Scala analysis: hi19marv
inverted smithgw_hahn19 in 1/4 kleismic tempering
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46.843 cents 46.842501 2: 115.587 cents 115.587047 3: 184.332 cents 184.331593 4: 231.174 cents 231.174094 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: 46.8425 cents 46.8425 2: 68.7445 cents 68.7445 3: 68.7445 cents 68.7445 4: 46.8425 cents 46.8425 5: 84.4672 cents 84.4672 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: 2 31.11985 cents 1: 5 46.84250 cents 1: 7 68.74455 cents 1: 5 84.46719 cents 2: 12 115.58705 cents 2: 2 131.30969 cents 2: 1 137.48909 cents 2: 4 153.21174 cents 3: 2 162.42955 cents 3: 8 184.33159 cents 3: 9 200.05424 cents 4: 7 231.17409 cents 4: 2 246.89674 cents 4: 10 268.79879 cents 5: 5 299.91864 cents 5: 11 315.64129 cents 5: 2 337.54333 cents 5: 1 353.26598 cents 6: 3 346.76114 cents 6: 1 362.48379 cents 6: 13 384.38583 cents 6: 2 400.10848 cents 7: 2 415.50569 cents 7: 9 431.22833 cents 7: 4 453.13038 cents 7: 4 468.85303 cents 8: 1 478.07084 cents 8: 13 499.97288 cents 8: 3 515.69553 cents 8: 2 537.59757 cents 9: 1 531.09273 cents 9: 5 546.81538 cents 9: 4 568.71743 cents 9: 9 584.44007 cents 10: 9 615.55993 cents 10: 4 631.28257 cents 10: 5 653.18462 cents 10: 1 668.90727 cents 11: 2 662.40243 cents 11: 3 684.30447 cents 11: 13 700.02712 cents 11: 1 721.92916 cents 12: 4 731.14697 cents 12: 4 746.86962 cents 12: 9 768.77167 cents 12: 2 784.49431 cents 13: 2 799.89152 cents 13: 13 815.61417 cents 13: 1 837.51621 cents 13: 3 853.23886 cents 14: 1 846.73402 cents 14: 2 862.45667 cents 14: 11 884.35871 cents 14: 5 900.08136 cents 15: 10 931.20121 cents 15: 2 953.10326 cents 15: 7 968.82591 cents 16: 9 999.94576 cents 16: 8 1015.66841 cents 16: 2 1037.57045 cents 17: 4 1046.78826 cents 17: 1 1062.51091 cents 17: 2 1068.69031 cents 17: 12 1084.41295 cents 18: 5 1115.53281 cents 18: 7 1131.25545 cents 18: 5 1153.15750 cents 18: 2 1168.88015 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.77778 = 34/9
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 : 46.8 115.6 184.3 231.2 315.6 384.4 431.2 500.0 584.4 615.6 700.0 768.8 815.6 884.4 931.2 999.9 1084.4 1115.5 1200.0 46.8 : 68.7 137.5 184.3 268.8 337.5 384.4 453.1 537.6 568.7 653.2 721.9 768.8 837.5 884.4 953.1 1037.6 1068.7 1153.2 1200.0 115.6 : 68.7 115.6 200.1 268.8 315.6 384.4 468.9 500.0 584.4 653.2 700.0 768.8 815.6 884.4 968.8 999.9 1084.4 1131.3 1200.0 184.3 : 46.8 131.3 200.1 246.9 315.6 400.1 431.2 515.7 584.4 631.3 700.0 746.9 815.6 900.1 931.2 1015.7 1062.5 1131.3 1200.0 231.2 : 84.5 153.2 200.1 268.8 353.3 384.4 468.9 537.6 584.4 653.2 700.0 768.8 853.2 884.4 968.8 1015.7 1084.4 1153.2 1200.0 315.6 : 68.7 115.6 184.3 268.8 299.9 384.4 453.1 500.0 568.7 615.6 684.3 768.8 799.9 884.4 931.2 999.9 1068.7 1115.5 1200.0 384.4 : 46.8 115.6 200.1 231.2 315.6 384.4 431.2 500.0 546.8 615.6 700.0 731.1 815.6 862.5 931.2 999.9 1046.8 1131.3 1200.0 431.2 : 68.7 153.2 184.3 268.8 337.5 384.4 453.1 500.0 568.7 653.2 684.3 768.8 815.6 884.4 953.1 999.9 1084.4 1153.2 1200.0 500.0 : 84.5 115.6 200.1 268.8 315.6 384.4 431.2 500.0 584.4 615.6 700.0 746.9 815.6 884.4 931.2 1015.7 1084.4 1131.3 1200.0 584.4 : 31.1 115.6 184.3 231.2 299.9 