Scala analysis: xen18-erlich-hanson-19
15L 4s MOS for Hanson, L=67.99, s=45.11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.990 cents 67.990000 2: 135.980 cents 135.980000 3: 181.090 cents 181.090000 4: 249.080 cents 249.080000 5: 317.070 cents 317.070000 6: 385.060 cents 385.060000 7: 453.050 cents 453.050000 8: 498.160 cents 498.160000 9: 566.150 cents 566.150000 10: 634.140 cents 634.140000 11: 702.130 cents 702.130000 12: 747.240 cents 747.240000 13: 815.230 cents 815.230000 14: 883.220 cents 883.220000 15: 951.210 cents 951.210000 16: 1019.200 cents 1019.200000 17: 1064.310 cents 1064.310000 18: 1132.300 cents 1132.300000 19: 1200.290 cents 1200.290000
SHOW/INTERVAL
0: 67.9900 cents 67.9900 1: 67.9900 cents 67.9900 2: 67.9900 cents 67.9900 3: 45.1100 cents 45.1100 4: 67.9900 cents 67.9900 5: 67.9900 cents 67.9900 6: 67.9900 cents 67.9900 7: 67.9900 cents 67.9900 8: 45.1100 cents 45.1100 9: 67.9900 cents 67.9900 10: 67.9900 cents 67.9900 11: 67.9900 cents 67.9900 12: 45.1100 cents 45.1100 13: 67.9900 cents 67.9900 14: 67.9900 cents 67.9900 15: 67.9900 cents 67.9900 16: 67.9900 cents 67.9900 17: 45.1100 cents 45.1100 18: 67.9900 cents 67.9900 19: 67.9900 cents 67.9900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 45.11000 cents 1: 15 67.99000 cents 2: 8 113.10000 cents 2: 11 135.98000 cents 3: 12 181.09000 cents 3: 7 203.97000 cents 4: 16 249.08000 cents 4: 3 271.96000 cents 5: 1 294.19000 cents 5: 18 317.07000 cents 6: 5 362.18000 cents 6: 14 385.06000 cents 7: 9 430.17000 cents 7: 10 453.05000 cents 8: 13 498.16000 cents 8: 6 521.04000 cents 9: 17 566.15000 cents 9: 2 589.03000 cents 10: 2 611.26000 cents 10: 17 634.14000 cents 11: 6 679.25000 cents 11: 13 702.13000 cents 12: 10 747.24000 cents 12: 9 770.12000 cents 13: 14 815.23000 cents 13: 5 838.11000 cents 14: 18 883.22000 cents 14: 1 906.10000 cents 15: 3 928.33000 cents 15: 16 951.21000 cents 16: 7 996.32000 cents 16: 12 1019.20000 cents 17: 11 1064.31000 cents 17: 8 1087.19000 cents 18: 15 1132.30000 cents 18: 4 1155.18000 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 18 19 0.0 : 68.0 136.0 181.1 249.1 317.1 385.1 453.0 498.2 566.1 634.1 702.1 747.2 815.2 883.2 951.2 1019.2 1064.3 1132.3 1200.3 68.0 : 68.0 113.1 181.1 249.1 317.1 385.1 430.2 498.2 566.1 634.1 679.3 747.2 815.2 883.2 951.2 996.3 1064.3 1132.3 1200.3 136.0 : 45.1 113.1 181.1 249.1 317.1 362.2 430.2 498.2 566.1 611.3 679.3 747.2 815.2 883.2 928.3 996.3 1064.3 1132.3 1200.3 181.1 : 68.0 136.0 204.0 272.0 317.1 385.1 453.0 521.0 566.1 634.1 702.1 770.1 838.1 883.2 951.2 1019.2 1087.2 1155.2 1200.3 249.1 : 68.0 136.0 204.0 249.1 317.1 385.1 453.1 498.2 566.1 634.1 702.1 770.1 815.2 883.2 951.2 1019.2 1087.2 1132.3 1200.3 317.1 : 68.0 136.0 181.1 249.1 317.1 385.1 430.2 498.2 566.1 634.1 702.1 747.2 815.2 883.2 951.2 1019.2 1064.3 1132.3 1200.3 385.1 : 68.0 113.1 181.1 249.1 317.1 362.2 430.2 498.2 566.1 634.1 679.2 747.2 815.2 883.2 951.2 996.3 1064.3 1132.3 1200.3 453.0 : 45.1 113.1 181.1 249.1 294.2 362.2 430.2 498.2 