Scala analysis: diff31-q
(31, 15, 7) type Q 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: 154.839 cents 154.838710 4: 193.548 cents 193.548390 5: 270.968 cents 270.967740 6: 309.677 cents 309.677420 7: 348.387 cents 348.387100 8: 387.097 cents 387.096770 9: 541.935 cents 541.935480 10: 619.355 cents 619.354840 11: 696.774 cents 696.774190 12: 735.484 cents 735.483870 13: 774.194 cents 774.193550 14: 967.742 cents 967.741940 15: 1083.871 cents 1083.870970 16: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 116.1290 cents 116.1290 1: 38.7097 cents 38.7097 2: 38.7097 cents 38.7097 3: 77.4194 cents 77.4194 4: 38.7097 cents 38.7097 5: 77.4193 cents 77.4193 6: 38.7097 cents 38.7097 7: 38.7097 cents 38.7097 8: 38.7097 cents 38.7097 9: 154.8387 cents 154.8387 10: 77.4194 cents 77.4194 11: 77.4193 cents 77.4193 12: 38.7097 cents 38.7097 13: 38.7097 cents 38.7097 14: 193.5484 cents 193.5484 15: 116.1290 cents 116.1290 16: 116.1290 cents 116.1290
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 38.70968 cents 1: 4 77.41936 cents 1: 2 116.12903 cents 1: 1 154.83871 cents 1: 1 193.54839 cents 2: 4 77.41935 cents 2: 5 116.12903 cents 2: 2 154.83871 cents 2: 1 193.54838 cents 2: 3 232.25807 cents 2: 1 309.67742 cents 3: 1 116.12903 cents 3: 5 154.83871 cents 3: 3 193.54839 cents 3: 1 232.25806 cents 3: 3 270.96774 cents 3: 1 309.67742 cents 3: 1 348.38710 cents 3: 1 425.80645 cents 4: 3 193.54839 cents 4: 3 232.25806 cents 4: 2 270.96774 cents 4: 2 309.67742 cents 4: 3 348.38709 cents 4: 1 387.09678 cents 4: 2 464.51613 cents 5: 1 232.25806 cents 5: 3 270.96774 cents 5: 1 309.67742 cents 5: 2 348.38709 cents 5: 4 387.09677 cents 5: 1 425.80646 cents 5: 1 464.51613 cents 5: 3 503.22581 cents 6: 3 309.67742 cents 6: 2 387.09677 cents 6: 5 425.80645 cents 6: 3 541.93549 cents 6: 3 580.64517 cents 7: 2 348.38710 cents 7: 1 425.80645 cents 7: 4 464.51613 cents 7: 2 503.22580 cents 7: 1 580.64516 cents 7: 4 619.35484 cents 7: 1 658.06452 cents 7: 1 696.77420 cents 8: 1 387.09677 cents 8: 1 464.51613 cents 8: 2 503.22580 cents 8: 4 541.93549 cents 8: 4 658.06452 cents 8: 2 696.77420 cents 8: 1 735.48387 cents 8: 1 812.90323 cents 9: 1 503.22580 cents 9: 1 541.93548 cents 9: 4 580.64516 cents 9: 1 619.35484 cents 9: 2 696.77420 cents 9: 4 735.48387 cents 9: 1 774.19355 cents 9: 2 851.61290 cents 10: 3 619.35484 cents 10: 3 658.06451 cents 10: 5 774.19355 cents 10: 2 812.90323 cents 10: 3 890.32258 cents 11: 3 696.77419 cents 11: 1 735.48387 cents 11: 1 774.19354 cents 11: 4 812.90323 cents 11: 2 851.61291 cents 11: 1 890.32258 cents 11: 3 929.03226 cents 11: 1 967.74194 cents 12: 2 735.48387 