Scala analysis: 16-miracle
16 out of 53 within 5/3 miracle scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.430 cents 83.430068 2: 116.802 cents 116.802094 3: 200.232 cents 200.232162 4: 233.604 cents 233.604188 5: 317.034 cents 317.034256 6: 350.406 cents 350.406282 7: 383.778 cents 383.778309 8: 467.208 cents 467.208375 9: 500.580 cents 500.580404 10: 584.010 cents 584.010471 11: 617.382 cents 617.382497 12: 700.813 cents 700.812565 13: 734.185 cents 734.184592 14: 767.557 cents 767.556618 15: 850.987 cents 850.986686 16: 5/3 884.358713 major sixth, BP sixth
SHOW/INTERVAL
0: 33.3720 cents 33.3720 1: 83.4301 cents 83.4301 2: 33.3720 cents 33.3720 3: 83.4301 cents 83.4301 4: 33.3720 cents 33.3720 5: 83.4301 cents 83.4301 6: 33.3720 cents 33.3720 7: 33.3720 cents 33.3720 8: 83.4301 cents 83.4301 9: 33.3720 cents 33.3720 10: 83.4301 cents 83.4301 11: 33.3720 cents 33.3720 12: 83.4301 cents 83.4301 13: 33.3720 cents 33.3720 14: 33.3720 cents 33.3720 15: 83.4301 cents 83.4301 16: 33.3720 cents 33.3720
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 33.37203 cents 1: 7 83.43007 cents 2: 2 66.74405 cents 2: 14 116.80209 cents 3: 11 150.17412 cents 3: 5 200.23216 cents 4: 4 183.54615 cents 4: 12 233.60419 cents 5: 13 266.97621 cents 5: 3 317.03426 cents 6: 6 300.34824 cents 6: 10 350.40628 cents 7: 15 383.77831 cents 7: 1 433.83635 cents 8: 8 417.15034 cents 8: 8 467.20838 cents 9: 1 450.52236 cents 9: 15 500.58040 cents 10: 10 533.95243 cents 10: 6 584.01047 cents 11: 3 567.32446 cents 11: 13 617.38250 cents 12: 12 650.75452 cents 12: 4 700.81256 cents 13: 5 684.12655 cents 13: 11 734.18459 cents 14: 14 767.55662 cents 14: 2 817.61466 cents 15: 7 800.92864 cents 15: 9 850.98669 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 0.0 : 83.4 116.8 200.2 233.6 317.0 350.4 383.8 467.2 500.6 584.0 617.4 700.8 734.2 767.6 851.0 884.4 83.4 : 33.4 116.8 150.2 233.6 267.0 300.3 383.8 417.2 500.6 534.0 617.4 650.8 684.1 767.6 800.9 884.4 116.8: 83.4 116.8 200.2 233.6 267.0 350.4 383.8 467.2 500.6 584.0 617.4 650.8 734.2 767.6 851.0 884.4 200.2: 33.4 116.8 150.2 183.5 267.0 300.3 383.8 417.2 500.6 534.0 567.3 650.8 684.1 767.6 800.9 884.4 233.6: 83.4 116.8 150.2 233.6 267.0 350.4 383.8 467.2 500.6 534.0 617.4 650.8 734.2 767.6 851.0 884.4 317.0: 33.4 66.7 150.2 183.5 267.0 300.3 383.8 417.2 450.5 534.0 567.3 650.8 684.1 767.6 800.9 884.4 350.4: 33.4 116.8 150.2 233.6 267.0 350.4 383.8 417.2 500.6 534.0 617.4 650.8 734.2 767.6 851.0 884.4 383.8: 83.4 116.8 200.2 233.6 317.0 350.4 383.8 467.2 500.6 584.0 617.4 700.8 734.2 817.6 851.0 884.4 467.2: 33.4 116.8 150.2 233.6 267.0 300.3 383.8 417.2 500.6 534.0 617.4 650.8 734.2 767.6 800.9 884.4 500.6: 83.4 116.8 200.2 233.6 267.0 350.4 383.8 467.2 500.6 584.0 617.4 700.8 734.2 767.6 851.0 884.4 584.0: 33.4 116.8 150.2 183.5 267.0 300.3 383.8 417.2 500.6 534.0 617.4 650.8 684.1 767.6 800.9 884.4 617.4: 83.4 116.8 150.2 233.6 267.0 350.4 383.8 467.2 500.6 584.0 617.4 650.8 734.2 767.6 851.0 884.4 700.8: 33.4 66.7 150.2 183.5 267.0 300.3 383.8 417.2 500.6 534.0 567.3 650.8 684.1 767.6 800.9 884.4 734.2: 33.4 116.8 150.2 233.6 267.0 350.4 383.8 467.2 500.6 534.0 617.4 650.8 734.2 767.6 851.0 884.4 767.6: 83.4 116.8 200.2 233.6 317.0 350.4 433.8 467.2 500.6 584.0 617.4 700.8 734.2 817.6 851.0 884.4 851.0: 33.4 116.8 150.2 233.6 267.0 350.4 383.8 417.2 500.6 534.0 617.4 650.8 734.2 767.6 800.9 884.4 884.4
