Scala analysis: wilson_class
Class Scale, Erv Wilson, 9 july 1967
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 28/25 196.198479 middle second 3: 7/6 266.870906 septimal minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 35/24 653.184619 septimal semi-diminished fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 7/4 968.825906 harmonic seventh 11: 28/15 1080.557192 grave major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 672/625 125.5261 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 15/14 119.4428 major diatonic semitone 5: 16/15 111.7313 minor diatonic semitone 6: 21/20 84.4672 minor semitone 7: 25/24 70.6724 classic chromatic semitone, minor chroma 8: 192/175 160.5017 septimal 4/5-tone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 21/20 84.4672 minor semitone 11: 16/15 111.7313 minor diatonic semitone 12: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 672/625 125.526 cents 1: 1 192/175 160.502 cents septimal 4/5-tone 2: 2 35/32 155.140 cents septimal neutral second 2: 2 125/112 190.115 cents classic augmented semitone 2: 4 28/25 196.198 cents middle second 2: 4 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 3 25/21 301.847 cents BP second, quasi-equal minor third 3: 6 6/5 315.641 cents minor third 4: 8 5/4 386.314 cents major third 4: 4 32/25 427.373 cents classic diminished fourth 5: 2 125/96 456.986 cents classic augmented third 5: 1 21/16 470.781 cents narrow fourth 5: 4 4/3 498.045 cents perfect fourth 5: 1 75/56 505.757 cents marvelous fourth 5: 2 168/125 511.840 cents 5: 2 48/35 546.815 cents septimal semi-augmented fourth 6: 6 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 6: 6 10/7 617.488 cents Euler's tritone 7: 2 35/24 653.185 cents septimal semi-diminished fifth 7: 2 125/84 688.160 cents 7: 1 112/75 694.243 cents marvelous fifth 7: 4 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 7: 2 192/125 743.014 cents classic diminished sixth 8: 4 25/16 772.627 cents classic augmented fifth 8: 8 8/5 813.686 cents minor sixth 9: 6 5/3 884.359 cents major sixth, BP sixth 9: 3 42/25 898.153 cents quasi-equal major sixth 9: 3 12/7 933.129 cents septimal major sixth 10: 4 7/4 968.826 cents harmonic seventh 10: 4 25/14 1003.802 cents middle minor seventh 10: 2 224/125 1009.885 cents 10: 2 64/35 1044.860 cents septimal neutral seventh 11: 1 175/96 1039.498 cents 11: 1 625/336 1074.474 cents 11: 2 28/15 1080.557 cents grave major seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 2 40/21 1115.533 cents acute major seventh 11: 4 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 70.7 196.2 266.9 386.3 498.0 582.5 653.2 813.7 884.4 968.8 1080.6 1200.0 70.7 : 125.5 196.2 315.6 427.4 511.8 582.5 743.0 813.7 898.2 1009.9 1129.3 1200.0 196.2 : 70.7 190.1 301.8 386.3 457.0 617.5 688.2 772.6 884.4 1003.8 1074.5 1200.0 266.9 : 119.4 231.2 315.6 386.3 546.8 617.5 702.0 813.7 933.1 1003.8 1129.3 1200.0 386.3 : 111.7 196.2 266.9 427.4 498.0 582.5 694.2 813.7 884.4 1009.9 1080.6 1200.0 498.0 : 84.5 155.1 315.6 386.3 470.8 582.5 702.0 772.6 898.2 968.8 1088.3 1200.0 582.5 : 70.7 231.2 301.8 386.3 498.0 617.5 688.2 813.7 884.4 1003.8 1115.5 1200.0 653.2 : 160.5 231.2 315.6 427.4 546.8 617.5 743.0 813.7 933.1 1044.9 1129.3 1200.0 813.7 : 70.7 155.1 266.9 386.3 457.0 582.5 653.2 772.6 884.4 968.8 1039.5 1200.0 884.4 : 84.5 196.2 315.6 386.3 511.8 582.5 702.0 813.7 898.2 968.8 1129.3 1200.0 968.8 : 111.7 231.2 301.8 427.4 498.0 617.5 729.2 813.7 884.4 1044.9 1115.5 1200.0 1080.6: 119.4 190.1 315.6 386.3 505.8 617.5 702.0 772.6 933.1 1003.8 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 160.5017 cents 4608/4375, 89.8292 cents 25/24, 70.6724 cents 2: 155.1396 .. 231.1741 cents 256/245, 76.0345 cents 6125/6144,-5.3620 cents 3: 266.8709 .. 315.6413 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 4: 386.3137 .. 427.3726 cents 128/125, 41.0589 cents 25/24, 70.6724 cents 5: 456.9861 .. 