Scala analysis: xen18-erlich-helmholtz-17
12L 5s MOS for Helmholtz, L=91.26, s=20.99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 91.260 cents 91.260000 2: 112.250 cents 112.250000 3: 203.510 cents 203.510000 4: 294.770 cents 294.770000 5: 386.030 cents 386.030000 6: 407.020 cents 407.020000 7: 498.280 cents 498.280000 8: 589.540 cents 589.540000 9: 610.530 cents 610.530000 10: 701.790 cents 701.790000 11: 793.050 cents 793.050000 12: 814.040 cents 814.040000 13: 905.300 cents 905.300000 14: 996.560 cents 996.560000 15: 1087.820 cents 1087.820000 16: 1108.810 cents 1108.810000 17: 1200.070 cents 1200.070000
SHOW/INTERVAL
0: 91.2600 cents 91.2600 1: 91.2600 cents 91.2600 2: 20.9900 cents 20.9900 3: 91.2600 cents 91.2600 4: 91.2600 cents 91.2600 5: 91.2600 cents 91.2600 6: 20.9900 cents 20.9900 7: 91.2600 cents 91.2600 8: 91.2600 cents 91.2600 9: 20.9900 cents 20.9900 10: 91.2600 cents 91.2600 11: 91.2600 cents 91.2600 12: 20.9900 cents 20.9900 13: 91.2600 cents 91.2600 14: 91.2600 cents 91.2600 15: 91.2600 cents 91.2600 16: 20.9900 cents 20.9900 17: 91.2600 cents 91.2600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 20.99000 cents 1: 12 91.26000 cents 2: 10 112.25000 cents 2: 7 182.52000 cents 3: 15 203.51000 cents 3: 2 273.78000 cents 4: 3 224.50000 cents 4: 14 294.77000 cents 5: 8 315.76000 cents 5: 9 386.03000 cents 6: 13 407.02000 cents 6: 4 477.29000 cents 7: 1 428.01000 cents 7: 16 498.28000 cents 8: 6 519.27000 cents 8: 11 589.54000 cents 9: 11 610.53000 cents 9: 6 680.80000 cents 10: 16 701.79000 cents 10: 1 772.06000 cents 11: 4 722.78000 cents 11: 13 793.05000 cents 12: 9 814.04000 cents 12: 8 884.31000 cents 13: 14 905.30000 cents 13: 3 975.57000 cents 14: 2 926.29000 cents 14: 15 996.56000 cents 15: 7 1017.55000 cents 15: 10 1087.82000 cents 16: 12 1108.81000 cents 16: 5 1179.08000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 91.3 112.3 203.5 294.8 386.0 407.0 498.3 589.5 610.5 701.8 793.1 814.0 905.3 996.6 1087.8 1108.8 1200.1 91.3 : 21.0 112.3 203.5 294.8 315.8 407.0 498.3 519.3 610.5 701.8 722.8 814.0 905.3 996.6 1017.6 1108.8 1200.1 112.3 : 91.3 182.5 273.8 294.8 386.0 477.3 498.3 589.5 680.8 701.8 793.0 884.3 975.6 996.6 1087.8 1179.1 1200.1 203.5 : 91.3 182.5 203.5 294.8 386.0 407.0 498.3 589.5 610.5 701.8 793.0 884.3 905.3 996.6 1087.8 1108.8 1200.1 294.8 : 91.3 112.3 203.5 294.8 315.8 407.0 498.3 519.3 610.5 701.8 793.1 814.0 905.3 996.6 1017.6 1108.8 1200.1 386.0 : 21.0 112.3 203.5 224.5 315.8 407.0 428.0 519.3 610.5 701.8 722.8 814.0 905.3 926.3 1017.5 1108.8 1200.1 407.0 : 91.3 182.5 203.5 294.8 386.0 407.0 498.3 589.5 680.8 701.8 793.0 884.3 905.3 996.6 1087.8 1179.1 1200.1 498.3 : 91.3 112.3 203.5 294.8 315.8 407.0 498.3 589.5 610.5 701.8 793.0 814.0 905.3 996.6 1087.8 1108.8 1200.1 589.5 : 21.0 112.3 203.5 224.5 315.8 407.0 498.3 519.3 610.5 