Scala analysis: bohpier25
Bohpier[25] in 41-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 87.805 cents 87.804878 2: 117.073 cents 117.073171 3: 146.341 cents 146.341463 4: 234.146 cents 234.146341 5: 263.415 cents 263.414634 6: 292.683 cents 292.682927 7: 380.488 cents 380.487805 8: 409.756 cents 409.756098 9: 439.024 cents 439.024390 10: 526.829 cents 526.829268 11: 556.098 cents 556.097561 12: 585.366 cents 585.365854 13: 673.171 cents 673.170732 14: 702.439 cents 702.439024 15: 731.707 cents 731.707317 16: 819.512 cents 819.512195 17: 848.780 cents 848.780488 18: 878.049 cents 878.048780 19: 965.854 cents 965.853659 20: 995.122 cents 995.121951 21: 1024.390 cents 1024.390244 22: 1112.195 cents 1112.195122 23: 1141.463 cents 1141.463415 24: 1170.732 cents 1170.731707 25: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 29.2683 cents 29.2683 1: 87.8049 cents 87.8049 2: 29.2683 cents 29.2683 3: 29.2683 cents 29.2683 4: 87.8049 cents 87.8049 5: 29.2683 cents 29.2683 6: 29.2683 cents 29.2683 7: 87.8049 cents 87.8049 8: 29.2683 cents 29.2683 9: 29.2683 cents 29.2683 10: 87.8049 cents 87.8049 11: 29.2683 cents 29.2683 12: 29.2683 cents 29.2683 13: 87.8049 cents 87.8049 14: 29.2683 cents 29.2683 15: 29.2683 cents 29.2683 16: 87.8049 cents 87.8049 17: 29.2683 cents 29.2683 18: 29.2683 cents 29.2683 19: 87.8049 cents 87.8049 20: 29.2683 cents 29.2683 21: 29.2683 cents 29.2683 22: 87.8049 cents 87.8049 23: 29.2683 cents 29.2683 24: 29.2683 cents 29.2683 25: 29.2683 cents 29.2683
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 17 29.26829 cents 1: 8 87.80488 cents 2: 9 58.53659 cents 2: 16 117.07317 cents 3: 1 87.80488 cents 3: 24 146.34146 cents 4: 18 175.60976 cents 4: 7 234.14634 cents 5: 10 204.87805 cents 5: 15 263.41463 cents 6: 2 234.14634 cents 6: 23 292.68293 cents 7: 19 321.95122 cents 7: 6 380.48780 cents 8: 11 351.21951 cents 8: 14 409.75610 cents 9: 3 380.48780 cents 9: 22 439.02439 cents 10: 20 468.29268 cents 10: 5 526.82927 cents 11: 12 497.56098 cents 11: 13 556.09756 cents 12: 4 526.82927 cents 12: 21 585.36585 cents 13: 21 614.63415 cents 13: 4 673.17073 cents 14: 13 643.90244 cents 14: 12 702.43902 cents 15: 5 673.17073 cents 15: 20 731.70732 cents 16: 22 760.97561 cents 16: 3 819.51220 cents 17: 14 790.24390 cents 17: 11 848.78049 cents 18: 6 819.51220 cents 18: 19 878.04878 cents 19: 23 907.31707 cents 19: 2 965.85366 cents 20: 15 936.58537 cents 20: 10 995.12195 cents 21: 7 965.85366 cents 21: 18 1024.39024 cents 22: 24 1053.65854 cents 22: 1 1112.19512 cents 23: 16 1082.92683 cents 23: 9 1141.46341 cents 24: 8 1112.19512 cents 24: 17 1170.73171 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 25 0.0 : 87.8 117.1 146.3 234.1 263.4 292.7 380.5 409.8 439.0 526.8 556.1 585.4 673.2 702.4 731.7 819.5 848.8 878.0 965.9 995.1 1024.4 1112.2 1141.5 1170.7 1200.0 87.8 : 29.3 58.5 146.3 175.6 204.9 292.7 322.0 351.2 439.0 468.3 497.6 585.4 614.6 643.9 731.7 761.0 790.2 878.0 907.3 936.6 