It is not sufficiently recognized, I believe, that each of these meantone temperaments possesses one or more Just intervals. Pythagorean tuning is known to contain pure 5ths and 4ths, of course, but each of the regular meantone temperaments given in Ex. 1b has some purity as well.
|
Regular Meantone version
|
Pure interval
|
Ratio
|
|
1/3 Comma
|
minor 3rd
|
6:5
|
|
Major 6th
|
5:3
|
|
|
2/7 Comma
|
minor semitone
|
25:24
|
|
1/4 Comma
|
Major 3rd
|
5:4
|
|
minor 6th
|
8:5
|
|
|
1/5 Comma
|
Major semitone
|
16:15
|
|
Major 7th
|
15:8
|
|
|
1/6 Comma
|
tritone
|
45:32
|
|
diminished 5th
|
64:45
|
The fact that each of these sytems found adherents in the Renaissance may have been due, in part, to the presence of these pure intervals and the consequent enhancement to certain modes and progressions.