Scala analysis: xen18-erlich-miracle-21
10L 11s MOS for Miracle, L=83.29, s=33.43
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33.430 cents 33.430000 2: 116.720 cents 116.720000 3: 150.150 cents 150.150000 4: 233.440 cents 233.440000 5: 266.870 cents 266.870000 6: 350.160 cents 350.160000 7: 383.590 cents 383.590000 8: 466.880 cents 466.880000 9: 500.310 cents 500.310000 10: 583.600 cents 583.600000 11: 617.030 cents 617.030000 12: 700.320 cents 700.320000 13: 733.750 cents 733.750000 14: 817.040 cents 817.040000 15: 850.470 cents 850.470000 16: 933.760 cents 933.760000 17: 967.190 cents 967.190000 18: 1050.480 cents 1050.480000 19: 1083.910 cents 1083.910000 20: 1167.200 cents 1167.200000 21: 1200.630 cents 1200.630000
SHOW/INTERVAL
0: 33.4300 cents 33.4300 1: 33.4300 cents 33.4300 2: 83.2900 cents 83.2900 3: 33.4300 cents 33.4300 4: 83.2900 cents 83.2900 5: 33.4300 cents 33.4300 6: 83.2900 cents 83.2900 7: 33.4300 cents 33.4300 8: 83.2900 cents 83.2900 9: 33.4300 cents 33.4300 10: 83.2900 cents 83.2900 11: 33.4300 cents 33.4300 12: 83.2900 cents 83.2900 13: 33.4300 cents 33.4300 14: 83.2900 cents 83.2900 15: 33.4300 cents 33.4300 16: 83.2900 cents 83.2900 17: 33.4300 cents 33.4300 18: 83.2900 cents 83.2900 19: 33.4300 cents 33.4300 20: 83.2900 cents 83.2900 21: 33.4300 cents 33.4300
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 33.43000 cents 1: 10 83.29000 cents 2: 1 66.86000 cents 2: 20 116.72000 cents 3: 12 150.15000 cents 3: 9 200.01000 cents 4: 2 183.58000 cents 4: 19 233.44000 cents 5: 13 266.87000 cents 5: 8 316.73000 cents 6: 3 300.30000 cents 6: 18 350.16000 cents 7: 14 383.59000 cents 7: 7 433.45000 cents 8: 4 417.02000 cents 8: 17 466.88000 cents 9: 15 500.31000 cents 9: 6 550.17000 cents 10: 5 533.74000 cents 10: 16 583.60000 cents 11: 16 617.03000 cents 11: 5 666.89000 cents 12: 6 650.46000 cents 12: 15 700.32000 cents 13: 17 733.75000 cents 13: 4 783.61000 cents 14: 7 767.18000 cents 14: 14 817.04000 cents 15: 18 850.47000 cents 15: 3 900.33000 cents 16: 8 883.90000 cents 16: 13 933.76000 cents 17: 19 967.19000 cents 17: 2 1017.05000 cents 18: 9 1000.62000 cents 18: 12 1050.48000 cents 19: 20 1083.91000 cents 19: 1 1133.77000 cents 20: 10 1117.34000 cents 20: 11 1167.20000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
