Scala analysis: 018_H5
Hyperenharmonic tetrachord 48/47 * 94/93 * 31/24
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 48/47 36.448379 2: 32/31 54.964428 Greek enharmonic 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 31/24 443.0806 1: 48/47 36.4484 2: 94/93 18.5160 3: 31/24 443.0806
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 94/93 18.516 cents 1: 1 48/47 36.448 cents 1: 1 31/24 443.081 cents 2: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 2: 1 47/36 461.597 cents 2: 1 62/47 479.529 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 : 36.4 55.0 498.0 36.4 : 18.5 461.6 498.0 55.0 : 443.1 479.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.5160 .. 443.0806 cents 961/752, 424.5645 cents 94/93, 18.5160 cents 2: 54.9644 .. 479.5290 cents 961/752, 424.5645 cents 768/961,-388.1161 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 94/93, 18.5160 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 31/24, 443.0806 cents Average / Smallest step : 8.966006 Largest / Average step : 2.668919 Largest / Smallest step : 23.929542 Median interval of one step : 48/47, 36.4484 cents, amount: 1 Least squares average step : 117.17945 cents, oct.: 351.53834 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1749-tone equal temperament with octave 4/3 degrees: 128 193 1749 Least number of segments generator : 875 of 249.165 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1685 of 479.820 cents and inv. generated superset size: 86 = 83 more = 2866.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 18.51605 cents Scale diversity : 0.081769 Lumma stability : 0.074355 Lumma impropriety factor : 0.779279 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 : 2232/2209, 17.9323 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 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 424.5645 cents: 2 -- Rational properties -- Prime limit : 47 Odd number limit : 93 (O: 47 U: 93) Highest odd numerator or denominator: 47 Scale harmonicity : 0.096774 Fundamental : 1/4371, -12.0937 octaves, 0.0599 Hz. Guide tone : 96, 6.5850 octaves, 25116.054 Hz. Exponens Consonantiae : 4.196160E+05, 18.67871 octaves Euler's gradus suavitatis : 86 Sum of Mann's harmonic distance : 82.5, average 27.50000 Mersenne's string divisions : 5985 Sum of van Prooijen's expressibility: 3.64058, average 1.21353 Sum of Tenney's harmonic distance : 7.42903, average 2.47634 Vogel's harmonic complexity : 58.66667 Wille's k value : 728 Wilson's harmonic complexity : 84 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 18.76409, average 3.12735 Lattice compactness (without 2's) : 6.00000, average 1.00000 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.66667 11 3: -1 .. 1 0.00000 2 1 31: -1 .. 0 -0.33333 1 1 47: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is JI-epimorphic with val: <7 11 33 38| Scale is weakly epimorphic with val: <7 11 33 41| Scale is weakly epimorphic with val: <7 11 34 37| Scale is weakly epimorphic with val: <7 11 34 40| Scale is weakly epimorphic with val: <7 11 34 43| Scale is weakly epimorphic with val: <7 11 36 38| Scale is weakly epimorphic with val: <7 11 36 41| Scale is weakly epimorphic with val: <7 11 37 37| Scale is weakly epimorphic with val: <7 11 37 40| Scale is weakly epimorphic with val: <7 11 37 43| Scale is weakly epimorphic with val: <7 11 39 41| Scale is weakly epimorphic with val: <7 12 34 37| Scale is weakly epimorphic with val: <7 12 37 37| Scale is weakly epimorphic with val: <8 11 33 40| Scale is weakly epimorphic with val: <8 11 36 40| Scale is weakly epimorphic with val: <8 11 37 39| Scale is weakly epimorphic with val: <8 11 37 42| Scale is weakly epimorphic with val: <8 11 39 40| Scale is weakly epimorphic with val: <8 12 35 41| Scale is weakly epimorphic with val: <8 12 37 39| Scale is weakly epimorphic with val: <8 12 37 42| Scale is weakly epimorphic with val: <8 12 38 41|