346.8 415.5 500.0 531.1 615.6 662.4 731.1 799.9 846.7 931.2 999.9 1046.8 1115.5 1200.0 615.6 : 84.5 153.2 200.1 268.8 315.6 384.4 468.9 500.0 584.4 631.3 700.0 768.8 815.6 900.1 968.8 1015.7 1084.4 1168.9 1200.0 700.0 : 68.7 115.6 184.3 231.2 299.9 384.4 415.5 500.0 546.8 615.6 684.3 731.1 815.6 884.4 931.2 999.9 1084.4 1115.5 1200.0 768.8 : 46.8 115.6 162.4 231.2 315.6 346.8 431.2 478.1 546.8 615.6 662.4 746.9 815.6 862.5 931.2 1015.7 1046.8 1131.3 1200.0 815.6 : 68.7 115.6 184.3 268.8 299.9 384.4 431.2 500.0 568.7 615.6 700.0 768.8 815.6 884.4 968.8 999.9 1084.4 1153.2 1200.0 884.4 : 46.8 115.6 200.1 231.2 315.6 362.5 431.2 500.0 546.8 631.3 700.0 746.9 815.6 900.1 931.2 1015.7 1084.4 1131.3 1200.0 931.2 : 68.7 153.2 184.3 268.8 315.6 384.4 453.1 500.0 584.4 653.2 700.0 768.8 853.2 884.4 968.8 1037.6 1084.4 1153.2 1200.0 999.9 : 84.5 115.6 200.1 246.9 315.6 384.4 431.2 515.7 584.4 631.3 700.0 784.5 815.6 900.1 968.8 1015.7 1084.4 1131.3 1200.0 1084.4: 31.1 115.6 162.4 231.2 299.9 346.8 431.2 500.0 546.8 615.6 700.0 731.1 815.6 884.4 931.2 999.9 1046.8 1115.5 1200.0 1115.5: 84.5 131.3 200.1 268.8 315.6 400.1 468.9 515.7 584.4 668.9 700.0 784.5 853.2 900.1 968.8 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 .. 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 .. 353.2660 cents 53.34734 cents 31.11985 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: 478.0708 .. 537.5976 cents 59.52674 cents 9.21781 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 .. 721.9292 cents 59.52674 cents -6.50484 cents 12: 731.1470 .. 784.4943 cents 53.34734 cents 9.21781 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: 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 .. 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: 7 Most common interval of one step : 68.74455 cents, amount: 7 Least squares average step : 62.86052 cents, oct.: 1194.34997 cents Scale is not proper Step pattern alph. order: ABBACBABCDCBABABCDC Step pattern size order : BCCBDCBCDADCBCBCDAD Scale is a Constant Structure, by a margin of 6.50484 cents Scale diversity : 1.385372 Lumma stability : 0.289787 Lumma impropriety factor : 0.021683 Number of different interval sizes : 68 = 3.77778 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.77778 = 34/9 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 6.17940 cents Number of recognisable fifths : 13, average 700.0271 cents Best minor thirds form a closed circle Formal octave complements present : 13 = 68.4211% -- 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: 11.8670 c. M:-21.4575 c. 24: 1 1 2 1 1 2 1 1 2 0 2 1 1 2 1 1 2 0 2 N D3 S SD: 14.2466 c. M:-18.8259 c. 25: 1 1 2 1 2 1 1 1 2 1 2 1 1 1 1 2 2 0 2 N D3 SD: 13.0639 c. M:-20.3587 c. 26: 1 1 2 1 2 1 1 2 2 0 2 2 1 1 1 2 1 1 2 N D3 SD: 12.7880 c. M: 23.2794 c. 27: 1 2 1 1 2 2 1 1 2 1 2 1 1 2 1 1 2 1 2 N D3 SD: 11.4402 c. M: 22.1680 c. 31: 1 2 2 1 2 2 1 2 2 1 2 2 1 2 1 2 2 1 2 P D3 S SD: 4.8349 c. M:-9.2168 c. 53: 2 3 3 2 4 3 2 3 4 1 4 3 2 3 2 3 4 1 4 N SD: 2.8583 c. M: 6.0988 c. 72: 3 4 4 3 5 4 3 4 5 2 5 4 3 4 3 4 5 2 5 P SD: 1.4405 c. M:-3.1575 c. 103: 4 6 6 4 7 6 4 6 7 3 7 6 4 6 4 6 7 3 7 P SD: 1.3440 c. M:-2.9138 c. 125: 5 7 7 5 9 7 5 7 9 3 9 7 5 7 5 