Scala analysis: xen18-erlich-ennealimmal-27
18L 9s MOS for Ennealimmal, L=49.024, s=35.289
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: 84.313 cents 84.313000 3: 133.337 cents 133.337000 4: 182.361 cents 182.361000 5: 217.650 cents 217.650000 6: 266.674 cents 266.674000 7: 315.698 cents 315.698000 8: 350.987 cents 350.987000 9: 400.011 cents 400.011000 10: 449.035 cents 449.035000 11: 484.324 cents 484.324000 12: 533.348 cents 533.348000 13: 582.372 cents 582.372000 14: 617.661 cents 617.661000 15: 666.685 cents 666.685000 16: 715.709 cents 715.709000 17: 750.998 cents 750.998000 18: 800.022 cents 800.022000 19: 849.046 cents 849.046000 20: 884.335 cents 884.335000 21: 933.359 cents 933.359000 22: 982.383 cents 982.383000 23: 1017.672 cents 1017.672000 24: 1066.696 cents 1066.696000 25: 1115.720 cents 1115.720000 26: 1151.009 cents 1151.009000 27: 1200.033 cents 1200.033000
SHOW/INTERVAL
0: 49.0240 cents 49.0240 1: 49.0240 cents 49.0240 2: 35.2890 cents 35.2890 3: 49.0240 cents 49.0240 4: 49.0240 cents 49.0240 5: 35.2890 cents 35.2890 6: 49.0240 cents 49.0240 7: 49.0240 cents 49.0240 8: 35.2890 cents 35.2890 9: 49.0240 cents 49.0240 10: 49.0240 cents 49.0240 11: 35.2890 cents 35.2890 12: 49.0240 cents 49.0240 13: 49.0240 cents 49.0240 14: 35.2890 cents 35.2890 15: 49.0240 cents 49.0240 16: 49.0240 cents 49.0240 17: 35.2890 cents 35.2890 18: 49.0240 cents 49.0240 19: 49.0240 cents 49.0240 20: 35.2890 cents 35.2890 21: 49.0240 cents 49.0240 22: 49.0240 cents 49.0240 23: 35.2890 cents 35.2890 24: 49.0240 cents 49.0240 25: 49.0240 cents 49.0240 26: 35.2890 cents 35.2890 27: 49.0240 cents 49.0240
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 35.28900 cents 1: 18 49.02400 cents 2: 18 84.31300 cents 2: 9 98.04800 cents 3: 27 133.33700 cents 4: 9 168.62600 cents 4: 18 182.36100 cents 5: 18 217.65000 cents 5: 9 231.38500 cents 6: 27 266.67400 cents 7: 9 301.96300 cents 7: 18 315.69800 cents 8: 18 350.98700 cents 8: 9 364.72200 cents 9: 27 400.01100 cents 10: 9 435.30000 cents 10: 18 449.03500 cents 11: 18 484.32400 cents 11: 9 498.05900 cents 12: 27 533.34800 cents 13: 9 568.63700 cents 13: 18 582.37200 cents 14: 18 617.66100 cents 14: 9 631.39600 cents 15: 27 666.68500 cents 16: 9 701.97400 cents 16: 18 715.70900 cents 17: 18 750.99800 cents 17: 9 764.73300 cents 18: 27 800.02200 cents 19: 9 835.31100 cents 19: 18 849.04600 cents 20: 18 884.33500 cents 20: 9 898.07000 cents 21: 27 933.35900 cents 22: 9 968.64800 cents 22: 18 982.38300 cents 23: 18 1017.67200 cents 23: 9 1031.40700 cents 24: 27 1066.69600 cents 25: 9 1101.98500 cents 25: 18 1115.72000 cents 26: 18 1151.00900 cents 26: 9 1164.74400 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.69231 = 22/13
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 25 26 27 0.0 : 49.0 84.3 133.3 182.4 217.6 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 49.0 : 35.3 84.3 133.3 168.6 217.7 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 84.3 : 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 133.3 : 49.0 84.3 133.3 182.4 217.6 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 182.4 : 35.3 84.3 133.3 168.6 217.6 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 217.6 : 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 266.7 : 49.0 84.3 133.3 182.4 