701.8 722.8 814.0 905.3 996.6 1017.5 1108.8 1200.1 610.5 : 91.3 182.5 203.5 294.8 386.0 477.3 498.3 589.5 680.8 701.8 793.0 884.3 975.6 996.6 1087.8 1179.1 1200.1 701.8 : 91.3 112.3 203.5 294.8 386.0 407.0 498.3 589.5 610.5 701.8 793.0 884.3 905.3 996.6 1087.8 1108.8 1200.1 793.1 : 21.0 112.3 203.5 294.8 315.8 407.0 498.3 519.3 610.5 701.8 793.0 814.0 905.3 996.6 1017.5 1108.8 1200.1 814.0 : 91.3 182.5 273.8 294.8 386.0 477.3 498.3 589.5 680.8 772.1 793.0 884.3 975.6 996.6 1087.8 1179.1 1200.1 905.3 : 91.3 182.5 203.5 294.8 386.0 407.0 498.3 589.5 680.8 701.8 793.0 884.3 905.3 996.6 1087.8 1108.8 1200.1 996.6 : 91.3 112.3 203.5 294.8 315.8 407.0 498.3 589.5 610.5 701.8 793.0 814.0 905.3 996.6 1017.5 1108.8 1200.1 1087.8: 21.0 112.2 203.5 224.5 315.8 407.0 498.3 519.3 610.5 701.8 722.8 814.0 905.3 926.3 1017.5 1108.8 1200.1 1108.8: 91.3 182.5 203.5 294.8 386.0 477.3 498.3 589.5 680.8 701.8 793.0 884.3 905.3 996.6 1087.8 1179.1 1200.1 1200.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.9900 .. 91.2600 cents 70.27000 cents 20.99000 cents 2: 112.2500 .. 182.5200 cents 70.27000 cents 20.99000 cents 3: 203.5100 .. 273.7800 cents 70.27000 cents 20.99000 cents 4: 224.5000 .. 294.7700 cents 70.27000 cents -49.28000 cents 5: 315.7600 .. 386.0300 cents 70.27000 cents 20.99000 cents 6: 407.0200 .. 477.2900 cents 70.27000 cents 20.99000 cents 7: 428.0100 .. 498.2800 cents 70.27000 cents -49.28000 cents 8: 519.2700 .. 589.5400 cents 70.27000 cents 20.99000 cents 9: 610.5300 .. 680.8000 cents 70.27000 cents 20.99000 cents 10: 701.7900 .. 772.0600 cents 70.27000 cents 20.99000 cents 11: 722.7800 .. 793.0500 cents 70.27000 cents -49.28000 cents 12: 814.0400 .. 884.3100 cents 70.27000 cents 20.99000 cents 13: 905.3000 .. 975.5700 cents 70.27000 cents 20.99000 cents 14: 926.2900 .. 996.5600 cents 70.27000 cents -49.28000 cents 15: 1017.5500 .. 1087.8200 cents 70.27000 cents 20.99000 cents 16: 1108.8100 .. 1179.0800 cents 70.27000 cents 20.99000 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 20.99000 cents, class 1 Average step (divided formal octave): 70.5924 cents Largest one step interval : 91.26000 cents Average / Smallest step : 3.363142 Largest / Average step : 1.292775 Largest / Smallest step : 4.347785 Median interval of one step : 91.26000 cents, amount: 12 Most common interval of one step : 91.26000 cents, amount: 12 Least squares average step : 70.51362 cents, oct.: 1198.73152 cents Scale is not proper Scale has Myhill's property chromas: 70.27000 cents and 49.28000 cents, ratio: 1.425933 generators: 7 of 498.28000 cents and 10 of 701.79000 cents ET pair of linear temperament : 12&53 Scale is distributional even Scale is a mode of a 1315-tone equal temperament with octave 1200.070 cents degrees: 100 123 223 323 423 446 546 646 669 769 869 892 992 1092 1192 1215 1315 generators: 546 and 