Scala analysis: shahin118
Shahin scale in 118-et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 101.695 cents 101.694915 2: 132.203 cents 132.203390 3: 203.390 cents 203.389831 4: 294.915 cents 294.915254 5: 335.593 cents 335.593220 6: 396.610 cents 396.610169 7: 498.305 cents 498.305085 8: 538.983 cents 538.983051 9: 610.169 cents 610.169492 10: 630.508 cents 630.508475 11: 701.695 cents 701.694915 12: 803.390 cents 803.389831 13: 854.237 cents 854.237288 14: 905.085 cents 905.084746 15: 986.441 cents 986.440678 16: 1047.458 cents 1047.457627 17: 1108.475 cents 1108.474576 18: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 91.5254 cents 91.5254 1: 101.6949 cents 101.6949 2: 30.5085 cents 30.5085 3: 71.1864 cents 71.1864 4: 91.5254 cents 91.5254 5: 40.6780 cents 40.6780 6: 61.0169 cents 61.0169 7: 101.6949 cents 101.6949 8: 40.6780 cents 40.6780 9: 71.1864 cents 71.1864 10: 20.3390 cents 20.3390 11: 71.1864 cents 71.1864 12: 101.6949 cents 101.6949 13: 50.8475 cents 50.8475 14: 50.8475 cents 50.8475 15: 81.3559 cents 81.3559 16: 61.0169 cents 61.0169 17: 61.0169 cents 61.0169 18: 91.5254 cents 91.5254
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20.33898 cents 1: 1 30.50847 cents 1: 2 40.67797 cents 1: 2 50.84746 cents 1: 3 61.01695 cents 1: 3 71.18644 cents 1: 1 81.35593 cents 1: 2 91.52542 cents 1: 3 101.69492 cents 2: 2 91.52542 cents 2: 3 101.69492 cents 2: 1 111.86441 cents 2: 1 122.03390 cents 2: 3 132.20339 cents 2: 2 142.37288 cents 2: 2 152.54237 cents 2: 2 162.71186 cents 2: 1 172.88136 cents 2: 1 193.22034 cents 3: 1 132.20339 cents 3: 1 162.71186 cents 3: 1 183.05085 cents 3: 4 193.22034 cents 3: 6 203.38983 cents 3: 2 213.55932 cents 3: 2 223.72881 cents 3: 1 254.23729 cents 4: 1 203.38983 cents 4: 2 233.89830 cents 4: 3 244.06780 cents 4: 1 254.23729 cents 4: 2 264.40678 cents 4: 2 274.57627 cents 4: 2 284.74576 cents 4: 4 294.91525 cents 4: 1 315.25424 cents 5: 3 294.91525 cents 5: 3 305.08475 cents 5: 2 315.25424 cents 5: 2 335.59322 cents 5: 3 345.76271 cents 5: 2 355.93220 cents 5: 1 366.10169 cents 5: 1 386.44068 cents 5: 1 396.61017 cents 6: 1 335.59322 cents 6: 1 355.93220 cents 6: 2 366.10169 cents 6: 1 376.27119 cents 6: 3 396.61017 cents 6: 4 406.77966 cents 6: 2 416.94915 cents 6: 2 427.11864 cents 6: 2 447.45763 cents 7: 2 406.77966 cents 7: 1 427.11864 cents 7: 2 437.28814 cents 7: 1 447.45763 cents 7: 1 457.62712 cents 7: 1 467.79661 cents 7: 3 477.96610 cents 7: 2 488.13559 cents 7: 4 498.30508 cents 