭) just like in [[Pythagorean tuning]], in contrast to meantone where sharps are flatter than or equal to the corresponding flats. [[17edo|10\17]], [[22edo|13\22]], and [[27edo|16\27]] are typical tunings of the generator.

Such a temperament without the [[5/1|5th harmonic]] is also called '''archy'''. If intervals of 5 are desired, the 5th harmonic is mapped to +9 generators through tempering out [[245/243]], so C–D♯ is 5/4. So superpyth is the "opposite" of meantone in several different ways: most notably, meantone (including [[12edo]]) has the fifth tuned flat so that intervals of harmonic 5 are simple while intervals of 7 are complex, while superpyth has the fifth tuned sharp so that intervals of 7 are simple while intervals of 5 are complex.

@@ Line 5: / Line 5: @@
 | ja =
 }}
-'''Superpyth''' is a [[regular temperament|temperament]] where [[~]][[3/2]] is a [[generator]], and the septimal comma ([[64/63]]) is [[tempering out|tempered out]], so that a stack of two perfect fifths [[octave reduction|octave-reduced]] gives a major whole tone that represents both [[9/8]] and [[8/7]] (likewise, two perfect fourths give a minor seventh that represents both [[7/4]] and [[16/9]], so intervals such as A–G and C–B♭ are harmonic sevenths). Since the generator is a perfect fifth, superpyth can be notated using the same standard [[chain-of-fifths notation]] that is also used for [[meantone]], with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭) just like in [[Pythagorean tuning]], in contrast to meantone where sharps are flatter than or equal to the corresponding flats. [[17edo|10\17]], [[22edo|13\22]], and [[27edo|16\27]] are typical tunings of the generator.
+'''Superpyth''' is a [[regular temperament|temperament]] where [[~]][[3/2]] is a [[generator]], and the septimal comma ([[64/63]]) is [[tempering out|tempered out]], so that a stack of two perfect fifths [[octave reduction|octave-reduced]] gives a major whole tone that represents both [[9/8]] and [[8/7]], and likewise, two perfect fourths give a minor seventh that represents both [[7/4]] and [[16/9]], so intervals such as A–G and C–B♭ are harmonic sevenths. Moreover, three fourths reach a subminor third that approximates [[7/6]], while four fifths reach a supermajor third that approximates [[9/7]].
-As a consequence of the fifth being tuned sharp, three fourths reach a subminor third that approximates 7/6 instead of 6/5, while four fifths reach a supermajor third that approximates 9/7.
+Since the generator is a perfect fifth, superpyth can be notated using the same standard [[chain-of-fifths notation]] that is also used for [[meantone]], with the understanding that sharps are sharper than flats (for example, A♯ is sharper than B♭) just like in [[Pythagorean tuning]], in contrast to meantone where sharps are flatter than or equal to the corresponding flats. [[17edo|10\17]], [[22edo|13\22]], and [[27edo|16\27]] are typical tunings of the generator.
 Such a temperament without the [[5/1|5th harmonic]] is also called '''archy'''. If intervals of 5 are desired, the 5th harmonic is mapped to +9 generators through tempering out [[245/243]], so C–D♯ is 5/4. So superpyth is the "opposite" of meantone in several different ways: most notably, meantone (including [[12edo]]) has the fifth tuned flat so that intervals of harmonic 5 are simple while intervals of 7 are complex, while superpyth has the fifth tuned sharp so that intervals of 7 are simple while intervals of 5 are complex.

Superpyth: Difference between revisions

FloraC (talk | contribs)