Commas and Generators
Meantone is the classic linear temperament. In the 5-limit it has comma 81/80, the comma of Didymus, which is the classic comma. In the 7-limit we have variants given by the comma sequence [81/80, 36/35], dominant; the sequence [81/80, 525/512], flattone; and the sequence [81/80, 126/125], meantone or standard septimal meantone. It has two strong contenders for an 11-limit version, huygens with comma sequence [81/80, 126/125, 99/98] and meanpop, or simply meantone, with sequence [81/80, 126/125, 385/384]. Meanpop has the same TOP tuning as 7-limit meantone and so may take the same name, but it is neither better nor worse than huygens; it is the mapping one would use for a fifth flatter than that of 31-equal, such as 50 or 69. For 43 one would use huygens; the two are identical in 31-equal which is a very practical solution for what tuning to use for 11-limit meantone.
The meantone generator is a flat fifth or sharp fourth, except for dominant where the fifth may be a trifle sharp; for instance the fifth of 41-equal.
Music in Meantone
The repertoire of 5-limit meantone, the standard tuning for hundreds of years of Western music, is vast. Any music in 12-equal making extensive use of seventh chords which can successfully be retuned to 70-equal may be regarded as in the dominant temperament. Twelve-note where the German sixth plays a major role, and where the three remote major triads before the wolf appears are made extensive use of, may be taken as in septimal meantone. Some of my versions of music either originally in meantone or adapted to it by me in various ways can be found here, here, here, and here. Other than that, you are on your own. Explore!
Table of Meantones
In the table below, a standard icon means a tuning map for a reduced pair of generators, and poptimal means a poptimal generator. The MOS given are valid for the optimized tunings of the particular version in question.
Period: Octave Generator: flat fifth or sharp fourth
5-limit: [81/80]
standard icon: [<1 2 4|, <0 -1 -4|]
poptimal: 34/81
MOS: 5, 7, 12, 19, 31, 50
7-limit
name: meantone, standard septimal meantone, 12&19
comma sequence: [81/80, 126/125]
wedgie: <<1 4 10 4 13 12||
standard icon: [<1 2 4 7|, <0 -1 -4 -10|] (fourth generator)
7&9 limit copoptimal generator: 5^(1/4) fifth (1/4 comma meantone)
7 limit poptimal: 86/205
9 limit poptimal: 47/112
TM basis: {81/80, 126/125}
MOS: 5, 7, 12, 19, 31, 50
name: dominant, dominant sevenths, 5&12
comma sequence: [81/80, 36/35]
wedgie: <<1 4 -2 4 -6 -16||
mapping: [<1 2 4 2|, <0 -1 -4 2|]
7&9 limit copoptimal generator: 29/70
TM basis: {36/35, 64/63}
MOS: 5, 7, 12, 17, 29
name: flattone, 19&26
comma sequence: [81/80, 525/512]
wedgie: <<1 4 -9 4 -17 -32||
standard icon: [<1 2 4 -1|, <0 -1 -4 9|]
7 limit poptimal: 46/109
9 limit poptimal: 27/64
TM basis: {81/80, 525/512}
MOS: 5, 7, 12, 19, 26, 45
11-limit
name: meantone, meanpop, 31&19
comma sequence: [81/80, 126/125, 385/384]
wedgie: <<1 4 10 -13 4 13 -24 12 -44 -71||
standard icon: <1 2 4 7 -2|, <0 -1 -4 -10 13|]
poptimal: 47/112
TM basis: {81/80, 126/125, 385/384}
MOS: 5, 7, 12, 19, 31, 50, 81
name: huygens, fokker, 31&12
comma sequence: [81/80, 126/125, 385/384] wedgie: <<1 4 10 18 4 13 25 12 28 16||
standard icon: [<1 2 4 7 11|, <0 -1 -4 -10 -18|]
poptimal: 13/31
TM basis: {81/80, 126/125, 99/98}
MOS: 5, 7, 12, 19, 31, 43
name: meanertone
wedgie: <<1 4 3 -1 4 2 -5 -4 -16 -13||
comma sequence: [81/80, 21/20, 33/32]
standard icon: [<1 2 4 4 3|, <0 -1 -4 -3 1|]
poptimal: 13/31
TM basis: {27/25, 21/20, 33/32}
MOS: 5, 7, 12, 19, 31, 43