Superpyth: Difference between revisions

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{{Infobox regtemp|Comma basis=[[64/63]] (2.3.7); <br> [[64/63]], [[245/243]] (2.3.5.7)|Edo join 1=5|Edo join 2=22|Generator=4/3|Generator tuning=~~487~~.4|Optimization method=DKW|Mapping=1; 1 9 -2|MOS scales=[[2L 3s]], [[5L 2s]], [[5L 7s]]|Subgroups=2.3.7, 2.3.5.7|Title=Archy; superpyth|Odd limit 1=(2.3.7) 9|Mistuning 1=?|Odd limit 2=9|Mistuning 2=?|Complexity 1=12|Complexity 2=27}}'''Archy''' is a [[regular temperament|temperament]] where the [[generator]] is [[4/3]], tuned flat so that stacking two of them gives the interval [[7/4]]. This means that intervals such as A–G and C–B♭ (notated in chain-of-fifths notation) are harmonic sevenths. Equivalently, two [[3/2]] perfect fifths [[octave reduction|octave-reduced]] gives [[8/7]]. Three fourths reach a subminor third that approximates [[7/6]], while four fifths reach a supermajor third that approximates [[9/7]]. This means that the septimal comma ([[64/63]]) is [[tempering out|tempered out]].

{{Infobox regtemp|Comma basis=[[64/63]] (2.3.7); <br> [[64/63]], [[245/243]] (2.3.5.7)|Edo join 1=5|Edo join 2=22|Generator=3/2|Generator tuning=712.6|Optimization method=DKW|Mapping=1; 1 9 -2|MOS scales=[[2L 3s]], [[5L 2s]], [[5L 7s]]|Subgroups=2.3.7, 2.3.5.7|Title=Archy; superpyth|Odd limit 1=(2.3.7) 9|Mistuning 1=?|Odd limit 2=9|Mistuning 2=?|Complexity 1=12|Complexity 2=27}}'''Archy''' is a [[regular temperament|temperament]] where the [[generator]] is [[4/3]], tuned flat so that stacking two of them gives the interval [[7/4]]. This means that intervals such as A–G and C–B♭ (notated in chain-of-fifths notation) are harmonic sevenths. Equivalently, two [[3/2]] perfect fifths [[octave reduction|octave-reduced]] gives [[8/7]]. Three fourths reach a subminor third that approximates [[7/6]], while four fifths reach a supermajor third that approximates [[9/7]]. This means that the septimal comma ([[64/63]]) is [[tempering out|tempered out]].

Since the generator is a perfect fourth or perfect fifth, archy 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. [[22edo|13\22]] and [[27edo|16\27]] are typical tunings of the generator.

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-{{Infobox regtemp|Comma basis=[[64/63]] (2.3.7); <br> [[64/63]], [[245/243]] (2.3.5.7)|Edo join 1=5|Edo join 2=22|Generator=4/3|Generator tuning=487.4|Optimization method=DKW|Mapping=1; 1 9 -2|MOS scales=[[2L 3s]], [[5L 2s]], [[5L 7s]]|Subgroups=2.3.7, 2.3.5.7|Title=Archy; superpyth|Odd limit 1=(2.3.7) 9|Mistuning 1=?|Odd limit 2=9|Mistuning 2=?|Complexity 1=12|Complexity 2=27}}'''Archy''' is a [[regular temperament|temperament]] where the [[generator]] is [[4/3]], tuned flat so that stacking two of them gives the interval [[7/4]]. This means that intervals such as A–G and C–B♭ (notated in chain-of-fifths notation) are harmonic sevenths. Equivalently, two [[3/2]] perfect fifths [[octave reduction|octave-reduced]] gives [[8/7]]. Three fourths reach a subminor third that approximates [[7/6]], while four fifths reach a supermajor third that approximates [[9/7]]. This means that the septimal comma ([[64/63]]) is [[tempering out|tempered out]].
+{{Infobox regtemp|Comma basis=[[64/63]] (2.3.7); <br> [[64/63]], [[245/243]] (2.3.5.7)|Edo join 1=5|Edo join 2=22|Generator=3/2|Generator tuning=712.6|Optimization method=DKW|Mapping=1; 1 9 -2|MOS scales=[[2L 3s]], [[5L 2s]], [[5L 7s]]|Subgroups=2.3.7, 2.3.5.7|Title=Archy; superpyth|Odd limit 1=(2.3.7) 9|Mistuning 1=?|Odd limit 2=9|Mistuning 2=?|Complexity 1=12|Complexity 2=27}}'''Archy''' is a [[regular temperament|temperament]] where the [[generator]] is [[4/3]], tuned flat so that stacking two of them gives the interval [[7/4]]. This means that intervals such as A–G and C–B♭ (notated in chain-of-fifths notation) are harmonic sevenths. Equivalently, two [[3/2]] perfect fifths [[octave reduction|octave-reduced]] gives [[8/7]]. Three fourths reach a subminor third that approximates [[7/6]], while four fifths reach a supermajor third that approximates [[9/7]]. This means that the septimal comma ([[64/63]]) is [[tempering out|tempered out]].
 Since the generator is a perfect fourth or perfect fifth, archy 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. [[22edo|13\22]] and [[27edo|16\27]] are typical tunings of the generator.