566.2 611.3 679.3 747.2 815.2 883.2 928.3 996.3 1064.3 1132.3 1200.3 498.2 : 68.0 136.0 204.0 249.1 317.1 385.1 453.0 521.0 566.1 634.1 702.1 770.1 838.1 883.2 951.2 1019.2 1087.2 1155.2 1200.3 566.1 : 68.0 136.0 181.1 249.1 317.1 385.1 453.1 498.2 566.1 634.1 702.1 770.1 815.2 883.2 951.2 1019.2 1087.2 1132.3 1200.3 634.1 : 68.0 113.1 181.1 249.1 317.1 385.1 430.2 498.2 566.1 634.1 702.1 747.2 815.2 883.2 951.2 1019.2 1064.3 1132.3 1200.3 702.1 : 45.1 113.1 181.1 249.1 317.1 362.2 430.2 498.2 566.1 634.1 679.3 747.2 815.2 883.2 951.2 996.3 1064.3 1132.3 1200.3 747.2 : 68.0 136.0 204.0 272.0 317.1 385.1 453.1 521.0 589.0 634.1 702.1 770.1 838.1 906.1 951.2 1019.2 1087.2 1155.2 1200.3 815.2 : 68.0 136.0 204.0 249.1 317.1 385.1 453.0 521.0 566.1 634.1 702.1 770.1 838.1 883.2 951.2 1019.2 1087.2 1132.3 1200.3 883.2 : 68.0 136.0 181.1 249.1 317.1 385.1 453.1 498.2 566.2 634.1 702.1 770.1 815.2 883.2 951.2 1019.2 1064.3 1132.3 1200.3 951.2 : 68.0 113.1 181.1 249.1 317.1 385.1 430.2 498.2 566.1 634.1 702.1 747.2 815.2 883.2 951.2 996.3 1064.3 1132.3 1200.3 1019.2: 45.1 113.1 181.1 249.1 317.1 362.2 430.2 498.2 566.1 634.1 679.3 747.2 815.2 883.2 928.3 996.3 1064.3 1132.3 1200.3 1064.3: 68.0 136.0 204.0 272.0 317.1 385.1 453.0 521.0 589.0 634.1 702.1 770.1 838.1 883.2 951.2 1019.2 1087.2 1155.2 1200.3 1132.3: 68.0 136.0 204.0 249.1 317.1 385.1 453.0 521.0 566.2 634.1 702.1 770.1 815.2 883.2 951.2 1019.2 1087.2 1132.3 1200.3 1200.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 45.1100 .. 67.9900 cents 22.88000 cents 45.11000 cents 2: 113.1000 .. 135.9800 cents 22.88000 cents 45.11000 cents 3: 181.0900 .. 203.9700 cents 22.88000 cents 45.11000 cents 4: 249.0800 .. 271.9600 cents 22.88000 cents 45.11000 cents 5: 294.1900 .. 317.0700 cents 22.88000 cents 22.23000 cents 6: 362.1800 .. 385.0600 cents 22.88000 cents 45.11000 cents 7: 430.1700 .. 453.0500 cents 22.88000 cents 45.11000 cents 8: 498.1600 .. 521.0400 cents 22.88000 cents 45.11000 cents 9: 566.1500 .. 589.0300 cents 22.88000 cents 45.11000 cents 10: 611.2600 .. 634.1400 cents 22.88000 cents 22.23000 cents 11: 679.2500 .. 702.1300 cents 22.88000 cents 45.11000 cents 12: 747.2400 .. 770.1200 cents 22.88000 cents 45.11000 cents 13: 815.2300 .. 838.1100 cents 22.88000 cents 45.11000 cents 14: 883.2200 .. 906.1000 cents 22.88000 cents 45.11000 cents 15: 928.3300 .. 951.2100 cents 22.88000 cents 22.23000 cents 16: 996.3200 .. 1019.2000 cents 22.88000 cents 45.11000 cents 17: 1064.3100 .. 1087.1900 cents 22.88000 cents 45.11000 cents 18: 1132.3000 .. 1155.1800 cents 22.88000 cents 45.11000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 45.11000 cents, class 1 Average step (divided formal octave): 63.1732 cents Largest one step interval : 67.99000 cents Average / Smallest step : 1.400425 Largest / Average step : 1.076248 Largest / Smallest step : 1.507205 Median interval of one step : 67.99000 cents, amount: 15 Most common interval of one step : 67.99000 cents, amount: 15 Least squares average step : 63.10832 