Topic: A 31edo approximation with some pure 5/4 and 7/5 intervals

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From: genewardsmith (2012-11-08)
Subject: A 31edo approximation with some pure 5/4 and 7/5 intervals

This has a gamut of 12 meantone (56/5)^(1/6) fifths, and so 6 = 12-6 pure 7/5s, and 18 1/4-comma 5^(1/4) fifths, and so 14 = 18-4 pure 5/4s. The difference between this and 31edo is subtle, but you can bring it out, eg by using two-part harmony. What Vicentino would have made of it I don't know.

! circle31.scl
!
Approximate 31edo with 18 5^(1/4) fifths, 12 (56/5)^(1/6) fifths, and a (4096/6125)*sqrt(5)
 31
!
 39.04564
 76.04900
 117.10786
 153.61881
 193.15686
 233.21637
 269.20586
 310.26471
 347.78954
 386.31371
 427.38710
 462.36271
 503.42157
 541.96027
 579.47057
 620.52943
 656.53344
 696.57843
 736.13100
 772.62743
 813.68629
 850.70417
 889.73529
 930.30173
 965.78428
 1006.84314
 1044.87491
 1082.89214
 1123.95100
 1159.44808
 1200.00000