Scala analysis: murat17
Murat[17] 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: 152.727 cents 152.727273 3: 196.364 cents 196.363636 4: 305.455 cents 305.454545 5: 349.091 cents 349.090909 6: 392.727 cents 392.727273 7: 501.818 cents 501.818182 8: 545.455 cents 545.454545 9: 654.545 cents 654.545455 10: 698.182 cents 698.181818 11: 807.273 cents 807.272727 12: 850.909 cents 850.909091 13: 894.545 cents 894.545455 14: 1003.636 cents 1003.636364 15: 1047.273 cents 1047.272727 16: 1156.364 cents 1156.363636 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 43.6364 cents 43.6364 1: 43.6364 cents 43.6364 2: 109.0909 cents 109.0909 3: 43.6364 cents 43.6364 4: 109.0909 cents 109.0909 5: 43.6364 cents 43.6364 6: 43.6364 cents 43.6364 7: 109.0909 cents 109.0909 8: 43.6364 cents 43.6364 9: 109.0909 cents 109.0909 10: 43.6364 cents 43.6364 11: 109.0909 cents 109.0909 12: 43.6364 cents 43.6364 13: 43.6364 cents 43.6364 14: 109.0909 cents 109.0909 15: 43.6364 cents 43.6364 16: 109.0909 cents 109.0909 17: 43.6364 cents 43.6364
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 43.63636 cents 1: 7 109.09091 cents 2: 3 87.27273 cents 2: 14 152.72727 cents 3: 13 196.36364 cents 3: 4 261.81818 cents 4: 6 240.00000 cents 4: 11 305.45455 cents 5: 16 349.09091 cents 5: 1 414.54545 cents 6: 9 392.72727 cents 6: 8 458.18182 cents 7: 2 436.36364 cents 7: 15 501.81818 cents 8: 12 545.45454 cents 8: 5 610.90909 cents 9: 5 589.09091 cents 9: 12 654.54545 cents 10: 15 698.18182 cents 10: 2 763.63636 cents 11: 8 741.81818 cents 11: 9 807.27273 cents 12: 1 785.45455 cents 12: 16 850.90909 cents 13: 11 894.54545 cents 13: 6 960.00000 cents 14: 4 938.18182 cents 14: 13 1003.63636 cents 15: 14 1047.27273 cents 15: 3 1112.72727 cents 16: 7 1090.90909 cents 16: 10 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 0.0 : 43.6 152.7 196.4 305.5 349.1 392.7 501.8 545.5 654.5 698.2 807.3 850.9 894.5 1003.6 1047.3 1156.4 1200.0 43.6 : 109.1 152.7 261.8 305.5 349.1 458.2 501.8 610.9 654.5 763.6 807.3 850.9 960.0 1003.6 1112.7 1156.4 1200.0 152.7 : 43.6 152.7 196.4 240.0 349.1 392.7 501.8 545.5 654.5 698.2 741.8 850.9 894.5 1003.6 1047.3 1090.9 1200.0 196.4 : 109.1 152.7 196.4 305.5 349.1 458.2 501.8 610.9 654.5 698.2 807.3 850.9 960.0 1003.6 1047.3 1156.4 1200.0 305.5 : 43.6 87.3 196.4 240.0 349.1 392.7 501.8 545.5 589.1 698.2 741.8 850.9 894.5 938.2 1047.3 1090.9 1200.0 349.1 : 43.6 152.7 196.4 305.5 349.1 458.2 501.8 545.5 654.5 698.2 807.3 850.9 894.5 1003.6 1047.3 1156.4 1200.0 392.7 : 109.1 152.7 261.8 305.5 414.5 458.2 501.8 610.9 654.5 763.6 807.3 850.9 960.0 1003.6 1112.7 1156.4 1200.0 501.8 : 43.6 152.7 196.4 305.5 349.1 392.7 501.8 545.5 654.5 698.2 741.8 850.9 894.5 1003.6 1047.3 1090.9 1200.0 545.5 : 109.1 152.7 261.8 305.5 349.1 458.2 501.8 610.9 654.5 698.2 807.3 850.9 960.0 1003.6 1047.3 1156.4 1200.0 654.5 : 43.6 152.7 196.4 240.0 349.1 392.7 501.8 545.5 589.1 698.2 741.8 850.9 894.5 938.2 1047.3 1090.9 1200.0 698.2 : 109.1 152.7 196.4 305.5 349.1 458.2 501.8 545.5 654.5 698.2 807.3 850.9 894.5 1003.6 1047.3 1156.4 1200.0 807.3 : 43.6 87.3 196.4 240.0 349.1 392.7 436.4 545.5 589.1 698.2 741.8 785.5 894.5 