cents 12: 1 812.90322 cents 12: 3 851.61291 cents 12: 2 890.32259 cents 12: 2 929.03226 cents 12: 3 967.74194 cents 12: 3 1006.45161 cents 13: 1 774.19355 cents 13: 1 851.61290 cents 13: 1 890.32258 cents 13: 3 929.03226 cents 13: 1 967.74194 cents 13: 3 1006.45162 cents 13: 5 1045.16129 cents 13: 1 1083.87097 cents 14: 1 890.32258 cents 14: 3 967.74194 cents 14: 1 1006.45162 cents 14: 2 1045.16129 cents 14: 5 1083.87097 cents 14: 4 1122.58065 cents 15: 1 1006.45161 cents 15: 1 1045.16129 cents 15: 2 1083.87097 cents 15: 4 1122.58064 cents 15: 8 1161.29032 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.80000 = 34/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 38.7 77.4 154.8 193.5 271.0 309.7 348.4 387.1 541.9 619.4 696.8 735.5 774.2 967.7 1083.9 1200.0 38.7 : 38.7 116.1 154.8 232.3 271.0 309.7 348.4 503.2 580.6 658.1 696.8 735.5 929.0 1045.2 1161.3 1200.0 77.4 : 77.4 116.1 193.5 232.3 271.0 309.7 464.5 541.9 619.4 658.1 696.8 890.3 1006.5 1122.6 1161.3 1200.0 154.8 : 38.7 116.1 154.8 193.5 232.3 387.1 464.5 541.9 580.6 619.4 812.9 929.0 1045.2 1083.9 1122.6 1200.0 193.5 : 77.4 116.1 154.8 193.5 348.4 425.8 503.2 541.9 580.6 774.2 890.3 1006.5 1045.2 1083.9 1161.3 1200.0 271.0 : 38.7 77.4 116.1 271.0 348.4 425.8 464.5 503.2 696.8 812.9 929.0 967.7 1006.5 1083.9 1122.6 1200.0 309.7 : 38.7 77.4 232.3 309.7 387.1 425.8 464.5 658.1 774.2 890.3 929.0 967.7 1045.2 1083.9 1161.3 1200.0 348.4 : 38.7 193.5 271.0 348.4 387.1 425.8 619.4 735.5 851.6 890.3 929.0 1006.5 1045.2 1122.6 1161.3 1200.0 387.1 : 154.8 232.3 309.7 348.4 387.1 580.6 696.8 812.9 851.6 890.3 967.7 1006.5 1083.9 1122.6 1161.3 1200.0 541.9 : 77.4 154.8 193.5 232.3 425.8 541.9 658.1 696.8 735.5 812.9 851.6 929.0 967.7 1006.5 1045.2 1200.0 619.4 : 77.4 116.1 154.8 348.4 464.5 580.6 619.4 658.1 735.5 774.2 851.6 890.3 929.0 967.7 1122.6 1200.0 696.8 : 38.7 77.4 271.0 387.1 503.2 541.9 580.6 658.1 696.8 774.2 812.9 851.6 890.3 1045.2 1122.6 1200.0 735.5 : 38.7 232.3 348.4 464.5 503.2 541.9 619.4 658.1 735.5 774.2 812.9 851.6 1006.5 1083.9 1161.3 1200.0 774.2 : 193.5 309.7 425.8 464.5 503.2 580.6 619.4 696.8 735.5 774.2 812.9 967.7 1045.2 1122.6 1161.3 1200.0 967.7 : 116.1 232.3 271.0 309.7 387.1 425.8 503.2 541.9 580.6 619.4 774.2 851.6 929.0 967.7 1006.5 1200.0 1083.9: 116.1 154.8 193.5 271.0 309.7 387.1 425.8 464.5 503.2 658.1 735.5 812.9 851.6 890.3 1083.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7097 .. 193.5484 cents 154.83871 cents 38.70968 cents 2: 77.4193 .. 309.6774 cents 232.25807 cents -116.12904 cents 3: 116.1290 .. 425.8064 cents 309.67742 cents -193.54839 cents 4: 193.5484 .. 