Scala analysis: 12_class
31 dyads covered by 4 tetrads (7-limit).
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 35/32 155.139620 septimal neutral second 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 21/16 470.780907 narrow fourth 6: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 7: 3/2 701.955001 perfect fifth 8: 25/16 772.627428 classic augmented fifth 9: 42/25 898.153480 quasi-equal major sixth 10: 7/4 968.825906 harmonic seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 21/20 84.4672 minor semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 192/175 160.5017 septimal 4/5-tone 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 21/20 84.4672 minor semitone 6: 16/15 111.7313 minor diatonic semitone 7: 15/14 119.4428 major diatonic semitone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 672/625 125.5261 10: 25/24 70.6724 classic chromatic semitone, minor chroma 11: 15/14 119.4428 major diatonic semitone 12: 16/15 111.7313 minor 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 : 84.5 155.1 315.6 386.3 470.8 582.5 702.0 772.6 898.2 968.8 1088.3 1200.0 84.5 : 70.7 231.2 301.8 386.3 498.0 617.5 688.2 813.7 884.4 1003.8 1115.5 1200.0 155.1 : 160.5 231.2 315.6 427.4 546.8 617.5 743.0 813.7 933.1 1044.9 1129.3 1200.0 315.6 : 70.7 155.1 266.9 386.3 457.0 582.5 653.2 772.6 884.4 968.8 1039.5 1200.0 386.3 : 84.5 196.2 315.6 386.3 511.8 582.5 702.0 813.7 898.2 968.8 1129.3 1200.0 470.8 : 111.7 231.2 301.8 427.4 498.0 617.5 729.2 813.7 884.4 1044.9 1115.5 1200.0 582.5 : 119.4 190.1 315.6 386.3 505.8 617.5 702.0 772.6 933.1 1003.8 1088.3 1200.0 702.0 : 70.7 196.2 266.9 386.3 498.0 582.5 653.2 813.7 884.4 968.8 1080.6 1200.0 772.6 : 125.5 196.2 315.6 427.4 511.8 582.5 743.0 813.7 898.2 1009.9 1129.3 1200.0 898.2 : 70.7 190.1 301.8 386.3 457.0 617.5 688.2 772.6 884.4 1003.8 1074.5 1200.0 968.8 : 119.4 231.2 315.6 386.3 546.8 617.5 702.0 813.7 933.1 1003.8 1129.3 1200.0 1088.3: 111.7 196.2 266.9 427.4 498.0 582.5 694.2 813.7 884.4 1009.9 1080.6 1200.0 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 : 98.42031 cents, oct.: 1181.04376 cents Scale is not proper Step pattern alph. order: ABCBADEBFBED Step pattern size order : BAFABCDAEADC 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 Length of longest harmonic part : 2 at degree 10 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 8.3333% 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 : 5 Inversional symmetry on intervals : 2-3 8-9 -- 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 : 0.163679 Specific harmonicity : 0.125333 Fundamental : 1/800, -9.6439 octaves, 0.3270 Hz. Guide tone : 1050, 10.0362 octaves, 274706.844 Hz. Exponens Consonantiae : 8.400000E+05, 19.68003 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 163.5, average 13.62500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.72574, average 0.97714 Sum of Tenney's harmonic distance : 22.74980, average 1.89582 Vogel's harmonic complexity : 18.33333 Wille's k value : 437 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 244.93703, average 3.14022 Lattice compactness (without 2's) : 132.59018, average 1.69987 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 1 -1.66667 26 1 3: 0 .. 1 0.50000 6 1 5: -2 .. 2 0.00000 10 4 7: 0 .. 