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The most common form of meantone temperament tunes all the major thirds to the just ratio of 4:5 (so, for instance, if A is tuned to 440 Hz, C#' is tuned to 550 Hz). This is achieved by tuning the perfect fifth a quarter of a syntonic comma flatter than the just ratio of 2:3. It is this that gives the system its name of quarter comma meantone or 1/4-comma meantone.
This system gives whole tones in the ratio 2:sqrt(5), diatonic semitones in the ratio ratio 5(5/4):8, and perfect fifths in the ratio of 1:5(1/4), which is 1.495349.., compared with a justly tuned fifth of 2:3, which is 1.5. One of the fifths will be a wolf interval, which means it will be so sharp it will not sound at all the same as a perfect fifth, and will not normally be used in common practice music. This is because twelve perfect fifths, each flattened by a quarter of a syntonic comma, do not add up to an exact number of octaves.
The term meantone temperament is sometimes used to refer specifically to 1/4-comma meantone. However, systems which flatten the fifth by differing amounts but which still equate the major whole tone, which in just intonation is 9/8, with the minor whole tone, tuned justly to 10/9, are also called meantone systems. Since (9/8)/(10/9) = 81/80, the syntonic comma, the fundamental character of a meantone tuning is that all intervals are generated from fifths, and the syntonic comma is tempered to a unison.
Meantones can be specified in various ways. We can, as above, specify what fraction (logarithmically) of a syntonic comma the fifth is being flattened by, what equal temperament has the meantone fifth in question, or what the ratio of the whole tone to the diatonic semitone is. This ratio was termed "R" by American composer, pianist and theoretician Easley Blackwood, but in effect has been in use for much longer than that. It is useful because it gives us an idea of the melodic qualities of the tuning, and because if R is a rational number, so is (3R+1)/(5R+2), which is the size of fifth in terms of logarithms base 2, and which immediately tells us what division of the octave we will have. If we multiply by 1200, we have the size of fifth in cents.
In these terms, some historically important meantone tunings are listed below. The relationship between the first two columns is exact, while that between them and the third is closely approximate.
| R | Equal temperament | Fraction of a comma |
|---|---|---|
| 2 | 7/12 | 1/11 |
| 9/5 | 32/55 | 1/6 |
| 7/4 | 25/43 | 1/5 |
| 5/3 | 18/31 | 7/29 |
| 33/20 | 119/205 | 1/4 |
| 8/5 | 29/50 | 2/7 |
| 3/2 | 11/19 | 1/3 |
Because of the wolf interval which arises when twelve notes to the octave are tuned to a meantone with fifths significantly flatter than the 1/11-comma of equal temperament, well temperaments and eventually equal temperament became more popular.