Scala analysis: diamond9plus-marvel
Marvel tempering of diamond9 plus secors up and down
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 115.587 cents 115.587050 2: 182.404 cents 182.403710 3: 201.339 cents 201.339490 4: 231.174 cents 231.174090 5: 268.156 cents 268.156160 6: 316.927 cents 316.926540 7: 383.743 cents 383.743210 8: 432.514 cents 432.513590 9: 499.330 cents 499.330250 10: 585.083 cents 585.082700 11: 614.917 cents 614.917300 12: 700.670 cents 700.669750 13: 767.486 cents 767.486410 14: 816.257 cents 816.256790 15: 883.073 cents 883.073460 16: 931.844 cents 931.843840 17: 968.826 cents 968.825910 18: 998.661 cents 998.660510 19: 1017.596 cents 1017.596290 20: 1084.413 cents 1084.412950 21: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 115.5871 cents 115.5871 1: 115.5871 cents 115.5871 2: 66.8167 cents 66.8167 3: 18.9358 cents 18.9358 4: 29.8346 cents 29.8346 5: 36.9821 cents 36.9821 6: 48.7704 cents 48.7704 7: 66.8167 cents 66.8167 8: 48.7704 cents 48.7704 9: 66.8167 cents 66.8167 10: 85.7525 cents 85.7525 11: 29.8346 cents 29.8346 12: 85.7525 cents 85.7525 13: 66.8167 cents 66.8167 14: 48.7704 cents 48.7704 15: 66.8167 cents 66.8167 16: 48.7704 cents 48.7704 17: 36.9821 cents 36.9821 18: 29.8346 cents 29.8346 19: 18.9358 cents 18.9358 20: 66.8167 cents 66.8167 21: 115.5871 cents 115.5871
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 18.93578 cents 1: 3 29.83460 cents 1: 2 36.98207 cents 1: 4 48.77038 cents 1: 6 66.81666 cents 1: 2 85.75245 cents 1: 2 115.58705 cents 2: 2 48.77038 cents 2: 2 66.81667 cents 2: 4 85.75244 cents 2: 8 115.58705 cents 2: 2 152.56911 cents 2: 2 182.40371 cents 2: 1 231.17410 cents 3: 2 85.75245 cents 3: 4 115.58704 cents 3: 2 152.56912 cents 3: 2 164.35743 cents 3: 4 182.40371 cents 3: 5 201.33949 cents 3: 2 297.99076 cents 4: 2 134.52283 cents 4: 2 152.56911 cents 4: 2 182.40372 cents 4: 2 201.33950 cents 4: 6 231.17409 cents 4: 4 268.15616 cents 4: 2 316.92654 cents 4: 1 364.80742 cents 5: 4 201.33949 cents 5: 2 231.17410 cents 5: 4 268.15616 cents 5: 2 297.99076 cents 5: 4 316.92654 cents 5: 1 334.97282 cents 5: 2 346.76114 cents 5: 2 383.74320 cents 6: 2 250.10988 cents 6: 2 268.15616 cents 6: 2 297.99076 cents 6: 2 316.92654 cents 6: 2 346.76114 cents 6: 2 353.90861 cents 6: 6 383.74321 cents 6: 1 402.67898 cents 6: 2 413.57780 cents 7: 4 316.92654 cents 7: 6 383.74321 cents 7: 7 432.51359 cents 7: 4 450.55987 cents 8: 2 383.74320 cents 8: 2 402.67899 cents 8: 2 413.57781 cents 8: 2 432.51359 cents 8: 1 462.34818 cents 8: 4 469.49566 cents 8: 8 499.33025 cents 9: 2 432.51359 cents 9: 2 469.49565 cents 9: 6 499.33025 cents 9: 2 518.26603 cents 9: 2 536.31232 cents 9: 4 548.10063 cents 9: 3 566.14692 cents 10: 2 499.33025 cents 10: 2 518.26604 cents 10: 1 536.31232 cents 10: 2 548.10063 cents 10: 2 566.14692 cents 10: 6 585.08270 cents 10: 6 614.91730 cents 11: 6 585.08270 cents 11: 6 614.91730 cents 11: 2 633.85308 cents 