Scala analysis: marvbiz
1/4 kleismic tempered marvel "byzantine" scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 84.467 cents 84.467193 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: 615.560 cents 615.559927 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: 999.946 cents 999.945760 17: 1084.413 cents 1084.412953 18: 1115.533 cents 1115.532807 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 84.4672 cents 84.4672 1: 84.4672 cents 84.4672 2: 31.1199 cents 31.1199 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: 31.1199 cents 31.1199 11: 84.4672 cents 84.4672 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: 68.7445 cents 68.7445 17: 84.4672 cents 84.4672 18: 31.1199 cents 31.1199 19: 84.4672 cents 84.4672
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 31.11985 cents 1: 4 46.84250 cents 1: 6 68.74455 cents 1: 6 84.46719 cents 2: 14 115.58705 cents 2: 4 153.21174 cents 2: 1 168.93439 cents 3: 2 162.42955 cents 3: 8 184.33159 cents 3: 9 200.05424 cents 4: 9 231.17409 cents 4: 8 268.79879 cents 4: 2 284.52143 cents 5: 6 299.91864 cents 5: 10 315.64129 cents 5: 1 337.54333 cents 5: 2 353.26598 cents 6: 4 346.76114 cents 6: 12 384.38583 cents 6: 3 400.10848 cents 7: 4 415.50569 cents 7: 7 431.22833 cents 7: 2 453.13038 cents 7: 6 468.85303 cents 8: 14 499.97288 cents 8: 4 515.69553 cents 8: 1 537.59757 cents 9: 2 531.09273 cents 9: 4 546.81538 cents 9: 3 568.71743 cents 9: 10 584.44007 cents 10: 10 615.55993 cents 10: 3 631.28257 cents 10: 4 653.18462 cents 10: 2 668.90727 cents 11: 1 662.40243 cents 11: 4 684.30447 cents 11: 14 700.02712 cents 12: 6 731.14697 cents 12: 2 746.86962 cents 12: 7 768.77167 cents 12: 4 784.49431 cents 13: 3 799.89152 cents 13: 12 815.61417 cents 13: 4 853.23886 cents 14: 2 846.73402 cents 14: 1 862.45667 cents 14: 10 884.35871 cents 14: 6 900.08136 cents 15: 2 915.47857 cents 15: 8 931.20121 cents 15: 9 968.82591 cents 16: 9 999.94576 cents 16: 8 1015.66841 cents 16: 2 1037.57045 cents 17: 1 1031.06561 cents 17: 4 1046.78826 cents 17: 14 1084.41295 cents 18: 6 1115.53281 cents 18: 6 1131.25545 cents 18: 4 1153.15750 cents 18: 3 1168.88015 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.44444 = 31/9
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 : 84.5 115.6 200.1 268.8 315.6 384.4 431.2 500.0 584.4 615.6 700.0 768.8 815.6 884.4 931.2 999.9 1084.4 1115.5 1200.0 84.5 : 31.1 115.6 184.3 231.2 299.9 346.8 415.5 500.0 531.1 615.6 684.3 731.1 799.9 846.7 915.5 999.9 1031.1 1115.5 1200.0 115.6 : 84.5 153.2 200.1 268.8 315.6 384.4 468.9 500.0 584.4 653.2 700.0 768.8 815.6 884.4 968.8 999.9 1084.4 1168.9 1200.0 200.1 : 68.7 115.6 184.3 231.2 299.9 384.4 415.5 500.0 568.7 