Scala analysis: 512_M20
Miscellaneous tetrachord 58/57 * 57/56 * 112/87
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58/57 30.109177 2: 29/28 60.751288 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/87 437.2937 1: 58/57 30.1092 2: 57/56 30.6421 Hendrix comma 3: 112/87 437.2937
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 58/57 30.109 cents 1: 1 57/56 30.642 cents Hendrix comma 1: 1 112/87 437.294 cents 2: 1 29/28 60.751 cents 2: 1 224/171 467.403 cents 2: 1 38/29 467.936 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 30.1 60.8 498.0 30.1 : 30.6 467.9 498.0 60.8 : 437.3 467.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.1092 .. 437.2937 cents 1064/841, 407.1845 cents 58/57, 30.1092 cents 2: 60.7513 .. 467.9358 cents 1064/841, 407.1845 cents 2523/3136,-376.5424 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 58/57, 30.1092 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/87, 437.2937 cents Average / Smallest step : 5.513767 Largest / Average step : 2.634061 Largest / Smallest step : 14.523602 Median interval of one step : 57/56, 30.6421 cents, amount: 1 Least squares average step : 117.55334 cents, oct.: 352.66002 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1869-tone equal temperament with octave 4/3 degrees: 113 228 1869 Least number of segments generator : 935 of 249.156 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1649 of 439.420 cents and inv. generated superset size: 70 = 67 more = 2333.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 30.10918 cents Scale diversity : 0.139751 Lumma stability : 0.120909 Lumma impropriety factor : 0.756041 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 3249/3248, 0.5329 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 406.6516 cents: 2 -- Rational properties -- Prime limit : 29 Odd number limit : 171 (O: 57 U: 171) Highest odd numerator or denominator: 57 Scale harmonicity : 0.009512 Average absolute harmonicity : 0.080081 Specific harmonicity : 0.042882 Fundamental : 1/1596, -10.6402 octaves, 0.1639 Hz. Guide tone : 116, 6.8580 octaves, 30348.566 Hz. Exponens Consonantiae : 1.851360E+05, 17.49823 octaves Euler's gradus suavitatis : 59 Sum of Mann's harmonic distance : 89.5, average 29.83333 Mersenne's string divisions : 45885 Sum of van Prooijen's expressibility: 3.69539, average 1.23180 Sum of Tenney's harmonic distance : 7.50804, average 2.50268 Vogel's harmonic complexity : 40.00000 Wille's k value : 826 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.24061, average 2.70677 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 0 -0.66667 2 1 7: -1 .. 0 -0.33333 1 19: -1 .. 0 -0.33333 1 29: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 28 33| Scale is weakly epimorphic with val: <6 10 18 30 37| Scale is weakly epimorphic with val: <6 10 18 31 33| Scale is weakly epimorphic with val: <6 10 19 28 35| Scale is weakly epimorphic with val: <6 10 19 29 34| Scale is weakly epimorphic with val: <6 10 19 31 38| Scale is weakly epimorphic with val: <6 10 19 32 34| Scale is weakly epimorphic with val: <6 10 20 29 36| Scale is weakly epimorphic with val: <6 10 20 30 35| Scale is weakly epimorphic with val: <6 10 20 33 35| Scale is weakly epimorphic with val: <6 10 21 28 36| Scale is weakly epimorphic with val: <6 10 21 30 37| Scale is weakly epimorphic with val: <6 10 21 31 36| Scale is weakly epimorphic with val: <6 10 21 34 36| Scale is weakly epimorphic with val: <6 10 22 28 35| Scale is weakly epimorphic with val: <6 10 22 29 37| Scale is