Scala analysis: dwarf19marv
Marvelous dwarf: 1/4 kleismic dwarf(<19 30 44|) = inverse wilson1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68.745 cents 68.744546 2: 115.587 cents 115.587047 3: 200.054 cents 200.054240 4: 268.799 cents 268.798786 5: 315.641 cents 315.641287 6: 384.386 cents 384.385833 7: 431.228 cents 431.228334 8: 499.973 cents 499.972880 9: 584.440 cents 584.440073 10: 631.283 cents 631.282574 11: 700.027 cents 700.027120 12: 768.772 cents 768.771666 13: 815.614 cents 815.614167 14: 884.359 cents 884.358713 15: 931.201 cents 931.201214 16: 1015.668 cents 1015.668407 17: 1084.413 cents 1084.412953 18: 1131.255 cents 1131.255454 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 68.7445 cents 68.7445 1: 68.7445 cents 68.7445 2: 46.8425 cents 46.8425 3: 84.4672 cents 84.4672 4: 68.7445 cents 68.7445 5: 46.8425 cents 46.8425 6: 68.7445 cents 68.7445 7: 46.8425 cents 46.8425 8: 68.7445 cents 68.7445 9: 84.4672 cents 84.4672 10: 46.8425 cents 46.8425 11: 68.7445 cents 68.7445 12: 68.7445 cents 68.7445 13: 46.8425 cents 46.8425 14: 68.7445 cents 68.7445 15: 46.8425 cents 46.8425 16: 84.4672 cents 84.4672 17: 68.7445 cents 68.7445 18: 46.8425 cents 46.8425 19: 68.7445 cents 68.7445
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 46.84250 cents 1: 9 68.74455 cents 1: 3 84.46719 cents 2: 11 115.58705 cents 2: 3 131.30969 cents 2: 2 137.48909 cents 2: 3 153.21174 cents 3: 2 162.42955 cents 3: 8 184.33159 cents 3: 9 200.05424 cents 4: 5 231.17409 cents 4: 4 246.89674 cents 4: 2 253.07614 cents 4: 8 268.79879 cents 5: 4 299.91864 cents 5: 12 315.64129 cents 5: 3 337.54333 cents 6: 1 346.76114 cents 6: 3 362.48379 cents 6: 15 384.38583 cents 7: 11 431.22833 cents 7: 6 453.13038 cents 7: 2 468.85303 cents 8: 14 499.97288 cents 8: 4 515.69553 cents 8: 1 537.59757 cents 9: 5 546.81538 cents 9: 1 562.53803 cents 9: 6 568.71743 cents 9: 7 584.44007 cents 10: 7 615.55993 cents 10: 6 631.28257 cents 10: 1 637.46197 cents 10: 5 653.18462 cents 11: 1 662.40243 cents 11: 4 684.30447 cents 11: 14 700.02712 cents 12: 2 731.14697 cents 12: 6 746.86962 cents 12: 11 768.77167 cents 13: 15 815.61417 cents 13: 3 837.51621 cents 13: 1 853.23886 cents 14: 3 862.45667 cents 14: 12 884.35871 cents 14: 4 900.08136 cents 15: 8 931.20121 cents 15: 2 946.92386 cents 15: 4 953.10326 cents 15: 5 968.82591 cents 16: 9 999.94576 cents 16: 8 1015.66841 cents 16: 2 1037.57045 cents 17: 3 1046.78826 cents 17: 2 1062.51091 cents 17: 3 1068.69031 cents 17: 11 1084.41295 cents 18: 3 1115.53281 cents 18: 9 1131.25545 cents 18: 7 1153.15750 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 68.7 115.6 200.1 268.8 315.6 384.4 431.2 500.0 584.4 631.3 700.0 768.8 815.6 884.4 931.2 1015.7 1084.4 1131.3 1200.0 68.7 : 46.8 131.3 200.1 246.9 315.6 