Scala analysis: xen18-erlich-ennealimmal-18
9L 9s MOS for Ennealimmal, L=84.313, s=49.024
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49.024 cents 49.024000 2: 133.337 cents 133.337000 3: 182.361 cents 182.361000 4: 266.674 cents 266.674000 5: 315.698 cents 315.698000 6: 400.011 cents 400.011000 7: 449.035 cents 449.035000 8: 533.348 cents 533.348000 9: 582.372 cents 582.372000 10: 666.685 cents 666.685000 11: 715.709 cents 715.709000 12: 800.022 cents 800.022000 13: 849.046 cents 849.046000 14: 933.359 cents 933.359000 15: 982.383 cents 982.383000 16: 1066.696 cents 1066.696000 17: 1115.720 cents 1115.720000 18: 1200.033 cents 1200.033000
SHOW/INTERVAL
0: 84.3130 cents 84.3130 1: 49.0240 cents 49.0240 2: 84.3130 cents 84.3130 3: 49.0240 cents 49.0240 4: 84.3130 cents 84.3130 5: 49.0240 cents 49.0240 6: 84.3130 cents 84.3130 7: 49.0240 cents 49.0240 8: 84.3130 cents 84.3130 9: 49.0240 cents 49.0240 10: 84.3130 cents 84.3130 11: 49.0240 cents 49.0240 12: 84.3130 cents 84.3130 13: 49.0240 cents 49.0240 14: 84.3130 cents 84.3130 15: 49.0240 cents 49.0240 16: 84.3130 cents 84.3130 17: 49.0240 cents 49.0240 18: 84.3130 cents 84.3130
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 49.02400 cents 1: 9 84.31300 cents 2: 18 133.33700 cents 3: 9 182.36100 cents 3: 9 217.65000 cents 4: 18 266.67400 cents 5: 9 315.69800 cents 5: 9 350.98700 cents 6: 18 400.01100 cents 7: 9 449.03500 cents 7: 9 484.32400 cents 8: 18 533.34800 cents 9: 9 582.37200 cents 9: 9 617.66100 cents 10: 18 666.68500 cents 11: 9 715.70900 cents 11: 9 750.99800 cents 12: 18 800.02200 cents 13: 9 849.04600 cents 13: 9 884.33500 cents 14: 18 933.35900 cents 15: 9 982.38300 cents 15: 9 1017.67200 cents 16: 18 1066.69600 cents 17: 9 1115.72000 cents 17: 9 1151.00900 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.52941 = 26/17
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.0 : 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 49.0 : 84.3 133.3 217.7 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 133.3 : 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 182.4 : 84.3 133.3 217.6 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 266.7 : 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 315.7 : 84.3 133.3 217.6 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 400.0 : 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 449.0 : 84.3 133.3 217.6 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 533.3 : 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 582.4 : 84.3 133.3 217.7 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 666.7 : 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 715.7 : 84.3 133.3 217.6 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 800.0 : 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 849.0 : 84.3 133.3 217.6 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 933.4 : 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 982.4 : 84.3 133.3 217.6 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 1066.7: 49.0 133.3 182.4 266.7 315.7 400.0 449.0 533.3 582.4 666.7 715.7 800.0 849.0 933.4 982.4 1066.7 1115.7 1200.0 1115.7: 84.3 133.3 217.6 266.7 351.0 400.0 484.3 533.3 617.7 666.7 751.0 800.0 884.3 933.4 1017.7 1066.7 1151.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 49.0240 .. 