Mercury meantone: Difference between revisions

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: ''Not to be confused with the [[Mercury|80th-octave temperament]] named after the same element.''

'''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⟩.

'''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 }}.

Revision as of 20:26, 4 March 2023 view source Fredg999 category edits (talk \| contribs) autopatrolled, Bots, emailconfirmed 4,330 edits m Removing from Category:Theory using Cat-a-lot ← Older edit		Latest revision as of 03:21, 17 January 2024 view source CompactStar (talk \| contribs) 5,020 edits Capitalization stuff applies here too
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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 ~~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⟩.		'''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 }}.