Scala analysis: diff31-h8
(31, 15, 7) type H8 cyclic difference set, 31edo
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38.710 cents 38.709680 2: 77.419 cents 77.419350 3: 116.129 cents 116.129030 4: 154.839 cents 154.838710 5: 232.258 cents 232.258060 6: 309.677 cents 309.677420 7: 464.516 cents 464.516130 8: 580.645 cents 580.645160 9: 619.355 cents 619.354840 10: 658.065 cents 658.064520 11: 890.323 cents 890.322580 12: 929.032 cents 929.032260 13: 1045.161 cents 1045.161290 14: 1122.581 cents 1122.580650 15: 1161.290 cents 1161.290320 16: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 38.7097 cents 38.7097 1: 38.7097 cents 38.7097 2: 38.7097 cents 38.7097 3: 38.7097 cents 38.7097 4: 38.7097 cents 38.7097 5: 77.4194 cents 77.4194 6: 77.4194 cents 77.4194 7: 154.8387 cents 154.8387 8: 116.1290 cents 116.1290 9: 38.7097 cents 38.7097 10: 38.7097 cents 38.7097 11: 232.2581 cents 232.2581 12: 38.7097 cents 38.7097 13: 116.1290 cents 116.1290 14: 77.4194 cents 77.4194 15: 38.7097 cents 38.7097 16: 38.7097 cents 38.7097
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 38.70968 cents 1: 3 77.41935 cents 1: 2 116.12903 cents 1: 1 154.83871 cents 1: 1 232.25806 cents 2: 6 77.41935 cents 2: 2 116.12903 cents 2: 3 154.83871 cents 2: 1 193.54839 cents 2: 1 232.25807 cents 2: 3 270.96774 cents 3: 4 116.12903 cents 3: 2 154.83871 cents 3: 2 193.54839 cents 3: 2 232.25807 cents 3: 4 309.67742 cents 3: 1 348.38710 cents 3: 1 387.09677 cents 4: 3 154.83871 cents 4: 2 193.54838 cents 4: 1 232.25807 cents 4: 2 270.96774 cents 4: 3 348.38710 cents 4: 1 387.09678 cents 4: 3 425.80645 cents 4: 1 464.51613 cents 5: 2 193.54838 cents 5: 2 232.25806 cents 5: 1 270.96774 cents 5: 2 309.67742 cents 5: 1 387.09678 cents 5: 1 425.80646 cents 5: 4 464.51613 cents 5: 2 503.22581 cents 5: 1 580.64516 cents 6: 1 232.25806 cents 6: 2 270.96774 cents 6: 1 309.67742 cents 6: 2 348.38710 cents 6: 1 425.80645 cents 6: 3 503.22581 cents 6: 3 541.93549 cents 6: 1 580.64516 cents 6: 1 619.35484 cents 6: 1 658.06452 cents 7: 2 309.67742 cents 7: 1 348.38710 cents 7: 2 387.09677 cents 7: 1 464.51613 cents 7: 3 541.93548 cents 7: 3 580.64516 cents 7: 1 658.06452 cents 7: 1 696.77420 cents 7: 2 735.48387 cents 8: 2 387.09677 cents 8: 2 425.80645 cents 8: 1 503.22581 cents 8: 3 580.64516 cents 8: 3 619.35484 cents 8: 1 696.77419 cents 8: 2 774.19355 cents 8: 2 812.90323 cents 9: 2 464.51613 cents 9: 1 503.22580 cents 9: 1 541.93548 cents 9: 3 619.35484 cents 9: 3 658.06452 cents 9: 1 735.48387 cents 9: 2 812.90323 cents 9: 1 851.61290 cents 9: 2 890.32258 cents 10: 1 541.93548 cents 10: 1 580.64516 cents 10: 1 619.35484 cents 10: 3 658.06452 cents 10: 3 696.77419 cents 10: 1 774.19355 cents 10: 2 