362.5 431.2 515.7 562.5 631.3 700.0 746.9 815.6 862.5 946.9 1015.7 1062.5 1131.3 1200.0 115.6 : 84.5 153.2 200.1 268.8 315.6 384.4 468.9 515.7 584.4 653.2 700.0 768.8 815.6 900.1 968.8 1015.7 1084.4 1153.2 1200.0 200.1 : 68.7 115.6 184.3 231.2 299.9 384.4 431.2 500.0 568.7 615.6 684.3 731.1 815.6 884.4 931.2 999.9 1068.7 1115.5 1200.0 268.8 : 46.8 115.6 162.4 231.2 315.6 362.5 431.2 500.0 546.8 615.6 662.4 746.9 815.6 862.5 931.2 999.9 1046.8 1131.3 1200.0 315.6 : 68.7 115.6 184.3 268.8 315.6 384.4 453.1 500.0 568.7 615.6 700.0 768.8 815.6 884.4 953.1 999.9 1084.4 1153.2 1200.0 384.4 : 46.8 115.6 200.1 246.9 315.6 384.4 431.2 500.0 546.8 631.3 700.0 746.9 815.6 884.4 931.2 1015.7 1084.4 1131.3 1200.0 431.2 : 68.7 153.2 200.1 268.8 337.5 384.4 453.1 500.0 584.4 653.2 700.0 768.8 837.5 884.4 968.8 1037.6 1084.4 1153.2 1200.0 500.0 : 84.5 131.3 200.1 268.8 315.6 384.4 431.2 515.7 584.4 631.3 700.0 768.8 815.6 900.1 968.8 1015.7 1084.4 1131.3 1200.0 584.4 : 46.8 115.6 184.3 231.2 299.9 346.8 431.2 500.0 546.8 615.6 684.3 731.1 815.6 884.4 931.2 999.9 1046.8 1115.5 1200.0 631.3 : 68.7 137.5 184.3 253.1 299.9 384.4 453.1 500.0 568.7 637.5 684.3 768.8 837.5 884.4 953.1 999.9 1068.7 1153.2 1200.0 700.0 : 68.7 115.6 184.3 231.2 315.6 384.4 431.2 500.0 568.7 615.6 700.0 768.8 815.6 884.4 931.2 999.9 1084.4 1131.3 1200.0 768.8 : 46.8 115.6 162.4 246.9 315.6 362.5 431.2 500.0 546.8 631.3 700.0 746.9 815.6 862.5 931.2 1015.7 1062.5 1131.3 1200.0 815.6 : 68.7 115.6 200.1 268.8 315.6 384.4 453.1 500.0 584.4 653.2 700.0 768.8 815.6 884.4 968.8 1015.7 1084.4 1153.2 1200.0 884.4 : 46.8 131.3 200.1 246.9 315.6 384.4 431.2 515.7 584.4 631.3 700.0 746.9 815.6 900.1 946.9 1015.7 1084.4 1131.3 1200.0 931.2 : 84.5 153.2 200.1 268.8 337.5 384.4 468.9 537.6 584.4 653.2 700.0 768.8 853.2 900.1 968.8 1037.6 1084.4 1153.2 1200.0 1015.7: 68.7 115.6 184.3 253.1 299.9 384.4 453.1 500.0 568.7 615.6 684.3 768.8 815.6 884.4 953.1 999.9 1068.7 1115.5 1200.0 1084.4: 46.8 115.6 184.3 231.2 315.6 384.4 431.2 500.0 546.8 615.6 700.0 746.9 815.6 884.4 931.2 999.9 1046.8 1131.3 1200.0 1131.3: 68.7 137.5 184.3 268.8 337.5 384.4 453.1 500.0 568.7 653.2 700.0 768.8 837.5 884.4 953.1 999.9 1084.4 1153.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 46.8425 .. 84.4672 cents 37.62469 cents 46.84250 cents 2: 115.5870 .. 153.2117 cents 37.62469 cents 31.11985 cents 3: 162.4295 .. 200.0542 cents 37.62469 cents 9.21781 cents 4: 231.1741 .. 268.7988 cents 37.62469 cents 31.11985 cents 5: 299.9186 .. 337.5433 cents 37.62469 cents 31.11985 cents 6: 346.7611 .. 384.3858 cents 37.62469 cents 9.21781 cents 7: 431.2283 .. 468.8530 cents 37.62469 cents 46.84250 cents 8: 499.9729 .. 537.5976 cents 37.62469 cents 31.11985 cents 9: 546.8154 .. 584.4401 cents 37.62469 cents 9.21781 cents 10: 615.5599 .. 