84.3130 cents 35.28900 cents 49.02400 cents 2: 133.3370 .. 133.3370 cents 1/1, 0.0000 cents 49.02400 cents 3: 182.3610 .. 217.6500 cents 35.28900 cents 49.02400 cents 4: 266.6740 .. 266.6740 cents 1/1, 0.0000 cents 49.02400 cents 5: 315.6980 .. 350.9870 cents 35.28900 cents 49.02400 cents 6: 400.0110 .. 400.0110 cents 1/1, 0.0000 cents 49.02400 cents 7: 449.0350 .. 484.3240 cents 35.28900 cents 49.02400 cents 8: 533.3480 .. 533.3480 cents 1/1, 0.0000 cents 49.02400 cents 9: 582.3720 .. 617.6610 cents 35.28900 cents 49.02400 cents 10: 666.6850 .. 666.6850 cents 1/1, 0.0000 cents 49.02400 cents 11: 715.7090 .. 750.9980 cents 35.28900 cents 49.02400 cents 12: 800.0220 .. 800.0220 cents 1/1, 0.0000 cents 49.02400 cents 13: 849.0460 .. 884.3350 cents 35.28900 cents 49.02400 cents 14: 933.3590 .. 933.3590 cents 1/1, 0.0000 cents 49.02400 cents 15: 982.3830 .. 1017.6720 cents 35.28900 cents 49.02400 cents 16: 1066.6960 .. 1066.6960 cents 1/1, 0.0000 cents 49.02400 cents 17: 1115.7200 .. 1151.0090 cents 35.28900 cents 49.02400 cents
SHOW DATA
Number of notes : 18 -- Interval properties -- Smallest interval : 49.02400 cents, class 1 Average step (divided formal octave): 66.6685 cents Largest one step interval : 84.31300 cents Average / Smallest step : 1.359916 Largest / Average step : 1.264660 Largest / Smallest step : 1.719831 Median interval of one step : 66.66850 cents, amount: 0 Least squares average step : 65.99083 cents, oct.: 1187.83495 cents Scale is strictly proper Scale has 9 repeating blocks of 2 notes Blocks have Myhill's property chromas: 35.28900 cents and 13.73500 cents, ratio: 2.569276 generator: 1 of 49.02400 cents ET pair of linear temperament : 99&171 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 612-tone equal temperament with octave 1200.033 cents degrees: 25 68 93 136 161 204 229 272 297 340 365 408 433 476 501 544 569 612 Least number of segments generator : 307 of 601.977 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 365 of 715.706 cents and inv. generated superset size: 546 = 528 more = 3033.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABABABAB Step pattern size order : SLSLSLSLSLSLSLSLSL Scale is a Constant Structure, by a margin of 49.02400 cents Scale diversity : 1.132995 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.735340 Number of different interval sizes : 26 = 1.52941 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.52941 = 26/17 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 35.28900 cents Scale is a chain of 9 triads 0.0 982.383 1066.696 cents Most common triad is 0.0 133.337 266.674 cents, amount: 18 Number of recognisable fifths : 9, average 715.7090 cents Number of appreciable fifths : 0 Number of recognisable fourths : 9, average 484.3240 cents Number of appreciable fourths : 0 Scale contains two identical disjunct "tetrachords" of 9 notes Best minor thirds form a closed circle Formal octave complements present : 9 = 50.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 2 4 6 8 10 12 14 16 Limited inverse transpositions : 1 3 5 7 9 11 13 15 17 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 -- Rational properties --
FIT/MODE
