Scala analysis: murat24
Murat[24] with 16/55 generator
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 43.636 cents 43.636364 2: 109.091 cents 109.090909 3: 152.727 cents 152.727273 4: 196.364 cents 196.363636 5: 240.000 cents 240.000000 6: 305.455 cents 305.454545 7: 349.091 cents 349.090909 8: 392.727 cents 392.727273 9: 458.182 cents 458.181818 10: 501.818 cents 501.818182 11: 545.455 cents 545.454545 12: 589.091 cents 589.090909 13: 654.545 cents 654.545455 14: 698.182 cents 698.181818 15: 741.818 cents 741.818182 16: 807.273 cents 807.272727 17: 850.909 cents 850.909091 18: 894.545 cents 894.545455 19: 960.000 cents 960.000000 20: 1003.636 cents 1003.636364 21: 1047.273 cents 1047.272727 22: 1090.909 cents 1090.909091 23: 1156.364 cents 1156.363636 24: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 43.6364 cents 43.6364 1: 43.6364 cents 43.6364 2: 65.4545 cents 65.4545 3: 43.6364 cents 43.6364 4: 43.6364 cents 43.6364 5: 43.6364 cents 43.6364 6: 65.4545 cents 65.4545 7: 43.6364 cents 43.6364 8: 43.6364 cents 43.6364 9: 65.4545 cents 65.4545 10: 43.6364 cents 43.6364 11: 43.6364 cents 43.6364 12: 43.6364 cents 43.6364 13: 65.4545 cents 65.4545 14: 43.6364 cents 43.6364 15: 43.6364 cents 43.6364 16: 65.4545 cents 65.4545 17: 43.6364 cents 43.6364 18: 43.6364 cents 43.6364 19: 65.4545 cents 65.4545 20: 43.6364 cents 43.6364 21: 43.6364 cents 43.6364 22: 43.6364 cents 43.6364 23: 65.4545 cents 65.4545 24: 43.6364 cents 43.6364
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 17 43.63636 cents 1: 7 65.45454 cents 2: 10 87.27273 cents 2: 14 109.09091 cents 3: 3 130.90909 cents 3: 21 152.72727 cents 4: 20 196.36364 cents 4: 4 218.18182 cents 5: 13 240.00000 cents 5: 11 261.81818 cents 6: 6 283.63636 cents 6: 18 305.45455 cents 7: 23 349.09091 cents 7: 1 370.90909 cents 8: 16 392.72727 cents 8: 8 414.54545 cents 9: 9 436.36364 cents 9: 15 458.18182 cents 10: 2 480.00000 cents 10: 22 501.81818 cents 11: 19 545.45454 cents 11: 5 567.27273 cents 12: 12 589.09091 cents 12: 12 610.90909 cents 13: 5 632.72727 cents 13: 19 654.54545 cents 14: 22 698.18182 cents 14: 2 720.00000 cents 15: 15 741.81818 cents 15: 9 763.63636 cents 16: 8 785.45455 cents 16: 16 807.27273 cents 17: 1 829.09091 cents 17: 23 850.90909 cents 18: 18 894.54545 cents 18: 6 916.36364 cents 19: 11 938.18182 cents 19: 13 960.00000 cents 20: 4 981.81818 cents 20: 20 1003.63636 cents 21: 21 1047.27273 cents 21: 3 1069.09091 cents 22: 14 1090.90909 cents 22: 10 1112.72727 cents 23: 7 1134.54545 cents 23: 17 1156.36364 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 20 21 22 23 24 0.0 : 43.6 109.1 152.7 196.4 240.0 305.5 349.1 392.7 458.2 501.8 545.5 589.1 654.5 698.2 741.8 807.3 850.9 894.5 960.0 1003.6 1047.3 1090.9 1156.4 1200.0 43.6 : 65.5 109.1 152.7 196.4 261.8 305.5 349.1 414.5 458.2 501.8 545.5 610.9 654.5 698.2 763.6 807.3 850.9 916.4 960.0 1003.6 1047.3 1112.7 1156.4 1200.0 109.1 : 43.6 87.3 130.9 196.4 240.0 283.6 349.1 392.7 436.4 480.0 545.5 589.1 632.7 698.2 741.8 785.5 850.9 894.5 938.2 981.8 1047.3 1090.9 1134.5 1200.0 152.7 : 43.6 87.3 152.7 196.4 240.0 305.5 349.1 392.7 436.4 501.8 545.5 589.1 654.5 698.2 741.8 807.3 850.9 894.5 938.2 