7: 1 508.47458 cents 8: 1 488.13559 cents 8: 3 498.30508 cents 8: 4 508.47458 cents 8: 1 518.64407 cents 8: 1 528.81356 cents 8: 1 538.98305 cents 8: 3 549.15254 cents 8: 1 569.49153 cents 8: 2 589.83051 cents 8: 1 600.00000 cents 9: 1 528.81356 cents 9: 1 549.15254 cents 9: 1 559.32203 cents 9: 3 569.49152 cents 9: 2 589.83051 cents 9: 2 600.00000 cents 9: 2 610.16949 cents 9: 3 630.50848 cents 9: 1 640.67797 cents 9: 1 650.84746 cents 9: 1 671.18644 cents 10: 1 600.00000 cents 10: 2 610.16949 cents 10: 1 630.50847 cents 10: 3 650.84746 cents 10: 1 661.01695 cents 10: 1 671.18644 cents 10: 1 681.35593 cents 10: 4 691.52542 cents 10: 3 701.69492 cents 10: 1 711.86441 cents 11: 1 691.52542 cents 11: 4 701.69491 cents 11: 2 711.86441 cents 11: 3 722.03390 cents 11: 1 732.20339 cents 11: 1 742.37288 cents 11: 1 752.54237 cents 11: 2 762.71186 cents 11: 1 772.88136 cents 11: 2 793.22034 cents 12: 2 752.54237 cents 12: 2 772.88136 cents 12: 2 783.05085 cents 12: 4 793.22034 cents 12: 3 803.38983 cents 12: 1 823.72881 cents 12: 2 833.89831 cents 12: 1 844.06780 cents 12: 1 864.40678 cents 13: 1 803.38983 cents 13: 1 813.55932 cents 13: 1 833.89831 cents 13: 2 844.06780 cents 13: 3 854.23729 cents 13: 2 864.40678 cents 13: 2 884.74576 cents 13: 3 894.91525 cents 13: 3 905.08475 cents 14: 1 884.74576 cents 14: 4 905.08475 cents 14: 2 915.25424 cents 14: 2 925.42373 cents 14: 2 935.59322 cents 14: 1 945.76271 cents 14: 3 955.93220 cents 14: 2 966.10170 cents 14: 1 996.61017 cents 15: 1 945.76271 cents 15: 2 976.27119 cents 15: 2 986.44068 cents 15: 6 996.61017 cents 15: 4 1006.77966 cents 15: 1 1016.94915 cents 15: 1 1037.28814 cents 15: 1 1067.79661 cents 16: 1 1006.77966 cents 16: 1 1027.11864 cents 16: 2 1037.28814 cents 16: 2 1047.45763 cents 16: 2 1057.62712 cents 16: 3 1067.79661 cents 16: 1 1077.96610 cents 16: 1 1088.13559 cents 16: 3 1098.30508 cents 16: 2 1108.47458 cents 17: 3 1098.30508 cents 17: 2 1108.47458 cents 17: 1 1118.64407 cents 17: 3 1128.81356 cents 17: 3 1138.98305 cents 17: 2 1149.15254 cents 17: 2 1159.32203 cents 17: 1 1169.49153 cents 17: 1 1179.66102 cents Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 9.35294 = 159/17