653.1846 cents 37.62469 cents 31.11985 cents 11: 662.4024 .. 700.0271 cents 37.62469 cents 9.21781 cents 12: 731.1470 .. 768.7717 cents 37.62469 cents 31.11985 cents 13: 815.6142 .. 853.2389 cents 37.62469 cents 46.84250 cents 14: 862.4567 .. 900.0814 cents 37.62469 cents 9.21781 cents 15: 931.2012 .. 968.8259 cents 37.62469 cents 31.11985 cents 16: 999.9458 .. 1037.5705 cents 37.62469 cents 31.11985 cents 17: 1046.7883 .. 1084.4130 cents 37.62469 cents 9.21781 cents 18: 1115.5328 .. 1153.1575 cents 37.62469 cents 31.11985 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 46.84250 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 84.46719 cents Average / Smallest step : 1.348303 Largest / Average step : 1.337397 Largest / Smallest step : 1.803217 Median interval of one step : 68.74455 cents, amount: 9 Most common interval of one step : 68.74455 cents, amount: 9 Least squares average step : 63.22950 cents, oct.: 1201.36047 cents Scale is strictly proper Step pattern alph. order: ABCABABACBAABABCABA Step pattern size order : MSLMSMSMLSMMSMSLMSM Scale is a Constant Structure, by a margin of 9.21781 cents Scale diversity : 1.315645 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.435630 Number of different interval sizes : 60 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 6.17940 cents Most common intervals : 384.38583 cents & inv., amount: 15 Most common triad is 0.0 384.386 815.614 cents, amount: 11 Number of recognisable fifths : 14, average 700.0271 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 15 = 78.9474% -- Rational properties --
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.0678 c. M: 16.1672 c. 31: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2 P M ME I SD: 5.6673 c. M: 11.9277 c. 49: 3 2 3 3 2 3 2 2 4 2 3 2 2 3 2 3 3 2 3 P T3 SD: 6.6826 c. M: 11.5868 c. 50: 3 2 3 3 2 3 2 3 3 2 3 3 2 3 2 3 3 2 3 SP M ME I SD: 4.6712 c. M: 8.4401 c. 53: 3 2 4 3 2 3 2 3 4 2 3 3 2 3 2 4 3 2 3 P T3 SD: 2.1994 c. M:-4.2392 c. 72: 4 3 5 4 3 4 3 4 5 3 4 4 3 4 3 5 4 3 4 SP T3 SD: 1.4450 c. M: 2.1321 c. 103: 6 4 7 6 4 6 4 6 7 4 6 6 4 6 4 7 6 4 6 SP SD: 1.1869 c. M: 2.1564 c. 125: 7 5 9 7 5 7 5 7 9 5 7 7 5 7 5 9 7 5 7 SP T3 SD: 1.1068 c. M:-2.3174 c. 156: 9 6 11 9 6 9 6 9 11 6 9 9 6 9 6 11 9 6 9 SP SD: 0.3217 c. M: 0.5133 c. 228: 13 9 16 13 9 13 9 13 16 9 13 13 9 13 9 16 13 9 13 SP SD: 0.2392 c. M: 0.3777 c. 384: 22 15 27 22 15 22 15 22 27 15 22 22 15 22 15 27 22 15 22 SP SD: 0.0332 c. M: 0.0651 c. 1973: 113 77 139 113 77 113 77 113 139 77 113 113 77 113 77 139 113 77 113 SP SD: 0.0274 c. M:-0.0506 c. 2357: 135 92 166 135 92 135 92 135 166 92 135 135 92 135 92 166 135 92 135 SP SD: 0.0178 c. M:-0.0317 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.9639 cents 3 .. 