1 0.50000 6 6 Average exponent except 2's : 12 / 12 = 1.00000 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: 21.8159 c. M:-44.8604 c. Twelve-tone Chromatic (1/11-comma) 14: 1 1 2 1 0 2 1 1 1 1 2 1 N D3 SD: 26.1073 c. M:-42.2577 c. 15: 1 1 2 1 1 1 2 1 1 1 2 1 P B ME SD: 16.6605 c. M:-31.7313 c. Augene-12 16: 1 1 2 1 1 2 1 1 2 1 1 2 P B ME S SD: 18.1910 c. M: 38.2687 c. 19: 1 1 3 1 1 2 2 1 2 1 2 2 N D3 SD: 17.0703 c. M: 28.8238 c. 20: 1 2 2 1 2 2 2 1 2 1 2 2 P D3 SD: 16.0058 c. M: 26.3137 c. 22: 2 1 3 1 2 2 2 1 3 1 2 2 P B D3 SD: 15.0013 c. M:-29.1192 c. 23: 2 1 3 1 2 2 2 2 2 2 2 2 P D3 SD: 13.7555 c. M: 23.6941 c. 24: 2 1 3 2 1 3 2 1 3 1 3 2 P T3 SD: 14.2846 c. M: 22.6274 c. 25: 2 1 4 1 2 2 3 1 3 1 3 2 N SD: 11.7914 c. M:-20.3587 c. 28: 2 2 3 2 2 3 2 2 3 2 2 3 SP B ME S SD: 11.7458 c. M:-17.4878 c. Demolished-12 31: 2 2 4 2 2 3 3 2 3 2 3 3 P D3 SD: 4.4704 c. M: 7.8309 c. 53: 4 3 7 3 4 5 5 3 6 3 5 5 P SD: 4.0963 c. M:-7.5069 c. 56: 4 3 8 3 4 5 6 3 6 3 6 5 N SD: 3.5496 c. M:-5.7873 c. 68: 5 4 9 4 5 6 7 4 7 4 7 6 P SD: 3.4010 c. M:-5.8489 c. 72: 5 4 10 4 5 7 7 4 8 4 7 7 N SD: 3.2535 c. M: 5.9608 c. 84: 6 5 11 5 6 8 8 5 9 5 8 8 P SD: 1.8350 c. M:-3.2021 c. 87: 6 5 12 5 6 8 9 5 9 5 9 8 N SD: 2.0086 c. M: 3.4155 c. 99: 7 6 13 6 7 9 10 6 10 6 10 9 P SD: 1.6615 c. M:-3.1301 c. 115: 8 7 15 7 8 11 11 7 12 7 11 11 P SD: 1.7127 c. M: 3.0513 c. 130: 9 8 17 8 9 12 13 8 13 8 13 12 P SD: 1.5198 c. M: 2.7689 c. 140: 10 8 19 8 10 13 14 8 15 8 14 13 N SD: 0.9684 c. M:-1.8465 c. 171: 12 10 23 10 12 16 17 10 18 10 17 16 N SD: 0.4231 c. M: 0.7537 c. 270: 19 16 36 16 19 25 27 16 28 16 27 25 N SD: 0.3649 c. M:-0.7059 c. 410: 29 24 55 24 29 38 41 24 43 24 41 38 N SD: 0.3194 c. M:-0.5118 c. 441: 31 26 59 26 31 41 44 26 46 26 44 41 N SD: 0.1206 c. M: 0.1993 c. 612: 43 36 82 36 43 57 61 36 64 36 61 57 N SD: 0.1310 c. M: 0.2377 c. 966: 68 57 129 57 68 90 96 57 101 57 96 90 N SD: 0.0776 c. M:-0.1399 c. 1137: 80 67 152 67 80 106 113 67 119 67 113 106 N SD: 0.0683 c. M: 0.1421 c. 1407: 99 83 188 83 99 131 140 83 147 83 140 131 N SD: 0.0505 c. M:-0.0843 c. 1547: 109 91 207 91 109 144 154 91 162 91 154 144 N SD: 0.0520 c. M:-0.1012 c. 1578: 111 93 211 93 111 147 157 93 165 93 157 147 N SD: 0.0392 c. M: 0.0585 c. 1988: 140 117 266 117 140 185 198 117 208 117 198 185 N SD: 0.0356 c. M:-0.0613 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: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 10.1851 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.0000 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 12.7505 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.5780 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 14.1953 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 10.2106 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.0127 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.3360 cents 11 x 12:13:14 x 15 x 17:18:19:21:22 SD: 9.7433 cents 12 x 13:14:15:16:17:18:19:20:21:23:24 SD: 7.0301 cents 13 x 14 x 16:17:18 x 20:22:23:24:26 S SD: 6.8546 cents 14:15 x 17 x 18:20:21:22:24:25:26:28 SD: 8.3420 cents 15:16 x 18:19:20:21 x 23:25:26:28:30 SD: 6.0007 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.3745 cents 19:20:21:23:24:25:27:29:30:32:33:36:38 SD: 4.8193 cents 20:21:22:24:25:26:28:30:31:34:35:38:40 SD: 3.2390 cents 32:34:35:38:40:42:45:48:50:54:56:60:64 SD: 2.4542 cents 40:42:44:48:50:53:56:60:63:67:70:75:80 SD: 2.0130 cents 44:46:48:53:55:58:62:66:69:74:77:83:88 SD: 1.7745 cents 55:58:60:66:69:72:77:83:86:92:96:103:110 SD: 1.5094 cents 60:63:66:72:75:79:84:90:94:101:105:113:120 SD: 1.2343 cents 64:67:70:77:80:84:90:96:100:108:112:120:128 SD: 1.0731 cents 80:84:88:96:100:105:112:120:125:134:140:150:160 SD: 0.9277 cents 96:101:105:115:120:126:134:144:150:161:168:180:192 SD: 0.6264 cents 128:134:140:154:160:168:179:192:200:215:224:240:256 SD: 0.5936 cents 140:147:153:168:175:184:196:210:219:235:245:263:280 SD: 0.4122 cents 160:168:175:192:200:210:224:240:250:269:280:300:320 SD: 0.1073 cents 480:504:525:576:600:630:672:720:750:806:840:900:960 SD: 0.0716 cents