615.6 684.3 731.1 799.9 884.4 915.5 999.9 1084.4 1115.5 1200.0 268.8 : 46.8 115.6 162.4 231.2 315.6 346.8 431.2 500.0 546.8 615.6 662.4 731.1 815.6 846.7 931.2 1015.7 1046.8 1131.3 1200.0 315.6 : 68.7 115.6 184.3 268.8 299.9 384.4 453.1 500.0 568.7 615.6 684.3 768.8 799.9 884.4 968.8 999.9 1084.4 1153.2 1200.0 384.4 : 46.8 115.6 200.1 231.2 315.6 384.4 431.2 500.0 546.8 615.6 700.0 731.1 815.6 900.1 931.2 1015.7 1084.4 1131.3 1200.0 431.2 : 68.7 153.2 184.3 268.8 337.5 384.4 453.1 500.0 568.7 653.2 684.3 768.8 853.2 884.4 968.8 1037.6 1084.4 1153.2 1200.0 500.0 : 84.5 115.6 200.1 268.8 315.6 384.4 431.2 500.0 584.4 615.6 700.0 784.5 815.6 900.1 968.8 1015.7 1084.4 1131.3 1200.0 584.4 : 31.1 115.6 184.3 231.2 299.9 346.8 415.5 500.0 531.1 615.6 700.0 731.1 815.6 884.4 931.2 999.9 1046.8 1115.5 1200.0 615.6 : 84.5 153.2 200.1 268.8 315.6 384.4 468.9 500.0 584.4 668.9 700.0 784.5 853.2 900.1 968.8 1015.7 1084.4 1168.9 1200.0 700.0 : 68.7 115.6 184.3 231.2 299.9 384.4 415.5 500.0 584.4 615.6 700.0 768.8 815.6 884.4 931.2 999.9 1084.4 1115.5 1200.0 768.8 : 46.8 115.6 162.4 231.2 315.6 346.8 431.2 515.7 546.8 631.3 700.0 746.9 815.6 862.5 931.2 1015.7 1046.8 1131.3 1200.0 815.6 : 68.7 115.6 184.3 268.8 299.9 384.4 468.9 500.0 584.4 653.2 700.0 768.8 815.6 884.4 968.8 999.9 1084.4 1153.2 1200.0 884.4 : 46.8 115.6 200.1 231.2 315.6 400.1 431.2 515.7 584.4 631.3 700.0 746.9 815.6 900.1 931.2 1015.7 1084.4 1131.3 1200.0 931.2 : 68.7 153.2 184.3 268.8 353.3 384.4 468.9 537.6 584.4 653.2 700.0 768.8 853.2 884.4 968.8 1037.6 1084.4 1153.2 1200.0 999.9 : 84.5 115.6 200.1 284.5 315.6 400.1 468.9 515.7 584.4 631.3 700.0 784.5 815.6 900.1 968.8 1015.7 1084.4 1131.3 1200.0 1084.4: 31.1 115.6 200.1 231.2 315.6 384.4 431.2 500.0 546.8 615.6 700.0 731.1 815.6 884.4 931.2 999.9 1046.8 1115.5 1200.0 1115.5: 84.5 168.9 200.1 284.5 353.3 400.1 468.9 515.7 584.4 668.9 700.0 784.5 853.2 900.1 968.8 1015.7 1084.4 1168.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1199 .. 84.4672 cents 53.34734 cents 31.11985 cents 2: 115.5870 .. 168.9344 cents 53.34734 cents 31.11985 cents 3: 162.4295 .. 200.0542 cents 37.62469 cents -6.50484 cents 4: 231.1741 .. 284.5214 cents 53.34734 cents 31.11985 cents 5: 299.9186 .. 353.2660 cents 53.34734 cents 15.39721 cents 6: 346.7611 .. 400.1085 cents 53.34734 cents -6.50484 cents 7: 415.5057 .. 468.8530 cents 53.34734 cents 15.39721 cents 8: 499.9729 .. 537.5976 cents 37.62469 cents 31.11985 cents 9: 531.0927 .. 584.4401 cents 53.34734 cents -6.50484 cents 10: 615.5599 .. 668.9073 cents 53.34734 cents 31.11985 cents 11: 662.4024 .. 700.0271 cents 37.62469 cents -6.50484 cents 12: 731.1470 .. 784.4943 cents 53.34734 cents 31.11985 cents 13: 799.8915 .. 