851.61290 cents 10: 1 890.32258 cents 10: 2 929.03226 cents 10: 1 967.74194 cents 11: 1 619.35484 cents 11: 2 696.77419 cents 11: 4 735.48387 cents 11: 1 774.19354 cents 11: 1 812.90322 cents 11: 2 890.32258 cents 11: 1 929.03226 cents 11: 2 967.74194 cents 11: 2 1006.45162 cents 12: 1 735.48387 cents 12: 3 774.19355 cents 12: 1 812.90322 cents 12: 3 851.61290 cents 12: 2 929.03226 cents 12: 1 967.74193 cents 12: 2 1006.45161 cents 12: 3 1045.16130 cents 13: 1 812.90323 cents 13: 1 851.61290 cents 13: 4 890.32258 cents 13: 2 967.74193 cents 13: 2 1006.45161 cents 13: 2 1045.16129 cents 13: 4 1083.87097 cents 14: 3 929.03226 cents 14: 1 967.74193 cents 14: 1 1006.45161 cents 14: 3 1045.16129 cents 14: 2 1083.87097 cents 14: 6 1122.58065 cents 15: 1 967.74194 cents 15: 1 1045.16129 cents 15: 2 1083.87097 cents 15: 3 1122.58065 cents 15: 9 1161.29032 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 7.73333 = 116/15
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 38.7 77.4 116.1 154.8 232.3 309.7 464.5 580.6 619.4 658.1 890.3 929.0 1045.2 1122.6 1161.3 1200.0 38.7 : 38.7 77.4 116.1 193.5 271.0 425.8 541.9 580.6 619.4 851.6 890.3 1006.5 1083.9 1122.6 1161.3 1200.0 77.4 : 38.7 77.4 154.8 232.3 387.1 503.2 541.9 580.6 812.9 851.6 967.7 1045.2 1083.9 1122.6 1161.3 1200.0 116.1 : 38.7 116.1 193.5 348.4 464.5 503.2 541.9 774.2 812.9 929.0 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 154.8 : 77.4 154.8 309.7 425.8 464.5 503.2 735.5 774.2 890.3 967.7 1006.5 1045.2 1083.9 1122.6 1161.3 1200.0 232.3 : 77.4 232.3 348.4 387.1 425.8 658.1 696.8 812.9 890.3 929.0 967.7 1006.5 1045.2 1083.9 1122.6 1200.0 309.7 : 154.8 271.0 309.7 348.4 580.6 619.4 735.5 812.9 851.6 890.3 929.0 967.7 1006.5 1045.2 1122.6 1200.0 464.5 : 116.1 154.8 193.5 425.8 464.5 580.6 658.1 696.8 735.5 774.2 812.9 851.6 890.3 967.7 1045.2 1200.0 580.6 : 38.7 77.4 309.7 348.4 464.5 541.9 580.6 619.4 658.1 696.8 735.5 774.2 851.6 929.0 1083.9 1200.0 619.4 : 38.7 271.0 309.7 425.8 503.2 541.9 580.6 619.4 658.1 696.8 735.5 812.9 890.3 1045.2 1161.3 1200.0 658.1 : 232.3 271.0 387.1 464.5 503.2 541.9 580.6 619.4 658.1 696.8 774.2 851.6 1006.5 1122.6 1161.3 1200.0 890.3 : 38.7 154.8 232.3 271.0 309.7 348.4 387.1 425.8 464.5 541.9 619.4 774.2 890.3 929.0 967.7 1200.0 929.0 : 116.1 193.5 232.3 271.0 309.7 348.4 387.1 425.8 503.2 580.6 735.5 851.6 890.3 929.0 1161.3 1200.0 1045.2: 77.4 116.1 154.8 193.5 232.3 271.0 309.7 387.1 464.5 619.4 735.5 774.2 812.9 1045.2 1083.9 1200.0 1122.6: 38.7 77.4 116.1 154.8 193.5 232.3 309.7 387.1 541.9 658.1 696.8 735.5 967.7 1006.5 1122.6 1200.0 1161.3: 38.7 77.4 116.1 154.8 193.5 271.0 348.4 503.2 619.4 658.1 696.8 929.0 967.7 1083.9 1161.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7097 .. 