Superpyth: Difference between revisions
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'''Superpyth''', a member of the [[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]] and [[12edo | '''Superpyth''', a member of the [[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]] and [[12edo]], with the understanding that, for example, A♯ is sharper than B♭ (in contrast to meantone where A♯ is flatter than B♭, or 12edo where they are identical). An interesting coincidence is that the [[Wikipedia: 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 through tempering out [[245/243]], so C-D♯ is 5/4. So superpyth is " | Such a temperament without the 5th harmonic is also called '''archy'''. If the 5th harmonic is used at all, it is mapped to -9 generators through tempering out [[245/243]], 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 | 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]]. | ||
[[MOS scale]]s of superpyth have cardinalities of 5, 7, 12, 17, or 22. | [[MOS scale]]s of superpyth have cardinalities of 5, 7, 12, 17, or 22. | ||
== Temperament data == | == Temperament data == | ||
{{ | {{Main| Archytas clan #Superpyth }} | ||
== Interval chains == | == Interval chains == | ||
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* [[Archy12]] | * [[Archy12]] | ||
* [[Supra12]] | * [[Supra12]] | ||
The boundary of propriety is [[17edo | The boundary of propriety is [[17edo]]. | ||
== Tuning spectrum == | == Tuning spectrum == | ||
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* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22study3.mp3 12of22study3 (children's story)] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22study3.mp3 12of22study3 (children's story)] | ||
* [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22study7.mp3 12of22study7] | * [http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/12of22study7.mp3 12of22study7] | ||
By [[Joel Grant Taylor]], all in Superpyth[12] in | By [[Joel Grant Taylor]], all in Superpyth[12] in 22edo tuning. | ||
* [https://m.soundcloud.com/lillianhearne/superpyth12-chromatic-riff <nowiki>Superpyth[12] chromatic riff</nowiki>] | * [https://m.soundcloud.com/lillianhearne/superpyth12-chromatic-riff <nowiki>Superpyth[12] chromatic riff</nowiki>] | ||
* [https://m.soundcloud.com/lillianhearne/trio-in-superpyth-temperament-for-irish-whistle-cello-and-piano Trio in Superpyth Temperament for Irish Whistle, Piano, and Cello] | * [https://m.soundcloud.com/lillianhearne/trio-in-superpyth-temperament-for-irish-whistle-cello-and-piano Trio in Superpyth Temperament for Irish Whistle, Piano, and Cello] | ||
Both by [[User:Lhearne|Lillian Hearne]] in | Both by [[User:Lhearne|Lillian Hearne]] in 22edo tuning | ||
== See also == | == See also == | ||
* [[ | * [[Ultrapyth]] | ||
{{IoT}} | |||
[[Category:Superpyth| ]] <!-- main article --> | [[Category:Superpyth| ]] <!-- main article --> | ||
[[Category:Archytas clan]] | [[Category:Archytas clan]] | ||
[[Category:Sensamagic clan]] | [[Category:Sensamagic clan]] | ||
[[Category:Orwellismic temperaments]] | [[Category:Orwellismic temperaments]] | ||