7 9 3 9 N SD: 1.0299 c. M: 1.9328 c. 156: 6 9 9 6 11 9 6 9 11 4 11 9 6 9 6 9 11 4 11 N SD: 0.3021 c. M: 0.6887 c. 228: 9 13 13 9 16 13 9 13 16 6 16 13 9 13 9 13 16 6 16 N SD: 0.2520 c. M:-0.5259 c. 384: 15 22 22 15 27 22 15 22 27 10 27 22 15 22 15 22 27 10 27 N SD: 0.0442 c. M:-0.0922 c. 924: 36 53 53 36 65 53 36 53 65 24 65 53 36 53 36 53 65 24 65 N SD: 0.0457 c. M: 0.0893 c. 1308: 51 75 75 51 92 75 51 75 92 34 92 75 51 75 51 75 92 34 92 N SD: 0.0377 c. M:-0.0721 c. 1692: 66 97 97 66 119 97 66 97 119 44 119 97 66 97 66 97 119 44 119 N SD: 0.0357 c. M:-0.0700 c. 1973: 77 113 113 77 139 113 77 113 139 51 139 113 77 113 77 113 139 51 139 N SD: 0.0342 c. M: 0.0741 c. 2201: 86 126 126 86 155 126 86 126 155 57 155 126 86 126 86 126 155 57 155 N SD: 0.0271 c. M: 0.0517 c. 2357: 92 135 135 92 166 135 92 135 166 61 166 135 92 135 92 135 166 61 166 N SD: 0.0216 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: 8.3503 cents 7 .. 14 match: 7 H SD: 2.7558 cents 8 .. 16 match: 8 H SD: 6.9505 cents 9 .. 18 match: 9 H SD: 4.5807 cents 10 .. 20 match: 10 H SD: 3.7431 cents 11 .. 22 match: 11 H SD: 7.7104 cents 12 .. 24 match: 12 H SD: 5.7052 cents 13 .. 26 match: 13 H SD: 6.1679 cents 14 .. 28 match: 14 H SD: 3.7341 cents 15 .. 30 match: 15 H SD: 4.3961 cents 16 .. 32 match: 14 SD: 5.0175 cents 17 .. 34 match: 14 SD: 5.0060 cents 18 .. 36 match: 16 S SD: 3.9304 cents 19 .. 38 match: 14 SD: 5.0669 cents 20 .. 40 match: 18 S SD: 3.6934 cents 21 .. 42 match: 18 SD: 3.7998 cents 22 .. 44 match: 17 SD: 4.3439 cents 23 .. 46 match: 18 SD: 4.0810 cents 24 .. 48 match: 17 SD: 3.1954 cents 25 .. 50 match: 19 SD: 3.1688 cents 27 .. 54 match: 18 SD: 2.8849 cents 28 .. 56 match: 19 SD: 2.2407 cents 29 .. 58 match: 18 SD: 2.6520 cents 30 .. 60 match: 19 SD: 2.4617 cents 32 .. 64 match: 19 SD: 2.2823 cents 35 .. 70 match: 19 SD: 2.0407 cents 36 .. 72 match: 19 SD: 2.0236 cents 40 .. 80 match: 19 SD: 1.9022 cents 42 .. 84 match: 19 SD: 1.5999 cents 45 .. 90 match: 19 SD: 1.3409 cents 56 .. 112 match: 19 SD: 1.3397 cents 60 .. 120 match: 19 SD: 1.1522 cents 63 .. 126 match: 19 SD: 1.0854 cents 70 .. 140 match: 19 SD: 0.8383 cents 84 .. 168 match: 19 SD: 0.7987 cents 96 .. 192 match: 19 SD: 0.7919 cents 98 .. 196 match: 19 SD: 0.7629 cents 100 .. 200 match: 19 SD: 0.6998 cents 104 .. 208 match: 19 SD: 0.6985 cents 105 .. 210 match: 19 SD: 0.5301 cents 134 .. 268 match: 19 SD: 0.5143 cents 140 .. 280 match: 19 SD: 0.5025 cents 141 .. 282 match: 19 SD: 0.4433 cents 145 .. 290 match: 19 SD: 0.4325 cents 170 .. 340 match: 19 SD: 0.3940 cents 176 .. 352 match: 19 SD: 0.3840 cents 177 .. 354 match: 19 SD: 0.3809 cents 188 .. 376 match: 19 SD: 0.3460 cents 215 .. 430 match: 19 SD: 0.3145 cents 216 .. 432 match: 19 SD: 0.2813 cents 251 .. 502 match: 19 SD: 0.2542 cents 261 .. 522 match: 19 SD: 0.2377 cents 286 .. 572 match: 19 SD: 0.2134 cents 293 .. 586 match: 19 SD: 0.1990 cents 329 .. 658 match: 19 SD: 0.1890 cents 349 .. 698 match: 19 SD: 0.1830 cents 365 .. 730 match: 19 SD: 0.1600 cents 434 .. 868 match: 19 SD: 0.1453 cents 435 .. 870 match: 19 SD: 0.1198 cents 510 .. 1020 match: 19 SD: 0.1149 cents 576 .. 1152 match: 19 SD: 0.1117 cents 580 .. 1160 match: 19 SD: 0.0866 cents