1003.6 1047.3 1090.9 1156.4 1200.0 196.4 : 43.6 109.1 152.7 196.4 261.8 305.5 349.1 392.7 458.2 501.8 545.5 610.9 654.5 698.2 763.6 807.3 850.9 894.5 960.0 1003.6 1047.3 1112.7 1156.4 1200.0 240.0 : 65.5 109.1 152.7 218.2 261.8 305.5 349.1 414.5 458.2 501.8 567.3 610.9 654.5 720.0 763.6 807.3 850.9 916.4 960.0 1003.6 1069.1 1112.7 1156.4 1200.0 305.5 : 43.6 87.3 152.7 196.4 240.0 283.6 349.1 392.7 436.4 501.8 545.5 589.1 654.5 698.2 741.8 785.5 850.9 894.5 938.2 1003.6 1047.3 1090.9 1134.5 1200.0 349.1 : 43.6 109.1 152.7 196.4 240.0 305.5 349.1 392.7 458.2 501.8 545.5 610.9 654.5 698.2 741.8 807.3 850.9 894.5 960.0 1003.6 1047.3 1090.9 1156.4 1200.0 392.7 : 65.5 109.1 152.7 196.4 261.8 305.5 349.1 414.5 458.2 501.8 567.3 610.9 654.5 698.2 763.6 807.3 850.9 916.4 960.0 1003.6 1047.3 1112.7 1156.4 1200.0 458.2 : 43.6 87.3 130.9 196.4 240.0 283.6 349.1 392.7 436.4 501.8 545.5 589.1 632.7 698.2 741.8 785.5 850.9 894.5 938.2 981.8 1047.3 1090.9 1134.5 1200.0 501.8 : 43.6 87.3 152.7 196.4 240.0 305.5 349.1 392.7 458.2 501.8 545.5 589.1 654.5 698.2 741.8 807.3 850.9 894.5 938.2 1003.6 1047.3 1090.9 1156.4 1200.0 545.5 : 43.6 109.1 152.7 196.4 261.8 305.5 349.1 414.5 458.2 501.8 545.5 610.9 654.5 698.2 763.6 807.3 850.9 894.5 960.0 1003.6 1047.3 1112.7 1156.4 1200.0 589.1 : 65.5 109.1 152.7 218.2 261.8 305.5 370.9 414.5 458.2 501.8 567.3 610.9 654.5 720.0 763.6 807.3 850.9 916.4 960.0 1003.6 1069.1 1112.7 1156.4 1200.0 654.5 : 43.6 87.3 152.7 196.4 240.0 305.5 349.1 392.7 436.4 501.8 545.5 589.1 654.5 698.2 741.8 785.5 850.9 894.5 938.2 1003.6 1047.3 1090.9 1134.5 1200.0 698.2 : 43.6 109.1 152.7 196.4 261.8 305.5 349.1 392.7 458.2 501.8 545.5 610.9 654.5 698.2 741.8 807.3 850.9 894.5 960.0 1003.6 1047.3 1090.9 1156.4 1200.0 741.8 : 65.5 109.1 152.7 218.2 261.8 305.5 349.1 414.5 458.2 501.8 567.3 610.9 654.5 698.2 763.6 807.3 850.9 916.4 960.0 1003.6 1047.3 1112.7 1156.4 1200.0 807.3 : 43.6 87.3 152.7 196.4 240.0 283.6 349.1 392.7 436.4 501.8 545.5 589.1 632.7 698.2 741.8 785.5 850.9 894.5 938.2 981.8 1047.3 1090.9 1134.5 1200.0 850.9 : 43.6 109.1 152.7 196.4 240.0 305.5 349.1 392.7 458.2 501.8 545.5 589.1 654.5 698.2 741.8 807.3 850.9 894.5 938.2 1003.6 1047.3 1090.9 1156.4 1200.0 894.5 : 65.5 109.1 152.7 196.4 261.8 305.5 349.1 414.5 458.2 501.8 545.5 610.9 654.5 698.2 763.6 807.3 850.9 894.5 960.0 1003.6 1047.3 1112.7 1156.4 1200.0 960.0 : 43.6 87.3 130.9 196.4 240.0 283.6 349.1 392.7 436.4 480.0 545.5 589.1 632.7 698.2 741.8 785.5 829.1 894.5 938.2 981.8 1047.3 1090.9 1134.5 1200.0 1003.6: 43.6 87.3 152.7 196.4 240.0 305.5 349.1 392.7 436.4 501.8 545.5 589.1 654.5 698.2 741.8 785.5 850.9 894.5 938.2 1003.6 1047.3 1090.9 1156.4 1200.0 1047.3: 43.6 109.1 152.7 196.4 261.8 305.5 349.1 392.7 458.2 501.8 545.5 610.9 654.5 698.2 741.8 807.3 850.9 894.5 960.0 1003.6 1047.3 1112.7 1156.4 1200.0 1090.9: 65.5 109.1 152.7 218.2 261.8 305.5 349.1 414.5 458.2 501.8 567.3 610.9 654.5 698.2 763.6 807.3 850.9 916.4 960.0 1003.6 1069.1 1112.7 1156.4 1200.0 1156.4: 43.6 87.3 152.7 196.4 240.0 283.6 349.1 392.7 436.4 501.8 545.5 589.1 632.7 698.2 741.8 785.5 850.9 894.5 938.2 1003.6 1047.3 1090.9 1134.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.6364 .. 