Topic: Another lattice-chord scale

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Thread (1 messages)

From: Gene Ward Smith (2004-02-15)
Subject: Another lattice-chord scale

The Canasta alternative I gave came from symmetry around a lattice
point of the tetrad lattice, which means it is also symmetrical around
a tetrad in the note-class lattice, which is a shallow hole. The deep
holes are hexanies, and corresponing to them are the holes of the
cubic lattice, the centers of the cubes. If we look at shells around
the holes, we get shells of size 8, 24, 24, 32, 48, 24 .... The 8
chord shell gives us the stellated hexany. The first two together give
us 32 chords, using 38 notes. The smallest four commas arising from
approximate 7-limit consonaces are 2401/2400, 6144/6125, 225/224,
1029/1024. The first and second together give hemiwuerschmidt, the
first and third, first and fourth, third and fourth all miralce, the
second and third orwell, the second and fourth valentine. It seems to
be a good candidate for both hemiwuerschmidt and miracle. It has no
2401/2400 steps, but does have 225/224, so miracle will boil it down. 

Here a the list of the step sizes:

[225/224, 1728/1715, 126/125, 875/864, 64/63, 50/49, 49/48, 
128/125, 36/35]

Here is the scale itself:

[49/48, 25/24, 21/20, 15/14, 35/32, 9/8, 147/128, 7/6, 75/64, 6/5,
49/40, 5/4, 245/192, 9/7, 21/16, 75/56, 175/128, 7/5, 45/32, 10/7,
35/24, 3/2, 49/32, 25/16, 63/40, 45/28, 105/64, 5/3, 12/7, 7/4, 25/14,
9/5, 175/96, 147/80, 15/8, 245/128, 63/32, 2]

Here it is tempered by TOP tuned hemiwuerschmidt:

! hemball.scl
Ball 2 around tetrad lattice hole, TOP hemiwuerschmidt tempered
38
!
36.757438
73.514875
83.550113
120.307550
157.064988
203.857663
240.615101
267.337304
277.372538
314.129979
350.887417
387.644854
424.402292
434.437529
471.194967
507.952404
544.709842
581.467283
591.502517
618.224720
654.982158
701.774833
738.532271
775.289708
785.324946
822.082383
858.839821
885.562024
932.354699
969.112137
1005.869574
1015.904812
1042.627012
1052.662250
1089.419687
1126.177125
1172.969800
1199.692003