546.8154 cents 4608/4375, 89.8292 cents 3125/3072, 29.6136 cents 6: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 49/48, 35.6968 cents 7: 653.1846 .. 743.0139 cents 4608/4375, 89.8292 cents 49/48, 35.6968 cents 8: 772.6274 .. 813.6863 cents 128/125, 41.0589 cents 3125/3072, 29.6136 cents 9: 884.3587 .. 933.1291 cents 36/35, 48.7704 cents 25/24, 70.6724 cents 10: 968.8259 .. 1044.8604 cents 256/245, 76.0345 cents 49/48, 35.6968 cents 11: 1039.4983 .. 1129.3276 cents 4608/4375, 89.8292 cents 6125/6144,-5.3620 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 192/175, 160.5017 cents Average / Smallest step : 1.414979 Largest / Average step : 1.605017 Largest / Smallest step : 2.271065 Median interval of one step : 98.09924 cents, amount: 0 Most common interval of one step : 25/24, 70.6724 cents, amount: 4 Least squares average step : 98.16867 cents, oct.: 1178.02402 cents Scale is not proper Step pattern alph. order: ABACDEAFAEDC Step pattern size order : AEADCBAFABCD Scale is a Constant Structure, by a margin of 5.36205 cents Scale diversity : 1.378034 Lumma stability : 0.403920 Lumma impropriety factor : 0.008937 Rothenberg efficiency : 0.356421 redundancy: 0.643579 Efficiency x scale size : 4.277056 Number of different interval sizes : 44 = 4.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.00000 = 4 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 6144/6125, 5.3620 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 8 Most common triad is 0.0 386.314 813.686 cents, amount: 4 Number of recognisable fifths : 7, average 696.9120 cents Number of appreciable fifths : 5, average 700.4127 cents Best fifths form a closed circle Scale contains a complete diamond : 1 5 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 10 Formal octave complements present : 3 = 25.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 7-8 -- Rational properties -- Prime limit : 7 Odd number limit : 625 (O: 625 U: 625) Highest odd numerator or denominator: 35 Scale harmonicity : 0.022445 Average absolute harmonicity : 0.162383 Specific harmonicity : 0.125706 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 1400, 10.4512 octaves, 366275.791 Hz. Exponens Consonantiae : 8.400000E+05, 19.68003 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 140.0, average 11.66667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.62536, average 0.88545 Sum of Tenney's harmonic distance : 21.24465, average 1.77039 Vogel's harmonic complexity : 17.91667 Wille's k value : 437 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 240.67232, average 3.08554 Lattice compactness (without 2's) : 132.51645, average 1.69893 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 -0.08333 21 1 3: -1 .. 0 -0.50000 6 1 5: -2 .. 2 0.00000 10 4 7: 0 .. 1 0.50000 6 6 Average exponent except 2's : 0 / 12 = 0.00000 Average absolute exponent except 2's: 22 / 12 = 1.83333 Scale is weakly epimorphic with val: <12 17 26 32| Scale is weakly epimorphic with val: <12 17 28 34| Scale is weakly epimorphic with val: <12 18 28 31| Scale is weakly epimorphic with val: <12 18 28 33| Scale is weakly epimorphic with val: <12 18 28 35| Scale is weakly epimorphic with val: <12 18 28 37| Scale is weakly epimorphic with val: <12 19 25 34| Scale is weakly epimorphic with val: <12 19 26 32| Scale is JI-epimorphic with val: <12 19 28 34| = patent Scale is weakly epimorphic with val: <12 20 26 31| Scale is weakly epimorphic with val: <12 20 26 33| Scale is weakly epimorphic with val: <12 20 26 35| Scale is weakly epimorphic with val: <12 20 26 37| Scale is weakly epimorphic with val: <12 20 29 35| Scale is weakly epimorphic with val: <12 21 26 32| Scale is weakly epimorphic with val: <12 21 28 34|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 23.1706 c. M:-46.8154 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 1 1 1 1 2 1 0 2 1 N D3 SD: 25.5265 c. M: 45.7490 c. 15: 1 1 1 2 1 1 1 2 1 1 1 2 P B ME SD: 20.9006 c. M: 40.5572 