Superpyth: Difference between revisions

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'''Superpyth''', a member of the [[Archytas_clan|Archytas clan]], has 4/3 as a generator, and the Archytas comma 64/63 is [[tempering_out|tempered out]], so two generators represents 7/4 in addition to 16/9. Since 4/3 is a generator we can use the same standard chain-of-fourths notation that is also used for [[Meantone|meantone]] and [[~~12edo|~~12edo]], with the understanding that, for example, A# is sharper than Bb (in contrast to meantone where A# is flatter than Bb, or 12edo where they are identical). An interesting coincidence is that the [http://en.wikipedia.org/wiki/Plastic_number plastic number]has a value of ~486.822 cents, which, taken as a generator and assuming an octave period, constitutes a variety of superpyth.

'''Superpyth''', a member of the [[Archytas_clan|Archytas clan]], has 4/3 as a generator, and the Archytas comma 64/63 is [[tempering_out|tempered out]], so two generators represents 7/4 in addition to 16/9. Since 4/3 is a generator we can use the same standard chain-of-fourths notation that is also used for [[Meantone|meantone]] and [[12edo]], with the understanding that, for example, A# is sharper than Bb (in contrast to meantone where A# is flatter than Bb, or 12edo where they are identical). An interesting coincidence is that the [http://en.wikipedia.org/wiki/Plastic_number plastic number]has a value of ~486.822 cents, which, taken as a generator and assuming an octave period, constitutes a variety of superpyth.

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.

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-'''Superpyth''', a member of the [[Archytas_clan|Archytas clan]], has 4/3 as a generator, and the Archytas comma 64/63 is [[tempering_out|tempered out]], so two generators represents 7/4 in addition to 16/9. Since 4/3 is a generator we can use the same standard chain-of-fourths notation that is also used for [[Meantone|meantone]] and [[12edo|12edo]], with the understanding that, for example, A# is sharper than Bb (in contrast to meantone where A# is flatter than Bb, or 12edo where they are identical). An interesting coincidence is that the [http://en.wikipedia.org/wiki/Plastic_number plastic number]has a value of ~486.822 cents, which, taken as a generator and assuming an octave period, constitutes a variety of superpyth.
+'''Superpyth''', a member of the [[Archytas_clan|Archytas clan]], has 4/3 as a generator, and the Archytas comma 64/63 is [[tempering_out|tempered out]], so two generators represents 7/4 in addition to 16/9. Since 4/3 is a generator we can use the same standard chain-of-fourths notation that is also used for [[Meantone|meantone]] and [[12edo]], with the understanding that, for example, A# is sharper than Bb (in contrast to meantone where A# is flatter than Bb, or 12edo where they are identical). An interesting coincidence is that the [http://en.wikipedia.org/wiki/Plastic_number plastic number]has a value of ~486.822 cents, which, taken as a generator and assuming an octave period, constitutes a variety of superpyth.
 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.

Superpyth: Difference between revisions

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