Mint temperaments: Difference between revisions
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= Ripple = | = Ripple = | ||
{{see also| Ripple family #Ripple }} | |||
{{see also| | |||
Period: 1\1 | Period: 1\1 | ||
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Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -5 -8 -2 }}] | Mapping: [{{val| 1 2 3 3 }}, {{val| 0 -5 -8 -2 }}] | ||
{{Multival|legend=1| 5 8 2 1 -11 -18 }} | |||
{{Val list|legend=1| 11c, 12 }} | {{Val list|legend=1| 11c, 12 }} | ||
Revision as of 02:26, 17 March 2021
These are low complexity, high error temperaments tempering out the septimal quarter-tone, 36/35. 36 is both a square and a triangular number, and this helps make 36/35 a septimal interval of considerable significance. Temperaments tempering it out include beep, dicot, dominant, father, diminished, august, hystrix, penta, hexadecimal, ripple and gorgo.
Progression
5-limit
Period: 1\1
Optimal (POTE) generators: ~25/24 = 140.995
EDO generators: 1\8, 1\9, 2\17
Scales:
Comma list: 3456/3125
POTE generator: ~25/24 = 140.995
Mapping: [⟨1 1 2], ⟨0 5 3]]
Badness: 0.2005
7-limit
Period: 1\1
Optimal (POTE) generators: ~15/14 = 140.927
EDO generators: 1\8, 1\9, 2\17
Scales:
Comma list: 36/35, 392/375
Mapping: [⟨1 1 2 2], ⟨0 5 3 7]]
Wedgie: ⟨⟨5 3 7 -7 -3 8]]
Badness: 0.0484
11-limit
Period: 1\1
Optimal (POTE) generators: ~12/11 = 140.747
EDO generators: 1\8, 1\9, 2\17
Scales:
Comma list: 36/35, 56/55, 77/75
Mapping: [⟨1 1 2 2 3], ⟨0 5 3 7 4]]
Badness: 0.0261
13-limit
Period: 1\1
Optimal (POTE) generators: ~13/12 = 140.751
EDO generators: 1\8, 1\9, 2\17
Scales:
Comma list: 26/25, 36/35, 56/55, 66/65
Mapping: [⟨1 1 2 2 3 3], ⟨0 5 3 7 4 6]]
Badness: 0.0182
17-limit
Period: 1\1
Optimal (POTE) generators: ~13/12 = 141.404
EDO generators: 1\8, 1\9, 2\17
Scales:
Comma list: 26/25, 36/35, 51/50, 56/55, 66/65
Mapping: [⟨1 1 2 2 3 3 4], ⟨0 5 3 7 4 6 1]]
Badness: 0.0167
19-limit
Period: 1\1
Optimal (POTE) generators: ~13/12 = 140.479
EDO generators: 1\8, 1\9, 2\17
Scales:
Comma list: 26/25, 36/35, 51/50, 56/55, 57/55, 66/65
Mapping: [⟨1 1 2 2 3 3 4 4], ⟨0 5 3 7 4 6 1 2]]
Badness: 0.0168
Ripple
Period: 1\1
Optimal (POTE) generators: ~21/20 = 99.483
EDO generators: 1\11, 1\12, 1\13
Scales:
Comma list: 36/35, 2560/2401
Mapping: [⟨1 2 3 3], ⟨0 -5 -8 -2]]
Wedgie: ⟨⟨ 5 8 2 1 -11 -18 ]]
Badness: 0.0597
11-limit
Period: 1\1
Optimal (POTE) generators: ~21/20 = 99.385
EDO generators: 1\11, 1\12, 1\13
Scales:
Comma list: 36/35, 80/77, 126/121
Mapping: [⟨1 2 3 3 4], ⟨0 -5 -8 -2 -6]]
Badness: 0.0388
13-limit
Period: 1\1
Optimal (POTE) generators: ~21/20 = 98.572
EDO generators: 1\11, 1\12, 1\13
Scales:
Comma list: 36/35, 40/39, 66/65, 147/143
Mapping: [⟨1 2 3 3 4 4], ⟨0 -5 -8 -2 -6 -3]]
Badness: 0.0316
Smate
5-limit
Period: 1\1
Optimal (POTE) generators: ~5/4 = 420.855
EDO generators: 5\14, 6\17, 7\20
Scales:
7-limit
Period: 1\1