769 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAABAABAAABA Step pattern size order : LSLLLSLLSLLSLLLSL Scale is a Constant Structure, by a margin of 20.99000 cents Ratio Whole / Half tone : 2.230002 Scale diversity : 1.130859 Lumma stability : 0.227378 Lumma impropriety factor : 0.164257 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 20.99000 cents Most common intervals : 498.28000 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 498.280 996.560 cents Most common triad is 0.0 498.280 701.790 cents, amount: 15 Number of recognisable fifths : 16, average 701.7900 cents Number of recognisable fourths : 16, average 498.2800 cents Scale contains two identical disjunct "tetrachords" of 8 notes Formal octave complements present : 17 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 8-9 -- Rational properties --
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 20.2501 c. M: 33.0682 c. 18: 1 1 1 1 2 0 1 2 0 2 1 0 2 1 1 1 1 N D3 I SD: 19.4126 c. M: 31.5861 c. 19: 1 1 1 2 1 0 2 1 1 1 2 0 1 2 1 1 1 N D3 I SD: 18.6527 c. M: 28.0984 c. 20: 2 0 1 2 1 1 1 2 0 2 1 1 1 2 1 0 2 N I SD: 18.0039 c. M: 28.7470 c. 21: 2 0 2 1 2 0 2 1 1 1 2 0 2 1 2 0 2 N T3 I SD: 15.6199 c. M: 25.0748 c. 22: 2 0 2 1 2 0 2 2 0 2 2 0 2 1 2 0 2 N I SD: 14.7311 c. M: 25.1795 c. 23: 2 0 2 2 1 1 2 1 1 1 2 1 1 2 2 0 2 N D3 I SD: 15.0711 c. M: 23.4896 c. 24: 2 0 2 2 2 0 2 2 0 2 2 0 2 2 2 0 2 N M DE I SD: 8.5691 c. M: 13.9933 c. 29: 2 1 2 2 2 1 2 2 1 2 2 1 2 2 2 1 2 P M ME I SD: 8.3249 c. M: 13.5945 c. 40: 3 1 3 3 3 1 3 3 0 3 3 1 3 3 3 1 3 N I SD: 8.1517 c. M: 13.0045 c. 41: 3 1 3 3 3 1 3 3 1 3 3 1 3 3 3 1 3 N M DE I SD: 3.3803 c. M: 5.5200 c. 53: 4 1 4 4 4 1 4 4 1 4 4 1 4 4 4 1 4 N M DE I SD: 0.6748 c. M: 1.1019 c. 118: 9 2 9 9 9 2 9 9 2 9 9 2 9 9 9 2 9 N M DE I SD: 0.2653 c. M: 0.4332 c. 171: 13 3 13 13 13 3 13 13 3 13 13 3 13 13 13 3 13 N M DE I SD: 0.0261 c. M: 0.0426 c. 802: 61 14 61 61 61 14 61 61 14 61 61 14 61 61 61 14 61 N M DE I SD: 0.0168 c. M: 0.0274 c. 973: 74 17 74 74 74 17 74 74 17 74 74 17 74 74 74 17 74 N M DE I SD: 0.0093 c. M: 0.0151 c. 1144: 87 20 87 87 87 20 87 87 20 87 87 20 87 87 87 20 87 N M DE I SD: 0.0040 c. M: 0.0065 c. 1315: 100 23 100 100 100 23 100 100 23 100 100 23 100 100 100 23 100 N M DE I SD: 0.0001 c. M: 0.0001 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0700 cents 2 .. 4 match: 2 H SD: 0.0896 cents 3 .. 6 match: 3 H SD: 6.9809 cents 4 .. 8 match: 4 H SD: 6.9340 cents 5 .. 10 match: 5 H SD: 6.0915 cents 6 .. 12 match: 6 H SD: 8.6537 cents 7 .. 14 match: 7 H SD: 7.4875 cents 8 .. 16 match: 8 H SD: 6.7687 cents 9 .. 18 match: 9 H SD: 6.9463 cents 10 .. 20 match: 10 H SD: 6.7349 cents 11 .. 22 match: 11 H SD: 9.4774 cents 12 .. 24 match: 12 H SD: 5.6073 cents 13 .. 26 match: 12 S SD: 7.5896 cents 14 .. 28 match: 13 S SD: 6.0975 cents 15 .. 30 match: 12 SD: 4.6085 cents 16 .. 