853.2389 cents 53.34734 cents 15.39721 cents 14: 846.7340 .. 900.0814 cents 53.34734 cents -6.50484 cents 15: 915.4786 .. 968.8259 cents 53.34734 cents 15.39721 cents 16: 999.9458 .. 1037.5705 cents 37.62469 cents 31.11985 cents 17: 1031.0656 .. 1084.4130 cents 53.34734 cents -6.50484 cents 18: 1115.5328 .. 1168.8801 cents 53.34734 cents 31.11985 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 31.11985 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 84.46719 cents Average / Smallest step : 2.029505 Largest / Average step : 1.337397 Largest / Smallest step : 2.714254 Median interval of one step : 68.74455 cents, amount: 6 Least squares average step : 62.95578 cents, oct.: 1196.15990 cents Scale is not proper Step pattern alph. order: ABACDCDCABACDCDCABA Step pattern size order : DADCBCBCDADCBCBCDAD Scale is a Constant Structure, by a margin of 6.50484 cents Scale diversity : 1.341138 Lumma stability : 0.284723 Lumma impropriety factor : 0.032524 Number of different interval sizes : 62 = 3.44444 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.44444 = 31/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 6.50484 cents Number of recognisable fifths : 14, average 700.0271 cents Scale contains two identical conjunct "tetrachords" of 9 notes Formal octave complements present : 19 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- 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: 12.0308 c. M: 21.3093 c. 24: 2 0 2 1 1 2 1 1 2 0 2 1 1 2 1 1 2 0 2 N D3 I SD: 14.2184 c. M: 18.7988 c. 25: 2 0 2 2 1 1 1 1 2 1 2 1 1 1 1 2 2 0 2 N T3 I SD: 13.9004 c. M:-20.3587 c. 27: 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 N D3 I SD: 12.2975 c. M:-22.1680 c. 28: 2 1 2 1 1 2 1 2 2 0 2 2 1 2 1 1 2 1 2 N D3 I SD: 11.2810 c. M:-15.6413 c. 30: 2 1 2 2 1 2 1 1 3 0 3 1 1 2 1 2 2 1 2 N I SD: 10.9817 c. M:-19.9729 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: 4.5224 c. M: 7.0478 c. 41: 3 1 3 2 2 2 2 2 3 1 3 2 2 2 2 2 3 1 3 P D3 I SD: 4.4494 c. M:-7.7961 c. 53: 4 1 4 3 2 3 2 3 4 1 4 3 2 3 2 3 4 1 4 N I SD: 3.0723 c. M:-6.0988 c. 72: 5 2 5 4 3 4 3 4 5 2 5 4 3 4 3 4 5 2 5 P I SD: 1.2488 c. M: 2.1321 c. 125: 9 3 9 7 5 7 5 7 9 3 9 7 5 7 5 7 9 3 9 N I SD: 1.0415 c. M:-1.9328 c. 156: 11 4 11 9 6 9 6 9 11 4 11 9 6 9 6 9 11 4 11 N I SD: 0.2541 c. M: 0.4591 c. 228: 16 6 16 13 9 13 9 13 16 6 16 13 9 13 9 13 16 6 16 N I SD: 0.2251 c. M: 0.3777 c. 384: 27 10 27 22 15 22 15 22 27 10 27 22 15 22 15 22 27 10 27 N I SD: 0.0471 c. M:-0.0922 c. 924: 65 24 65 53 36 53 36 53 65 24 65 53 36 53 36 53 65 24 65 N I SD: 0.0406 c. M: 0.0595 c. 1308: 92 34 92 75 51 75 51 75 92 34 92 75 51 75 51 75 92 34 92 N I SD: 0.0367 c. M:-0.0635 c. 2201: 155 57 155 126 86 126 86 126 155 57 155 126 86 126 86 126 155 57 155 N I SD: 0.0254 c. M:-0.0398 c. 2357: 166 61 166 135 92 135 92 135 166 61 166 135 92 135 92 135 166 61 166 N I SD: 0.0233 c. M:-0.0470 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: 7.8098 cents 5 .. 