FIT/MODE
3: 0 0 3 N M DE S SD: 38.0770 c. M: 54.9644 c. 6: 0 1 5 N G T3 SD: 26.5512 c. M: 36.4484 c. 7: 1 0 6 N G T3 SD: 22.1066 c. M:-34.7009 c. 8: 1 0 7 N G T3 SD: 15.4831 c. M:-25.8072 c. 9: 1 0 8 N G T3 SD: 10.9083 c. M:-18.8900 c. 10: 1 0 9 N G T3 SD: 8.2666 c. M:-13.3561 c. 11: 1 0 10 N G T3 SD: 7.5673 c. M: 9.6876 c. 15: 1 1 13 N M DE S SD: 6.8664 c. M:-11.4416 c. 16: 1 1 14 N M DE S SD: 5.2112 c. M:-7.2912 c. 17: 1 1 15 N M DE S SD: 4.6302 c. M: 7.1516 c. 18: 1 1 16 N M DE S SD: 5.0733 c. M: 8.7792 c. 24: 2 1 21 N T3 SD: 5.1224 c. M:-7.2912 c. 25: 2 1 22 N T3 SD: 3.3949 c. M:-4.8010 c. 26: 2 1 23 N T3 SD: 1.8011 c. M:-2.5023 c. 27: 2 1 24 N T3 SD: 0.3351 c. M:-0.4438 c. 82: 6 3 73 N T3 SD: 0.1738 c. M: 0.3010 c. 109: 8 4 97 N T3 SD: 0.0983 c. M: 0.1338 c. 136: 10 5 121 N T3 SD: 0.1014 c. M:-0.1726 c. 245: 18 9 218 N T3 SD: 0.0938 c. M:-0.1427 c. 354: 26 13 315 N T3 SD: 0.0935 c. M:-0.1312 c. 425: 31 16 378 N T3 SD: 0.0955 c. M: 0.1204 c. 452: 33 17 402 N T3 SD: 0.0898 c. M:-0.1290 c. 453: 33 17 403 N T3 SD: 0.0965 c. M: 0.1670 c. 463: 34 17 412 N T3 SD: 0.0940 c. M:-0.1251 c. 479: 35 18 426 N T3 SD: 0.0888 c. M:-0.1428 c. 480: 35 18 427 N T3 SD: 0.0782 c. M: 0.1326 c. 507: 37 19 451 N T3 SD: 0.0647 c. M: 0.1019 c. 534: 39 20 475 N T3 SD: 0.0563 c. M: 0.0743 c. 561: 41 21 499 N T3 SD: 0.0533 c. M:-0.0780 c. 589: 43 22 524 N T3 SD: 0.0511 c. M: 0.0886 c. 616: 45 23 548 N T3 SD: 0.0386 c. M: 0.0652 c. 643: 47 24 572 N T3 SD: 0.0306 c. M: 0.0438 c. 670: 49 25 596 N T3 SD: 0.0288 c. M:-0.0435 c. 725: 53 27 645 N T3 SD: 0.0233 c. M: 0.0396 c. 752: 55 28 669 N T3 SD: 0.0133 c. M: 0.0222 c. 779: 57 29 693 N T3 SD: 0.0114 c. M:-0.0187 c. 861: 63 32 766 N T3 SD: 0.0076 c. M: 0.0117 c. 888: 65 33 790 N T3 SD: 0.0044 c. M:-0.0076 c. 1640: 120 61 1459 N T3 SD: 0.0038 c. M: 0.0061 c. 1749: 128 65 1556 N T3 SD: 0.0034 c. M: 0.0058 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: 105.9532 cents 7 x 8:9 S SD: 93.5600 cents 8 x 9:11 SD: 79.0930 cents 9 x 10:12 S SD: 63.7196 cents 10 x 11:13 SD: 59.2240 cents 11 x 12:15 S SD: 51.6404 cents 12 x 13:16 SD: 41.8041 cents 13 x 14:17 SD: 40.3360 cents 14 x 15:19 SD: 35.6945 cents 15 x 16:20 S SD: 28.3834 cents 16 x 17:21 SD: 28.4712 cents 17 x 18:23 SD: 25.3668 cents 18 x 19:24 SD: 19.3193 cents 19 x 20:25 S SD: 20.4371 cents 20 x 21:27 SD: 18.2547 cents 21 x 22:28 SD: 12.7863 cents 22 x 23:29 SD: 14.7912 cents 23 x 24:31 SD: 13.2344 cents 24 x 25:32 SD: 7.8540 cents 25 x 26:33 SD: 10.8406 cents 26 x 27:35 SD: 9.7732 cents 27 x 28:36 SD: 3.9982 cents 28 x 29:37 SD: 8.2851 cents 29 x 30:39 SD: 7.6604 cents 30 x 31:40 SD: 0.9012 cents 31 x 32:41 SD: 7.0091 cents 32 x 33:43 SD: 6.7892 cents 33 x 34:44 SD: 1.6410 cents 34 x 35:45 SD: 6.8208 cents 35 x 36:47 SD: 6.8956 cents 36 x 37:48 SD: 3.7652 cents 37 x 38:49 SD: 7.3335 cents 38:39 x 51 SD: 7.0973 cents 39:40 x 52 SD: 3.6913 cents 40:41 x 53 SD: 6.2751 cents 41:42 x 55 SD: 5.8850 cents 42:43 x 56 SD: 2.1442 cents 43:44 x 57 SD: 5.3183 cents 44:45 x 59 SD: 5.0559 cents 45:46 x 60 SD: 0.8011 cents 46:47 x 61 SD: 4.7335 cents 51:52:53:68 SD: 3.9898 cents 54:55:56:72 SD: 3.0887 cents 57:58:59:76 SD: 2.6383 cents 71 x 73:95 SD: 4.5893 cents 72 x 74:96 SD: 3.7652 cents 73 x 75:97 SD: 5.0509 cents 74 x 76:99 SD: 5.2786 cents 75:77 x 100 SD: 4.5565 cents 76:78 x 101 SD: 5.1271 cents 77:79 x 103 SD: 4.8634 cents 78:80:81:104 SD: 4.2440 cents 80:82:83:107 SD: 4.0245 cents 81:83:84:108 SD: 3.2887 cents 83:85:86:111 SD: 3.2011 cents 84:86:87:112 SD: 2.4009 cents 87:89:90:116 SD: 1.5740 cents 90:92:93:120 SD: 0.8039 cents 93:95:96:124 SD: 0.1293 cents 468:478:483:624 SD: 0.1265 cents 561:573:579:748 SD: 0.1159 cents