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More microtempered scales

🔗Gene W Smith <genewardsmith@juno.com>

6/10/2002 2:43:50 PM

Here are more microtempered scales, to drive the idea home and perhaps
people nuts. These make use of the comma 4375/4374~1; I give 19-tone JI
scales, and corresponding scales in the 1547-et. I would not leap to the
conclusion that since 31 and 72 were not found to be adequitely close to
JI, the same must be true of 1547. I give the scale, which are Fokker
blocks, the number of intervals and triads in the 7 and 9 limits, and the
commas used to create the blocks.

Scale A
1, 250/243, 27/25, 10/9, 125/108, 6/5, 5/4, 162/125, 4/3, 25/18, 36/25,
3/2, 125/81, 8/5, 5/3, 216/125, 9/5, 50/27, 243/125

7: 14, 0
9: 26, 0

Commas {81/80, 126/125, 4375/4374};

Scale B
1, 36/35, 175/162, 10/9, 81/70, 6/5, 5/4, 35/27, 4/3, 243/175, 350/243,
3/2, 54/35, 8/5, 5/3, 140/81, 9/5, 324/175, 35/18

7: 10, 0
9: 24, 0

Commas {81/80, 245/243, 4375/4374};

A = B in the 1547 et
[0, 63, 172, 235, 326, 407, 498, 579, 642, 733, 814, 905, 968, 1049,
1140, 1221, 1312, 1375, 1484]

7: 45, 28
9: 70, 83

Scale C
1, 36/35, 27/25, 10/9, 7/6, 6/5, 63/50, 162/125, 4/3, 7/5, 10/7, 3/2,
125/81, 100/63, 5/3, 12/7, 9/5, 50/27, 35/18

Commas {49/48, 126/125, 4375/4374};

7: 18, 0
9: 30, 6

Scale D
1, 36/35, 175/162, 10/9, 7/6, 6/5, 1225/972, 35/27, 4/3, 7/5, 10/7, 3/2,
54/35, 1944/1225, 5/3, 12/7, 9/5, 324/175, 35/18

Commas {49/48, 245/243, 4375/4374};

7: 14, 0
9: 28, 6

C = D in the 1547 et
[0, 63, 172, 235, 344, 407, 516, 579, 642, 751, 796, 905, 968, 1031,
1140, 1203, 1312, 1375, 1484]

7: 43, 26
9: 62, 61

Scale E
1, 28/27, 27/25, 10/9, 125/108, 6/5, 5/4, 162/125, 4/3, 25/18, 36/25,
3/2, 125/81, 8/5, 5/3, 216/125, 9/5, 50/27, 27/14

7: 14, 0
9: 26, 0

Commas {126/125, 225/224, 4375/4374};

Scale F
[1, 28/27, 175/162, 10/9, 81/70, 6/5, 5/4, 35/27, 4/3, 25/18, 36/25, 3/2,
54/35, 8/5, 5/3, 140/81, 9/5, 324/175, 27/14

Commas {245/243, 225/224, 4375/4374};

7: 12, 0
9: 26, 0

E = F in the 1547 et
[0, 81, 172, 235, 326, 407, 498, 579, 642, 733, 814, 905, 968, 1049,
1140, 1221, 1312, 1375, 1466]

7: 41, 22
9: 62, 59

Scale G
[1, 25/24, 27/25, 10/9, 125/108, 6/5, 5/4, 162/125, 4/3, 25/18, 36/25,
3/2, 125/81, 8/5, 5/3, 216/125, 9/5, 50/27, 48/25

7: 16, 0
9: 28, 0

Commas {81/80, 225/224, 4375/4374};

Scale G in the 1547 et
[0, 91, 172, 235, 326, 407, 498, 579, 642, 733, 814, 905, 968, 1049,
1140, 1221, 1312, 1375, 1456]

7: 43, 24
9: 66, 71

Scale H
[1, 36/35, 175/162, 10/9, 8/7, 6/5, 100/81, 35/27, 4/3, 48/35, 35/24,
3/2, 54/35, 81/50, 5/3, 7/4, 9/5, 324/175, 35/18

7: 8, 0
9: 20, 0

Commas {49/48, 81/80, 4375/4374};

Scale H in the 1547 et
r1 := [0, 63, 172, 235, 298, 407, 470, 579, 642, 705, 842, 905, 968,
1077,
1140, 1249, 1312, 1375, 1484];

7: 43, 24
9: 62, 57