217.6 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 315.7 : 35.3 84.3 133.3 168.6 217.6 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 351.0 : 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 400.0 : 49.0 84.3 133.3 182.4 217.6 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 449.0 : 35.3 84.3 133.3 168.6 217.6 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 484.3 : 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 533.3 : 49.0 84.3 133.3 182.4 217.6 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 582.4 : 35.3 84.3 133.3 168.6 217.7 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 617.7 : 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 666.7 : 49.0 84.3 133.3 182.4 217.7 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 715.7 : 35.3 84.3 133.3 168.6 217.6 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 751.0 : 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 800.0 : 49.0 84.3 133.3 182.4 217.6 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 849.0 : 35.3 84.3 133.3 168.6 217.6 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 884.3 : 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 933.4 : 49.0 84.3 133.3 182.4 217.6 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 982.4 : 35.3 84.3 133.3 168.6 217.6 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 1017.7: 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 1066.7: 49.0 84.3 133.3 182.4 217.6 266.7 315.7 351.0 400.0 449.0 484.3 533.3 582.4 617.7 666.7 715.7 751.0 800.0 849.0 884.3 933.4 982.4 1017.7 1066.7 1115.7 1151.0 1200.0 1115.7: 35.3 84.3 133.3 168.6 217.6 266.7 302.0 351.0 400.0 435.3 484.3 533.3 568.6 617.7 666.7 702.0 751.0 800.0 835.3 884.3 933.4 968.6 1017.7 1066.7 1102.0 1151.0 1200.0 1151.0: 49.0 98.0 133.3 182.4 231.4 266.7 315.7 364.7 400.0 449.0 498.1 533.3 582.4 631.4 666.7 715.7 764.7 800.0 849.0 898.1 933.4 982.4 1031.4 1066.7 1115.7 1164.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.2890 .. 49.0240 cents 13.73500 cents 35.28900 cents 2: 84.3130 .. 98.0480 cents 13.73500 cents 35.28900 cents 3: 133.3370 .. 133.3370 cents 1/1, 0.0000 cents 35.28900 cents 4: 168.6260 .. 182.3610 cents 13.73500 cents 35.28900 cents 5: 217.6500 .. 231.3850 cents 13.73500 cents 35.28900 cents 6: 266.6740 .. 266.6740 cents 1/1, 0.0000 cents 35.28900 cents 7: 301.9630 .. 315.6980 cents 13.73500 cents 35.28900 cents 8: 350.9870 .. 364.7220 cents 13.73500 cents 35.28900 cents 9: 400.0110 .. 400.0110 cents 1/1, 0.0000 cents 35.28900 cents 10: 435.3000 .. 449.0350 cents 13.73500 cents 35.28900 cents 11: 484.3240 .. 498.0590 cents 13.73500 cents 35.28900 cents 12: 533.3480 .. 533.3480 cents 1/1, 0.0000 cents 35.28900 cents 13: 568.6370 .. 582.3720 cents 13.73500 cents 35.28900 cents 14: 617.6610 .. 631.3960 cents 13.73500 cents 35.28900 cents 15: 666.6850 .. 666.6850 cents 1/1, 0.0000 cents 35.28900 cents 16: 701.9740 .. 715.7090 cents 13.73500 cents 35.28900 cents 17: 750.9980 .. 764.7330 cents 13.73500 cents 35.28900 cents 18: 800.0220 .. 800.0220 cents 1/1, 0.0000 cents 35.28900 cents 19: 835.3110 .. 849.0460 cents 13.73500 cents 35.28900 cents 20: 884.3350 .. 898.0700 cents 13.73500 cents 35.28900 cents 21: 933.3590 .. 933.3590 cents 1/1, 0.0000 cents 35.28900 cents 22: 968.6480 .. 982.3830 cents 13.73500 cents 35.28900 cents 23: 1017.6720 .. 1031.4070 cents 13.73500 cents 35.28900 cents 24: 1066.6960 .. 1066.6960 cents 1/1, 0.0000 cents 35.28900 cents 25: 1101.9850 .. 1115.7200 cents 13.73500 cents 35.28900 cents 26: 1151.0090 .. 1164.7440 cents 13.73500 cents 35.28900 cents
