Würschmidt family: Difference between revisions

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The [[5-limit]] parent comma for the '''würschmidt family''' (würschmidt is sometimes spelled '''wuerschmidt''') is [[393216/390625]], known as Würschmidt's comma, and named after José Würschmidt. ~~Its [[monzo]] is {{monzo| 17 1 -8 }}, and flipping that yields {{multival| 8 1 17 }} for the wedgie. This tells us the~~ [[generator]] is a classic major third, and ~~that~~ to get to the interval class of fifths ~~will require~~ eight of these. In fact, (5/4)<sup>8</sup> × 393216/390625 = 6.

The [[5-limit]] parent comma for the '''würschmidt family''' (würschmidt is sometimes spelled '''wuerschmidt''') is [[393216/390625]], known as Würschmidt's comma, and named after José Würschmidt. The [[generator]] is a classic major third, and to get to the interval class of fifths requires eight of these. In fact, (5/4)<sup>8</sup> × 393216/390625 = 6.

Similar to [[meantone]], würschmidt implies that 3/2 will be tempered flat and/or 5/4 will be tempered sharp, and therefore 6/5 will be tempered flat. Unlike meantone, it is far more accurate. Combining würschmidt with meantone gives [[31edo]] as the first practical tuning with a generator of 10\31, but increasingly good 5-limit edo generators are [[34edo|11\34]] and especially [[65edo|21\65]], which notably is the point where it is combined with [[schismic]]/[[nestoria]] and [[gravity]]/[[larry]]. Other edo tunings include [[96edo]], [[99edo]] and [[164edo]].

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	The [[5-limit]] parent comma for the '''würschmidt family''' (würschmidt is sometimes spelled '''wuerschmidt''') is [[393216/390625]], known as Würschmidt's comma, and named after José Würschmidt. ~~Its [[monzo]] is {{monzo\| 17 1 -8 }}, and flipping that yields {{multival\| 8 1 17 }} for the wedgie. This tells us the~~ [[generator]] is a classic major third, and ~~that~~ to get to the interval class of fifths ~~will require~~ eight of these. In fact, (5/4)<sup>8</sup> × 393216/390625 = 6.		The [[5-limit]] parent comma for the '''würschmidt family''' (würschmidt is sometimes spelled '''wuerschmidt''') is [[393216/390625]], known as Würschmidt's comma, and named after José Würschmidt. The [[generator]] is a classic major third, and to get to the interval class of fifths requires eight of these. In fact, (5/4)<sup>8</sup> × 393216/390625 = 6.

	Similar to [[meantone]], würschmidt implies that 3/2 will be tempered flat and/or 5/4 will be tempered sharp, and therefore 6/5 will be tempered flat. Unlike meantone, it is far more accurate. Combining würschmidt with meantone gives [[31edo]] as the first practical tuning with a generator of 10\31, but increasingly good 5-limit edo generators are [[34edo\|11\34]] and especially [[65edo\|21\65]], which notably is the point where it is combined with [[schismic]]/[[nestoria]] and [[gravity]]/[[larry]]. Other edo tunings include [[96edo]], [[99edo]] and [[164edo]].		Similar to [[meantone]], würschmidt implies that 3/2 will be tempered flat and/or 5/4 will be tempered sharp, and therefore 6/5 will be tempered flat. Unlike meantone, it is far more accurate. Combining würschmidt with meantone gives [[31edo]] as the first practical tuning with a generator of 10\31, but increasingly good 5-limit edo generators are [[34edo\|11\34]] and especially [[65edo\|21\65]], which notably is the point where it is combined with [[schismic]]/[[nestoria]] and [[gravity]]/[[larry]]. Other edo tunings include [[96edo]], [[99edo]] and [[164edo]].