6 match: 3 H SD: 0.6426 cents 4 .. 8 match: 4 H SD: 9.4308 cents 5 .. 10 match: 5 H SD: 0.6678 cents 6 .. 12 match: 6 H SD: 5.6433 cents 7 .. 14 match: 7 H SD: 5.5827 cents 8 .. 16 match: 8 H SD: 7.0384 cents 9 .. 18 match: 9 H SD: 5.0033 cents 10 .. 20 match: 10 H SD: 4.8288 cents 11 .. 22 match: 11 H SD: 6.7291 cents 12 .. 24 match: 12 H SD: 5.1809 cents 13 .. 26 match: 13 H SD: 5.9085 cents 14 .. 28 match: 14 H SD: 4.2767 cents 15 .. 30 match: 15 H SD: 3.7628 cents 16 .. 32 match: 15 SD: 4.1732 cents 17 .. 34 match: 15 SD: 4.4687 cents 18 .. 36 match: 17 S SD: 3.4356 cents 19 .. 38 match: 15 SD: 5.3414 cents 20 .. 40 match: 18 S SD: 3.7717 cents 21 .. 42 match: 17 SD: 3.7713 cents 22 .. 44 match: 18 SD: 4.1210 cents 23 .. 46 match: 19 SD: 3.6276 cents 24 .. 48 match: 19 SD: 2.6532 cents 25 .. 50 match: 19 SD: 2.2272 cents 27 .. 54 match: 18 SD: 2.8449 cents 28 .. 56 match: 19 SD: 2.7138 cents 29 .. 58 match: 19 SD: 2.6836 cents 30 .. 60 match: 19 SD: 2.2358 cents 39 .. 78 match: 19 SD: 2.0868 cents 40 .. 80 match: 19 SD: 1.8652 cents 41 .. 82 match: 19 SD: 1.8389 cents 45 .. 90 match: 19 SD: 1.6112 cents 48 .. 96 match: 19 SD: 1.2941 cents 60 .. 120 match: 19 SD: 1.1291 cents 70 .. 140 match: 19 SD: 1.0277 cents 72 .. 144 match: 19 SD: 0.9248 cents 75 .. 150 match: 19 SD: 0.8365 cents 84 .. 168 match: 19 SD: 0.7970 cents 90 .. 180 match: 19 SD: 0.7815 cents 96 .. 192 match: 19 SD: 0.7757 cents 99 .. 198 match: 19 SD: 0.7578 cents 100 .. 200 match: 19 SD: 0.5835 cents 114 .. 228 match: 19 SD: 0.5695 cents 120 .. 240 match: 19 SD: 0.5335 cents 125 .. 250 match: 19 SD: 0.4956 cents 145 .. 290 match: 19 SD: 0.4487 cents 149 .. 298 match: 19 SD: 0.4320 cents 170 .. 340 match: 19 SD: 0.3853 cents 173 .. 346 match: 19 SD: 0.3666 cents 201 .. 402 match: 19 SD: 0.3438 cents 202 .. 404 match: 19 SD: 0.3306 cents 204 .. 408 match: 19 SD: 0.3160 cents 219 .. 438 match: 19 SD: 0.2968 cents 244 .. 488 match: 19 SD: 0.2778 cents 245 .. 490 match: 19 SD: 0.2596 cents 261 .. 522 match: 19 SD: 0.2323 cents 286 .. 572 match: 19 SD: 0.2311 cents 293 .. 586 match: 19 SD: 0.2111 cents 319 .. 638 match: 19 SD: 0.2085 cents 346 .. 692 match: 19 SD: 0.1938 cents 350 .. 700 match: 19 SD: 0.1910 cents 361 .. 722 match: 19 SD: 0.1797 cents 375 .. 750 match: 19 SD: 0.1679 cents 418 .. 836 match: 19 SD: 0.1672 cents 421 .. 842 match: 19 SD: 0.1621 cents 424 .. 848 match: 19 SD: 0.1582 cents 434 .. 868 match: 19 SD: 0.1571 cents 435 .. 870 match: 19 SD: 0.1475 cents 463 .. 926 match: 19 SD: 0.1459 cents 465 .. 930 match: 19 SD: 0.1430 cents 466 .. 932 match: 19 SD: 0.1308 cents 490 .. 980 match: 19 SD: 0.1228 cents 495 .. 990 match: 19 SD: 0.1205 cents 540 .. 1080 match: 19 SD: 0.1101 cents 570 .. 1140 match: 19 SD: 0.1080 cents 595 .. 1190 match: 19 SD: 0.0964 cents