1024.4 1053.7 1082.9 1112.2 1200.0 117.1 : 29.3 117.1 146.3 175.6 263.4 292.7 322.0 409.8 439.0 468.3 556.1 585.4 614.6 702.4 731.7 761.0 848.8 878.0 907.3 995.1 1024.4 1053.7 1082.9 1170.7 1200.0 146.3 : 87.8 117.1 146.3 234.1 263.4 292.7 380.5 409.8 439.0 526.8 556.1 585.4 673.2 702.4 731.7 819.5 848.8 878.0 965.9 995.1 1024.4 1053.7 1141.5 1170.7 1200.0 234.1 : 29.3 58.5 146.3 175.6 204.9 292.7 322.0 351.2 439.0 468.3 497.6 585.4 614.6 643.9 731.7 761.0 790.2 878.0 907.3 936.6 965.9 1053.7 1082.9 1112.2 1200.0 263.4 : 29.3 117.1 146.3 175.6 263.4 292.7 322.0 409.8 439.0 468.3 556.1 585.4 614.6 702.4 731.7 761.0 848.8 878.0 907.3 936.6 1024.4 1053.7 1082.9 1170.7 1200.0 292.7 : 87.8 117.1 146.3 234.1 263.4 292.7 380.5 409.8 439.0 526.8 556.1 585.4 673.2 702.4 731.7 819.5 848.8 878.0 907.3 995.1 1024.4 1053.7 1141.5 1170.7 1200.0 380.5 : 29.3 58.5 146.3 175.6 204.9 292.7 322.0 351.2 439.0 468.3 497.6 585.4 614.6 643.9 731.7 761.0 790.2 819.5 907.3 936.6 965.9 1053.7 1082.9 1112.2 1200.0 409.8 : 29.3 117.1 146.3 175.6 263.4 292.7 322.0 409.8 439.0 468.3 556.1 585.4 614.6 702.4 731.7 761.0 790.2 878.0 907.3 936.6 1024.4 1053.7 1082.9 1170.7 1200.0 439.0 : 87.8 117.1 146.3 234.1 263.4 292.7 380.5 409.8 439.0 526.8 556.1 585.4 673.2 702.4 731.7 761.0 848.8 878.0 907.3 995.1 1024.4 1053.7 1141.5 1170.7 1200.0 526.8 : 29.3 58.5 146.3 175.6 204.9 292.7 322.0 351.2 439.0 468.3 497.6 585.4 614.6 643.9 673.2 761.0 790.2 819.5 907.3 936.6 965.9 1053.7 1082.9 1112.2 1200.0 556.1 : 29.3 117.1 146.3 175.6 263.4 292.7 322.0 409.8 439.0 468.3 556.1 585.4 614.6 643.9 731.7 761.0 790.2 878.0 907.3 936.6 1024.4 1053.7 1082.9 1170.7 1200.0 585.4 : 87.8 117.1 146.3 234.1 263.4 292.7 380.5 409.8 439.0 526.8 556.1 585.4 614.6 702.4 731.7 761.0 848.8 878.0 907.3 995.1 1024.4 1053.7 1141.5 1170.7 1200.0 673.2 : 29.3 58.5 146.3 175.6 204.9 292.7 322.0 351.2 439.0 468.3 497.6 526.8 614.6 643.9 673.2 761.0 790.2 819.5 907.3 936.6 965.9 1053.7 1082.9 1112.2 1200.0 702.4 : 29.3 117.1 146.3 175.6 263.4 292.7 322.0 409.8 439.0 468.3 497.6 585.4 614.6 643.9 731.7 761.0 790.2 878.0 907.3 936.6 1024.4 1053.7 1082.9 1170.7 1200.0 731.7 : 87.8 117.1 146.3 234.1 263.4 292.7 380.5 409.8 439.0 468.3 556.1 585.4 614.6 702.4 731.7 761.0 848.8 878.0 907.3 995.1 1024.4 1053.7 1141.5 1170.7 1200.0 819.5 : 29.3 58.5 146.3 175.6 204.9 292.7 322.0 351.2 380.5 468.3 497.6 526.8 614.6 643.9 673.2 761.0 790.2 819.5 907.3 936.6 965.9 1053.7 1082.9 1112.2 1200.0 848.8 : 29.3 117.1 146.3 175.6 263.4 292.7 322.0 351.2 439.0 468.3 497.6 585.4 614.6 643.9 731.7 761.0 790.2 878.0 907.3 936.6 1024.4 1053.7 1082.9 1170.7 1200.0 878.0 : 87.8 117.1 146.3 234.1 263.4 292.7 322.0 409.8 439.0 468.3 556.1 585.4 614.6 702.4 731.7 761.0 848.8 878.0 907.3 995.1 1024.4 1053.7 1141.5 1170.7 1200.0 965.9 : 29.3 58.5 146.3 175.6 204.9 234.1 322.0 351.2 380.5 468.3 497.6 526.8 614.6 643.9 673.2 761.0 790.2 819.5 907.3 936.6 965.9 1053.7 1082.9 1112.2 1200.0 995.1 : 29.3 117.1 146.3 