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

20 scales

Thread (1 messages)

From: Keenan Pepper (2011-07-26)
Subject: Examples of good (and small) rank-3 3DE scales

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