464.5161 cents 270.96774 cents -232.25806 cents 5: 232.2581 .. 503.2258 cents 270.96775 cents -232.25807 cents 6: 309.6774 .. 580.6452 cents 270.96775 cents -193.54839 cents 7: 348.3871 .. 696.7742 cents 348.38710 cents -232.25807 cents 8: 387.0968 .. 812.9032 cents 425.80646 cents -309.67743 cents 9: 503.2258 .. 851.6129 cents 348.38710 cents -309.67743 cents 10: 619.3548 .. 890.3226 cents 270.96774 cents -232.25806 cents 11: 696.7742 .. 967.7419 cents 270.96775 cents -193.54839 cents 12: 735.4839 .. 1006.4516 cents 270.96774 cents -232.25807 cents 13: 774.1935 .. 1083.8710 cents 309.67742 cents -232.25806 cents 14: 890.3226 .. 1122.5807 cents 232.25807 cents -193.54839 cents 15: 1006.4516 .. 1161.2903 cents 154.83871 cents -116.12904 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 : 193.54839 cents Average / Smallest step : 1.937500 Largest / Average step : 2.580645 Largest / Smallest step : 5.000001 Median interval of one step : 58.06452 cents, amount: 0 Most common interval of one step : 38.70968 cents, amount: 8 Least squares average step : 64.71451 cents, oct.: 1035.43212 cents Scale is not proper Scale is a mode of a 31-tone equal temperament with octave 1200.000 cents degrees: 1 2 4 5 7 8 9 10 14 16 18 19 20 25 28 31 Least number of segments generator : 16 of 619.355 cents and inv. number of contiguous generator circle segments: 4 Shortest superset generator : 16 of 619.355 cents and inv. generated superset size: 27 = 11 more = 168.750% Number of contiguous 1-step segments: 4 Step pattern alph. order: AABABAAACBBAADEE Step pattern size order : AABABAAADBBAAECC Interval vector is [ 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 ] 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 : 8 Mean interval variety : 6.80000 = 34/5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 38.70967 cents Most common triad is 0.0 116.129 154.839 cents, amount: 5 Number of recognisable fifths : 8, average 696.7742 cents Formal octave complements present : 1 = 6.2500% -- Rational properties --
FIT/MODE
16: 0 1 1 0 1 1 0 1 2 1 1 0 1 3 1 2 N SD: 30.3084 c. M: 60.4839 c. 17: 1 0 1 1 1 0 1 0 3 1 1 0 1 3 1 2 N SD: 20.0457 c. M: 34.1556 c. 21: 1 0 2 0 2 0 1 1 2 2 1 1 1 3 2 2 N SD: 16.2275 c. M: 27.6498 c. 22: 1 0 2 1 1 1 0 1 3 1 2 0 1 4 2 2 N SD: 15.4899 c. M: 26.3930 c. 23: 1 0 2 1 1 1 1 0 3 2 1 1 1 4 2 2 N SD: 14.8164 c. M: 25.2454 c. 24: 1 1 1 1 1 1 1 1 3 1 2 1 0 4 3 2 N SD: 14.1990 c. M: 24.1935 c. 26: 1 1 1 1 2 1 1 0 4 1 2 1 1 4 2 3 N SD: 13.1068 c. M: 22.3325 c. 27: 1 1 1 1 2 1 1 1 3 2 2 1 0 5 2 3 N SD: 12.6214 c. M: 21.5054 c. 29: 1 1 2 1 2 0 1 1 4 2 2 1 1 4 3 3 N SD: 11.7509 c. M: 20.0222 c. 30: 1 1 2 1 2 1 1 1 4 1 2 1 1 5 3 3 N SD: 11.3592 c. M: 19.3548 c. 31: 1 1 2 1 2 1 1 1 4 2 2 1 1 5 3 3 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: 2.5904 cents 3 .. 