175.6 204.9 292.7 322.0 351.2 439.0 468.3 497.6 585.4 614.6 643.9 731.7 761.0 790.2 878.0 907.3 936.6 1024.4 1053.7 1082.9 1170.7 1200.0 1024.4: 87.8 117.1 146.3 175.6 263.4 292.7 322.0 409.8 439.0 468.3 556.1 585.4 614.6 702.4 731.7 761.0 848.8 878.0 907.3 995.1 1024.4 1053.7 1141.5 1170.7 1200.0 1112.2: 29.3 58.5 87.8 175.6 204.9 234.1 322.0 351.2 380.5 468.3 497.6 526.8 614.6 643.9 673.2 761.0 790.2 819.5 907.3 936.6 965.9 1053.7 1082.9 1112.2 1200.0 1141.5: 29.3 58.5 146.3 175.6 204.9 292.7 322.0 351.2 439.0 468.3 497.6 585.4 614.6 643.9 731.7 761.0 790.2 878.0 907.3 936.6 1024.4 1053.7 1082.9 1170.7 1200.0 1170.7: 29.3 117.1 146.3 175.6 263.4 292.7 322.0 409.8 439.0 468.3 556.1 585.4 614.6 702.4 731.7 761.0 848.8 878.0 907.3 995.1 1024.4 1053.7 1141.5 1170.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.2683 .. 87.8049 cents 58.53659 cents 29.26829 cents 2: 58.5366 .. 117.0732 cents 58.53659 cents -29.26829 cents 3: 87.8049 .. 146.3415 cents 58.53659 cents -29.26829 cents 4: 175.6098 .. 234.1463 cents 58.53659 cents 29.26829 cents 5: 204.8780 .. 263.4146 cents 58.53659 cents -29.26829 cents 6: 234.1463 .. 292.6829 cents 58.53659 cents -29.26829 cents 7: 321.9512 .. 380.4878 cents 58.53659 cents 29.26829 cents 8: 351.2195 .. 409.7561 cents 58.53659 cents -29.26829 cents 9: 380.4878 .. 439.0244 cents 58.53659 cents -29.26829 cents 10: 468.2927 .. 526.8293 cents 58.53659 cents 29.26829 cents 11: 497.5610 .. 556.0976 cents 58.53659 cents -29.26829 cents 12: 526.8293 .. 585.3659 cents 58.53659 cents -29.26829 cents 13: 614.6341 .. 673.1707 cents 58.53659 cents 29.26829 cents 14: 643.9024 .. 702.4390 cents 58.53659 cents -29.26829 cents 15: 673.1707 .. 731.7073 cents 58.53659 cents -29.26829 cents 16: 760.9756 .. 819.5122 cents 58.53659 cents 29.26829 cents 17: 790.2439 .. 848.7805 cents 58.53659 cents -29.26829 cents 18: 819.5122 .. 878.0488 cents 58.53659 cents -29.26829 cents 19: 907.3171 .. 965.8537 cents 58.53659 cents 29.26829 cents 20: 936.5854 .. 995.1220 cents 58.53659 cents -29.26829 cents 21: 965.8537 .. 1024.3902 cents 58.53659 cents -29.26829 cents 22: 1053.6585 .. 1112.1951 cents 58.53659 cents 29.26829 cents 23: 1082.9268 .. 1141.4634 cents 58.53659 cents -29.26829 cents 24: 1112.1951 .. 1170.7317 cents 58.53659 cents -29.26829 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 29.26829 cents, class 1 Average step (divided formal octave): 48.0000 cents Largest one step interval : 87.80488 cents Average / Smallest step : 1.640000 Largest / Average step : 1.829268 Largest / Smallest step : 3.000000 Median interval of one step : 29.26829 cents, amount: 17 Most common interval of one step : 29.26829 cents, amount: 17 Least squares average step : 49.69518 cents, oct.: 1242.37943 cents Scale is not proper Scale has Myhill's property chromas: 58.53659 cents and 29.26829 cents, ratio: 2.000000 generators: 3 of 146.34146 cents and 1053.65854 cents ET pair of linear temperament : 41&41 Scale is