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 : 33.4 116.7 150.1 233.4 266.9 350.2 383.6 466.9 500.3 583.6 617.0 700.3 733.7 817.0 850.5 933.8 967.2 1050.5 1083.9 1167.2 1200.6 33.4 : 83.3 116.7 200.0 233.4 316.7 350.2 433.4 466.9 550.2 583.6 666.9 700.3 783.6 817.0 900.3 933.8 1017.1 1050.5 1133.8 1167.2 1200.6 116.7 : 33.4 116.7 150.1 233.4 266.9 350.2 383.6 466.9 500.3 583.6 617.0 700.3 733.7 817.0 850.5 933.8 967.2 1050.5 1083.9 1117.3 1200.6 150.1 : 83.3 116.7 200.0 233.4 316.7 350.2 433.5 466.9 550.2 583.6 666.9 700.3 783.6 817.0 900.3 933.8 1017.1 1050.5 1083.9 1167.2 1200.6 233.4 : 33.4 116.7 150.2 233.4 266.9 350.2 383.6 466.9 500.3 583.6 617.0 700.3 733.8 817.0 850.5 933.8 967.2 1000.6 1083.9 1117.3 1200.6 266.9 : 83.3 116.7 200.0 233.4 316.7 350.2 433.5 466.9 550.2 583.6 666.9 700.3 783.6 817.0 900.3 933.8 967.2 1050.5 1083.9 1167.2 1200.6 350.2 : 33.4 116.7 150.1 233.4 266.9 350.2 383.6 466.9 500.3 583.6 617.0 700.3 733.8 817.0 850.5 883.9 967.2 1000.6 1083.9 1117.3 1200.6 383.6 : 83.3 116.7 200.0 233.4 316.7 350.2 433.4 466.9 550.2 583.6 666.9 700.3 783.6 817.0 850.5 933.8 967.2 1050.5 1083.9 1167.2 1200.6 466.9 : 33.4 116.7 150.1 233.4 266.9 350.2 383.6 466.9 500.3 583.6 617.0 700.3 733.7 767.2 850.5 883.9 967.2 1000.6 1083.9 1117.3 1200.6 500.3 : 83.3 116.7 200.0 233.4 316.7 350.2 433.4 466.9 550.2 583.6 666.9 700.3 733.8 817.0 850.5 933.8 967.2 1050.5 1083.9 1167.2 1200.6 583.6 : 33.4 116.7 150.1 233.4 266.9 350.2 383.6 466.9 500.3 583.6 617.0 650.5 733.7 767.2 850.5 883.9 967.2 1000.6 1083.9 1117.3 1200.6 617.0 : 83.3 116.7 200.0 233.4 316.7 350.2 433.5 466.9 550.2 583.6 617.0 700.3 733.7 817.0 850.5 933.8 967.2 1050.5 1083.9 1167.2 1200.6 700.3 : 33.4 116.7 150.1 233.4 266.9 350.2 383.6 466.9 500.3 533.7 617.0 650.5 733.7 767.2 850.5 883.9 967.2 1000.6 1083.9 1117.3 1200.6 733.7 : 83.3 116.7 200.0 233.4 316.7 350.2 433.5 466.9 500.3 583.6 617.0 700.3 733.7 817.0 850.5 933.8 967.2 1050.5 1083.9 1167.2 1200.6 817.0 : 33.4 116.7 150.1 233.4 266.9 350.2 383.6 417.0 500.3 533.7 617.0 650.5 733.7 767.2 850.5 883.9 967.2 1000.6 1083.9 1117.3 1200.6 850.5 : 83.3 116.7 200.0 233.4 316.7 350.2 383.6 466.9 500.3 583.6 617.0 700.3 733.7 817.0 850.5 933.8 967.2 1050.5 1083.9 1167.2 1200.6 933.8 : 33.4 116.7 150.2 233.4 266.9 300.3 383.6 417.0 500.3 533.7 617.0 650.5 733.8 767.2 850.5 883.9 967.2 1000.6 1083.9 1117.3 1200.6 967.2 : 83.3 116.7 200.0 233.4 266.9 350.2 383.6 466.9 500.3 583.6 617.0 700.3 733.7 817.0 850.5 933.8 967.2 1050.5 1083.9 1167.2 1200.6 1050.5: 33.4 116.7 150.1 183.6 266.9 300.3 383.6 417.0 500.3 533.7 617.0 650.5 733.7 767.2 850.5 883.9 967.2 1000.6 1083.9 1117.3 1200.6 1083.9: 83.3 116.7 150.2 233.4 266.9 350.2 383.6 466.9 500.3 583.6 617.0 700.3 733.7 817.0 850.5 933.8 967.2 1050.5 1083.9 1167.2 1200.6 1167.2: 33.4 66.9 150.2 183.6 266.9 300.3 383.6 417.0 500.3 533.7 617.0 650.5 733.7 767.2 850.5 883.9 967.2 1000.6 1083.9 1117.3 1200.6 1200.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.4300 .. 83.2900 cents 49.86000 cents 33.43000 cents 2: 66.8600 .. 