Optimal (POTE) generators: ~5/4 = 422.275
EDO generators: 5\14, 6\17, 7\20
Scales:
Comma list: 36/35, 2048/1875
Mapping: [⟨1 3 2 6], ⟨0 -4 1 -9]]
Wedgie: ⟨⟨4 -1 9 -11 3 24]]
Badness: 0.0779
11-limit
Period: 1\1
Optimal (POTE) generators: ~5/4 = 422.217
EDO generators: 5\14, 6\17, 7\20
Scales:
Comma list: 36/35, 56/55, 243/242
Mapping: [⟨1 3 2 6 7], ⟨0 -4 1 -9 -10]]
Badness: 0.0425
13-limit
Period: 1\1
Optimal (POTE) generators: ~5/4 = 423.020
EDO generators: 5\14, 6\17, 7\20
Scales:
Comma list: 26/25, 36/35, 56/55, 243/242
Mapping: [⟨1 3 2 6 7 3], ⟨0 -4 1 -9 -10 2]]
Badness: 0.0368
Hemismate
Period: 1\1
Optimal (POTE) generators: ~8/7 = 210.452
EDO generators: 2\11, 3\17, 4\23
Scales:
Comma list: 256/245, 392/375
Mapping: [⟨1 3 2 3], ⟨0 -8 2 -1]]
Wedgie: ⟨⟨8 -2 1 -22 -21 8]]
Badness: 0.1543
11-limit
Period: 1\1
Optimal (POTE) generators: ~8/7 = 210.481
EDO generators: 2\11, 3\17, 4\23
Scales:
Comma list: 56/55, 77/75, 256/245
Mapping: [⟨1 3 2 3 4], ⟨0 -8 2 -1 -3]]
Badness: 0.0655
13-limit
Period: 1\1
Optimal (POTE) generators: ~8/7 = 210.974
EDO generators: 2\11, 3\17, 4\23
Scales:
Comma list: 26/25, 56/55, 77/75, 256/245
Mapping: [⟨1 3 2 3 4 3], ⟨0 -8 2 -1 -3 4]]
Badness: 0.0505
Subklei
5-limit
Period: 1\1
Optimal (POTE) generators: ~6/5 = 284.293
Scales:
7-limit
Period: 1\1
Optimal (POTE) generators: ~6/5 = 284.219
Scales:
Comma list: 36/35, 1029/1000
Mapping: [⟨1 3 4 4], ⟨0 -6 -7 -5]]
Wedgie: ⟨⟨6 7 5 -3 -9 -8]]
Badness: 0.0611
11-limit
Period: 1\1
Optimal (POTE) generators: ~6/5 = 283.253
Scales:
Comma list: 36/35, 77/75, 352/343
Mapping: [⟨1 3 4 4 7], ⟨0 -6 -7 -5 -15]]
Badness: 0.0447
13-limit
Period: 1\1
Optimal (POTE) generators: ~6/5 = 282.856
Scales:
Comma list: 26/25, 36/35, 66/65, 352/343
POTE generator: ~6/5 = 282.856
Mapping: [⟨1 3 4 4 7 7], ⟨0 -6 -7 -5 -15 -14]]
Badness: 0.0323
Subkla
Period: 1\1
Optimal (POTE) generators: ~6/5 = 283.822
Scales:
Comma list: 36/35, 56/55, 1029/1000
Mapping: [⟨1 3 4 4 3], ⟨0 -6 -7 -5 2]]
Badness: 0.0472
13-limit
Period: 1\1
Optimal (POTE) generators: ~6/5 = 283.882
Scales:
Comma list: 36/35, 56/55, 66/65, 640/637
Mapping: [⟨1 3 4 4 3 3], ⟨0 -6 -7 -5 2 3]]
Badness: 0.0367
Slurpee
5-limit
Period: 1\1
Optimal (POTE) generators: ~27/25 = 72.742
EDO generators: 1\16, 1\17, 2\33
Scales:
7-limit
Period: 1\1
Optimal (POTE) generators: ~21/20 = 72.303
EDO generators: 1\16, 1\17, 2\33
Scales:
Comma list: 36/35, 51200/50421
Mapping: [⟨1 2 3 3], ⟨0 -7 -11 -3]]
Wedgie: ⟨⟨7 11 3 1 -15 -24]]
Badness: 0.1149
11-limit
Period: 1\1
Optimal (POTE) generators: ~21/20 = 72.297
EDO generators: 1\16, 1\17, 2\33
Scales:
Comma list: 36/35, 121/120, 352/343
Mapping: [⟨1 2 3 3 4], ⟨0 -7 -11 -3 -9]]
Badness: 0.0505
13-limit
Period: 1\1
Optimal (POTE) generators: ~21/20 = 72.409
EDO generators: 1\16, 1\17, 2\33
Scales:
Comma list: 36/35. 66/65, 143/140, 352/343
Mapping: [⟨1 2 3 3 4 4], ⟨0 -7 -11 -3 -9 -5]]
Badness: 0.0331