Talk:Meantone: Difference between revisions

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Are historical well temperaments not a form of meantone temperament? -- [[User:VectorGraphics|VectorGraphics]] ([[User talk:VectorGraphics|talk]]) 19:24, 17 June 2025 (UTC)

: ~~More properly speaking~~, ~~they~~ would be derivatives of meantone temperament rather than meantone itself. They could be viewed as finite note subsets of rank-3 or higher (depending upon the number of different fifth sizes) ~~derivatives of~~ meantone, which is rank-2 (all fifths the same). The exception would be something like 12 note 1/6-comma meantone that has a single wolf fifth that is just what is left over to close the ~~circle~~ of fifths (and technically it's a diminished sixth) that ~~(barely)~~ isn't so far off as to put it out of diatonic range. ~~That~~ would qualify as a finite note subset of a rank-2 temperament (meantone) while being usable as a circulating temperament. The same would be true if anybody had come up with an even less-flattened meantone to use as-is with a likewise shoehorned circle and no purposely-resized second size of fifth~~, but as far as~~ I know 1/6-comma meantone ~~was the only one actually~~ used that way. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 20:06, 17 June 2025 (UTC)

: If I understand correctly (including from my reading of the article here about well temperaments), most well temperaments (historical and otherwise) would be derivatives of meantone temperament rather than meantone itself. They could be viewed as finite note subsets of rank-3 or higher (depending upon the number of different fifth sizes) temperaments derived from meantone, which is rank-2 (having all fifths the same). The exception would be something like 12 note 1/6-comma meantone that has a single wolf fifth that is just what is left over to close a finite section of the helix of fifths into a circle (and technically it's a diminished sixth rather than a real fifth), with the proviso that it isn't so far off from a real fifth as to put it out of diatonic range. Since this is sufficient for a circulating temperament, that kind of well temperament would qualify as a finite note subset of a rank-2 temperament (meantone) while being usable (even if not very good) as a circulating temperament. The same would be true if anybody had come up with an even less-flattened meantone to use as-is with a likewise finite subset of the helix of fifths being shoehorned into circle (and no purposely-resized second size of fifth). I don't know of anything other than 1/6-comma meantone being used that way in actual practice, but the [[historical temperaments]] page here mentions Romieu and 1/7-comma meantone (of which the 12 note subset would be more circulation-friendly than 12 note 1/6-comma meantone), so depending upon whether that got into actual performance, that might be another example. [[User:Lucius Chiaraviglio|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio|talk]]) 21:05, 17 June 2025 (UTC)

Revision as of 20:06, 17 June 2025 view source Lucius Chiaraviglio (talk \| contribs) 1,167 edits →Meantone and being regular/rank-2: 1/6-comma meantone ← Older edit		Revision as of 21:05, 17 June 2025 view source Lucius Chiaraviglio (talk \| contribs) 1,167 edits →Meantone and being regular/rank-2: Flesh this out a bit more Newer edit →
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	Are historical well temperaments not a form of meantone temperament? -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 19:24, 17 June 2025 (UTC)		Are historical well temperaments not a form of meantone temperament? -- [[User:VectorGraphics\|VectorGraphics]] ([[User talk:VectorGraphics\|talk]]) 19:24, 17 June 2025 (UTC)

	: ~~More properly speaking~~, ~~they~~ would be derivatives of meantone temperament rather than meantone itself. They could be viewed as finite note subsets of rank-3 or higher (depending upon the number of different fifth sizes) ~~derivatives of~~ meantone, which is rank-2 (all fifths the same). The exception would be something like 12 note 1/6-comma meantone that has a single wolf fifth that is just what is left over to close the ~~circle~~ of fifths (and technically it's a diminished sixth) that ~~(barely)~~ isn't so far off as to put it out of diatonic range. ~~That~~ would qualify as a finite note subset of a rank-2 temperament (meantone) while being usable as a circulating temperament. The same would be true if anybody had come up with an even less-flattened meantone to use as-is with a likewise shoehorned circle and no purposely-resized second size of fifth~~, but as far as~~ I know 1/6-comma meantone ~~was the only one actually~~ used that way. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 20:06, 17 June 2025 (UTC)		: If I understand correctly (including from my reading of the article here about well temperaments), most well temperaments (historical and otherwise) would be derivatives of meantone temperament rather than meantone itself. They could be viewed as finite note subsets of rank-3 or higher (depending upon the number of different fifth sizes) temperaments derived from meantone, which is rank-2 (having all fifths the same). The exception would be something like 12 note 1/6-comma meantone that has a single wolf fifth that is just what is left over to close a finite section of the helix of fifths into a circle (and technically it's a diminished sixth rather than a real fifth), with the proviso that it isn't so far off from a real fifth as to put it out of diatonic range. Since this is sufficient for a circulating temperament, that kind of well temperament would qualify as a finite note subset of a rank-2 temperament (meantone) while being usable (even if not very good) as a circulating temperament. The same would be true if anybody had come up with an even less-flattened meantone to use as-is with a likewise finite subset of the helix of fifths being shoehorned into circle (and no purposely-resized second size of fifth). I don't know of anything other than 1/6-comma meantone being used that way in actual practice, but the [[historical temperaments]] page here mentions Romieu and 1/7-comma meantone (of which the 12 note subset would be more circulation-friendly than 12 note 1/6-comma meantone), so depending upon whether that got into actual performance, that might be another example. [[User:Lucius Chiaraviglio\|Lucius Chiaraviglio]] ([[User talk:Lucius Chiaraviglio\|talk]]) 21:05, 17 June 2025 (UTC)