116.7200 cents 49.86000 cents -16.43000 cents 3: 150.1500 .. 200.0100 cents 49.86000 cents 33.43000 cents 4: 183.5800 .. 233.4400 cents 49.86000 cents -16.43000 cents 5: 266.8700 .. 316.7300 cents 49.86000 cents 33.43000 cents 6: 300.3000 .. 350.1600 cents 49.86000 cents -16.43000 cents 7: 383.5900 .. 433.4500 cents 49.86000 cents 33.43000 cents 8: 417.0200 .. 466.8800 cents 49.86000 cents -16.43000 cents 9: 500.3100 .. 550.1700 cents 49.86000 cents 33.43000 cents 10: 533.7400 .. 583.6000 cents 49.86000 cents -16.43000 cents 11: 617.0300 .. 666.8900 cents 49.86000 cents 33.43000 cents 12: 650.4600 .. 700.3200 cents 49.86000 cents -16.43000 cents 13: 733.7500 .. 783.6100 cents 49.86000 cents 33.43000 cents 14: 767.1800 .. 817.0400 cents 49.86000 cents -16.43000 cents 15: 850.4700 .. 900.3300 cents 49.86000 cents 33.43000 cents 16: 883.9000 .. 933.7600 cents 49.86000 cents -16.43000 cents 17: 967.1900 .. 1017.0500 cents 49.86000 cents 33.43000 cents 18: 1000.6200 .. 1050.4800 cents 49.86000 cents -16.43000 cents 19: 1083.9100 .. 1133.7700 cents 49.86000 cents 33.43000 cents 20: 1117.3400 .. 1167.2000 cents 49.86000 cents -16.43000 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 33.43000 cents, class 1 Average step (divided formal octave): 57.1729 cents Largest one step interval : 83.29000 cents Average / Smallest step : 1.710226 Largest / Average step : 1.456810 Largest / Smallest step : 2.491475 Median interval of one step : 33.43000 cents, amount: 11 Most common interval of one step : 33.43000 cents, amount: 11 Least squares average step : 57.44894 cents, oct.: 1206.42767 cents Scale is not proper Scale has Myhill's property chromas: 49.86000 cents and 16.43000 cents, ratio: 3.034693 generators: 2 of 116.72000 cents and 19 of 1083.91000 cents ET pair of linear temperament : 10&31 Scale is distributional even Scale is a mode of a 1975-tone equal temperament with octave 1200.630 cents degrees: 55 192 247 384 439 576 631 768 823 960 1015 1152 1207 1344 1399 1536 1591 1728 1783 1920 1975 generators: 192 and 1783 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABABABABABA Step pattern size order : SLSLSLSLSLSLSLSLSLSLS Scale is a Constant Structure, by a margin of 16.43000 cents Scale diversity : 1.199577 Lumma stability : 0.306281 Lumma impropriety factor : 0.136845 Rothenberg efficiency : 0.698413 redundancy: 0.301587 Efficiency x scale size : 14.666667 Number of different interval sizes : 40 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.43000 cents Most common intervals : 116.72000 cents & inv., amount: 20 Scale is a chain of 10 triads 0.0 116.720 233.440 cents Most common triad is 0.0 116.720 1083.910 cents, amount: 19 Number of recognisable fifths : 15, average 700.3200 cents Number of recognisable fourths : 15, average 500.3100 cents Scale contains two identical disjunct "tetrachords" of 10 notes Formal octave complements present : 21 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 10-11 -- Rational properties --