938.2 1047.3 1090.9 1200.0 850.9 : 43.6 152.7 196.4 305.5 349.1 392.7 501.8 545.5 654.5 698.2 741.8 850.9 894.5 1003.6 1047.3 1156.4 1200.0 894.5 : 109.1 152.7 261.8 305.5 349.1 458.2 501.8 610.9 654.5 698.2 807.3 850.9 960.0 1003.6 1112.7 1156.4 1200.0 1003.6: 43.6 152.7 196.4 240.0 349.1 392.7 501.8 545.5 589.1 698.2 741.8 850.9 894.5 1003.6 1047.3 1090.9 1200.0 1047.3: 109.1 152.7 196.4 305.5 349.1 458.2 501.8 545.5 654.5 698.2 807.3 850.9 960.0 1003.6 1047.3 1156.4 1200.0 1156.4: 43.6 87.3 196.4 240.0 349.1 392.7 436.4 545.5 589.1 698.2 741.8 850.9 894.5 938.2 1047.3 1090.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.6364 .. 109.0909 cents 65.45455 cents 43.63636 cents 2: 87.2727 .. 152.7273 cents 65.45454 cents -21.81818 cents 3: 196.3636 .. 261.8182 cents 65.45455 cents 43.63636 cents 4: 240.0000 .. 305.4545 cents 65.45454 cents -21.81818 cents 5: 349.0909 .. 414.5455 cents 65.45454 cents 43.63636 cents 6: 392.7273 .. 458.1818 cents 65.45454 cents -21.81818 cents 7: 436.3636 .. 501.8182 cents 65.45454 cents -21.81818 cents 8: 545.4545 .. 610.9091 cents 65.45455 cents 43.63636 cents 9: 589.0909 .. 654.5455 cents 65.45455 cents -21.81818 cents 10: 698.1818 .. 763.6364 cents 65.45454 cents 43.63636 cents 11: 741.8182 .. 807.2727 cents 65.45455 cents -21.81818 cents 12: 785.4545 .. 850.9091 cents 65.45454 cents -21.81818 cents 13: 894.5455 .. 960.0000 cents 65.45454 cents 43.63636 cents 14: 938.1818 .. 1003.6364 cents 65.45455 cents -21.81818 cents 15: 1047.2727 .. 1112.7273 cents 65.45455 cents 43.63636 cents 16: 1090.9091 .. 1156.3636 cents 65.45455 cents -21.81818 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 43.63636 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 109.09091 cents Average / Smallest step : 1.617647 Largest / Average step : 1.545455 Largest / Smallest step : 2.500000 Median interval of one step : 43.63636 cents, amount: 10 Most common interval of one step : 43.63636 cents, amount: 10 Least squares average step : 70.80825 cents, oct.: 1203.74026 cents Scale is not proper Scale has Myhill's property chromas: 65.45455 cents and 21.81818 cents, ratio: 3.000000 generators: 5 of 349.09091 cents and 12 of 850.90909 cents ET pair of linear temperament : 24&31 Scale is distributional even Scale is a mode of a 55-tone equal temperament with octave 1200.000 cents degrees: 2 7 9 14 16 18 23 25 30 32 37 39 41 46 48 53 55 generators: 16 and 39 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABABABAABABA Step pattern size order : SLSLSSLSLSLSSLSLS Interval vector is [ 0 10 0 3 7 0 14 0 13 0 6 4 0 11 0 16 0 9 1 2 8 0 15 0 12 0 5 ] Scale is a Constant Structure, by a margin of 21.81818 cents Scale diversity : 1.206950 Lumma stability : 0.290909 Lumma impropriety factor : 0.163636 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 : 21.81818 cents Most common intervals : 349.09091 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 392.727 850.909 cents Most common triad is 0.0 349.091 850.909 cents, amount: 15 Number of recognisable fifths : 15, average 698.1818 cents Scale contains two identical conjunct "tetrachords" of 8 notes Formal octave complements present : 