weakly epimorphic with val: <6 10 22 31 38| Scale is weakly epimorphic with val: <6 10 22 32 37| Scale is weakly epimorphic with val: <6 11 18 29 33| Scale is weakly epimorphic with val: <6 11 18 30 38| Scale is weakly epimorphic with val: <6 11 18 32 33| Scale is weakly epimorphic with val: <6 11 19 28 36| Scale is weakly epimorphic with val: <6 11 19 30 34| Scale is weakly epimorphic with val: <6 11 19 33 34| Scale is weakly epimorphic with val: <6 11 20 28 35| Scale is weakly epimorphic with val: <6 11 20 29 37| Scale is weakly epimorphic with val: <6 11 20 31 35| Scale is weakly epimorphic with val: <6 11 20 34 35| Scale is weakly epimorphic with val: <6 11 21 29 36| Scale is weakly epimorphic with val: <6 11 21 30 38| Scale is weakly epimorphic with val: <6 11 21 32 36| Scale is weakly epimorphic with val: <6 11 22 28 36| Scale is weakly epimorphic with val: <6 11 22 30 37| Scale is weakly epimorphic with val: <6 11 22 33 37| Scale is weakly epimorphic with val: <7 10 18 28 34| Scale is weakly epimorphic with val: <7 10 18 30 35| Scale is weakly epimorphic with val: <7 10 18 31 37| Scale is weakly epimorphic with val: <7 10 18 33 35| Scale is weakly epimorphic with val: <7 10 19 28 36| Scale is weakly epimorphic with val: <7 10 19 29 35| Scale is weakly epimorphic with val: <7 10 19 31 36| Scale is weakly epimorphic with val: <7 10 19 32 38| Scale is weakly epimorphic with val: <7 10 19 34 36| Scale is weakly epimorphic with val: <7 10 20 29 37| Scale is weakly epimorphic with val: <7 10 20 30 36| Scale is weakly epimorphic with val: <7 10 20 32 37| Scale is weakly epimorphic with val: <7 10 21 28 34| Scale is weakly epimorphic with val: <7 10 21 30 38| Scale is weakly epimorphic with val: <7 10 21 31 37| Scale is weakly epimorphic with val: <7 10 21 33 38| Scale is weakly epimorphic with val: <7 10 22 29 35| Scale is weakly epimorphic with val: <7 10 22 32 38| Scale is JI-epimorphic with val: <7 11 18 29 34| Scale is weakly epimorphic with val: <7 11 18 29 37| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 18 30 36| Scale is weakly epimorphic with val: <7 11 18 32 34| Scale is weakly epimorphic with val: <7 11 18 32 37| Scale is weakly epimorphic with val: <7 11 18 33 33| Scale is weakly epimorphic with val: <7 11 18 33 36| Scale is weakly epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 28 37| Scale is weakly epimorphic with val: <7 11 19 30 32| Scale is JI-epimorphic with val: <7 11 19 30 35| Scale is weakly epimorphic with val: <7 11 19 30 38| Scale is weakly epimorphic with val: <7 11 19 31 34| Scale is weakly epimorphic with val: <7 11 19 31 37| Scale is weakly epimorphic with val: <7 11 19 33 35| Scale is weakly epimorphic with val: <7 11 19 33 38| Scale is weakly epimorphic with val: <7 11 19 34 34| Scale is weakly epimorphic with val: <7 11 19 34 37| Scale is weakly epimorphic with val: <7 11 20 28 33| Scale is weakly epimorphic with val: <7 11 20 28 36| Scale is weakly epimorphic with val: <7 11 20 29 32| Scale is weakly epimorphic with val: <7 11 20 29 35| Scale is weakly epimorphic with val: <7 11 20 29 38| Scale is weakly epimorphic with val: <7 11 20 31 33| Scale is JI-epimorphic with val: <7 11 20 31 36| Scale is weakly epimorphic with val: <7 11 20 32 32| Scale is weakly epimorphic with val: <7 11 20 32 35| Scale is weakly epimorphic with val: <7 11 20 32 38| Scale is weakly epimorphic with val: <7 11 20 34 36| Scale is weakly epimorphic with val: <7 11 21 29 34| Scale is weakly epimorphic with val: <7 11 21 29 37| Scale is weakly