232.2581 cents 193.54838 cents 38.70968 cents 2: 77.4193 .. 270.9677 cents 193.54839 cents -154.83871 cents 3: 116.1290 .. 387.0968 cents 270.96774 cents -154.83871 cents 4: 154.8387 .. 464.5161 cents 309.67742 cents -232.25806 cents 5: 193.5484 .. 580.6452 cents 387.09678 cents -270.96775 cents 6: 232.2581 .. 658.0645 cents 425.80646 cents -348.38710 cents 7: 309.6774 .. 735.4839 cents 425.80645 cents -348.38710 cents 8: 387.0968 .. 812.9032 cents 425.80646 cents -348.38710 cents 9: 464.5161 .. 890.3226 cents 425.80645 cents -348.38710 cents 10: 541.9355 .. 967.7419 cents 425.80646 cents -348.38710 cents 11: 619.3548 .. 1006.4516 cents 387.09678 cents -348.38710 cents 12: 735.4839 .. 1045.1613 cents 309.67743 cents -270.96775 cents 13: 812.9032 .. 1083.8710 cents 270.96774 cents -232.25807 cents 14: 929.0323 .. 1122.5806 cents 193.54839 cents -154.83871 cents 15: 967.7419 .. 1161.2903 cents 193.54838 cents -154.83871 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 38.70967 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 232.25806 cents Average / Smallest step : 1.937500 Largest / Average step : 3.096774 Largest / Smallest step : 6.000001 Median interval of one step : 38.70968 cents, amount: 9 Most common interval of one step : 38.70968 cents, amount: 9 Least squares average step : 74.26255 cents, oct.: 1188.20079 cents Scale is not proper Scale is a mode of a 31-tone equal temperament with octave 1200.000 cents degrees: 1 2 3 4 6 8 12 15 16 17 23 24 27 29 30 31 Least number of segments generator : 23 of 890.323 cents and inv. number of contiguous generator circle segments: 3 Shortest superset generator : 16 of 619.355 cents and inv. generated superset size: 26 = 10 more = 162.500% Number of contiguous 1-step segments: 3 Step pattern alph. order: AAAABBCDAAEADBAA Step pattern size order : AAAABBDCAAEACBAA Interval vector is [ 9 9 8 9 7 8 8 9 7 7 7 8 7 8 9 ] Scale is not a Constant Structure Scale diversity : 1.238549 Lumma stability : 0.064516 Lumma impropriety factor : 0.870968 Rothenberg efficiency : 0.708333 redundancy: 0.291667 Efficiency x scale size : 11.333333 Number of different interval sizes : 30 = 2.00000 / class Number of one step interval sizes : 5 Highest interval variety : 10 Mean interval variety : 7.73333 = 116/15 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 38.70967 cents Number of recognisable fifths : 7, average 696.7742 cents Formal octave complements present : 11 = 68.7500% -- Rational properties --
FIT/MODE