17 = 100.0000% 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: 18.8624 c. M: 30.8021 c. 19: 1 1 1 2 1 0 2 1 1 1 2 0 1 2 1 1 1 N D3 I SD: 18.3225 c. M:-29.8565 c. 21: 1 2 0 2 1 1 2 1 1 1 2 1 1 2 0 2 1 N D3 I SD: 17.0309 c. M:-25.9740 c. 22: 1 2 1 2 0 1 2 1 2 1 2 1 0 2 1 2 1 N T3 I SD: 14.9671 c. M:-21.8182 c. 24: 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 P M ME I SD: 4.4536 c. M: 7.2727 c. 31: 1 3 1 3 1 1 3 1 3 1 3 1 1 3 1 3 1 N M DE I SD: 3.4480 c. M: 5.6305 c. 55: 2 5 2 5 2 2 5 2 5 2 5 2 2 5 2 5 2 N M DE I 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: 8.8992 cents 5 .. 10 match: 5 H SD: 8.2778 cents 6 .. 12 match: 6 H SD: 6.7192 cents 7 .. 14 match: 7 H SD: 12.0193 cents 8 .. 16 match: 8 H SD: 7.0122 cents 9 .. 18 match: 8 S SD: 6.2352 cents 10 .. 20 match: 9 S SD: 7.6375 cents 11 .. 22 match: 9 S SD: 5.5603 cents 12 .. 24 match: 11 S SD: 5.8341 cents 13 .. 26 match: 12 SD: 6.8727 cents 14 .. 28 match: 13 SD: 6.7094 cents 15 .. 30 match: 12 SD: 5.5880 cents 16 .. 32 match: 13 SD: 5.3420 cents 17 .. 34 match: 12 SD: 4.6788 cents 18 .. 36 match: 15 SD: 5.4180 cents 19 .. 38 match: 14 SD: 4.7437 cents 20 .. 40 match: 14 SD: 4.4080 cents 21 .. 42 match: 15 SD: 4.9766 cents 22 .. 44 match: 17 SD: 3.5715 cents 23 .. 46 match: 16 SD: 4.2196 cents 24 .. 48 match: 16 SD: 2.7915 cents 25 .. 50 match: 16 SD: 3.6714 cents 26 .. 52 match: 17 SD: 3.5816 cents 27 .. 54 match: 17 SD: 3.1081 cents 28 .. 56 match: 16 SD: 3.1660 cents 29 .. 58 match: 15 SD: 3.4661 cents 30 .. 60 match: 17 SD: 2.6232 cents 32 .. 64 match: 17 SD: 1.9418 cents 35 .. 70 match: 17 SD: 1.8988 cents 40 .. 80 match: 17 SD: 1.8955 cents 41 .. 82 match: 17 SD: 1.5719 cents 52 .. 104 match: 17 SD: 1.5031 cents 57 .. 114 match: 17 SD: 1.4993 cents 59 .. 118 match: 17 SD: 1.4661 cents 62 .. 124 match: 17 SD: 1.4076 cents 63 .. 126 match: 17 SD: 1.3588 cents 65 .. 130 match: 17 SD: 1.3333 cents 66 .. 132 match: 17 SD: 1.1100 cents 74 .. 148 match: 17 SD: 0.9656 cents 76 .. 152 match: 17 SD: 0.9167 cents 83 .. 166 match: 17 SD: 0.8111 cents 89 .. 178 match: 17 SD: 0.7923 cents 98 .. 196 match: 17 SD: 0.7476 cents 107 .. 214 match: 17 SD: 0.6655 cents 117 .. 234 match: 17 SD: 0.6278 cents 118 .. 236 match: 17 SD: 0.5525 cents 143 .. 286 match: 17 SD: 0.5195 cents 149 .. 298 match: 17 SD: 0.5077 cents 151 .. 302 match: 17 SD: 0.5054 cents 157 .. 314 match: 17 SD: 0.4686 cents 161 .. 322 match: 17 SD: 0.3780 cents 192 .. 384 match: 17 SD: 0.3466 cents 197 .. 394 match: 17 SD: 0.3114 cents 224 .. 448 match: 17 SD: 0.2937 cents 232 .. 464 match: 17 SD: 0.2911 cents 238 .. 476 match: 17 SD: 0.2841 cents 259 .. 518 match: 17 SD: 0.2525 cents 274 .. 548 match: 17 SD: 0.2425 cents 300 .. 600 match: 17 SD: 0.2398 cents 306 .. 612 match: 17 SD: 0.2319 cents 315 .. 630 match: 17 SD: 0.2265 cents 318 .. 636 match: 17 SD: 0.1830 cents 357 .. 714 match: 17 SD: 0.1807 cents 389 .. 778 match: 17 SD: 0.1445 cents 466 .. 932 match: 17 SD: 0.1445 cents 467 .. 934 match: 17 SD: 0.1322 cents 507 .. 1014 match: 17 SD: 0.1287 cents 542 .. 1084 match: 17 SD: 0.1159 cents 550 .. 1100 match: 17 SD: 0.0974 cents 586 .. 1172 match: 17 SD: 0.0966 cents