Talk:Meantone temperament
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This is what was in the article before I edited. I don't really understand it, and what I do understand doesn't seem strictly relevant to meantone, so I'm moving it here. I've replaced it with a stubby entry for now, but I'll be expanding it in time. --Camembert
Original article text follows
In a modern 12 note equal temperament the semitone is exactly half a tone logarithmically.
If the semitone is allowed to be more than half a tone, one can get a better approximation to just intonation.
If the semitone is a rational fraction of a tone logarithmically, one gets a finite number of notes in an octave.
Semitone/Tone Notes
1/2 12
4/7 43
3/5 31
5/8 50
2/3 19
One can make some intervals perfectly tuned. In Pythagorean tuning, 1:2 (the Octave) and 2:3 (the Fifth) are perfect and 9:10 is approximated by 8:9. This gives a semitone of 243:256, a tone of 8:9, and a major Third of 64:81 (1.265625). Quarter comma meantone tunes 1:2 and 4:5 (the major Third) perfectly, giving a tone ratio 2:sqrt(5), a semitone ratio 5^(5/4):8, and a Fifth of 5^(1/4) (1.495349).
[edit] Notation and the wolf
The page as it stands has a nonstandard notation for accidentals (black notes). The usual is to notate all accidentals on the flatward side of the wolf as sharps, and vice versa. That is, if the wolf is between G# and Eb, you use F#, C#, G#, Eb, Bb. This is also easier to understand because A# is an unfamiliar note whereas Bb is very common. Then the flats and sharps form a mnemonic for which intervals are 'bad': the fifth G#-Eb is bad as are all thirds where the root is a sharp or where the third is a flat. --Tdent 21:53, 14 Apr 2005 (UTC)
[edit] Definition and history
The definition of meantone should not imply that the major 3rd is 'just', since in 1/5 comma, 1/6 comma, etc. etc. (all of which were historically referred to as mean-tone) it is not. The correct definition is that each perfect fifth is an equal interval apart from the wolf, with a corollary that the fifths are narrower than equal-tempered. (Otherwise Pythagorean tuning and equal temperament would also qualify.)
It would be useful to indicate the historical uses of (the various types of) mean-tone, which was widespread in the Renaissance, Baroque and early Classical eras. Even though keyboards began to be tuned to other types of temperament in the 18th century, vocal and wind/string instrument intonation was still taught according to a 1/6-comma meantone scheme in the time of Mozart. It appears likely that keyboard instruments were tuned to a slightly altered form of meantone through the 19th century, for example temperaments based on 1/8 comma meantone. --Tdent 22:24, 14 Apr 2005 (UTC)