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.0 : 101.7 132.2 203.4 294.9 335.6 396.6 498.3 539.0 610.2 630.5 701.7 803.4 854.2 905.1 986.4 1047.5 1108.5 1200.0 101.7 : 30.5 101.7 193.2 233.9 294.9 396.6 437.3 508.5 528.8 600.0 701.7 752.5 803.4 884.7 945.8 1006.8 1098.3 1200.0 132.2 : 71.2 162.7 203.4 264.4 366.1 406.8 478.0 498.3 569.5 671.2 722.0 772.9 854.2 915.3 976.3 1067.8 1169.5 1200.0 203.4 : 91.5 132.2 193.2 294.9 335.6 406.8 427.1 498.3 600.0 650.8 701.7 783.1 844.1 905.1 996.6 1098.3 1128.8 1200.0 294.9 : 40.7 101.7 203.4 244.1 315.3 335.6 406.8 508.5 559.3 610.2 691.5 752.5 813.6 905.1 1006.8 1037.3 1108.5 1200.0 335.6 : 61.0 162.7 203.4 274.6 294.9 366.1 467.8 518.6 569.5 650.8 711.9 772.9 864.4 966.1 996.6 1067.8 1159.3 1200.0 396.6 : 101.7 142.4 213.6 233.9 305.1 406.8 457.6 508.5 589.8 650.8 711.9 803.4 905.1 935.6 1006.8 1098.3 1139.0 1200.0 498.3 : 40.7 111.9 132.2 203.4 305.1 355.9 406.8 488.1 549.2 610.2 701.7 803.4 833.9 905.1 996.6 1037.3 1098.3 1200.0 539.0 : 71.2 91.5 162.7 264.4 315.3 366.1 447.5 508.5 569.5 661.0 762.7 793.2 864.4 955.9 996.6 1057.6 1159.3 1200.0 610.2 : 20.3 91.5 193.2 244.1 294.9 376.3 437.3 498.3 589.8 691.5 722.0 793.2 884.7 925.4 986.4 1088.1 1128.8 1200.0 630.5 : 71.2 172.9 223.7 274.6 355.9 416.9 478.0 569.5 671.2 701.7 772.9 864.4 905.1 966.1 1067.8 1108.5 1179.7 1200.0 701.7 : 101.7 152.5 203.4 284.7 345.8 406.8 498.3 600.0 630.5 701.7 793.2 833.9 894.9 996.6 1037.3 1108.5 1128.8 1200.0 803.4 : 50.8 101.7 183.1 244.1 305.1 396.6 498.3 528.8 600.0 691.5 732.2 793.2 894.9 935.6 1006.8 1027.1 1098.3 1200.0 854.2 : 50.8 132.2 193.2 254.2 345.8 447.5 478.0 549.2 640.7 681.4 742.4 844.1 884.7 955.9 976.3 1047.5 1149.2 1200.0 905.1 : 81.4 142.4 203.4 294.9 396.6 427.1 498.3 589.8 630.5 691.5 793.2 833.9 905.1 925.4 996.6 1098.3 1149.2 1200.0 986.4 : 61.0 122.0 213.6 315.3 345.8 416.9 508.5 549.2 610.2 711.9 752.5 823.7 844.1 915.3 1016.9 1067.8 1118.6 1200.0 1047.5: 61.0 152.5 254.2 284.7 355.9 447.5 488.1 549.2 650.8 691.5 762.7 783.1 854.2 955.9 1006.8 1057.6 1139.0 1200.0 1108.5: 91.5 193.2 223.7 294.9 386.4 427.1 488.1 589.8 630.5 701.7 722.0 793.2 894.9 945.8 996.6 1078.0 1139.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.3390 .. 101.6949 cents 81.35593 cents 20.33898 cents 2: 91.5254 .. 193.2203 cents 101.69492 cents -10.16949 cents 3: 132.2034 .. 254.2373 cents 122.03390 cents -61.01695 cents 4: 203.3898 .. 315.2542 cents 111.86441 cents -50.84746 cents 5: 294.9153 .. 396.6102 cents 101.69492 cents -20.33898 cents 6: 335.5932 .. 447.4576 cents 111.86441 cents -61.01695 cents 7: 406.7797 .. 508.4746 cents 101.69492 cents -40.67797 cents 8: 488.1356 .. 600.0000 cents 111.86441 cents -20.33898 cents 9: 528.8136 .. 671.1864 cents 142.37288 cents -71.18644 cents 10: 600.0000 .. 