Scala analysis: stellar
stellar scale in 1/4 kleismic marvel tempering
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 115.587 cents 115.587047 2: 153.212 cents 153.211740 3: 200.054 cents 200.054240 4: 231.174 cents 231.174094 5: 268.799 cents 268.798786 6: 315.641 cents 315.641287 7: 384.386 cents 384.385833 8: 468.853 cents 468.853027 9: 499.973 cents 499.972880 10: 584.440 cents 584.440073 11: 615.560 cents 615.559927 12: 700.027 cents 700.027120 13: 768.772 cents 768.771666 14: 815.614 cents 815.614167 15: 853.239 cents 853.238860 16: 884.359 cents 884.358713 17: 931.201 cents 931.201214 18: 968.826 cents 968.825906 19: 1084.413 cents 1084.412953 20: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 115.5870 cents 115.5870 1: 115.5870 cents 115.5870 2: 37.6247 cents 37.6247 3: 46.8425 cents 46.8425 4: 31.1199 cents 31.1199 5: 37.6247 cents 37.6247 6: 46.8425 cents 46.8425 7: 68.7445 cents 68.7445 8: 84.4672 cents 84.4672 9: 31.1199 cents 31.1199 10: 84.4672 cents 84.4672 11: 31.1199 cents 31.1199 12: 84.4672 cents 84.4672 13: 68.7445 cents 68.7445 14: 46.8425 cents 46.8425 15: 37.6247 cents 37.6247 16: 31.1199 cents 31.1199 17: 46.8425 cents 46.8425 18: 37.6247 cents 37.6247 19: 115.5870 cents 115.5870 20: 115.5870 cents 115.5870
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 31.11985 cents 1: 4 37.62469 cents 1: 4 46.84250 cents 1: 2 68.74455 cents 1: 3 84.46719 cents 1: 3 115.58705 cents 2: 2 68.74455 cents 2: 2 77.96235 cents 2: 4 84.46719 cents 2: 6 115.58705 cents 2: 4 153.21174 cents 2: 2 231.17409 cents 3: 6 115.58705 cents 3: 1 146.70690 cents 3: 2 153.21174 cents 3: 2 184.33159 cents 3: 6 200.05424 cents 3: 2 268.79879 cents 3: 1 346.76114 cents 4: 2 153.21174 cents 4: 2 162.42955 cents 4: 2 184.33159 cents 4: 6 231.17409 cents 4: 2 237.67893 cents 4: 2 268.79879 cents 4: 2 315.64129 cents 4: 2 384.38583 cents 5: 2 200.05424 cents 5: 2 231.17409 cents 5: 6 268.79879 cents 5: 2 299.91864 cents 5: 3 315.64129 cents 5: 2 346.76114 cents 5: 1 422.01053 cents 5: 2 431.22833 cents 6: 2 268.79879 cents 6: 2 299.91864 cents 6: 4 315.64129 cents 6: 2 346.76114 cents 6: 2 353.26598 cents 6: 4 384.38583 cents 6: 2 462.34819 cents 6: 2 468.85303 cents 7: 2 346.76114 cents 7: 2 353.26598 cents 7: 6 384.38583 cents 7: 4 431.22833 cents 7: 1 453.13038 cents 7: 4 499.97288 cents 7: 1 515.69553 cents 8: 2 384.38583 cents 8: 2 415.50569 cents 8: 2 431.22833 cents 8: 4 468.85303 cents 8: 4 499.97288 cents 8: 2 537.59757 cents 8: 4 546.81538 cents 9: 2 462.34819 cents 9: 2 468.85303 cents 9: 4 499.97288 cents 9: 2 537.59757 cents 9: 1 546.81538 cents 9: 1 577.93523 cents 9: 6 584.44007 cents 9: 2 615.55993 cents 10: 2 499.97288 cents 10: 2 546.81538 cents 10: 2 568.71743 cents 10: 4 584.44007 cents 