Mercury meantone: Difference between revisions
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: ''Not to be confused with the [[Mercury|80th-octave temperament]] named after the same element.'' | : ''Not to be confused with the [[Mercury|80th-octave temperament]] named after the same element.'' | ||
'''Mercury | '''Mercury meantone''' is a [[non-octave]] [[tuning]] 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, its imperfect octaves actually become an advantage over theoretically perfect ones. It exceeds the octave by [[557122275/556583944]], or the mercurial comma. Its 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 {{monzo| 1 -3 -3 0 0 0 5 0 0 -2 }}. | ||
[[Category:19-limit]] | [[Category:19-limit]] | ||
[[Category:Temperaments]] | [[Category:Temperaments]] | ||
[[Category:Meantone]] | [[Category:Meantone]] | ||
[[Category:Mercurial]] | [[Category:Mercurial]] | ||
Latest revision as of 03:21, 17 January 2024
- Not to be confused with the 80th-octave temperament named after the same element.
Mercury meantone is a non-octave tuning 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, its imperfect octaves actually become an advantage over theoretically perfect ones. It exceeds the octave by 557122275/556583944, or the mercurial comma. Its 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⟩.