epimorphic with val: <7 11 21 30 33| Scale is weakly epimorphic with val: <7 11 21 30 36| Scale is weakly epimorphic with val: <7 11 21 32 34| Scale is JI-epimorphic with val: <7 11 21 32 37| Scale is weakly epimorphic with val: <7 11 21 33 33| Scale is weakly epimorphic with val: <7 11 21 33 36| Scale is weakly epimorphic with val: <7 11 22 28 34| Scale is weakly epimorphic with val: <7 11 22 28 37| Scale is weakly epimorphic with val: <7 11 22 30 32| Scale is weakly epimorphic with val: <7 11 22 30 35| Scale is weakly epimorphic with val: <7 11 22 30 38| Scale is weakly epimorphic with val: <7 11 22 31 34| Scale is weakly epimorphic with val: <7 11 22 31 37| Scale is weakly epimorphic with val: <7 11 22 33 35| Scale is JI-epimorphic with val: <7 11 22 33 38| Scale is weakly epimorphic with val: <7 11 22 34 34| Scale is weakly epimorphic with val: <7 11 22 34 37| Scale is weakly epimorphic with val: <7 12 18 28 36| Scale is weakly epimorphic with val: <7 12 18 29 35| Scale is weakly epimorphic with val: <7 12 18 32 35| Scale is weakly epimorphic with val: <7 12 19 29 37| Scale is weakly epimorphic with val: <7 12 19 30 36| Scale is weakly epimorphic with val: <7 12 19 33 36| Scale is weakly epimorphic with val: <7 12 20 28 37| Scale is weakly epimorphic with val: <7 12 20 30 38| Scale is weakly epimorphic with val: <7 12 20 31 37| Scale is weakly epimorphic with val: <7 12 20 34 37| Scale is weakly epimorphic with val: <7 12 21 28 36| Scale is weakly epimorphic with val: <7 12 21 29 38| Scale is weakly epimorphic with val: <7 12 21 32 38| Scale is weakly epimorphic with val: <7 12 22 29 37| Scale is weakly epimorphic with val: <8 11 18 29 35| Scale is weakly epimorphic with val: <8 11 18 30 37| Scale is weakly epimorphic with val: <8 11 18 32 38| Scale is weakly epimorphic with val: <8 11 18 33 37| Scale is weakly epimorphic with val: <8 11 19 28 38| Scale is weakly epimorphic with val: <8 11 19 30 36| Scale is weakly epimorphic with val: <8 11 19 31 38| Scale is weakly epimorphic with val: <8 11 19 34 38| Scale is weakly epimorphic with val: <8 11 20 28 34| Scale is weakly epimorphic with val: <8 11 20 31 37| Scale is weakly epimorphic with val: <8 11 21 29 35| Scale is weakly epimorphic with val: <8 11 21 32 38| Scale is weakly epimorphic with val: <8 11 22 30 36| Scale is weakly epimorphic with val: <8 12 18 28 37| Scale is weakly epimorphic with val: <8 12 18 29 36| Scale is weakly epimorphic with val: <8 12 18 31 37| Scale is weakly epimorphic with val: <8 12 18 34 37| Scale is weakly epimorphic with val: <8 12 19 29 38| Scale is weakly epimorphic with val: <8 12 19 30 37| Scale is weakly epimorphic with val: <8 12 19 32 38| Scale is weakly epimorphic with val: <8 12 20 28 35| Scale is weakly epimorphic with val: <8 12 20 31 38| Scale is weakly epimorphic with val: <8 12 21 29 36| Scale is weakly epimorphic with val: <8 12 22 30 37|
FIT/MODE
3: 0 0 3 N M DE S SD: 39.1462 c. M: 60.7513 c. 6: 0 1 5 N G T3 SD: 21.6171 c. M: 30.1092 c. 7: 0 1 6 N G T3 SD: 18.3909 c. M: 30.1092 c. 8: 0 1 7 N G T3 SD: 17.4052 c. M: 30.1092 c. 9: 0 1 8 N G T3 SD: 17.6622 c. M: 30.1092 c. 10: 0 1 9 N G T3 SD: 18.4968 c. M: 30.1092 c. 11: 1 0 10 N G T3 SD: 12.5102 c. M: 15.4745 c. 13: 1 1 11 N M DE S SD: 10.3144 c. M:-15.8710 c. 14: 1 1 12 N M DE S SD: 6.7821 c. M:-10.3980 c. 15: 1 1 13 N M DE S SD: 3.7214 c. M:-5.6547 c. 16: 1 1 14 N M DE S SD: 1.0489 c. M:-1.5043 c. 33: 2 2 29 N M DE S SD: 0.2249 c. M: 0.3822 c. 49: 3 3 43 N M DE S SD: 0.2593 c. M:-0.3834 c. 82: 5 5 72 N M DE S