711.8644 cents 111.86441 cents -71.18644 cents 11: 691.5254 .. 793.2203 cents 101.69492 cents -20.33898 cents 12: 752.5424 .. 864.4068 cents 111.86441 cents -40.67797 cents 13: 803.3898 .. 905.0847 cents 101.69492 cents -61.01695 cents 14: 884.7458 .. 996.6102 cents 111.86441 cents -20.33898 cents 15: 945.7627 .. 1067.7966 cents 122.03390 cents -50.84746 cents 16: 1006.7797 .. 1108.4746 cents 101.69492 cents -61.01695 cents 17: 1098.3051 .. 1179.6610 cents 81.35593 cents -10.16949 cents
SHOW DATA
Number of notes : 18 -- Interval properties -- Smallest interval : 20.33898 cents, class 1 Average step (divided formal octave): 66.6667 cents Largest one step interval : 101.69492 cents Average / Smallest step : 3.277778 Largest / Average step : 1.525424 Largest / Smallest step : 5.000000 Median interval of one step : 66.10169 cents, amount: 0 Least squares average step : 65.88230 cents, oct.: 1185.88133 cents Scale is not proper Scale is a mode of a 118-tone equal temperament with octave 1200.000 cents degrees: 10 13 20 29 33 39 49 53 60 62 69 79 84 89 97 103 109 118 Least number of segments generator : 69 of 701.695 cents and inv. number of contiguous generator circle segments: 2 Shortest superset generator : 91 of 925.424 cents and inv. generated superset size: 80 = 62 more = 444.444% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFAECGCAHHIFFD Step pattern size order : IBFHCEICFAFIDDGEEH Interval vector is [ 0 1 1 2 2 3 3 1 4 6 1 1 4 2 2 3 1 1 5 7 2 2 2 3 2 2 2 2 7 3 3 0 3 3 3 3 1 1 4 6 2 3 2 3 1 1 3 3 7 5 1 2 1 4 1 4 0 4 2 ] Scale is not a Constant Structure Scale diversity : 1.617036 Lumma stability : 0.033898 Lumma impropriety factor : 0.559322 Number of different interval sizes : 111 = 6.52941 / class Number of one step interval sizes : 9 Highest interval variety : 11 Mean interval variety : 9.35294 = 159/17 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 10.16949 cents Number of recognisable fifths : 15, average 700.3390 cents Formal octave complements present : 7 = 38.8889% -- Rational properties --
FIT/MODE
18: 2 0 1 2 0 1 2 0 1 1 1 1 1 1 1 1 1 1 N T3 SD: 21.4887 c. M:-38.4181 c. 20: 2 0 1 2 0 1 2 1 1 0 2 1 1 1 1 1 1 2 N SD: 21.6140 c. M: 36.6102 c. 21: 2 0 2 1 1 1 2 0 2 0 1 2 1 1 1 1 1 2 N SD: 14.7768 c. M:-25.1816 c. 22: 2 0 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 N D3 SD: 14.7695 c. M:-24.0370 c. 24: 2 1 1 2 1 1 2 1 1 1 1 2 1 1 2 1 1 2 N D3 I SD: 9.1405 c. M:-19.4915 c. 28: 2 1 2 2 1 1 3 1 1 1 1 3 1 1 2 1 2 2 N SD: 11.1183 c. M: 