11: 2 651.89937 cents 11: 1 663.68768 cents 11: 2 681.73396 cents 11: 2 700.66975 cents 12: 3 633.85308 cents 12: 4 651.89936 cents 12: 2 663.68768 cents 12: 2 681.73397 cents 12: 6 700.66975 cents 12: 2 730.50435 cents 12: 2 767.48641 cents 13: 8 700.66974 cents 13: 4 730.50435 cents 13: 1 737.65182 cents 13: 2 767.48641 cents 13: 2 786.42219 cents 13: 2 797.32101 cents 13: 2 816.25680 cents 14: 4 749.44013 cents 14: 7 767.48641 cents 14: 6 816.25679 cents 14: 4 883.07346 cents 15: 2 786.42220 cents 15: 1 797.32102 cents 15: 6 816.25679 cents 15: 2 846.09139 cents 15: 2 853.23886 cents 15: 2 883.07346 cents 15: 2 902.00924 cents 15: 2 931.84384 cents 15: 2 949.89012 cents 16: 2 816.25680 cents 16: 2 853.23886 cents 16: 1 865.02718 cents 16: 4 883.07346 cents 16: 2 902.00924 cents 16: 4 931.84384 cents 16: 2 968.82590 cents 16: 4 998.66051 cents 17: 1 835.19258 cents 17: 2 883.07346 cents 17: 4 931.84384 cents 17: 6 968.82591 cents 17: 2 998.66050 cents 17: 2 1017.59628 cents 17: 2 1047.43089 cents 17: 2 1065.47717 cents 18: 2 902.00924 cents 18: 5 998.66051 cents 18: 4 1017.59629 cents 18: 2 1035.64257 cents 18: 2 1047.43088 cents 18: 4 1084.41296 cents 18: 2 1114.24755 cents 19: 1 968.82590 cents 19: 2 1017.59629 cents 19: 2 1047.43089 cents 19: 8 1084.41295 cents 19: 4 1114.24756 cents 19: 2 1133.18333 cents 19: 2 1151.22962 cents 20: 2 1084.41295 cents 20: 2 1114.24755 cents 20: 6 1133.18334 cents 20: 4 1151.22962 cents 20: 2 1163.01793 cents 20: 3 1170.16540 cents 20: 2 1181.06422 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 7.10000 = 71/10
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 0.0 : 115.6 182.4 201.3 231.2 268.2 316.9 383.7 432.5 499.3 585.1 614.9 700.7 767.5 816.3 883.1 931.8 968.8 998.7 1017.6 1084.4 1200.0 115.6 : 66.8 85.8 115.6 152.6 201.3 268.2 316.9 383.7 469.5 499.3 585.1 651.9 700.7 767.5 816.3 853.2 883.1 902.0 968.8 1084.4 1200.0 182.4 : 18.9 48.8 85.8 134.5 201.3 250.1 316.9 402.7 432.5 518.3 585.1 633.9 700.7 749.4 786.4 816.3 835.2 902.0 1017.6 1133.2 1200.0 201.3 : 29.8 66.8 115.6 182.4 231.2 298.0 383.7 413.6 499.3 566.1 614.9 681.7 730.5 767.5 797.3 816.3 883.1 998.7 1114.2 1181.1 1200.0 231.2 : 37.0 85.8 152.6 201.3 268.2 353.9 383.7 469.5 536.3 585.1 651.9 700.7 737.7 767.5 786.4 853.2 968.8 1084.4 1151.2 1170.2 1200.0 268.2 : 48.8 115.6 164.4 231.2 316.9 346.8 432.5 499.3 548.1 614.9 663.7 700.7 730.5 749.4 816.3 931.8 1047.4 1114.2 1133.2 1163.0 1200.0 316.9 : 66.8 115.6 182.4 268.2 298.0 383.7 450.6 499.3 566.1 614.9 651.9 681.7 700.7 767.5 883.1 998.7 1065.5 1084.4 1114.2 1151.2 1200.0 383.7 : 48.8 115.6 201.3 231.2 316.9 383.7 432.5 499.3 548.1 585.1 614.9 633.9 700.7 816.3 931.8 998.7 1017.6 1047.4 1084.4 1133.2 1200.0 432.5 : 66.8 152.6 182.4 268.2 335.0 383.7 450.6 499.3 536.3 566.1 585.1 651.9 767.5 883.1 949.9 968.8 998.7 1035.6 1084.4 1151.2 1200.0 499.3 : 85.8 115.6 201.3 268.2 316.9 383.7 432.5 469.5 499.3 518.3 585.1 700.7 816.3 