18: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 12.4765 c. M:-17.6445 c. 24: 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 P B D3 SD: 13.6262 c. M:-17.6445 c. 27: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 SP B ME SD: 3.2374 c. M: 4.5783 c. 45: 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 3 SP B ME SD: 3.0482 c. M:-4.3108 c. 72: 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 5 SP B DE SD: 0.6911 c. M:-0.9774 c. 99: 4 7 4 7 4 7 4 7 4 7 4 7 4 7 4 7 4 7 SP B DE SD: 0.3803 c. M: 0.5378 c. 171: 7 12 7 12 7 12 7 12 7 12 7 12 7 12 7 12 7 12 SP B DE SD: 0.0708 c. M:-0.1002 c. 441: 18 31 18 31 18 31 18 31 18 31 18 31 18 31 18 31 18 31 SP B DE SD: 0.0304 c. M: 0.0431 c. 612: 25 43 25 43 25 43 25 43 25 43 25 43 25 43 25 43 25 43 SP B DE SD: 0.0022 c. M: 0.0030 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0330 cents 2 .. 4 match: 2 H SD: 6.8770 cents 3 .. 6 match: 3 H SD: 16.6443 cents 4 .. 8 match: 4 H SD: 5.9192 cents 5 .. 10 match: 5 H SD: 7.5544 cents 6 .. 12 match: 6 H SD: 9.1027 cents 7 .. 14 match: 7 H SD: 7.8512 cents 8 .. 16 match: 8 H SD: 5.4282 cents 9 .. 18 match: 9 H SD: 8.6342 cents 10 .. 20 match: 10 H SD: 4.6701 cents 11 .. 22 match: 11 H SD: 5.8105 cents 12 .. 24 match: 12 H SD: 5.2305 cents 13 .. 26 match: 13 H SD: 5.3354 cents 14 .. 28 match: 14 H SD: 4.9812 cents 15 .. 30 match: 14 S SD: 5.6324 cents 16 .. 32 match: 13 S SD: 5.4400 cents 17 .. 34 match: 16 S SD: 4.3397 cents 18 .. 36 match: 15 SD: 5.5833 cents 19 .. 38 match: 17 SD: 4.2425 cents 20 .. 40 match: 17 SD: 3.8312 cents 21 .. 42 match: 15 SD: 4.3367 cents 22 .. 44 match: 16 SD: 3.8566 cents 24 .. 48 match: 18 SD: 3.1298 cents 25 .. 50 match: 17 SD: 2.5872 cents 27 .. 54 match: 17 SD: 2.4951 cents 30 .. 60 match: 18 SD: 2.3715 cents 34 .. 68 match: 18 SD: 2.1182 cents 35 .. 70 match: 18 SD: 1.8767 cents 41 .. 82 match: 18 SD: 1.8144 cents 47 .. 94 match: 18 SD: 1.5927 cents 53 .. 106 match: 18 SD: 1.5210 cents 55 .. 110 match: 18 SD: 1.3287 cents 60 .. 120 match: 18 SD: 1.1500 cents 61 .. 122 match: 18 SD: 1.1378 cents 65 .. 130 match: 18 SD: 1.1265 cents 66 .. 132 match: 18 SD: 1.1185 cents 70 .. 140 match: 18 SD: 1.0347 cents 72 .. 144 match: 18 SD: 0.9726 cents 73 .. 146 match: 18 SD: 0.9281 cents 85 .. 170 match: 18 SD: 0.9271 cents 88 .. 176 match: 18 SD: 0.9096 cents 90 .. 180 match: 18 SD: 0.8800 cents 92 .. 184 match: 18 SD: 0.8737 cents 95 .. 190 match: 18 SD: 0.8541 cents 96 .. 192 match: 18 SD: 0.8517 cents 97 .. 194 match: 18 SD: 0.7971 cents 100 .. 200 match: 18 SD: 0.6637 cents 108 .. 216 match: 18 SD: 0.6605 cents 109 .. 218 match: 18 SD: 0.6217 cents 115 .. 230 match: 18 SD: 0.5575 cents 135 .. 270 match: 18 SD: 0.5298 cents 136 .. 272 match: 18 SD: 0.4728 cents 150 .. 300 match: 18 SD: 0.4639 cents 162 .. 324 match: 18 SD: 0.4411 cents 170 .. 340 match: 18 SD: 0.4202 cents 172 .. 344 match: 18 SD: 0.4055 cents 180 .. 360 match: 18 SD: 0.3946 cents 196 .. 392 match: 18 SD: 0.3892 cents 199 .. 398 match: 18 SD: 0.3404 cents 200 .. 400 match: 18 SD: 0.3381 cents 215 .. 430 match: 18 SD: 0.2971 cents 235 .. 470 match: 18 SD: 0.2876 cents 250 .. 500 match: 18 SD: 0.2376 cents 277 .. 554 match: 18 SD: 0.2259 cents 305 .. 610 match: 18 SD: 0.2068 cents 349 .. 698 match: 18 SD: 0.1938 cents 350 .. 700 match: 18 SD: 0.1915 cents 377 .. 754 match: 18 SD: 0.1852 cents 385 .. 770 match: 18 SD: 0.1117 cents 588 .. 1176 match: 18 SD: 0.0995 cents