cents, oct.: 1199.05800 cents Scale is strictly proper Scale has Myhill's property chromas: 22.88000 cents and 22.23000 cents, ratio: 1.029240 generators: 5 of 317.07000 cents and 14 of 883.22000 cents ET pair of linear temperament : 15&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1783-tone equal temperament with octave 1200.290 cents degrees: 101 202 269 370 471 572 673 740 841 942 1043 1110 1211 1312 1413 1514 1581 1682 1783 generators: 471 and 1312 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAABAAABAAAABAA Step pattern size order : LLSLLLLSLLLSLLLLSLL Scale is a Constant Structure, by a margin of 22.23000 cents Scale diversity : 1.188798 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.656883 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 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 : 22.23000 cents Most common intervals : 317.07000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 453.050 883.220 cents Most common triad is 0.0 317.070 883.220 cents, amount: 17 Number of recognisable fifths : 13, average 702.1300 cents Number of recognisable fourths : 13, average 498.1600 cents Scale contains two identical disjunct "tetrachords" of 9 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 19 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties --
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.5957 c. M:-10.8379 c. 34: 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 P M ME I SD: 3.5811 c. M:-5.8844 c. 53: 3 3 2 3 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3 SP M ME I SD: 0.0672 c. M:-0.1104 c. 935: 53 53 35 53 53 53 53 35 53 53 53 35 53 53 53 53 35 53 53 SP M DE I SD: 0.0655 c. M:-0.1076 c. 988: 56 56 37 56 56 56 56 37 56 56 56 37 56 56 56 56 37 56 56 SP M DE I SD: 0.0584 c. M:-0.0959 c. 1041: 59 59 39 59 59 59 59 39 59 59 59 39 59 59 59 59 39 59 59 SP M DE I SD: 0.0520 c. M:-0.0854 c. 1094: 62 62 41 62 62 62 62 41 62 62 62 41 62 62 62 62 41 62 62 SP M DE I SD: 0.0462 c. M:-0.0759 c. 1147: 65 65 43 65 65 65 65 43 65 65 65 43 65 65 65 65 43 65 65 SP M DE I SD: 0.0410 c. M:-0.0673 c. 1200: 68 68 45 68 68 68 68 45 68 68 68 45 68 68 68 68 45 68 68 SP M DE I SD: 0.0362 c. M:-0.0595 c. 1253: 71 71 47 71 71 71 71 47 71 71 71 47 71 71 71 71 47 71 71 SP M DE I SD: 0.0318 c. M:-0.0523 c. 1306: 74 74 49 74 74 74 74 49 74 74 74 49 74 74 74 74 49 74 74 SP M DE I SD: 0.0278 c. M:-0.0457 c. 1359: 77 77 51 77 77 77 77 51 77 77 77 51 77 77 77 77 51 77 77 SP M DE I SD: 0.0241 c. M:-0.0396 c. 1412: 80 80 53 80 80 80 80 53 80 80 80 53 80 80 80 80 53 80 80 SP M DE I SD: 0.0207 c. M:-0.0340 c. 1465: 83 83 55 83 83 83 83 55 83 83 83 55 83 83 83 83 55 83 83 SP M DE I SD: 0.0175 c. M:-0.0288 c. 1518: 86 86 57 86 86 86 86 57 86 86 86 57 86 86 86 86 57 86 86 SP M DE I SD: 0.0145 c. M:-0.0239 c. 1571: 89 89 59 89 89 89 89 59 89 89 89 59 89 89 89 89 59 89 89 SP M DE I SD: 0.0118 c. M:-0.0194 c. 1624: 92 92 61 92 92 92 92 61 92 92 92 61 92 92 92 92 61 92 92 SP M DE I SD: 0.0092 c. M:-0.0151 c. 1677: 95 95 63 95 95 95 95 63 95 