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3720 .. 83.4301 cents 50.05804 cents 33.37203 cents 2: 66.7441 .. 116.8021 cents 50.05804 cents -16.68602 cents 3: 150.1741 .. 200.2322 cents 50.05804 cents 33.37203 cents 4: 183.5461 .. 233.6042 cents 50.05804 cents -16.68602 cents 5: 266.9762 .. 317.0343 cents 50.05804 cents 33.37203 cents 6: 300.3482 .. 350.4063 cents 50.05804 cents -16.68602 cents 7: 383.7783 .. 433.8364 cents 50.05804 cents 33.37203 cents 8: 417.1503 .. 467.2084 cents 50.05804 cents -16.68602 cents 9: 450.5224 .. 500.5804 cents 50.05804 cents -16.68601 cents 10: 533.9524 .. 584.0105 cents 50.05804 cents 33.37203 cents 11: 567.3245 .. 617.3825 cents 50.05804 cents -16.68601 cents 12: 650.7545 .. 700.8126 cents 50.05804 cents 33.37203 cents 13: 684.1266 .. 734.1846 cents 50.05804 cents -16.68601 cents 14: 767.5566 .. 817.6147 cents 50.05804 cents 33.37203 cents 15: 800.9286 .. 850.9867 cents 50.05804 cents -16.68602 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 33.37203 cents, class 1 Average step (divided formal octave): 55.2724 cents Largest one step interval : 83.43007 cents Average / Smallest step : 1.656250 Largest / Average step : 1.509434 Largest / Smallest step : 2.500000 Median interval of one step : 33.37203 cents, amount: 9 Most common interval of one step : 33.37203 cents, amount: 9 Least squares average step : 56.62760 cents, oct.: 906.04161 cents Scale is not proper Scale has Myhill's property chromas: 50.05804 cents and 16.68602 cents, ratio: 2.999999 generators: 7 of 383.77831 cents and 9 of 500.58040 cents ET pair of linear temperament : 23&30 Scale is distributional even Scale is a mode of a 53-tone equal temperament with octave 5/3 degrees: 5 7 12 14 19 21 23 28 30 35 37 42 44 46 51 53 generators: 23 and 30 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABBABABABBAB Step pattern size order : LSLSLSSLSLSLSSLS Interval vector is [ 0 9 0 2 7 0 14 0 11 0 4 5 0 12 0 13 0 6 3 0 10 0 15 0 8 1 ] Scale is a Constant Structure, by a margin of 16.68601 cents Scale diversity : 0.893937 Lumma stability : 0.301887 Lumma impropriety factor : 0.150943 Rothenberg efficiency : 0.708333 redundancy: 0.291667 Efficiency x scale size : 11.333333 Number of different interval sizes : 30 = 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 : 16.68601 cents Most common intervals : 383.77831 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 33.372 500.580 cents Most common triad is 0.0 383.778 500.580 cents, amount: 14 Number of recognisable fifths : 4, average 700.8126 cents Number of recognisable fourths : 15, average 500.5804 cents Formal octave complements present : 5 = 31.2500% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 9-10 -- Rational properties -- Prime limit : 5 (not all pitches rational)
FIT/MODE