883.1 902.0 931.8 968.8 1017.6 1084.4 1133.2 1200.0 585.1 : 29.8 115.6 182.4 231.2 298.0 346.8 383.7 413.6 432.5 499.3 614.9 730.5 797.3 816.3 846.1 883.1 931.8 998.7 1047.4 1114.2 1200.0 614.9 : 85.8 152.6 201.3 268.2 316.9 353.9 383.7 402.7 469.5 585.1 700.7 767.5 786.4 816.3 853.2 902.0 968.8 1017.6 1084.4 1170.2 1200.0 700.7 : 66.8 115.6 182.4 231.2 268.2 298.0 316.9 383.7 499.3 614.9 681.7 700.7 730.5 767.5 816.3 883.1 931.8 998.7 1084.4 1114.2 1200.0 767.5 : 48.8 115.6 164.4 201.3 231.2 250.1 316.9 432.5 548.1 614.9 633.9 663.7 700.7 749.4 816.3 865.0 931.8 1017.6 1047.4 1133.2 1200.0 816.3 : 66.8 115.6 152.6 182.4 201.3 268.2 383.7 499.3 566.1 585.1 614.9 651.9 700.7 767.5 816.3 883.1 968.8 998.7 1084.4 1151.2 1200.0 883.1 : 48.8 85.8 115.6 134.5 201.3 316.9 432.5 499.3 518.3 548.1 585.1 633.9 700.7 749.4 816.3 902.0 931.8 1017.6 1084.4 1133.2 1200.0 931.8 : 37.0 66.8 85.8 152.6 268.2 383.7 450.6 469.5 499.3 536.3 585.1 651.9 700.7 767.5 853.2 883.1 968.8 1035.6 1084.4 1151.2 1200.0 968.8 : 29.8 48.8 115.6 231.2 346.8 413.6 432.5 462.3 499.3 548.1 614.9 663.7 730.5 816.3 846.1 931.8 998.7 1047.4 1114.2 1163.0 1200.0 998.7 : 18.9 85.8 201.3 316.9 383.7 402.7 432.5 469.5 518.3 585.1 633.9 700.7 786.4 816.3 902.0 968.8 1017.6 1084.4 1133.2 1170.2 1200.0 1017.6: 66.8 182.4 298.0 364.8 383.7 413.6 450.6 499.3 566.1 614.9 681.7 767.5 797.3 883.1 949.9 998.7 1065.5 1114.2 1151.2 1181.1 1200.0 1084.4: 115.6 231.2 298.0 316.9 346.8 383.7 432.5 499.3 548.1 614.9 700.7 730.5 816.3 883.1 931.8 998.7 1047.4 1084.4 1114.2 1133.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.9358 .. 115.5871 cents 96.65127 cents 18.93578 cents 2: 48.7704 .. 231.1741 cents 182.40372 cents -66.81667 cents 3: 85.7524 .. 297.9908 cents 212.23831 cents -145.42165 cents 4: 134.5228 .. 364.8074 cents 230.28459 cents -163.46793 cents 5: 201.3395 .. 383.7432 cents 182.40371 cents -163.46793 cents 6: 250.1099 .. 413.5778 cents 163.46792 cents -133.63332 cents 7: 316.9265 .. 450.5599 cents 133.63333 cents -96.65126 cents 8: 383.7432 .. 499.3302 cents 115.58705 cents -66.81667 cents 9: 432.5136 .. 566.1469 cents 133.63333 cents -66.81666 cents 10: 499.3302 .. 614.9173 cents 115.58705 cents -66.81667 cents 11: 585.0827 .. 700.6698 cents 115.58705 cents -29.83460 cents 12: 633.8531 .. 767.4864 cents 133.63333 cents -66.81667 cents 13: 700.6697 .. 816.2568 cents 115.58706 cents -66.81667 cents 14: 749.4401 .. 883.0735 cents 133.63333 cents -66.81667 cents 15: 786.4222 .. 949.8901 cents 163.46792 cents -96.65126 cents 16: 816.2568 .. 998.6605 cents 182.40371 cents -133.63332 cents 17: 835.1926 .. 1065.4772 cents 230.28459 cents -163.46793 cents 18: 902.0092 .. 1114.2476 cents 212.23831 cents -163.46793 cents 19: 968.8259 .. 1151.2296 cents 182.40372 cents -145.42165 cents 20: 1084.4129 .. 