95 95 63 95 95 95 95 63 95 95 SP M DE I SD: 0.0068 c. M:-0.0112 c. 1730: 98 98 65 98 98 98 98 65 98 98 98 65 98 98 98 98 65 98 98 SP M DE I SD: 0.0045 c. M:-0.0074 c. 1783: 101 101 67 101 101 101 101 67 101 101 101 67 101 101 101 101 67 101 101 SP M DE I SD: 0.0024 c. M:-0.0039 c. 1836: 104 104 69 104 104 104 104 69 104 104 104 69 104 104 104 104 69 104 104 SP M DE I SD: 0.0004 c. M:-0.0006 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.2900 cents 2 .. 4 match: 2 H SD: 0.1694 cents 3 .. 6 match: 3 H SD: 0.3936 cents 4 .. 8 match: 4 H SD: 4.4159 cents 5 .. 10 match: 5 H SD: 3.3154 cents 6 .. 12 match: 6 H SD: 3.8778 cents 7 .. 14 match: 7 H SD: 6.9607 cents 8 .. 16 match: 8 H SD: 5.9513 cents 9 .. 18 match: 9 H SD: 5.8299 cents 10 .. 20 match: 10 H SD: 4.5176 cents 11 .. 22 match: 11 H SD: 6.1163 cents 12 .. 24 match: 12 H SD: 3.9550 cents 13 .. 26 match: 13 H SD: 4.4590 cents 14 .. 28 match: 14 H SD: 4.9319 cents 15 .. 30 match: 15 H SD: 4.0730 cents 16 .. 32 match: 16 H SD: 4.5876 cents 17 .. 34 match: 15 SD: 5.7237 cents 18 .. 36 match: 17 SD: 3.8888 cents 19 .. 38 match: 16 SD: 4.2549 cents 20 .. 40 match: 18 SD: 2.8064 cents 21 .. 42 match: 17 S SD: 3.4630 cents 22 .. 44 match: 17 SD: 4.2478 cents 23 .. 46 match: 18 SD: 3.8138 cents 24 .. 48 match: 19 SD: 2.7356 cents 25 .. 50 match: 18 SD: 2.8681 cents 26 .. 52 match: 19 SD: 2.5214 cents 31 .. 62 match: 18 SD: 2.7821 cents 33 .. 66 match: 19 SD: 2.4584 cents 34 .. 68 match: 19 SD: 2.3570 cents 36 .. 72 match: 19 SD: 2.0328 cents 39 .. 78 match: 19 SD: 1.9982 cents 40 .. 80 match: 19 SD: 1.9792 cents 44 .. 88 match: 19 SD: 1.7218 cents 45 .. 90 match: 19 SD: 1.5554 cents 48 .. 96 match: 19 SD: 1.5174 cents 50 .. 100 match: 19 SD: 1.4858 cents 52 .. 104 match: 19 SD: 1.3301 cents 60 .. 120 match: 19 SD: 1.1600 cents 70 .. 140 match: 19 SD: 1.0005 cents 72 .. 144 match: 19 SD: 0.9052 cents 80 .. 160 match: 19 SD: 0.8900 cents 90 .. 180 match: 19 SD: 0.7633 cents 96 .. 192 match: 19 SD: 0.7368 cents 98 .. 196 match: 19 SD: 0.7144 cents 100 .. 200 match: 19 SD: 0.6398 cents 108 .. 216 match: 19 SD: 0.6016 cents 120 .. 240 match: 19 SD: 0.5041 cents 144 .. 288 match: 19 SD: 0.4594 cents 156 .. 312 match: 19 SD: 0.4200 cents 168 .. 336 match: 19 SD: 0.4123 cents 170 .. 340 match: 19 SD: 0.4095 cents 173 .. 346 match: 19 SD: 0.3951 cents 174 .. 348 match: 19 SD: 0.3502 cents 180 .. 360 match: 19 SD: 0.3382 cents 194 .. 388 match: 19 SD: 0.3350 cents 198 .. 396 match: 19 SD: 0.3289 cents 218 .. 436 match: 19 SD: 0.3257 cents 220 .. 440 match: 19 SD: 0.2886 cents 228 .. 456 match: 19 SD: 0.2719 cents 244 .. 488 match: 19 SD: 0.2707 cents 246 .. 492 match: 19 SD: 0.2452 cents 258 .. 516 match: 19 SD: 0.2448 cents 272 .. 544 match: 19 SD: 0.2328 cents 298 .. 596 match: 19 SD: 0.1970 cents 318 .. 636 match: 19 SD: 0.1742 cents 344 .. 688 match: 19 SD: 0.1608 cents 354 .. 708 match: 19 SD: 0.1494 cents 418 .. 836 match: 19 SD: 0.1474 cents 452 .. 904 match: 19 SD: 0.1189 cents 574 .. 1148 match: 19 SD: 0.1110 cents