65.4545 cents 21.81818 cents 43.63636 cents 2: 87.2727 .. 109.0909 cents 21.81818 cents 21.81818 cents 3: 130.9091 .. 152.7273 cents 21.81818 cents 21.81818 cents 4: 196.3636 .. 218.1818 cents 21.81818 cents 43.63636 cents 5: 240.0000 .. 261.8182 cents 21.81818 cents 21.81818 cents 6: 283.6364 .. 305.4545 cents 21.81818 cents 21.81818 cents 7: 349.0909 .. 370.9091 cents 21.81818 cents 43.63636 cents 8: 392.7273 .. 414.5455 cents 21.81818 cents 21.81818 cents 9: 436.3636 .. 458.1818 cents 21.81818 cents 21.81818 cents 10: 480.0000 .. 501.8182 cents 21.81818 cents 21.81818 cents 11: 545.4545 .. 567.2727 cents 21.81818 cents 43.63636 cents 12: 589.0909 .. 610.9091 cents 21.81818 cents 21.81818 cents 13: 632.7273 .. 654.5455 cents 21.81818 cents 21.81818 cents 14: 698.1818 .. 720.0000 cents 21.81818 cents 43.63636 cents 15: 741.8182 .. 763.6364 cents 21.81818 cents 21.81818 cents 16: 785.4545 .. 807.2727 cents 21.81818 cents 21.81818 cents 17: 829.0909 .. 850.9091 cents 21.81818 cents 21.81818 cents 18: 894.5455 .. 916.3636 cents 21.81818 cents 43.63636 cents 19: 938.1818 .. 960.0000 cents 21.81818 cents 21.81818 cents 20: 981.8182 .. 1003.6364 cents 21.81818 cents 21.81818 cents 21: 1047.2727 .. 1069.0909 cents 21.81818 cents 43.63636 cents 22: 1090.9091 .. 1112.7273 cents 21.81818 cents 21.81818 cents 23: 1134.5455 .. 1156.3636 cents 21.81818 cents 21.81818 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 43.63636 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 65.45454 cents Average / Smallest step : 1.145833 Largest / Average step : 1.309091 Largest / Smallest step : 1.500000 Median interval of one step : 43.63636 cents, amount: 17 Most common interval of one step : 43.63636 cents, amount: 17 Least squares average step : 49.98590 cents, oct.: 1199.66160 cents Scale is strictly proper Scale has Myhill's property chromas: 21.81818 cents and 21.81818 cents, ratio: 1.000000 generators: 7 of 349.09091 cents and 17 of 850.90909 cents Scale is maximally even in 55-tone equal temperament ET pair of linear temperament : 24&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 55-tone equal temperament with octave 1200.000 cents degrees: 2 5 7 9 11 14 16 18 21 23 25 27 30 32 34 37 39 41 44 46 48 50 53 55 generators: 16 and 39 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAABAAABAABAABAAABA Step pattern size order : SLSSSLSSLSSSLSSLSSLSSSLS Interval vector is [ 0 17 7 10 14 3 21 0 20 4 13 11 6 18 0 23 1 16 8 9 15 2 22 0 19 5 12 ] Scale is a Constant Structure, by a margin of 21.81818 cents Scale diversity : 1.180592 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.581818 Rothenberg efficiency : 0.694444 redundancy: 0.305556 Efficiency x scale size : 16.666667 Number of different interval sizes : 46 = 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 : 21.81818 cents Most common intervals : 349.09091 cents & inv., amount: 23 Scale is a chain of 12 triads 0.0 240.000 850.909 cents Most common triad is 0.0 349.091 850.909 cents, amount: 22 Number of recognisable fifths : 24, average 700.0000 cents Number of appreciable fifths : 22, average 698.1818 cents Formal octave complements present : 23 = 95.8333% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 15-16 -- Rational properties --