10: 4 615.55993 cents 10: 2 631.28257 cents 10: 2 653.18462 cents 10: 2 700.02712 cents 11: 2 584.44007 cents 11: 6 615.55993 cents 11: 1 622.06477 cents 11: 1 653.18462 cents 11: 2 662.40243 cents 11: 4 700.02712 cents 11: 2 731.14697 cents 11: 2 737.65181 cents 12: 4 653.18462 cents 12: 2 662.40243 cents 12: 4 700.02712 cents 12: 4 731.14697 cents 12: 2 768.77167 cents 12: 2 784.49431 cents 12: 2 815.61417 cents 13: 1 684.30447 cents 13: 4 700.02712 cents 13: 1 746.86962 cents 13: 4 768.77167 cents 13: 6 815.61417 cents 13: 2 846.73402 cents 13: 2 853.23886 cents 14: 2 731.14697 cents 14: 2 737.65181 cents 14: 4 815.61417 cents 14: 2 846.73402 cents 14: 2 853.23886 cents 14: 4 884.35871 cents 14: 2 900.08136 cents 14: 2 931.20121 cents 15: 2 768.77167 cents 15: 1 777.98947 cents 15: 2 853.23886 cents 15: 3 884.35871 cents 15: 2 900.08136 cents 15: 6 931.20121 cents 15: 2 968.82591 cents 15: 2 999.94576 cents 16: 2 815.61417 cents 16: 2 884.35871 cents 16: 2 931.20121 cents 16: 2 962.32107 cents 16: 6 968.82591 cents 16: 2 1015.66841 cents 16: 2 1037.57045 cents 16: 2 1046.78826 cents 17: 1 853.23886 cents 17: 2 931.20121 cents 17: 6 999.94576 cents 17: 2 1015.66841 cents 17: 2 1046.78826 cents 17: 1 1053.29310 cents 17: 6 1084.41295 cents 18: 2 968.82591 cents 18: 4 1046.78826 cents 18: 6 1084.41295 cents 18: 4 1115.53281 cents 18: 2 1122.03765 cents 18: 2 1131.25545 cents 19: 3 1084.41295 cents 19: 3 1115.53281 cents 19: 2 1131.25545 cents 19: 4 1153.15750 cents 19: 4 1162.37531 cents 19: 4 1168.88015 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.26316 = 138/19
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.0 : 115.6 153.2 200.1 231.2 268.8 315.6 384.4 468.9 500.0 584.4 615.6 700.0 768.8 815.6 853.2 884.4 931.2 968.8 1084.4 1200.0 115.6 : 37.6 84.5 115.6 153.2 200.1 268.8 353.3 384.4 468.9 500.0 584.4 653.2 700.0 737.7 768.8 815.6 853.2 968.8 1084.4 1200.0 153.2 : 46.8 78.0 115.6 162.4 231.2 315.6 346.8 431.2 462.3 546.8 615.6 662.4 700.0 731.1 778.0 815.6 931.2 1046.8 1162.4 1200.0 200.1 : 31.1 68.7 115.6 184.3 268.8 299.9 384.4 415.5 500.0 568.7 615.6 653.2 684.3 731.1 768.8 884.4 999.9 1115.5 1153.2 1200.0 231.2 : 37.6 84.5 153.2 237.7 268.8 353.3 384.4 468.9 537.6 584.4 622.1 653.2 700.0 737.7 853.2 968.8 1084.4 1122.0 1168.9 1200.0 268.8 : 46.8 115.6 200.1 231.2 315.6 346.8 431.2 500.0 546.8 584.4 615.6 662.4 700.0 815.6 931.2 1046.8 1084.4 1131.3 1162.4 1200.0 315.6 : 68.7 153.2 184.3 268.8 299.9 384.4 453.1 500.0 537.6 568.7 615.6 653.2 768.8 884.4 999.9 1037.6 1084.4 1115.5 1153.2 1200.0 384.4 : 84.5 115.6 200.1 231.2 315.6 384.4 431.2 468.9 500.0 546.8 584.4 700.0 815.6 931.2 968.8 1015.7 1046.8 1084.4 1131.3 1200.0 468.9 : 31.1 115.6 146.7 231.2 299.9 346.8 384.4 415.5 462.3 500.0 