distributional even Scale is a mode of a 41-tone equal temperament with octave 1200.000 cents degrees: 3 4 5 8 9 10 13 14 15 18 19 20 23 24 25 28 29 30 33 34 35 38 39 40 41 generators: 5 and 36 Number of contiguous 1-step segments: 8 Step pattern alph. order: ABBABBABBABBABBABBABBABBB Step pattern size order : LSSLSSLSSLSSLSSLSSLSSLSSS Interval vector is [ 17 9 9 16 24 18 10 9 15 23 19 11 9 14 22 20 12 9 13 21 ] Scale is not a Constant Structure Scale diversity : 1.153686 Lumma stability : 0.219512 Lumma impropriety factor : 0.390244 Number of different interval sizes : 40 = 1.66667 / 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 : 29.26829 cents Most common intervals : 146.34146 cents & inv., amount: 24 Scale is a chain of 12 triads 0.0 556.098 1053.659 cents Most common triad is 0.0 146.341 1053.659 cents, amount: 23 Number of recognisable fifths : 12, average 702.4390 cents Scale contains two identical disjunct "tetrachords" of 11 notes Formal octave complements present : 9 = 36.0000% Limited inverse transpositions : 22 Inversional symmetry on degrees : 11 Inversional symmetry on intervals : 23-24 -- Rational properties --
FIT/MODE
25: 2 0 1 2 0 1 2 0 1 2 1 0 2 1 0 2 1 0 2 1 0 2 1 0 1 N T3 SD: 12.9883 c. M: 25.7561 c. 26: 2 1 0 2 1 0 2 1 1 1 1 1 2 0 1 2 0 1 2 1 0 2 1 0 1 N T3 SD: 12.9020 c. M:-22.5141 c. 27: 2 1 0 2 1 1 2 0 1 2 1 0 2 1 0 2 1 1 2 0 1 2 1 0 1 N SD: 12.5521 c. M:-21.6802 c. 28: 2 1 0 2 1 1 2 1 0 2 1 1 2 0 1 2 1 0 3 0 1 2 1 0 1 N SD: 12.1973 c. M: 20.9059 c. 29: 2 1 1 2 0 1 2 1 1 2 0 1 2 1 1 2 1 0 2 1 1 2 1 0 1 N T3 SD: 11.5532 c. M:-20.1850 c. 30: 2 1 1 2 1 0 3 0 1 2 1 1 2 1 0 3 0 1 2 1 1 2 1 0 1 N S SD: 11.4774 c. M:-20.4878 c. 31: 2 1 1 2 1 1 2 1 0 3 0 1 2 1 1 2 1 1 2 1 0 3 0 1 1 N SD: 10.8473 c. M: 18.8828 c. 32: 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 0 3 1 0 3 0 1 1 N SD: 10.3576 c. M:-18.2927 c. 33: 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 1 P M ME S SD: 12.4169 c. M: 21.2860 c. 36: 3 1 0 3 1 1 2 1 1 3 1 1 2 1 1 3 0 1 3 1 1 2 1 1 1 N SD: 9.5493 c. M:-16.2602 c. 38: 3 1 1 2 1 1 3 1 1 3 1 1 2 1 1 3 1 1 3 1 0 3 1 1 1 N SD: 8.9994 c. M:-15.4044 c. 39: 3 1 1 3 1 1 2 1 1 3 1 1 3 1 1 3 1 1 2 1 1 3 1 1 1 N SD: 8.7673 c. M:-15.0094 c. 40: 3 1 1 3 1 1 3 1 1 3 1 1 2 1 1 3 1 1 3 1 1 3 1 1 1 N SD: 8.5782 c. M:-14.6341 c. 41: 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 3 1 1 1 N M DE S 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: 0.2420 cents 3 .. 6 match: 3 H SD: 9.8226 cents 4 .. 8 match: 4 H SD: 1.6395 cents 5 .. 10 match: 5 H SD: 4.9612 cents 6 .. 12 match: 6 H SD: 6.4639 cents 7 .. 14 match: 7 H SD: 10.2393 cents 8 .. 16 match: 8 H SD: 5.0322 cents 9 .. 18 match: 9 H SD: 8.4819 cents 10 .. 20 match: 10 H SD: 5.3323 cents 11 .. 22 match: 11 H SD: 3.8995 cents 12 .. 24 match: 12 H SD: 4.3234 cents 13 .. 26 match: 12 SD: 4.7438 cents 14 .. 28 match: 13 SD: 5.7580 cents 15 .. 30 match: 14 SD: 3.3300 cents 16 .. 32 match: 14 S SD: 4.2933 cents 17 .. 