16: 1 1 1 1 1 1 0 2 1 1 1 1 1 0 2 1 N T3 SD: 28.6554 c. M: 52.1438 c. 17: 2 0 2 0 2 1 0 2 1 1 1 1 1 1 1 1 N D3 SD: 15.0386 c. M: 25.5198 c. 20: 2 1 2 0 2 1 1 2 0 2 1 2 1 0 2 1 N T3 SD: 12.5336 c. M:-20.8575 c. 21: 2 1 2 1 2 0 1 2 1 2 1 2 0 1 2 1 N SD: 11.6321 c. M:-19.8643 c. 22: 2 1 2 1 2 1 1 2 0 3 0 2 1 1 2 1 N SD: 11.6454 c. M:-18.9614 c. 23: 2 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 5.2063 c. M: 9.4312 c. 30: 3 1 3 1 3 1 1 3 1 3 1 3 1 1 3 1 N M DE SD: 3.9915 c. M:-7.2306 c. 53: 5 2 5 2 5 2 2 5 2 5 2 5 2 2 5 2 N M DE SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 315.6413 cents 2 .. 3 match: 1 H SD: 1.1424 cents 3 .. 5 match: 2 H SD: 1.2677 cents 4 .. 7 match: 3 H SD: 28.1710 cents 5 .. 8 match: 3 H SD: 12.4522 cents 6 .. 10 match: 4 H SD: 8.3457 cents 7 .. 12 match: 5 H SD: 12.0657 cents 8 .. 13 match: 5 H SD: 6.9266 cents 9 .. 15 match: 6 H SD: 4.4417 cents 10 .. 17 match: 7 H SD: 9.0147 cents 11 .. 18 match: 7 H SD: 10.6479 cents 12 .. 20 match: 8 H SD: 6.3562 cents 13 .. 22 match: 9 H SD: 6.7394 cents 14 .. 23 match: 9 H SD: 5.3687 cents 15 .. 25 match: 9 SD: 5.4609 cents 16 .. 27 match: 11 H SD: 4.3981 cents 17 .. 28 match: 10 S SD: 6.4784 cents 18 .. 30 match: 11 S SD: 4.8076 cents 19 .. 32 match: 12 SD: 5.0532 cents 20 .. 33 match: 12 SD: 4.4531 cents 21 .. 35 match: 12 S SD: 4.0136 cents 22 .. 37 match: 11 SD: 4.8007 cents 23 .. 38 match: 13 S SD: 4.1105 cents 24 .. 40 match: 12 SD: 3.6382 cents 25 .. 42 match: 14 SD: 3.4845 cents 26 .. 43 match: 14 SD: 3.5366 cents 27 .. 45 match: 16 S SD: 3.3731 cents 28 .. 47 match: 14 SD: 3.3322 cents 29 .. 48 match: 13 SD: 3.6038 cents 30 .. 50 match: 14 SD: 2.7786 cents 31 .. 52 match: 13 SD: 3.4692 cents 32 .. 53 match: 15 SD: 2.5601 cents 33 .. 55 match: 14 SD: 2.8046 cents 34 .. 57 match: 13 SD: 2.9932 cents 35 .. 58 match: 15 SD: 2.5938 cents 36 .. 60 match: 16 SD: 2.4815 cents 37 .. 62 match: 15 SD: 3.2618 cents 38 .. 63 match: 14 SD: 2.5712 cents 39 .. 65 match: 16 SD: 2.2488 cents 40 .. 67 match: 16 SD: 1.7776 cents 54 .. 90 match: 16 SD: 1.6383 cents 55 .. 92 match: 16 SD: 1.6277 cents 56 .. 93 match: 16 SD: 1.5980 cents 57 .. 95 match: 16 SD: 1.4154 cents 68 .. 113 match: 16 SD: 1.1804 cents 74 .. 123 match: 16 SD: 1.1383 cents 75 .. 125 match: 16 SD: 1.0863 cents 80 .. 133 match: 16 SD: 1.0310 cents 84 .. 140 match: 16 SD: 0.7418 cents 104 .. 173 match: 16 SD: 0.6935 cents 120 .. 200 match: 16 SD: 0.6699 cents 125 .. 208 match: 16 SD: 0.6273 cents 129 .. 215 match: 16 SD: 0.5537 cents 138 .. 230 match: 16 SD: 0.5389 cents 140 .. 233 match: 16 SD: 0.5107 cents 161 .. 268 match: 16 SD: 0.4599 cents 186 .. 310 match: 16 SD: 0.4417 cents 187 .. 312 match: 16 SD: 0.4213 cents 200 .. 333 match: 16 SD: 0.4158 cents 201 .. 335 match: 16 SD: 0.3991 cents 214 .. 357 match: 16 SD: 0.3602 cents 227 .. 378 match: 16 SD: 0.3470 cents 229 .. 382 match: 16 SD: 0.2996 cents 242 .. 403 match: 16 SD: 0.2974 cents 262 .. 437 match: 16 SD: 0.2860 cents 269 .. 448 match: 16 SD: 0.2739 cents 285 .. 475 match: 16 SD: 0.2646 cents 299 .. 498 match: 16 SD: 0.2377 cents 303 .. 505 match: 16 SD: 0.2236 cents 339 .. 565 match: 16 SD: 0.2193 cents 343 .. 572 match: 16 SD: 0.2083 cents 367 .. 612 match: 16 SD: 0.2005 cents 387 .. 645 match: 16 SD: 0.1868 cents 423 .. 705 match: 16 SD: 0.1791 cents 432 .. 720 match: 16 SD: 0.1789 cents 441 .. 735 match: 16 SD: 0.1714 cents 443 .. 738 match: 16 SD: 0.1697 cents 471 .. 785 match: 16 SD: 0.1368 cents 504 .. 840 match: 16 SD: 0.1260 cents 513 .. 855 match: 16 SD: 0.1188 cents 588 .. 980 match: 16 SD: 0.0941 cents