SD: 0.1500 c. M:-0.2594 c. 115: 7 7 101 N M DE S SD: 0.1379 c. M:-0.2066 c. 148: 9 9 130 N M DE S SD: 0.1452 c. M: 0.1782 c. 197: 12 12 173 N M DE S SD: 0.1390 c. M:-0.2286 c. 312: 19 19 274 N M DE S SD: 0.1379 c. M:-0.2205 c. 427: 26 26 375 N M DE S SD: 0.1377 c. M:-0.2167 c. 459: 28 28 403 N M DE S SD: 0.1576 c. M:-0.2727 c. 466: 28 29 409 N T3 SD: 0.1439 c. M: 0.1837 c. 476: 29 29 418 N M DE S SD: 0.1402 c. M:-0.2339 c. 483: 29 30 424 N T3 SD: 0.1289 c. M: 0.2059 c. 499: 30 31 438 N T3 SD: 0.1227 c. M: 0.1666 c. 500: 30 31 439 N T3 SD: 0.1309 c. M: 0.2265 c. 515: 31 32 452 N T3 SD: 0.1256 c. M:-0.1746 c. 516: 31 32 453 N T3 SD: 0.1133 c. M: 0.1879 c. 532: 32 33 467 N T3 SD: 0.1049 c. M: 0.1516 c. 533: 32 33 468 N T3 SD: 0.1202 c. M: 0.2078 c. 548: 33 34 481 N T3 SD: 0.1060 c. M:-0.1411 c. 549: 33 34 482 N T3 SD: 0.1008 c. M: 0.1720 c. 565: 34 35 496 N T3 SD: 0.0900 c. M: 0.1383 c. 581: 35 36 510 N T3 SD: 0.0889 c. M:-0.1114 c. 582: 35 36 511 N T3 SD: 0.0913 c. M: 0.1580 c. 598: 36 37 525 N T3 SD: 0.0779 c. M: 0.1265 c. 614: 37 38 539 N T3 SD: 0.0743 c. M: 0.0967 c. 615: 37 38 540 N T3 SD: 0.0844 c. M: 0.1455 c. 630: 38 39 553 N T3 SD: 0.0802 c. M:-0.1209 c. 631: 38 39 554 N T3 SD: 0.0684 c. M: 0.1160 c. 647: 39 40 568 N T3 SD: 0.0618 c. M: 0.0879 c. 664: 40 41 583 N T3 SD: 0.0615 c. M: 0.1065 c. 680: 41 42 597 N T3 SD: 0.0515 c. M: 0.0800 c. 696: 42 43 611 N T3 SD: 0.0528 c. M:-0.0732 c. 697: 42 43 612 N T3 SD: 0.0571 c. M: 0.0979 c. 713: 43 44 626 N T3 SD: 0.0436 c. M: 0.0728 c. 729: 44 45 640 N T3 SD: 0.0414 c. M:-0.0526 c. 746: 45 46 655 N T3 SD: 0.0383 c. M: 0.0662 c. 762: 46 47 669 N T3 SD: 0.0318 c. M: 0.0435 c. 779: 47 48 684 N T3 SD: 0.0357 c. M: 0.0602 c. 795: 48 49 698 N T3 SD: 0.0242 c. M: 0.0385 c. 828: 50 51 727 N T3 SD: 0.0196 c. M: 0.0340 c. 844: 51 52 741 N T3 SD: 0.0186 c. M:-0.0291 c. 861: 52 53 756 N T3 SD: 0.0190 c. M: 0.0298 c. 877: 53 54 770 N T3 SD: 0.0100 c. M:-0.0136 c. 910: 55 56 799 N T3 SD: 0.0044 c. M: 0.0076 c. 1853: 112 114 1627 N T3 SD: 0.0056 c. M: 0.0075 c. 1869: 113 115 1641 N T3 SD: 0.0035 c. M:-0.0054 c. 1902: 115 117 1670 N T3 SD: 0.0024 c. M:-0.0040 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 103.0598 cents 7 x 8:9 S SD: 90.8405 cents 8 x 9:11 SD: 76.3748 cents 9 x 10:12 S SD: 60.8262 cents 10 x 11:13 SD: 56.5461 cents 11 x 12:15 S SD: 48.9722 cents 12 x 13:16 SD: 38.9107 cents 13 x 14:17 SD: 37.7250 cents 14 x 15:19 SD: 33.1045 cents 15 x 16:20 S SD: 25.4900 cents 16 x 17:21 SD: 25.9679 cents 17 x 18:23 SD: 22.9034 cents 18 x 19:24 SD: 16.4259 cents 19 x 20:25 S SD: 18.1148 cents 20 x 21:27 SD: 16.0075 cents 21 x 22:28 SD: 9.8929 cents 22 x 23:29 SD: 12.7875 cents 23 x 24:31 SD: 11.3739 cents 24 x 25:32 SD: 4.9606 cents 25 x 26:33 SD: 9.4054 cents 26 x 27:35 SD: 8.5950 cents 27 x 28:36 SD: 1.1048 cents 28 x 29:37 SD: 7.7634 cents 29 x 30:39 SD: 7.5013 cents 30 x 31:40 SD: 1.9922 cents 31 x 32:41 SD: 7.5828 cents 32 x 33:43 SD: 7.7045 cents 33 x 34:44 SD: 4.5344 cents 34 x 35:45 SD: 8.2902 cents 35 x 36:47 SD: 8.5932 cents 36 x 37:48 SD: 6.6586 cents 37 x 38:49 SD: 9.3596 cents 38:39 x 51 SD: 9.3503 cents 39:40 x 52 SD: 6.8609 cents 40:41 x 53 SD: 8.3302 cents 41:42 x 55 SD: 7.8348 cents 42:43:44:56 SD: 7.4864 cents 44:45:46:59 SD: 6.9618 cents 45:46:47:60 SD: 5.5200 cents 47:48:49:63 SD: 5.3162 cents 48:49:50:64 SD: 3.7955 cents 51:52:53:68 SD: 2.2717 cents 54:55:56:72 SD: 0.9207 cents 57:58:59:76 SD: 0.3492 cents 111:113:115:148 SD: 0.3231 cents 168:171:174:224 SD: 0.1776 cents 225:229:233:300 SD: 0.1594 cents