SHOW DATA
Number of notes : 27 -- Interval properties -- Smallest interval : 35.28900 cents, class 1 Average step (divided formal octave): 44.4457 cents Largest one step interval : 49.02400 cents Average / Smallest step : 1.259477 Largest / Average step : 1.103010 Largest / Smallest step : 1.389215 Median interval of one step : 49.02400 cents, amount: 18 Most common interval of one step : 49.02400 cents, amount: 18 Least squares average step : 44.43972 cents, oct.: 1199.87246 cents Scale is strictly proper Scale has 9 repeating blocks of 3 notes Blocks have Myhill's property chromas: 13.73500 cents and 21.55400 cents, ratio: 1.569276 generators: 1 of 49.02400 cents and 2 of 84.31300 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 43 68 93 111 136 161 179 204 229 247 272 297 315 340 365 383 408 433 451 476 501 519 544 569 587 612 Least number of segments generator : 311 of 609.821 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 365 of 715.706 cents and inv. generated superset size: 547 = 520 more = 2025.926% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABAABAABAABAABAABAABA Step pattern size order : LSLLSLLSLLSLLSLLSLLSLLSLLSL Scale is a Constant Structure, by a margin of 35.28900 cents Scale diversity : 1.110781 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.793981 Number of different interval sizes : 44 = 1.69231 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.69231 = 22/13 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 13.73500 cents Most common triad is 0.0 133.337 266.674 cents, amount: 27 Number of recognisable fifths : 27, average 711.1307 cents Number of appreciable fifths : 9, average 701.9740 cents Number of recognisable fourths : 27, average 488.9023 cents Number of appreciable fourths : 9, average 498.0590 cents Scale contains two identical disjunct "tetrachords" of 12 notes Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 27 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 3 6 9 12 15 18 21 24 Limited inverse transpositions : 3 6 9 12 15 18 21 24 Inversional symmetry on degrees : 0 3 6 9 12 15 18 21 24 Inversional symmetry on intervals : 1-2 4-5 7-8 10-11 13-14 16-17 19-20 22-23 25-26 -- Rational properties --
FIT/MODE
27: 1 1 1 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: 3.7382 c. M: 4.5783 c. 45: 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 2 1 2 SP B ME I SD: 3.5198 c. M: 4.3108 c. 72: 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 SP B ME I SD: 0.7980 c. M: 0.9774 c. 99: 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 4 3 4 SP B ME I SD: 0.4391 c. M: 0.5378 c. 171: 7 5 7 7 5 7 7 5 7 7 5 7 7 5 7 7 5 7 7 5 7 7 5 7 7 5 7 SP B DE I SD: 0.0818 c. M: 0.1002 c. 441: 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 18 13 18 SP B DE I SD: 0.0352 c. M: 0.0431 c. 612: 25 18 25 25 18 25 25 18 25 25 18 25 25 18 25 25 18 25 25 18 25 25 18 25 25 18 25 SP B DE I SD: 0.0025 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: 4.5737 cents 4 .. 8 match: 4 H SD: 5.9192 cents 5 .. 