c. Augment-12 16: 1 2 1 1 2 1 1 2 1 1 2 1 P B ME I SD: 22.3010 c. M:-44.4428 c. Flavell's Blues 18: 1 2 1 2 1 2 1 2 1 2 1 2 SP B ME SD: 16.7211 c. M: 31.3783 c. 19: 1 2 1 2 2 1 1 3 1 1 2 2 N D3 SD: 11.6838 c. M: 21.6057 c. 22: 1 3 1 2 2 2 1 3 1 2 2 2 P B D3 SD: 11.5033 c. M:-21.9833 c. 24: 1 3 1 3 2 2 1 3 2 1 3 2 P T3 SD: 14.1360 c. M: 20.6724 c. 27: 2 2 2 3 2 2 2 3 2 2 2 3 SP B ME SD: 11.6456 c. M: 18.4207 c. 30: 2 3 2 3 2 3 1 4 2 2 3 3 P SD: 11.3686 c. M: 18.0450 c. 31: 2 3 2 3 3 2 2 4 2 2 3 3 P D3 SD: 3.7905 c. M:-6.7469 c. 68: 4 7 4 7 6 5 4 9 4 5 6 7 P SD: 2.1554 c. M: 4.0866 c. 72: 4 8 4 7 7 5 4 10 4 5 7 7 N SD: 2.5226 c. M: 4.0058 c. 84: 5 9 5 8 8 6 5 11 5 6 8 8 P SD: 2.9078 c. M:-5.1571 c. 87: 5 9 5 9 8 6 5 12 5 6 8 9 N SD: 2.9959 c. M: 4.9088 c. 99: 6 10 6 10 9 7 6 13 6 7 9 10 P SD: 1.3505 c. M: 2.2591 c. 140: 8 15 8 14 13 10 8 19 8 10 13 14 N SD: 1.0805 c. M: 2.1010 c. 171: 10 18 10 17 16 12 10 23 10 12 16 17 N SD: 0.3127 c. M: 0.5530 c. 373: 22 39 22 37 35 26 22 50 22 26 35 37 N SD: 0.3036 c. M:-0.6145 c. 410: 24 43 24 41 38 29 24 55 24 29 38 41 N SD: 0.3521 c. M: 0.5572 c. 441: 26 46 26 44 41 31 26 59 26 31 41 44 N SD: 0.1572 c. M: 0.2851 c. 612: 36 64 36 61 57 43 36 82 36 43 57 61 N SD: 0.1353 c. M: 0.2434 c. 935: 55 98 55 93 87 66 55 125 55 66 87 93 N SD: 0.0990 c. M:-0.1652 c. 1106: 65 116 65 110 103 78 65 148 65 78 103 110 N SD: 0.0931 c. M:-0.1849 c. 1137: 67 119 67 113 106 80 67 152 67 80 106 113 N SD: 0.0945 c. M:-0.1816 c. 1205: 71 126 71 120 112 85 71 161 71 85 112 120 N SD: 0.0731 c. M:-0.1367 c. 1376: 81 144 81 137 128 97 81 184 81 97 128 137 N SD: 0.0414 c. M: 0.0799 c. 1547: 91 162 91 154 144 109 91 207 91 109 144 154 N SD: 0.0432 c. M: 0.0842 c. 1578: 93 165 93 157 147 111 93 211 93 111 147 157 N SD: 0.0358 c. M:-0.0539 c. 1749: 103 183 103 174 163 123 103 234 103 123 163 174 N SD: 0.0358 c. M:-0.0682 c. 2019: 119 211 119 201 188 142 119 270 119 142 188 201 N SD: 0.0331 c. M: 0.0618 c. 2190: 129 229 129 218 204 154 129 293 129 154 204 218 N SD: 0.0302 c. M: 0.0588 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 24.3852 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 12.1926 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.7943 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.6489 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.0804 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.0923 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 8.2552 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 11.0201 cents 11 x 12:13:14:15 x 16 x 18:19:21:22 SD: 10.0104 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.8313 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 7.9329 cents 14:15:16 x 18:19:20 x 22:23:25:26:28 SD: 10.5062 cents 15:16:17:18:19:20:21:22:24:25:26:28:30 S SD: 6.1134 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.9330 cents 20:21:22:23:25:27:28:29:32:33:35:37:40 SD: 4.4789 cents 23:24:26:27:29:31:32:34:37:38:40:43:46 SD: 3.7872 cents 24:25:27:28:30:32:34:35:38:40:42:45:48 SD: 2.4542 cents 40:42:45:47:50:53:56:58:64:67:70:75:80 SD: 2.2850 cents 42:44:47:49:53:56:59:61:67:70:74:78:84 SD: 2.1989 cents 43:45:48:50:54:57:60:63:69:72:75:80:86 SD: 1.9566 cents 48:50:54:56:60:64:67:70:77:80:84:90:96 SD: 1.0731 cents 72:75:81:84:90:96:101:105:115:120:126:134:144 SD: 0.8617 cents 92:96:103:107:115:123:129:134:147:153:161:172:184 SD: 0.8307 cents 100:104:112:117:125:133:140:146:160:167:175:187:200 SD: 0.7278 cents 115:120:129:134:144:153:161:168:184:192:201:215:230 SD: 0.7173 cents 120:125:134:140:150:160:168:175:192:200:210:224:240 SD: 0.4300 cents 168:175:188:196:210:224:235:245:269:280:294:314:336 SD: 0.2747 cents 192:200:215:224:240:256:269:280:307:320:336:358:384 SD: 0.2168 cents 240:250:269:280:300:320:336:350:384:400:420:448:480 SD: 0.1073 cents 360:375:403:420:450:480:504:525:576:600:630:672:720 SD: 0.0716 cents 600:625:672:700:750:800:840:875:960:1000:1050:1120:1200 SD: 0.0000 cents