10 match: 5 H SD: 3.5720 cents 6 .. 12 match: 6 H SD: 5.8681 cents 7 .. 14 match: 7 H SD: 5.2305 cents 8 .. 16 match: 8 H SD: 6.5232 cents 9 .. 18 match: 9 H SD: 4.9783 cents 10 .. 20 match: 10 H SD: 4.7498 cents 11 .. 22 match: 11 H SD: 7.6086 cents 12 .. 24 match: 12 H SD: 4.8709 cents 13 .. 26 match: 13 H SD: 6.2484 cents 14 .. 28 match: 14 H SD: 4.3456 cents 15 .. 30 match: 15 H SD: 4.4297 cents 16 .. 32 match: 14 SD: 4.8265 cents 17 .. 34 match: 14 SD: 4.4124 cents 18 .. 36 match: 16 S SD: 3.1821 cents 19 .. 38 match: 14 SD: 4.8661 cents 20 .. 40 match: 18 S SD: 3.8930 cents 21 .. 42 match: 17 SD: 3.6291 cents 22 .. 44 match: 17 SD: 4.0621 cents 23 .. 46 match: 19 SD: 3.5930 cents 24 .. 48 match: 18 SD: 2.6108 cents 27 .. 54 match: 17 SD: 3.2978 cents 28 .. 56 match: 19 SD: 2.8484 cents 29 .. 58 match: 18 SD: 3.1208 cents 30 .. 60 match: 18 SD: 2.3479 cents 31 .. 62 match: 18 SD: 2.5020 cents 32 .. 64 match: 18 SD: 2.0551 cents 33 .. 66 match: 18 SD: 2.5474 cents 34 .. 68 match: 18 SD: 2.7217 cents 35 .. 70 match: 18 SD: 2.1086 cents 36 .. 72 match: 18 SD: 2.0438 cents 40 .. 80 match: 19 SD: 1.5985 cents 42 .. 84 match: 19 SD: 1.5130 cents 50 .. 100 match: 18 SD: 1.6292 cents 54 .. 108 match: 19 SD: 1.4337 cents 56 .. 112 match: 19 SD: 1.2390 cents 59 .. 118 match: 19 SD: 1.2009 cents 60 .. 120 match: 19 SD: 0.9184 cents 75 .. 150 match: 19 SD: 0.9124 cents 84 .. 168 match: 19 SD: 0.6955 cents 100 .. 200 match: 19 SD: 0.6442 cents 105 .. 210 match: 19 SD: 0.6103 cents 114 .. 228 match: 19 SD: 0.5649 cents 120 .. 240 match: 19 SD: 0.5351 cents 138 .. 276 match: 19 SD: 0.5137 cents 141 .. 282 match: 19 SD: 0.4803 cents 145 .. 290 match: 19 SD: 0.4604 cents 155 .. 310 match: 19 SD: 0.4447 cents 156 .. 312 match: 19 SD: 0.3837 cents 180 .. 360 match: 19 SD: 0.3732 cents 197 .. 394 match: 19 SD: 0.3583 cents 201 .. 402 match: 19 SD: 0.2901 cents 220 .. 440 match: 19 SD: 0.2900 cents 244 .. 488 match: 19 SD: 0.2748 cents 261 .. 522 match: 19 SD: 0.1958 cents 358 .. 716 match: 19 SD: 0.1853 cents 361 .. 722 match: 19 SD: 0.1644 cents 379 .. 758 match: 19 SD: 0.1640 cents 417 .. 834 match: 19 SD: 0.1523 cents 435 .. 870 match: 19 SD: 0.1355 cents 463 .. 926 match: 19 SD: 0.1331 cents 480 .. 960 match: 19 SD: 0.1270 cents 495 .. 990 match: 19 SD: 0.1269 cents 540 .. 1080 match: 19 SD: 0.1168 cents 555 .. 1110 match: 19 SD: 0.1043 cents 580 .. 1160 match: 19 SD: 0.0982 cents