32 match: 14 S SD: 4.7816 cents 17 .. 34 match: 13 SD: 5.3303 cents 18 .. 36 match: 14 SD: 4.5570 cents 19 .. 38 match: 12 SD: 5.1492 cents 20 .. 40 match: 13 SD: 4.6204 cents 21 .. 42 match: 15 SD: 4.3717 cents 22 .. 44 match: 13 SD: 2.9362 cents 23 .. 46 match: 16 SD: 3.9263 cents 24 .. 48 match: 14 SD: 3.8285 cents 25 .. 50 match: 15 SD: 4.1067 cents 26 .. 52 match: 15 SD: 3.4744 cents 27 .. 54 match: 13 SD: 3.7087 cents 28 .. 56 match: 15 SD: 2.9978 cents 29 .. 58 match: 14 SD: 3.3770 cents 30 .. 60 match: 16 SD: 2.7723 cents 31 .. 62 match: 14 SD: 2.4584 cents 32 .. 64 match: 14 SD: 1.8579 cents 33 .. 66 match: 16 SD: 2.2482 cents 34 .. 68 match: 14 SD: 2.8295 cents 35 .. 70 match: 14 SD: 2.8574 cents 36 .. 72 match: 15 SD: 2.4843 cents 37 .. 74 match: 15 SD: 2.3483 cents 38 .. 76 match: 17 SD: 2.1488 cents 39 .. 78 match: 14 SD: 2.1711 cents 40 .. 80 match: 17 SD: 1.8896 cents 41 .. 82 match: 16 SD: 2.0296 cents 42 .. 84 match: 17 SD: 1.7795 cents 43 .. 86 match: 16 SD: 2.2488 cents 44 .. 88 match: 16 SD: 2.1978 cents 45 .. 90 match: 17 SD: 1.8253 cents 46 .. 92 match: 16 SD: 2.2593 cents 47 .. 94 match: 15 SD: 1.6698 cents 48 .. 96 match: 16 SD: 1.2615 cents 49 .. 98 match: 16 SD: 1.6450 cents 50 .. 100 match: 16 SD: 1.6124 cents 51 .. 102 match: 16 SD: 2.0690 cents 52 .. 104 match: 16 SD: 1.6590 cents 53 .. 106 match: 16 SD: 1.8422 cents 54 .. 108 match: 17 SD: 1.4891 cents 55 .. 110 match: 17 SD: 1.4503 cents 56 .. 112 match: 17 SD: 1.4359 cents 57 .. 114 match: 17 SD: 1.1603 cents 64 .. 128 match: 17 SD: 1.1218 cents 65 .. 130 match: 16 SD: 1.3912 cents 66 .. 132 match: 16 SD: 1.4696 cents 67 .. 134 match: 16 SD: 1.4159 cents 69 .. 138 match: 17 SD: 1.2688 cents 71 .. 142 match: 17 SD: 1.0223 cents 72 .. 144 match: 17 SD: 0.9001 cents 87 .. 174 match: 17 SD: 0.8328 cents 88 .. 176 match: 17 SD: 0.8249 cents 90 .. 180 match: 17 SD: 0.7903 cents 96 .. 192 match: 17 SD: 0.7760 cents 108 .. 216 match: 17 SD: 0.6776 cents 118 .. 236 match: 17 SD: 0.6684 cents 120 .. 240 match: 17 SD: 0.6349 cents 128 .. 256 match: 17 SD: 0.4990 cents 135 .. 270 match: 17 SD: 0.4967 cents 144 .. 288 match: 17 SD: 0.4773 cents 150 .. 300 match: 17 SD: 0.4618 cents 166 .. 332 match: 17 SD: 0.4539 cents 167 .. 334 match: 17 SD: 0.4160 cents 168 .. 336 match: 17 SD: 0.3874 cents 184 .. 368 match: 17 SD: 0.3781 cents 192 .. 384 match: 17 SD: 0.3659 cents 200 .. 400 match: 17 SD: 0.3631 cents 208 .. 416 match: 17 SD: 0.3100 cents 222 .. 444 match: 17 SD: 0.3014 cents 253 .. 506 match: 17 SD: 0.2989 cents 256 .. 512 match: 17 SD: 0.2692 cents 272 .. 544 match: 17 SD: 0.2594 cents 280 .. 560 match: 17 SD: 0.2477 cents 296 .. 592 match: 17 SD: 0.2143 cents 312 .. 624 match: 17 SD: 0.1822 cents 392 .. 784 match: 17 SD: 0.1537 cents 464 .. 928 match: 17 SD: 0.1312 cents 480 .. 960 match: 17 SD: 0.1064 cents