FIT/MODE
24: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.3093 c. M:-10.9091 c. 31: 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1 P M ME SD: 4.8846 c. M: 8.4457 c. 55: 2 3 2 2 2 3 2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 2 3 2 SP M ME 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: 1.8866 cents 3 .. 6 match: 3 H SD: 3.6210 cents 4 .. 8 match: 4 H SD: 2.8860 cents 5 .. 10 match: 5 H SD: 3.9144 cents 6 .. 12 match: 6 H SD: 4.8838 cents 7 .. 14 match: 7 H SD: 7.9832 cents 8 .. 16 match: 8 H SD: 2.3026 cents 9 .. 18 match: 9 H SD: 4.0526 cents 10 .. 20 match: 10 H SD: 3.9447 cents 11 .. 22 match: 11 H SD: 4.3486 cents 12 .. 24 match: 12 H SD: 4.0922 cents 13 .. 26 match: 13 H SD: 3.9605 cents 14 .. 28 match: 14 H SD: 4.5958 cents 15 .. 30 match: 15 H SD: 2.7188 cents 16 .. 32 match: 16 H SD: 3.2996 cents 17 .. 34 match: 17 H SD: 3.4867 cents 18 .. 36 match: 18 H SD: 3.7051 cents 19 .. 38 match: 19 H SD: 3.0100 cents 20 .. 40 match: 20 H SD: 2.9941 cents 21 .. 42 match: 19 SD: 3.9562 cents 22 .. 44 match: 21 SD: 2.9000 cents 23 .. 46 match: 20 SD: 3.3388 cents 24 .. 48 match: 22 SD: 2.6035 cents 25 .. 50 match: 21 SD: 3.1663 cents 26 .. 52 match: 23 SD: 2.8214 cents 27 .. 54 match: 23 SD: 2.2592 cents 28 .. 56 match: 23 SD: 2.6770 cents 29 .. 58 match: 22 SD: 2.8992 cents 30 .. 60 match: 23 SD: 2.0509 cents 32 .. 64 match: 24 SD: 1.6125 cents 41 .. 82 match: 24 SD: 1.5084 cents 42 .. 84 match: 24 SD: 1.4526 cents 46 .. 92 match: 24 SD: 1.4150 cents 47 .. 94 match: 24 SD: 1.3540 cents 52 .. 104 match: 24 SD: 1.3380 cents 59 .. 118 match: 24 SD: 1.1692 cents 62 .. 124 match: 24 SD: 1.0867 cents 66 .. 132 match: 24 SD: 0.9105 cents 74 .. 148 match: 24 SD: 0.8209 cents 76 .. 152 match: 24 SD: 0.7751 cents 89 .. 178 match: 24 SD: 0.6452 cents 106 .. 212 match: 24 SD: 0.6333 cents 107 .. 214 match: 24 SD: 0.5739 cents 108 .. 216 match: 24 SD: 0.5492 cents 109 .. 218 match: 24 SD: 0.5427 cents 121 .. 242 match: 24 SD: 0.5035 cents 140 .. 280 match: 24 SD: 0.4548 cents 148 .. 296 match: 24 SD: 0.4349 cents 155 .. 310 match: 24 SD: 0.3884 cents 161 .. 322 match: 24 SD: 0.3723 cents 181 .. 362 match: 24 SD: 0.3610 cents 183 .. 366 match: 24 SD: 0.3513 cents 185 .. 370 match: 24 SD: 0.3473 cents 197 .. 394 match: 24 SD: 0.2816 cents 224 .. 448 match: 24 SD: 0.2759 cents 227 .. 454 match: 24 SD: 0.2745 cents 228 .. 456 match: 24 SD: 0.2732 cents 232 .. 464 match: 24 SD: 0.2646 cents 247 .. 494 match: 24 SD: 0.2610 cents 259 .. 518 match: 24 SD: 0.2598 cents 260 .. 520 match: 24 SD: 0.2540 cents 264 .. 528 match: 24 SD: 0.2397 cents 274 .. 548 match: 24 SD: 0.2116 cents 310 .. 620 match: 24 SD: 0.2019 cents 318 .. 636 match: 24 SD: 0.1761 cents 350 .. 700 match: 24 SD: 0.1655 cents 357 .. 714 match: 24 SD: 0.1585 cents 383 .. 766 match: 24 SD: 0.1548 cents 389 .. 778 match: 24 SD: 0.1396 cents 443 .. 886 match: 24 SD: 0.1369 cents 466 .. 932 match: 24 SD: 0.1287 cents 475 .. 950 match: 24 SD: 0.1223 cents 476 .. 952 match: 24 SD: 0.1170 cents 518 .. 1036 match: 24 SD: 0.1043 cents 550 .. 1100 match: 24 SD: 0.0942 cents