Mercury meantone: Difference between revisions

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Mercury Meantone is a non-octave variant of [[meantone]] that sharpens the octave slightly so the individual tones and semitones are the relatively simple pure ratios of [[19/17]] and [[15/14]]. The ratio between large and small steps is 1.61213228, extremely close to the golden ratio phi, and so mercury meantone is extremely close to [[~~Golden_meantone|~~golden meantone]] in sound, only with more consonant small steps and slightly less consonant 3rds & 5ths. On instruments which have slightly inharmonic partials, which as a result are often tuned with slightly stretched octaves to compensate like pianos, it's imperfect octaves actually become an advantage over theoretically perfect ones. It exceeds the octave by [[557122275/556583944]], or the mercurial comma. It's superpyth counterpart uses ratios of [[17/15]] and [[30/29]], for a L/s ratio of 3.717820234, and exceeds an octave by [[2839714/2838375]] or [1 -3 -3 0 0 0 5 0 0 -2⟩.

'''Mercury Meantone''' is a non-octave variant of [[meantone]] that sharpens the octave slightly so the individual tones and semitones are the relatively simple pure ratios of [[19/17]] and [[15/14]]. The ratio between large and small steps is 1.61213228, extremely close to the golden ratio phi, and so mercury meantone is extremely close to [[golden meantone]] in sound, only with more consonant small steps and slightly less consonant 3rds & 5ths. On instruments which have slightly inharmonic partials, which as a result are often tuned with slightly stretched octaves to compensate like pianos, it's imperfect octaves actually become an advantage over theoretically perfect ones. It exceeds the octave by [[557122275/556583944]], or the mercurial comma. It's superpyth counterpart uses ratios of [[17/15]] and [[30/29]], for a L/s ratio of 3.717820234, and exceeds an octave by [[2839714/2838375]] or [1 -3 -3 0 0 0 5 0 0 -2⟩.

[[Category:Theory]]

[[Category:19-limit]]

[[Category:~~Interval]]~~

[[Category:Temperament]]

~~[[Category:Ratio]]~~

~~[[Category:Just interval~~]]

[[Category:Meantone]]

[[Category:Mercurial]]

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-Mercury Meantone is a non-octave variant of [[meantone]] that sharpens the octave slightly so the individual tones and semitones are the relatively simple pure ratios of [[19/17]] and [[15/14]]. The ratio between large and small steps is 1.61213228, extremely close to the golden ratio phi, and so mercury meantone is extremely close to [[Golden_meantone|golden meantone]] in sound, only with more consonant small steps and slightly less consonant 3rds & 5ths. On instruments which have slightly inharmonic partials, which as a result are often tuned with slightly stretched octaves to compensate like pianos, it's imperfect octaves actually become an advantage over theoretically perfect ones. It exceeds the octave by [[557122275/556583944]], or the mercurial comma. It's superpyth counterpart uses ratios of [[17/15]] and [[30/29]], for a L/s ratio of 3.717820234, and exceeds an octave by [[2839714/2838375]] or [1 -3 -3 0 0 0 5 0 0 -2⟩.
+'''Mercury Meantone''' is a non-octave variant of [[meantone]] that sharpens the octave slightly so the individual tones and semitones are the relatively simple pure ratios of [[19/17]] and [[15/14]]. The ratio between large and small steps is 1.61213228, extremely close to the golden ratio phi, and so mercury meantone is extremely close to [[golden meantone]] in sound, only with more consonant small steps and slightly less consonant 3rds & 5ths. On instruments which have slightly inharmonic partials, which as a result are often tuned with slightly stretched octaves to compensate like pianos, it's imperfect octaves actually become an advantage over theoretically perfect ones. It exceeds the octave by [[557122275/556583944]], or the mercurial comma. It's superpyth counterpart uses ratios of [[17/15]] and [[30/29]], for a L/s ratio of 3.717820234, and exceeds an octave by [[2839714/2838375]] or [1 -3 -3 0 0 0 5 0 0 -2⟩.
 [[Category:Theory]]
 [[Category:19-limit]]
-[[Category:Interval]]
+[[Category:Temperament]]
-[[Category:Ratio]]
-[[Category:Just interval]]
 [[Category:Meantone]]
 [[Category:Mercurial]]