Tungsten meantone: Difference between revisions

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'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S6 of an octave, where S6is the sixth [[Wikipedia: Metallic mean|metallic mean]], equal to (6 + sqrt (10)~~)/2~~ or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S6 of an octave, where S6 is the sixth [[Wikipedia: Metallic mean|metallic mean]], equal to 3 + sqrt (10) or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.

Revision as of 10:48, 2 February 2021 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 25,500 edits m General cleanup ← Older edit		Revision as of 15:52, 13 January 2022 view source FloraC (talk \| contribs) autopatrolled, Bureaucrats, Interface administrators, Sysops 25,500 edits Correction Newer edit →
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	'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<sub>6</sub> of an octave, where S<sub>6</sub>is the sixth [[Wikipedia: Metallic mean\|metallic mean]], equal to (6 + sqrt (10)~~)/2~~ or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.		'''Tungsten meantone''' is the name given by Mason Green in 2016 to the variant of meantone in which the size of the tempered whole tone is equal to 1/S<sub>6</sub> of an octave, where S<sub>6</sub> is the sixth [[Wikipedia: Metallic mean\|metallic mean]], equal to 3 + sqrt (10) or about 6.162. This gives a whole tone of ~194.733 cents, and a generator width of ~697.367 cents.

	Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.		Tungsten meantone has the unique property that the ratio between the sizes of its fifth and fourth is the same as the ratio between the sizes of its diatonic and chromatic semitones; therefore, the whole tone may be divided into two chromatic semitones and a diesis in a manner exactly proportional to that in which the octave divides into two fourths and a whole tone. Successive MOSes thus become self-similar, with the whole tone looking like a scaled-down version of the the octave, and the diesis eventually looking like a scaled-down version of the whole tone, etc. Tungsten meantone is thus a cousin to [[golden meantone]], since in each case the same ratios between interval sizes appear repeatedly and the scale is thus self-similar.