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Jake Freivald’s explanation of the tuning.
MEANTONE
http://xenharmonic.wikispaces.com/Meantone+family
We all know the basics of meantone, so I won’t go into a lot of detail. Septimal meantone takes us to 7/4 by stacking 10 fifths — 7-limit intervals are complex / costly / precious.
Meantone[19] in 31 EDO (i.e., using 18\31, or the 18th step of 31 EDO) gives us lots of accurate 8/7s, 7/6s, 7/4s, 7/5s, 10/7s, and so on. The 9/7 is about 10 cents flat. A few neutrals creep in.
This is the “Ionian” mode: If you play the 1/1, 9/8, 5/4, 4/3, 3/2, 5/3, 15/8, and 2/1 of this mode, you’ll have a standard 5-limit major scale. You can do a I-IV-V, ii-V-I, etc. using this scale.
! C:\Freivald\music\Tuning\scales\meantone[19].scl
!
Meantone[19] in 31 EDO.
19
!
38.70972
116.12905
193.54838
232.25810
309.67743
387.09676
425.80648
503.22581
541.93553
619.35486
696.77419
735.48391
812.90324
890.32257
929.03229
1006.45162
1083.87095
1122.58067
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