FIT/MODE
21: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.3770 c. M: 23.7429 c. 24: 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 N D3 I SD: 13.6090 c. M: 16.7387 c. 26: 1 2 0 2 1 2 0 2 1 2 0 2 1 2 0 2 1 2 0 2 1 N D3 I SD: 13.1638 c. M: 21.8142 c. 27: 1 2 0 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 0 2 1 N D3 I SD: 12.9441 c. M: 22.2022 c. 29: 1 2 1 2 0 2 1 2 1 2 1 2 1 2 1 2 0 2 1 2 1 N I SD: 12.1994 c. M: 18.9517 c. 31: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME I SD: 3.2093 c. M: 5.3000 c. 41: 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 3 1 N M DE I SD: 2.5107 c. M: 4.1463 c. 72: 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 5 2 N M DE I SD: 0.0479 c. M: 0.0792 c. 1111: 31 77 31 77 31 77 31 77 31 77 31 77 31 77 31 77 31 77 31 77 31 N M DE I SD: 0.0429 c. M: 0.0709 c. 1183: 33 82 33 82 33 82 33 82 33 82 33 82 33 82 33 82 33 82 33 82 33 N M DE I SD: 0.0374 c. M: 0.0618 c. 1255: 35 87 35 87 35 87 35 87 35 87 35 87 35 87 35 87 35 87 35 87 35 N M DE I SD: 0.0325 c. M: 0.0537 c. 1327: 37 92 37 92 37 92 37 92 37 92 37 92 37 92 37 92 37 92 37 92 37 N M DE I SD: 0.0282 c. M: 0.0465 c. 1399: 39 97 39 97 39 97 39 97 39 97 39 97 39 97 39 97 39 97 39 97 39 N M DE I SD: 0.0242 c. M: 0.0400 c. 1471: 41 102 41 102 41 102 41 102 41 102 41 102 41 102 41 102 41 102 41 102 41 N M DE I SD: 0.0207 c. M: 0.0342 c. 1543: 43 107 43 107 43 107 43 107 43 107 43 107 43 107 43 107 43 107 43 107 43 N M DE I SD: 0.0175 c. M: 0.0289 c. 1615: 45 112 45 112 45 112 45 112 45 112 45 112 45 112 45 112 45 112 45 112 45 N M DE I SD: 0.0146 c. M: 0.0241 c. 1687: 47 117 47 117 47 117 47 117 47 117 47 117 47 117 47 117 47 117 47 117 47 N M DE I SD: 0.0119 c. M: 0.0197 c. 1759: 49 122 49 122 49 122 49 122 49 122 49 122 49 122 49 122 49 122 49 122 49 N M DE I SD: 0.0095 c. M: 0.0156 c. 1831: 51 127 51 127 51 127 51 127 51 127 51 127 51 127 51 127 51 127 51 127 51 N M DE I SD: 0.0072 c. M: 0.0119 c. 1903: 53 132 53 132 53 132 53 132 53 132 53 132 53 132 53 132 53 132 53 132 53 N M DE I SD: 0.0051 c. M: 0.0085 c. 1975: 55 137 55 137 55 137 55 137 55 137 55 137 55 137 55 137 55 137 55 137 55 N M DE I SD: 0.0032 c. M: 0.0053 c. 2047: 57 142 57 142 57 142 57 142 57 142 57 142 57 142 57 142 57 142 57 142 57 N M DE I SD: 0.0014 c. M: 0.0023 c. 2119: 59 147 59 147 59 147 59 147 59 147 59 147 59 147 59 147 59 147 59 147 59 N M DE I SD: 0.0003 c. M: 0.0005 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.6300 cents 2 .. 