1181.0642 cents 96.65127 cents -66.81667 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 18.93578 cents, class 1 Average step (divided formal octave): 57.1429 cents Largest one step interval : 115.58705 cents Average / Smallest step : 3.017719 Largest / Average step : 2.022773 Largest / Smallest step : 6.104161 Median interval of one step : 48.77038 cents, amount: 4 Most common interval of one step : 66.81666 cents, amount: 6 Least squares average step : 56.52181 cents, oct.: 1186.95810 cents Scale is not proper Step pattern alph. order: ABCDEFBFBGDGBFBFEDCBA Step pattern size order : GEABCDEDEFBFEDEDCBAEG Scale is not a Constant Structure Scale diversity : 1.351474 Lumma stability : 0.031560 Lumma impropriety factor : 0.887156 Number of different interval sizes : 68 = 3.40000 / class Number of one step interval sizes : 7 Highest interval variety : 9 Mean interval variety : 7.10000 = 71/10 Median interval variety : 5.5 Lowest interval variety : 4 Smallest interval difference : 7.14747 cents Number of recognisable fifths : 16, average 700.6698 cents Formal octave complements present : 21 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 10-11 -- Rational properties --
FIT/MODE
21: 2 1 0 1 0 1 1 1 1 2 0 2 1 1 1 1 0 1 0 1 3 N SD: 31.7672 c. M: 55.8415 c. 22: 2 1 1 0 1 1 1 1 1 2 0 2 1 1 1 1 1 0 1 1 2 N I SD: 11.0703 c. M: 18.7673 c. 31: 3 2 0 1 1 1 2 1 2 2 1 2 2 1 2 1 1 1 0 2 3 N I SD: 5.6731 c. M: 11.1447 c. 41: 4 2 1 1 1 2 2 2 2 3 1 3 2 2 2 2 1 1 1 2 4 N I SD: 4.0667 c. M: 6.7940 c. 53: 5 3 1 1 2 2 3 2 3 4 1 4 3 2 3 2 2 1 1 3 5 N I SD: 2.5741 c. M: 4.7590 c. 72: 7 4 1 2 2 3 4 3 4 5 2 5 4 3 4 3 2 2 1 4 7 N I SD: 1.2001 c. M: 2.1592 c. 125: 12 7 2 3 4 5 7 5 7 9 3 9 7 5 7 5 4 3 2 7 12 N I SD: 0.4211 c. M: 0.7741 c. 197: 19 11 3 5 6 8 11 8 11 14 5 14 11 8 11 8 6 5 3 11 19 N I SD: 0.2189 c. M: 0.3374 c. 322: 31 18 5 8 10 13 18 13 18 23 8 23 18 13 18 13 10 8 5 18 31 N I SD: 0.1316 c. M:-0.2155 c. 519: 50 29 8 13 16 21 29 21 29 37 13 37 29 21 29 21 16 13 8 29 50 N I SD: 0.1298 c. M: 0.2552 c. 685: 66 38 11 17 21 28 38 28 38 49 17 49 38 28 38 28 21 17 11 38 66 N I SD: 0.1210 c. M: 0.2139 c. 810: 78 45 13 20 25 33 45 33 45 58 20 58 45 33 45 33 25 20 13 45 78 N I SD: 0.0945 c. M: 0.1815 c. 882: 85 49 14 22 27 36 49 36 49 63 22 63 49 36 49 36 27 22 14 49 85 N I SD: 0.0851 c. M:-0.1395 c. 1007: 97 56 16 25 31 41 56 41 56 72 25 72 56 41 56 41 31 25 16 56 97 N I SD: 0.0420 c. M: 0.0800 c. 1132: 109 63 18 28 35 46 63 46 63 81 28 81 63 46 63 46 35 28 18 63 109 N I SD: 0.0521 c. M: 0.0787 c. 1204: 116 67 19 30 37 49 67 49 67 86 30 86 67 49 67 49 37 30 19 67 116 N I SD: 0.0315 c. M:-0.0551 c. 1329: 128 74 21 33 41 54 74 54 74 95 33 95 74 54 74 54 41 33 21 74 128 N I SD: 0.0129 c. M: 0.0228 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.6426 cents 3 .. 6 match: 3 H SD: 0.6059 cents 4 .. 8 match: 4 H SD: 0.7185 cents 5 .. 10 match: 5 H SD: 0.7712 cents 6 .. 12 match: 6 H SD: 5.3117 cents 7 .. 14 match: 7 H SD: 2.8629 cents 8 .. 16 match: 8 H SD: 5.2424 cents 9 .. 18 match: 9 H SD: 4.5720 cents 10 .. 20 match: 10 H SD: 4.1012 cents 11 .. 