34 match: 16 S SD: 3.8108 cents 18 .. 36 match: 16 SD: 4.4962 cents 19 .. 38 match: 16 SD: 3.9719 cents 20 .. 40 match: 17 SD: 2.8987 cents 21 .. 42 match: 17 SD: 2.5511 cents 22 .. 44 match: 20 S SD: 3.0501 cents 23 .. 46 match: 18 SD: 2.7355 cents 24 .. 48 match: 18 SD: 3.0189 cents 25 .. 50 match: 18 SD: 2.6880 cents 26 .. 52 match: 21 SD: 2.8288 cents 27 .. 54 match: 20 SD: 2.0630 cents 28 .. 56 match: 20 SD: 2.0984 cents 29 .. 58 match: 19 SD: 2.4230 cents 30 .. 60 match: 23 SD: 2.1884 cents 31 .. 62 match: 20 SD: 2.1312 cents 32 .. 64 match: 22 SD: 1.6023 cents 33 .. 66 match: 21 SD: 1.9927 cents 34 .. 68 match: 22 SD: 1.8821 cents 35 .. 70 match: 21 SD: 1.8364 cents 36 .. 72 match: 22 SD: 1.6121 cents 37 .. 74 match: 23 SD: 1.8543 cents 38 .. 76 match: 22 SD: 1.6280 cents 39 .. 78 match: 22 SD: 2.0301 cents 40 .. 80 match: 24 SD: 1.6323 cents 41 .. 82 match: 24 SD: 1.7603 cents 42 .. 84 match: 25 SD: 1.2852 cents 43 .. 86 match: 24 SD: 1.6598 cents 44 .. 88 match: 25 SD: 1.3965 cents 45 .. 90 match: 24 SD: 1.4889 cents 46 .. 92 match: 24 SD: 1.6730 cents 48 .. 96 match: 25 SD: 1.2828 cents 49 .. 98 match: 24 SD: 1.4332 cents 50 .. 100 match: 24 SD: 1.4143 cents 53 .. 106 match: 25 SD: 1.2467 cents 55 .. 110 match: 25 SD: 1.1116 cents 56 .. 112 match: 25 SD: 1.0603 cents 60 .. 120 match: 25 SD: 1.0448 cents 68 .. 136 match: 25 SD: 0.9784 cents 70 .. 140 match: 25 SD: 0.9770 cents 71 .. 142 match: 25 SD: 0.9690 cents 72 .. 144 match: 25 SD: 0.9290 cents 74 .. 148 match: 25 SD: 0.8843 cents 76 .. 152 match: 25 SD: 0.8028 cents 82 .. 164 match: 25 SD: 0.6916 cents 90 .. 180 match: 25 SD: 0.6312 cents 98 .. 196 match: 25 SD: 0.6016 cents 110 .. 220 match: 25 SD: 0.5830 cents 112 .. 224 match: 25 SD: 0.5695 cents 114 .. 228 match: 25 SD: 0.5132 cents 124 .. 248 match: 25 SD: 0.5095 cents 130 .. 260 match: 25 SD: 0.5029 cents 134 .. 268 match: 25 SD: 0.4871 cents 135 .. 270 match: 25 SD: 0.4503 cents 139 .. 278 match: 25 SD: 0.4229 cents 146 .. 292 match: 25 SD: 0.4106 cents 152 .. 304 match: 25 SD: 0.4028 cents 158 .. 316 match: 25 SD: 0.3565 cents 171 .. 342 match: 25 SD: 0.3544 cents 172 .. 344 match: 25 SD: 0.3448 cents 188 .. 376 match: 25 SD: 0.3431 cents 191 .. 382 match: 25 SD: 0.3387 cents 194 .. 388 match: 25 SD: 0.3098 cents 206 .. 412 match: 25 SD: 0.2970 cents 212 .. 424 match: 25 SD: 0.2861 cents 213 .. 426 match: 25 SD: 0.2733 cents 228 .. 456 match: 25 SD: 0.2384 cents 256 .. 512 match: 25 SD: 0.2132 cents 270 .. 540 match: 25 SD: 0.2121 cents 284 .. 568 match: 25 SD: 0.2016 cents 304 .. 608 match: 25 SD: 0.1688 cents 330 .. 660 match: 25 SD: 0.1662 cents 385 .. 770 match: 25 SD: 0.1426 cents 419 .. 838 match: 25 SD: 0.1397 cents 430 .. 860 match: 25 SD: 0.1345 cents 444 .. 888 match: 25 SD: 0.1281 cents 456 .. 912 match: 25 SD: 0.1253 cents 498 .. 996 match: 25 SD: 0.1096 cents 512 .. 1024 match: 25 SD: 0.1094 cents 517 .. 1034 match: 25 SD: 0.1033 cents 554 .. 1108 match: 25 SD: 0.0942 cents