16: 1 0 1 0 1 1 2 2 0 1 3 0 2 1 0 1 N SD: 19.6363 c. M:-36.2903 c. 23: 1 0 1 1 1 2 3 2 1 1 4 1 2 2 0 1 N SD: 13.6600 c. M:-25.2454 c. 27: 1 1 1 0 2 2 3 3 1 1 5 1 3 1 1 1 N SD: 11.6363 c. M:-21.5054 c. 29: 1 1 1 1 2 1 4 3 1 1 6 0 3 2 1 1 N SD: 10.8338 c. M:-20.0222 c. 30: 1 1 1 1 2 2 4 3 0 1 6 1 3 2 1 1 N SD: 10.4727 c. M:-19.3548 c. 31: 1 1 1 1 2 2 4 3 1 1 6 1 3 2 1 1 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 21.9452 cents 3 .. 6 match: 3 H SD: 11.3517 cents 4 .. 8 match: 4 H SD: 24.2165 cents 5 .. 10 match: 5 H SD: 16.3365 cents 6 .. 12 match: 6 H SD: 10.9314 cents 7 .. 14 match: 6 S SD: 6.6502 cents 8 .. 16 match: 8 H SD: 15.1573 cents 9 .. 18 match: 8 SD: 10.0878 cents 10 .. 20 match: 9 SD: 6.2581 cents 11 .. 22 match: 10 S SD: 8.0466 cents 12 .. 24 match: 10 S SD: 8.0196 cents 13 .. 26 match: 10 SD: 6.2085 cents 14 .. 28 match: 10 SD: 5.8865 cents 15 .. 30 match: 11 SD: 5.0905 cents 16 .. 32 match: 10 SD: 5.2953 cents 17 .. 34 match: 11 SD: 5.8368 cents 18 .. 36 match: 13 SD: 5.9447 cents 19 .. 38 match: 12 SD: 4.0891 cents 20 .. 40 match: 13 SD: 3.2778 cents 21 .. 42 match: 14 SD: 3.3037 cents 22 .. 44 match: 13 SD: 2.9866 cents 23 .. 46 match: 14 SD: 3.6615 cents 24 .. 48 match: 13 SD: 3.6589 cents 25 .. 50 match: 14 SD: 3.3418 cents 26 .. 52 match: 14 SD: 3.2105 cents 27 .. 54 match: 14 SD: 3.5078 cents 28 .. 56 match: 15 SD: 3.0820 cents 29 .. 58 match: 14 SD: 3.4764 cents 30 .. 60 match: 15 SD: 2.3660 cents 31 .. 62 match: 15 SD: 3.0318 cents 32 .. 64 match: 15 SD: 2.8209 cents 33 .. 66 match: 15 SD: 2.7021 cents 34 .. 68 match: 15 SD: 2.8542 cents 35 .. 70 match: 15 SD: 2.2172 cents 36 .. 72 match: 15 SD: 2.6019 cents 37 .. 74 match: 15 SD: 2.4896 cents 39 .. 78 match: 16 SD: 2.3612 cents 40 .. 80 match: 16 SD: 2.0056 cents 41 .. 82 match: 16 SD: 1.6888 cents 42 .. 84 match: 16 SD: 1.3037 cents 70 .. 140 match: 16 SD: 1.2775 cents 71 .. 142 match: 16 SD: 1.2131 cents 72 .. 144 match: 16 SD: 1.1636 cents 76 .. 152 match: 16 SD: 1.1341 cents 82 .. 164 match: 16 SD: 0.9228 cents 85 .. 170 match: 16 SD: 0.8937 cents 86 .. 172 match: 16 SD: 0.8144 cents 88 .. 176 match: 16 SD: 0.7605 cents 116 .. 232 match: 16 SD: 0.7212 cents 117 .. 234 match: 16 SD: 0.6383 cents 127 .. 254 match: 16 SD: 0.5799 cents 128 .. 256 match: 16 SD: 0.4733 cents 158 .. 316 match: 16 SD: 0.4702 cents 169 .. 338 match: 16 SD: 0.4498 cents 173 .. 346 match: 16 SD: 0.3535 cents 214 .. 428 match: 16 SD: 0.2893 cents 256 .. 512 match: 16 SD: 0.2784 cents 266 .. 532 match: 16 SD: 0.2754 cents 286 .. 572 match: 16 SD: 0.2377 cents 311 .. 622 match: 16 SD: 0.2339 cents 321 .. 642 match: 16 SD: 0.2092 cents 342 .. 684 match: 16 SD: 0.2081 cents 363 .. 726 match: 16 SD: 0.1877 cents 404 .. 808 match: 16 SD: 0.1822 cents 432 .. 864 match: 16 SD: 0.1807 cents 439 .. 878 match: 16 SD: 0.1445 cents 480 .. 960 match: 16 SD: 0.1318 cents 562 .. 1124 match: 16 SD: 0.1313 cents 565 .. 1130 match: 16 SD: 0.1174 cents