4 match: 2 H SD: 0.8761 cents 3 .. 6 match: 3 H SD: 11.3234 cents 4 .. 8 match: 4 H SD: 0.9071 cents 5 .. 10 match: 5 H SD: 9.5618 cents 6 .. 12 match: 6 H SD: 5.6713 cents 7 .. 14 match: 7 H SD: 6.9396 cents 8 .. 16 match: 8 H SD: 5.6529 cents 9 .. 18 match: 9 H SD: 7.6058 cents 10 .. 20 match: 10 H SD: 6.0355 cents 11 .. 22 match: 11 H SD: 7.0728 cents 12 .. 24 match: 11 S SD: 4.0251 cents 13 .. 26 match: 12 S SD: 5.1548 cents 14 .. 28 match: 13 S SD: 5.0805 cents 15 .. 30 match: 14 S SD: 5.3711 cents 16 .. 32 match: 15 S SD: 4.7001 cents 17 .. 34 match: 17 H SD: 4.5617 cents 18 .. 36 match: 15 SD: 4.1342 cents 19 .. 38 match: 16 SD: 4.3522 cents 20 .. 40 match: 18 SD: 4.0165 cents 21 .. 42 match: 16 SD: 4.3200 cents 22 .. 44 match: 15 SD: 2.9490 cents 23 .. 46 match: 20 SD: 3.4274 cents 24 .. 48 match: 19 SD: 3.5561 cents 25 .. 50 match: 17 SD: 3.1902 cents 26 .. 52 match: 16 SD: 3.4078 cents 27 .. 54 match: 20 SD: 3.2073 cents 28 .. 56 match: 20 SD: 2.6391 cents 29 .. 58 match: 19 SD: 2.9036 cents 30 .. 60 match: 20 SD: 2.2223 cents 31 .. 62 match: 20 SD: 2.7049 cents 32 .. 64 match: 20 SD: 1.9610 cents 34 .. 68 match: 19 SD: 2.7345 cents 35 .. 70 match: 21 SD: 2.0715 cents 36 .. 72 match: 20 SD: 1.7103 cents 37 .. 74 match: 20 SD: 2.4178 cents 38 .. 76 match: 19 SD: 2.2018 cents 40 .. 80 match: 21 SD: 1.7895 cents 42 .. 84 match: 21 SD: 1.5022 cents 48 .. 96 match: 21 SD: 1.3231 cents 53 .. 106 match: 21 SD: 1.2569 cents 54 .. 108 match: 21 SD: 1.2187 cents 55 .. 110 match: 21 SD: 1.1212 cents 68 .. 136 match: 21 SD: 0.9083 cents 84 .. 168 match: 21 SD: 0.7184 cents 98 .. 196 match: 21 SD: 0.5870 cents 110 .. 220 match: 21 SD: 0.5566 cents 132 .. 264 match: 21 SD: 0.5411 cents 133 .. 266 match: 21 SD: 0.5187 cents 140 .. 280 match: 21 SD: 0.4957 cents 144 .. 288 match: 21 SD: 0.4392 cents 152 .. 304 match: 21 SD: 0.4216 cents 161 .. 322 match: 21 SD: 0.3886 cents 186 .. 372 match: 21 SD: 0.3597 cents 187 .. 374 match: 21 SD: 0.3156 cents 210 .. 420 match: 21 SD: 0.2695 cents 242 .. 484 match: 21 SD: 0.2478 cents 254 .. 508 match: 21 SD: 0.2472 cents 262 .. 524 match: 21 SD: 0.2302 cents 290 .. 580 match: 21 SD: 0.2187 cents 299 .. 598 match: 21 SD: 0.1953 cents 317 .. 634 match: 21 SD: 0.1916 cents 355 .. 710 match: 21 SD: 0.1669 cents 407 .. 814 match: 21 SD: 0.1628 cents 432 .. 864 match: 21 SD: 0.1623 cents 449 .. 898 match: 21 SD: 0.1541 cents 451 .. 902 match: 21 SD: 0.1535 cents 456 .. 912 match: 21 SD: 0.1313 cents 504 .. 1008 match: 21 SD: 0.1099 cents 561 .. 1122 match: 21 SD: 0.1089 cents 576 .. 1152 match: 21 SD: 0.1057 cents