615.6 731.1 846.7 884.4 931.2 962.3 999.9 1046.8 1115.5 1200.0 500.0 : 84.5 115.6 200.1 268.8 315.6 353.3 384.4 431.2 468.9 584.4 700.0 815.6 853.2 900.1 931.2 968.8 1015.7 1084.4 1168.9 1200.0 584.4 : 31.1 115.6 184.3 231.2 268.8 299.9 346.8 384.4 500.0 615.6 731.1 768.8 815.6 846.7 884.4 931.2 999.9 1084.4 1115.5 1200.0 615.6 : 84.5 153.2 200.1 237.7 268.8 315.6 353.3 468.9 584.4 700.0 737.7 784.5 815.6 853.2 900.1 968.8 1053.3 1084.4 1168.9 1200.0 700.0 : 68.7 115.6 153.2 184.3 231.2 268.8 384.4 500.0 615.6 653.2 700.0 731.1 768.8 815.6 884.4 968.8 999.9 1084.4 1115.5 1200.0 768.8 : 46.8 84.5 115.6 162.4 200.1 315.6 431.2 546.8 584.4 631.3 662.4 700.0 746.9 815.6 900.1 931.2 1015.7 1046.8 1131.3 1200.0 815.6 : 37.6 68.7 115.6 153.2 268.8 384.4 500.0 537.6 584.4 615.6 653.2 700.0 768.8 853.2 884.4 968.8 999.9 1084.4 1153.2 1200.0 853.2 : 31.1 78.0 115.6 231.2 346.8 462.3 500.0 546.8 577.9 615.6 662.4 731.1 815.6 846.7 931.2 962.3 1046.8 1115.5 1162.4 1200.0 884.4 : 46.8 84.5 200.1 315.6 431.2 468.9 515.7 546.8 584.4 631.3 700.0 784.5 815.6 900.1 931.2 1015.7 1084.4 1131.3 1168.9 1200.0 931.2 : 37.6 153.2 268.8 384.4 422.0 468.9 500.0 537.6 584.4 653.2 737.7 768.8 853.2 884.4 968.8 1037.6 1084.4 1122.0 1153.2 1200.0 968.8 : 115.6 231.2 346.8 384.4 431.2 462.3 500.0 546.8 615.6 700.0 731.1 815.6 846.7 931.2 999.9 1046.8 1084.4 1115.5 1162.4 1200.0 1084.4: 115.6 231.2 268.8 315.6 346.8 384.4 431.2 500.0 584.4 615.6 700.0 731.1 815.6 884.4 931.2 968.8 999.9 1046.8 1084.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1199 .. 115.5870 cents 84.46719 cents 31.11985 cents 2: 68.7445 .. 231.1741 cents 162.42955 cents -46.84250 cents 3: 115.5870 .. 346.7611 cents 231.17409 cents -115.58705 cents 4: 153.2117 .. 384.3858 cents 231.17409 cents -193.54940 cents 5: 200.0542 .. 431.2283 cents 231.17409 cents -184.33159 cents 6: 268.7988 .. 468.8530 cents 200.05424 cents -162.42955 cents 7: 346.7611 .. 515.6955 cents 168.93439 cents -122.09189 cents 8: 384.3858 .. 546.8154 cents 162.42955 cents -131.30969 cents 9: 462.3482 .. 615.5599 cents 153.21174 cents -84.46719 cents 10: 499.9729 .. 700.0271 cents 200.05424 cents -115.58705 cents 11: 584.4401 .. 737.6518 cents 153.21174 cents -115.58705 cents 12: 653.1846 .. 815.6142 cents 162.42955 cents -84.46719 cents 13: 684.3045 .. 853.2389 cents 168.93439 cents -131.30969 cents 14: 731.1470 .. 931.2012 cents 200.05424 cents -122.09189 cents 15: 768.7717 .. 999.9458 cents 231.17409 cents -162.42955 cents 16: 815.6142 .. 1046.7883 cents 231.17409 cents -184.33159 cents 17: 853.2389 .. 1084.4130 cents 231.17409 cents -193.54940 cents 18: 968.8259 .. 1131.2555 cents 162.42955 cents -115.58705 cents 19: 1084.4130 .. 1168.8801 cents 84.46719 cents -46.84250 cents
SHOW DATA