18.8862 c. 29: 2 1 2 2 1 2 2 1 2 0 2 2 2 1 2 1 2 2 N SD: 10.0648 c. M: 18.9363 c. 31: 3 0 2 3 1 1 3 1 2 0 2 3 1 1 2 2 2 2 N SD: 10.9819 c. M: 18.6987 c. 33: 3 1 2 2 1 2 3 1 2 0 2 3 2 1 2 2 1 3 N SD: 9.9614 c. M:-18.4900 c. 34: 3 1 2 2 2 1 3 1 2 1 2 3 1 2 2 2 1 3 N SD: 9.3336 c. M:-17.3480 c. 36: 3 1 2 3 1 2 3 1 2 1 2 3 2 1 3 1 2 3 N SD: 6.8886 c. M: 14.1243 c. 45: 4 1 3 3 2 2 4 1 3 1 2 4 2 2 3 2 3 3 N SD: 6.3973 c. M:-11.5254 c. 46: 4 1 3 3 2 2 4 2 2 1 3 4 2 2 3 2 2 4 N SD: 6.2225 c. M: 12.8224 c. 48: 4 1 3 4 1 3 4 1 3 1 3 4 2 2 3 3 2 4 N SD: 6.7302 c. M: 13.9831 c. 49: 4 1 3 4 2 2 4 2 3 1 3 4 2 2 3 3 2 4 N SD: 5.6837 c. M: 9.7544 c. 53: 5 1 3 4 2 3 4 2 3 1 3 5 2 2 4 2 3 4 N SD: 5.8787 c. M:-11.7045 c. 55: 5 1 3 4 2 3 5 2 3 1 3 5 2 2 4 3 3 4 N SD: 5.6076 c. M: 11.2789 c. 57: 5 1 4 4 2 3 5 2 3 1 3 5 3 2 4 3 3 4 N SD: 5.0575 c. M:-8.9206 c. 61: 5 2 3 5 2 3 5 2 4 1 4 5 2 3 4 3 3 5 N SD: 4.7258 c. M: 8.3356 c. 65: 5 2 4 5 2 3 6 2 4 1 4 5 3 3 4 4 3 5 N SD: 4.7934 c. M: 9.5437 c. 69: 6 2 4 5 2 4 6 2 4 1 4 6 3 3 5 3 4 5 N SD: 4.0363 c. M:-6.9270 c. 70: 6 2 4 5 3 3 6 3 4 1 4 6 3 3 5 3 4 5 N SD: 4.6150 c. M:-9.5884 c. 72: 6 2 4 6 2 4 6 2 5 1 4 6 3 3 5 4 4 5 N SD: 3.9755 c. M:-8.1921 c. 73: 6 2 4 6 2 4 6 3 4 1 5 6 3 3 5 4 3 6 N SD: 3.9435 c. M: 7.1047 c. 81: 7 2 5 6 3 4 7 2 5 2 4 7 4 3 6 4 4 6 N SD: 4.1132 c. M:-6.5286 c. 82: 7 2 5 6 3 4 7 3 5 1 5 7 3 4 5 5 4 6 N SD: 3.0243 c. M:-6.2009 c. 89: 8 2 5 7 3 4 8 3 5 2 5 8 3 4 6 5 4 7 N SD: 3.2796 c. M:-6.1703 c. 90: 8 2 5 7 3 5 7 3 6 1 6 7 4 4 6 5 4 7 N SD: 3.4590 c. M:-5.8757 c. 91: 8 2 5 7 3 5 8 3 5 2 5 8 4 4 6 4 5 7 N SD: 3.4517 c. M: 5.9229 c. 93: 8 2 6 7 3 5 8 3 5 2 5 8 4 4 6 5 5 7 N SD: 3.0993 c. M: 5.7955 c. 94: 8 2 6 7 3 5 8 3 6 1 6 8 4 4 6 5 5 7 N SD: 2.3337 c. M: 4.9766 c. 105: 9 3 6 8 3 6 9 3 6 2 6 9 5 4 7 6 5 8 N SD: 3.2223 c. M:-4.9395 c. 106: 9 3 6 8 4 5 9 4 6 2 6 9 5 4 7 6 5 8 N SD: 2.7215 c. M:-6.1401 c. 110: 9 3 7 8 4 5 10 3 7 2 6 10 4 5 7 6 6 8 N SD: 3.0426 c. M: 4.6225 c. 111: 9 3 7 8 4 6 9 4 6 2 7 9 5 5 7 6 5 9 N SD: 2.9068 c. M: 5.7719 c. 114: 10 3 6 9 4 6 9 4 7 2 7 9 5 5 8 6 5 9 N SD: 2.8918 c. M:-5.1740 c. 118: 10 3 7 9 4 6 10 4 7 2 7 10 5 5 8 6 6 9 N 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: 0.1300 cents 3 .. 6 match: 3 H SD: 6.9092 cents 4 .. 8 match: 4 H SD: 5.1013 cents 5 .. 10 match: 5 H SD: 9.2967 cents 6 .. 12 match: 6 H SD: 5.8210 cents 7 .. 14 match: 7 H SD: 9.1660 cents 8 .. 16 match: 8 H SD: 4.2665 cents 9 .. 18 match: 9 H SD: 5.7473 cents 10 .. 20 match: 10 H SD: 7.3293 cents 11 .. 