22 match: 11 H SD: 7.6553 cents 12 .. 24 match: 11 S SD: 4.1869 cents 13 .. 26 match: 12 S SD: 6.4774 cents 14 .. 28 match: 13 S SD: 3.6352 cents 15 .. 30 match: 14 S SD: 4.0684 cents 16 .. 32 match: 15 S SD: 4.1802 cents 17 .. 34 match: 16 S SD: 4.5717 cents 18 .. 36 match: 16 S SD: 3.2408 cents 19 .. 38 match: 14 SD: 4.9320 cents 20 .. 40 match: 18 SD: 3.5050 cents 21 .. 42 match: 18 SD: 3.7713 cents 22 .. 44 match: 16 SD: 4.1414 cents 23 .. 46 match: 18 SD: 3.7491 cents 24 .. 48 match: 17 SD: 2.4776 cents 25 .. 50 match: 18 SD: 2.5962 cents 26 .. 52 match: 18 SD: 3.4139 cents 27 .. 54 match: 19 SD: 2.8192 cents 28 .. 56 match: 19 SD: 2.2008 cents 29 .. 58 match: 18 SD: 2.5157 cents 30 .. 60 match: 19 SD: 2.3425 cents 31 .. 62 match: 20 SD: 2.5511 cents 32 .. 64 match: 19 SD: 2.0725 cents 33 .. 66 match: 19 SD: 2.5320 cents 34 .. 68 match: 19 SD: 2.6656 cents 35 .. 70 match: 20 SD: 1.9757 cents 36 .. 72 match: 20 SD: 1.8665 cents 37 .. 74 match: 20 SD: 2.4020 cents 38 .. 76 match: 19 SD: 2.2285 cents 39 .. 78 match: 21 SD: 2.1401 cents 40 .. 80 match: 21 SD: 1.7296 cents 41 .. 82 match: 20 SD: 1.7900 cents 42 .. 84 match: 20 SD: 1.6121 cents 43 .. 86 match: 19 SD: 1.8547 cents 44 .. 88 match: 20 SD: 1.7590 cents 45 .. 90 match: 20 SD: 1.3852 cents 50 .. 100 match: 20 SD: 1.5253 cents 51 .. 102 match: 20 SD: 1.8851 cents 52 .. 104 match: 20 SD: 1.5791 cents 53 .. 106 match: 21 SD: 1.5770 cents 54 .. 108 match: 21 SD: 1.3015 cents 55 .. 110 match: 21 SD: 1.2827 cents 56 .. 112 match: 21 SD: 1.0733 cents 59 .. 118 match: 20 SD: 1.2431 cents 60 .. 120 match: 20 SD: 1.0210 cents 68 .. 136 match: 20 SD: 1.1323 cents 70 .. 140 match: 21 SD: 0.9460 cents 72 .. 144 match: 21 SD: 0.8849 cents 77 .. 154 match: 20 SD: 0.9476 cents 80 .. 160 match: 21 SD: 0.9191 cents 84 .. 168 match: 21 SD: 0.6815 cents 99 .. 198 match: 21 SD: 0.6733 cents 105 .. 210 match: 21 SD: 0.6120 cents 113 .. 226 match: 21 SD: 0.6071 cents 114 .. 228 match: 21 SD: 0.5932 cents 119 .. 238 match: 21 SD: 0.5686 cents 120 .. 240 match: 21 SD: 0.5036 cents 144 .. 288 match: 21 SD: 0.4410 cents 154 .. 308 match: 21 SD: 0.4383 cents 155 .. 310 match: 21 SD: 0.4357 cents 161 .. 322 match: 21 SD: 0.3448 cents 201 .. 402 match: 21 SD: 0.3194 cents 204 .. 408 match: 21 SD: 0.2785 cents 209 .. 418 match: 21 SD: 0.2763 cents 233 .. 466 match: 21 SD: 0.2440 cents 251 .. 502 match: 21 SD: 0.2247 cents 279 .. 558 match: 21 SD: 0.2178 cents 299 .. 598 match: 21 SD: 0.2087 cents 314 .. 628 match: 21 SD: 0.1988 cents 317 .. 634 match: 21 SD: 0.1909 cents 323 .. 646 match: 21 SD: 0.1785 cents 335 .. 670 match: 21 SD: 0.1620 cents 359 .. 718 match: 21 SD: 0.1493 cents 443 .. 886 match: 21 SD: 0.1446 cents 448 .. 896 match: 21 SD: 0.1237 cents 511 .. 1022 match: 21 SD: 0.1210 cents 520 .. 1040 match: 21 SD: 0.1206 cents 532 .. 1064 match: 21 SD: 0.1132 cents 567 .. 1134 match: 21 SD: 0.1098 cents 568 .. 1136 match: 21 SD: 0.0937 cents