Number of notes : 20 -- Interval properties -- Smallest interval : 31.11985 cents, class 1 Average step (divided formal octave): 60.0000 cents Largest one step interval : 115.58705 cents Average / Smallest step : 1.928030 Largest / Average step : 1.926451 Largest / Smallest step : 3.714254 Median interval of one step : 46.84250 cents, amount: 4 Least squares average step : 56.92542 cents, oct.: 1138.50845 cents Scale is not proper Step pattern alph. order: ABCDBCEFDFDFECBDCBAA Step pattern size order : FBCABCDEAEAEDCBACBFF Scale is not a Constant Structure Scale diversity : 1.309547 Lumma stability : 0.051866 Lumma impropriety factor : 0.885426 Number of different interval sizes : 66 = 3.47368 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 7.26316 = 138/19 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 6.50484 cents Most common intervals : 115.58705 cents & inv., amount: 15 Most common triad is 0.0 115.587 1084.413 cents, amount: 10 Number of recognisable fifths : 14, average 700.0271 cents Formal octave complements present : 15 = 75.0000% Limited inverse transpositions : 19 Inversional symmetry on intervals : 9-10 19-20 -- Rational properties --
FIT/MODE
20: 1 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 2 2 N SD: 33.4277 c. M: 55.5870 c. 21: 2 1 1 0 1 1 1 1 1 1 1 1 1 1 1 0 1 1 2 2 N SD: 16.2412 c. M:-28.5172 c. 22: 2 1 1 0 1 1 1 2 0 2 0 2 1 1 1 0 1 1 2 2 N SD: 11.6514 c. M:-22.0561 c. 25: 2 1 1 1 1 1 1 2 0 2 1 2 1 1 1 0 1 1 3 2 N SD: 13.8210 c. M:-20.3587 c. 27: 3 0 2 0 1 1 2 2 0 2 1 2 1 1 1 1 1 1 2 3 N SD: 12.6538 c. M:-22.1680 c. 30: 3 1 1 1 1 1 2 2 0 3 0 3 1 1 1 1 1 1 3 3 N SD: 11.5669 c. M:-19.9729 c. 31: 3 1 1 1 1 1 2 2 1 2 1 2 2 1 1 1 1 1 3 3 N SD: 3.4926 c. M: 6.5059 c. 53: 5 2 2 1 2 2 3 4 1 4 1 4 3 2 2 1 2 2 5 5 N SD: 3.5914 c. M:-7.1385 c. 72: 7 2 3 2 2 3 4 5 2 5 2 5 4 3 2 2 3 2 7 7 N SD: 1.6961 c. M: 3.2389 c. 103: 10 3 4 3 3 4 6 7 3 7 3 7 6 4 3 3 4 3 10 10 N SD: 1.4866 c. M: 2.8336 c. 125: 12 4 5 3 4 5 7 9 3 9 3 9 7 5 4 3 5 4 12 12 N SD: 0.8730 c. M:-1.5470 c. 156: 15 5 6 4 5 6 9 11 4 11 4 11 9 6 5 4 6 5 15 15 N SD: 0.3325 c. M:-0.6344 c. 228: 22 7 9 6 7 9 13 16 6 16 6 16 13 9 7 6 9 7 22 22 N SD: 0.3103 c. M: 0.6073 c. 353: 34 11 14 9 11 14 20 25 9 25 9 25 20 14 11 9 14 11 34 34 N SD: 0.2886 c. M:-0.5123 c. 384: 37 12 15 10 12 15 22 27 10 27 10 27 22 15 12 10 15 12 37 37 N SD: 0.0567 c. M: 0.1139 c. 924: 89 29 36 24 29 36 53 65 24 65 24 65 53 36 29 24 36 29 89 89 N SD: 0.0327 c. M:-0.0595 c. 1308: 126 41 51 34 41 51 75 92 34 92 34 92 75 51 41 34 51 41 126 126 N SD: 0.0291 c. M: 0.0542 c. 2201: 212 69 86 57 69 86 126 155 57 155 57 155 126 86 69 57 86 69 212 212 N SD: 0.0196 c. M:-0.0366 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: 0.6816 cents 5 .. 10 match: 5 H SD: 9.7693 cents 6 .. 