22 match: 10 S SD: 5.5154 cents 12 .. 24 match: 12 H SD: 3.8259 cents 13 .. 26 match: 13 H SD: 7.0094 cents 14 .. 28 match: 14 H SD: 5.3119 cents 15 .. 30 match: 13 SD: 6.1218 cents 16 .. 32 match: 15 S SD: 3.7781 cents 17 .. 34 match: 14 SD: 4.2344 cents 18 .. 36 match: 15 SD: 4.3213 cents 19 .. 38 match: 15 SD: 3.8863 cents 20 .. 40 match: 15 SD: 4.3514 cents 21 .. 42 match: 16 SD: 4.6816 cents 22 .. 44 match: 18 SD: 3.2562 cents 23 .. 46 match: 16 SD: 3.6936 cents 24 .. 48 match: 18 S SD: 3.5085 cents 25 .. 50 match: 15 SD: 3.3002 cents 26 .. 52 match: 15 SD: 3.1759 cents 27 .. 54 match: 17 SD: 2.8267 cents 28 .. 56 match: 16 SD: 3.0311 cents 29 .. 58 match: 17 SD: 3.3188 cents 30 .. 60 match: 15 SD: 2.3259 cents 31 .. 62 match: 17 SD: 2.5224 cents 32 .. 64 match: 17 SD: 2.3585 cents 34 .. 68 match: 18 SD: 2.3500 cents 35 .. 70 match: 16 SD: 2.5361 cents 36 .. 72 match: 18 SD: 2.0383 cents 37 .. 74 match: 17 SD: 2.5667 cents 38 .. 76 match: 18 SD: 1.7076 cents 42 .. 84 match: 16 SD: 1.5805 cents 43 .. 86 match: 17 SD: 2.1067 cents 44 .. 88 match: 16 SD: 2.1386 cents 46 .. 92 match: 18 SD: 1.8340 cents 47 .. 94 match: 18 SD: 1.4056 cents 48 .. 96 match: 18 SD: 1.3392 cents 51 .. 102 match: 17 SD: 1.6790 cents 52 .. 104 match: 18 SD: 1.4473 cents 54 .. 108 match: 18 SD: 1.4210 cents 58 .. 116 match: 17 SD: 1.6261 cents 59 .. 118 match: 18 SD: 1.5651 cents 60 .. 120 match: 18 SD: 1.4105 cents 61 .. 122 match: 18 SD: 1.3046 cents 64 .. 128 match: 18 SD: 1.0469 cents 66 .. 132 match: 18 SD: 0.7279 cents 98 .. 196 match: 18 SD: 0.7111 cents 102 .. 204 match: 18 SD: 0.5662 cents 112 .. 224 match: 18 SD: 0.5438 cents 135 .. 270 match: 18 SD: 0.4973 cents 144 .. 288 match: 18 SD: 0.4937 cents 150 .. 300 match: 18 SD: 0.4529 cents 162 .. 324 match: 18 SD: 0.4514 cents 166 .. 332 match: 18 SD: 0.4369 cents 168 .. 336 match: 18 SD: 0.3697 cents 178 .. 356 match: 18 SD: 0.3408 cents 201 .. 402 match: 18 SD: 0.3386 cents 210 .. 420 match: 18 SD: 0.3090 cents 216 .. 432 match: 18 SD: 0.2896 cents 230 .. 460 match: 18 SD: 0.2820 cents 249 .. 498 match: 18 SD: 0.2445 cents 279 .. 558 match: 18 SD: 0.2394 cents 280 .. 560 match: 18 SD: 0.2149 cents 303 .. 606 match: 18 SD: 0.2141 cents 312 .. 624 match: 18 SD: 0.1846 cents 350 .. 700 match: 18 SD: 0.1774 cents 378 .. 756 match: 18 SD: 0.1413 cents 513 .. 1026 match: 18 SD: 0.1397 cents 516 .. 1032 match: 18 SD: 0.1373 cents 528 .. 1056 match: 18 SD: 0.0939 cents 594 .. 1188 match: 18 SD: 0.0664 cents