6 match: 3 H SD: 31.4097 cents 4 .. 8 match: 4 H SD: 1.3377 cents 5 .. 10 match: 5 H SD: 14.7487 cents 6 .. 12 match: 5 SD: 11.2442 cents 7 .. 14 match: 7 H SD: 10.2389 cents 8 .. 16 match: 8 H SD: 8.5180 cents 9 .. 18 match: 8 S SD: 7.4311 cents 10 .. 20 match: 9 SD: 11.5177 cents 11 .. 22 match: 9 SD: 7.2186 cents 12 .. 24 match: 10 SD: 6.4429 cents 13 .. 26 match: 9 SD: 7.2460 cents 14 .. 28 match: 11 S SD: 7.4648 cents 15 .. 30 match: 10 SD: 7.0744 cents 16 .. 32 match: 11 SD: 3.1904 cents 17 .. 34 match: 12 SD: 5.0354 cents 18 .. 36 match: 12 SD: 5.2204 cents 19 .. 38 match: 13 S SD: 4.2710 cents 20 .. 40 match: 12 SD: 4.3506 cents 21 .. 42 match: 12 SD: 3.3277 cents 22 .. 44 match: 13 SD: 4.6310 cents 23 .. 46 match: 14 SD: 3.2112 cents 24 .. 48 match: 14 SD: 3.0385 cents 25 .. 50 match: 14 SD: 3.1175 cents 26 .. 52 match: 15 SD: 3.9946 cents 27 .. 54 match: 13 SD: 3.3460 cents 28 .. 56 match: 13 SD: 2.8647 cents 29 .. 58 match: 13 SD: 3.7559 cents 30 .. 60 match: 15 SD: 3.0163 cents 31 .. 62 match: 15 SD: 3.0065 cents 32 .. 64 match: 15 SD: 2.2213 cents 33 .. 66 match: 15 SD: 3.1943 cents 34 .. 68 match: 16 SD: 3.1611 cents 35 .. 70 match: 16 SD: 2.4051 cents 36 .. 72 match: 16 SD: 2.2300 cents 38 .. 76 match: 15 SD: 3.1031 cents 39 .. 78 match: 16 SD: 2.4439 cents 40 .. 80 match: 16 SD: 1.6964 cents 41 .. 82 match: 16 SD: 1.5320 cents 60 .. 120 match: 16 SD: 1.3664 cents 67 .. 134 match: 16 SD: 1.3345 cents 71 .. 142 match: 16 SD: 1.2876 cents 75 .. 150 match: 16 SD: 1.2317 cents 76 .. 152 match: 16 SD: 0.9630 cents 84 .. 168 match: 16 SD: 0.9304 cents 85 .. 170 match: 16 SD: 0.8612 cents 87 .. 174 match: 16 SD: 0.7787 cents 107 .. 214 match: 16 SD: 0.7117 cents 117 .. 234 match: 16 SD: 0.6282 cents 128 .. 256 match: 16 SD: 0.5631 cents 147 .. 294 match: 16 SD: 0.5167 cents 160 .. 320 match: 16 SD: 0.5081 cents 170 .. 340 match: 16 SD: 0.4449 cents 172 .. 344 match: 16 SD: 0.3918 cents 179 .. 358 match: 16 SD: 0.3422 cents 220 .. 440 match: 16 SD: 0.3364 cents 236 .. 472 match: 16 SD: 0.3342 cents 255 .. 510 match: 16 SD: 0.2739 cents 270 .. 540 match: 16 SD: 0.2664 cents 302 .. 604 match: 16 SD: 0.2477 cents 307 .. 614 match: 16 SD: 0.2317 cents 323 .. 646 match: 16 SD: 0.2056 cents 353 .. 706 match: 16 SD: 0.1981 cents 372 .. 744 match: 16 SD: 0.1897 cents 395 .. 790 match: 16 SD: 0.1474 cents 438 .. 876 match: 16 SD: 0.1405 cents 484 .. 968 match: 16 SD: 0.1332 cents 525 .. 1050 match: 16 SD: 0.1002 cents