10 match: 5 H SD: 2.7331 cents 6 .. 12 match: 6 H SD: 4.3395 cents 7 .. 14 match: 7 H SD: 3.8065 cents 8 .. 16 match: 8 H SD: 5.0160 cents 9 .. 18 match: 9 H SD: 3.7800 cents 10 .. 20 match: 10 H SD: 3.0676 cents 11 .. 22 match: 11 H SD: 4.0132 cents 12 .. 24 match: 12 H SD: 3.1446 cents 13 .. 26 match: 13 H SD: 3.7385 cents 14 .. 28 match: 14 H SD: 3.0560 cents 15 .. 30 match: 15 H SD: 2.7532 cents 16 .. 32 match: 16 H SD: 3.8385 cents 17 .. 34 match: 17 H SD: 2.9701 cents 18 .. 36 match: 18 H SD: 3.1031 cents 19 .. 38 match: 19 H SD: 2.5076 cents 20 .. 40 match: 20 H SD: 2.7538 cents 21 .. 42 match: 21 H SD: 2.6916 cents 22 .. 44 match: 22 H SD: 2.4596 cents 23 .. 46 match: 20 SD: 2.8009 cents 24 .. 48 match: 23 S SD: 2.3084 cents 25 .. 50 match: 24 S SD: 2.3748 cents 26 .. 52 match: 24 SD: 2.6036 cents 27 .. 54 match: 25 S SD: 2.3606 cents 28 .. 56 match: 25 S SD: 2.2476 cents 29 .. 58 match: 24 SD: 2.6006 cents 30 .. 60 match: 26 SD: 1.8856 cents 31 .. 62 match: 26 SD: 2.0643 cents 32 .. 64 match: 26 SD: 2.4498 cents 33 .. 66 match: 25 SD: 2.2742 cents 34 .. 68 match: 27 SD: 1.9918 cents 35 .. 70 match: 27 SD: 1.5357 cents 41 .. 82 match: 26 SD: 1.5004 cents 46 .. 92 match: 27 SD: 1.4703 cents 47 .. 94 match: 27 SD: 1.4677 cents 53 .. 106 match: 27 SD: 1.2001 cents 55 .. 110 match: 27 SD: 1.1650 cents 59 .. 118 match: 27 SD: 1.1344 cents 60 .. 120 match: 27 SD: 1.0098 cents 61 .. 122 match: 27 SD: 0.9218 cents 66 .. 132 match: 27 SD: 0.8959 cents 72 .. 144 match: 27 SD: 0.8418 cents 74 .. 148 match: 27 SD: 0.7955 cents 80 .. 160 match: 27 SD: 0.7615 cents 84 .. 168 match: 27 SD: 0.7357 cents 90 .. 180 match: 27 SD: 0.7223 cents 95 .. 190 match: 27 SD: 0.7222 cents 96 .. 192 match: 27 SD: 0.6550 cents 98 .. 196 match: 27 SD: 0.6329 cents 100 .. 200 match: 27 SD: 0.6186 cents 102 .. 204 match: 27 SD: 0.5830 cents 114 .. 228 match: 27 SD: 0.5584 cents 115 .. 230 match: 27 SD: 0.5224 cents 125 .. 250 match: 27 SD: 0.4991 cents 126 .. 252 match: 27 SD: 0.4981 cents 134 .. 268 match: 27 SD: 0.4776 cents 135 .. 270 match: 27 SD: 0.4526 cents 136 .. 272 match: 27 SD: 0.4233 cents 155 .. 310 match: 27 SD: 0.4012 cents 161 .. 322 match: 27 SD: 0.3809 cents 164 .. 328 match: 27 SD: 0.3618 cents 177 .. 354 match: 27 SD: 0.3484 cents 179 .. 358 match: 27 SD: 0.3344 cents 180 .. 360 match: 27 SD: 0.3063 cents 199 .. 398 match: 27 SD: 0.2850 cents 200 .. 400 match: 27 SD: 0.2828 cents 210 .. 420 match: 27 SD: 0.2802 cents 215 .. 430 match: 27 SD: 0.2628 cents 235 .. 470 match: 27 SD: 0.2601 cents 236 .. 472 match: 27 SD: 0.2538 cents 240 .. 480 match: 27 SD: 0.2373 cents 245 .. 490 match: 27 SD: 0.2282 cents 270 .. 540 match: 27 SD: 0.2184 cents 276 .. 552 match: 27 SD: 0.1984 cents 285 .. 570 match: 27 SD: 0.1983 cents 300 .. 600 match: 27 SD: 0.1921 cents 313 .. 626 match: 27 SD: 0.1893 cents 315 .. 630 match: 27 SD: 0.1745 cents 350 .. 700 match: 27 SD: 0.1709 cents 360 .. 720 match: 27 SD: 0.1583 cents 378 .. 756 match: 27 SD: 0.1503 cents 385 .. 770 match: 27 SD: 0.1377 cents 424 .. 848 match: 27 SD: 0.1361 cents 449 .. 898 match: 27 SD: 0.1244 cents 462 .. 924 match: 27 SD: 0.1243 cents 480 .. 960 match: 27 SD: 0.1162 cents 485 .. 970 match: 27 SD: 0.1045 cents 558 .. 1116 match: 27 SD: 0.0985 cents 560 .. 1120 match: 27 SD: 0.0846 cents