12 match: 6 H SD: 5.8681 cents 7 .. 14 match: 7 H SD: 5.5284 cents 8 .. 16 match: 8 H SD: 4.4997 cents 9 .. 18 match: 9 H SD: 5.8822 cents 10 .. 20 match: 10 H SD: 6.0152 cents 11 .. 22 match: 10 SD: 7.5283 cents 12 .. 24 match: 11 S SD: 4.0835 cents 13 .. 26 match: 12 S SD: 6.0561 cents 14 .. 28 match: 13 S SD: 4.8786 cents 15 .. 30 match: 13 S SD: 4.4443 cents 16 .. 32 match: 14 S SD: 3.4848 cents 17 .. 34 match: 14 SD: 4.3950 cents 18 .. 36 match: 15 S SD: 4.0771 cents 19 .. 38 match: 14 SD: 4.7325 cents 20 .. 40 match: 17 SD: 3.4433 cents 21 .. 42 match: 16 SD: 3.8611 cents 22 .. 44 match: 15 SD: 3.6341 cents 23 .. 46 match: 17 SD: 3.2779 cents 24 .. 48 match: 17 S SD: 2.7469 cents 25 .. 50 match: 17 SD: 2.5559 cents 26 .. 52 match: 17 SD: 3.5541 cents 27 .. 54 match: 18 SD: 3.0424 cents 28 .. 56 match: 18 SD: 2.5458 cents 29 .. 58 match: 18 SD: 2.7164 cents 30 .. 60 match: 19 SD: 2.1304 cents 31 .. 62 match: 18 SD: 2.5036 cents 32 .. 64 match: 19 SD: 2.0592 cents 34 .. 68 match: 19 SD: 2.6124 cents 35 .. 70 match: 20 SD: 2.0937 cents 37 .. 74 match: 17 SD: 2.5283 cents 38 .. 76 match: 19 SD: 2.4610 cents 39 .. 78 match: 20 SD: 2.2011 cents 40 .. 80 match: 20 SD: 1.8567 cents 41 .. 82 match: 20 SD: 1.7366 cents 42 .. 84 match: 20 SD: 1.5651 cents 45 .. 90 match: 19 SD: 1.4787 cents 48 .. 96 match: 20 SD: 1.4773 cents 54 .. 108 match: 20 SD: 1.4350 cents 55 .. 110 match: 20 SD: 1.2448 cents 60 .. 120 match: 20 SD: 1.2330 cents 63 .. 126 match: 20 SD: 1.2176 cents 64 .. 128 match: 20 SD: 1.1595 cents 65 .. 130 match: 20 SD: 1.1201 cents 72 .. 144 match: 20 SD: 0.9145 cents 75 .. 150 match: 20 SD: 0.8931 cents 77 .. 154 match: 20 SD: 0.8660 cents 84 .. 168 match: 20 SD: 0.6898 cents 100 .. 200 match: 20 SD: 0.6331 cents 105 .. 210 match: 20 SD: 0.6066 cents 120 .. 240 match: 20 SD: 0.5542 cents 129 .. 258 match: 20 SD: 0.4790 cents 132 .. 264 match: 20 SD: 0.4389 cents 160 .. 320 match: 20 SD: 0.4377 cents 161 .. 322 match: 20 SD: 0.3491 cents 204 .. 408 match: 20 SD: 0.2975 cents 229 .. 458 match: 20 SD: 0.2864 cents 245 .. 490 match: 20 SD: 0.2605 cents 251 .. 502 match: 20 SD: 0.2601 cents 261 .. 522 match: 20 SD: 0.2181 cents 279 .. 558 match: 20 SD: 0.2116 cents 309 .. 618 match: 20 SD: 0.2030 cents 334 .. 668 match: 20 SD: 0.1820 cents 379 .. 758 match: 20 SD: 0.1651 cents 399 .. 798 match: 20 SD: 0.1631 cents 421 .. 842 match: 20 SD: 0.1581 cents 424 .. 848 match: 20 SD: 0.1551 cents 433 .. 866 match: 20 SD: 0.1537 cents 434 .. 868 match: 20 SD: 0.1466 cents 435 .. 870 match: 20 SD: 0.1341 cents 463 .. 926 match: 20 SD: 0.1311 cents 490 .. 980 match: 20 SD: 0.1298 cents 520 .. 1040 match: 20 SD: 0.1217 cents 540 .. 1080 match: 20 SD: 0.1013 cents 595 .. 1190 match: 20 SD: 0.0798 cents