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Examples of good (and small) rank-3 3DE scales

🔗Keenan Pepper <keenanpepper@gmail.com>

7/26/2011 12:26:17 PM

Here are some small examples I cooked up of N=3 distributionally even scales in temperaments that work well for it. The reason I don't have any scales in marvel, or breed, or other familiar rank-3 temperaments is because I believe it's impossible to have an arbitrarily large 3DE scale in them that contains complete otonal/utonal chords. 3DE is too strong of a constraint for them. But certain temperaments work anyway.

Sonic15 should be particularly interesting for you porcupine lovers. It's porcupine but with abundant and accurate intervals of 7, added in a coherent way. (Plus it has a really cute name.)

Index:
archytas7
archytas8
archytas12
didymus9
jubilee10sym1, -sym2, -asym1, -asym2, -asym3, -asym4
jubilee12sym
orwellian9
orwellian13
sonic13
sonic15
starling7
starling11
supermagic7
supermagic10
supermagic11

! archytas7.scl
!
A distributionally even scale in archytas (64/63 planar) temperament, abacabc
7
!
174.29000
392.38000
489.44000
707.53000
881.82000
978.88000
1196.97000

! archytas8.scl
!
A distributionally even scale in archytas (64/63 planar) temperament, abacbabc
8
!
121.03000
392.38000
489.44000
610.47000
707.53000
978.88000
1099.91000
1196.97000

! archytas12.scl
!
A distributionally even scale in archytas (64/63 planar) temperament, ababacbababc
12
!
121.03000
218.09000
271.35000
392.38000
489.44000
610.47000
707.53000
828.56000
881.82000
978.88000
1099.91000
1196.97000

! didymus9.scl
!
A distributionally even scale in didymus (81/80 planar) temperament, aabacabac
9
!
192.70000
385.40000
461.68000
654.38000
697.04000
889.74000
966.02000
1158.72000
1201.38000

! jubilee10sym1.scl
!
A distributionally even scale in jubilee (50/49 planar) temperament, aabacaabac
10
!
102.92000
205.84000
380.63000
483.55000
599.67000
702.59000
805.51000
980.30000
1083.22000
1199.34000

! jubilee10sym2.scl
!
A distributionally even scale in jubilee (50/49 planar) temperament, aabacaabac
10
!
102.92000
205.84000
277.70000
380.62000
599.66000
702.58000
805.50000
877.36000
980.28000
1199.32000

! jubilee10asym1.scl
!
A distributionally even scale in jubilee (50/49 planar) temperament, aabaacabac
10
!
102.92000
205.84000
380.63000
483.55000
586.47000
702.59000
805.51000
980.30000
1083.22000
1199.34000

! jubilee10asym2.scl
!
A distributionally even scale in jubilee (50/49 planar) temperament, aabaacabac
10
!
102.92000
205.84000
380.63000
483.55000
599.67000
702.59000
877.38000
980.30000
1083.22000
1199.34000

! jubilee10asym3.scl
!
A distributionally even scale in jubilee (50/49 planar) temperament, aabaacabac
10
!
102.92000
205.84000
277.70000
380.62000
483.54000
702.58000
805.50000
877.36000
980.28000
1199.32000

! jubilee10asym4.scl
!
A distributionally even scale in jubilee (50/49 planar) temperament, aabaacabac
10
!
102.92000
205.84000
277.70000
380.62000
599.66000
702.58000
774.44000
877.36000
980.28000
1199.32000

! jubilee12sym.scl
!
A distributionally even scale in jubilee (50/49 planar) temperament, aabaacaabaac
12
!
102.92000
205.84000
277.70000
380.62000
483.54000
599.66000
702.58000
805.50000
877.36000
980.28000
1083.20000
1199.32000

! orwellian9.scl
!
A distributionally even scale in orwellian temperament, ababababc
9
!
43.33000
270.47000
387.99000
431.32000
658.46000
701.79000
928.93000
972.26000
1199.40000

! orwellian13.scl
!
A distributionally even scale in orwellian temperament, abacbacabcabc
13
!
43.33000
160.85000
270.47000
387.99000
431.32000
540.94000
658.46000
701.79000
819.31000
928.93000
972.26000
1089.78000
1199.40000

! sonic13.scl
!
A distributionally even scale in sonic temperament, ababababababc
13
!
96.02000
311.62000
379.72000
475.74000
543.84000
639.86000
707.96000
803.98000
872.08000
968.10000
1036.20000
1132.22000
1200.32000

! sonic15.scl
!
A distributionally even scale in sonic temperament, abababababababc
15
!
96.02000
164.12000
215.60000
311.62000
379.72000
475.74000
543.84000
639.86000
707.96000
803.98000
872.08000
968.10000
1036.20000
1132.22000
1200.32000

! starling7.scl
!
A distributionally even scale in starling temperament, abababc
7
!
78.93000
311.10000
390.03000
622.20000
701.13000
967.62000
1199.79000

! starling11.scl
!
A distributionally even scale in starling temperament, abacbabcabc
11
!
78.93000
266.49000
311.10000
390.03000
577.59000
656.52000
701.13000
888.69000
967.62000
1155.18000
1199.79000

! supermagic7.scl
!
A distributionally even scale in supermagic temperament, abababc
7
!
59.11000
321.68000
380.79000
643.36000
702.47000
965.04000
1201.03000

! supermagic10.scl
!
A distributionally even scale in supermagic temperament, abacbacabc
10
!
59.11000
85.69000
321.68000
380.79000
616.78000
643.36000
702.47000
938.46000
965.04000
1201.03000

! supermagic11.scl
!
A distributionally even scale in supermagic temperament, abacbabcabc
11
!
85.70000
144.81000
321.69000
380.80000
466.50000
643.38000
702.49000
788.19000
965.07000
1024.18000
1201.06000

Enjoy!

Keenan