Scala analysis: 043_H11
Hyperenharmonic tetrachord 75/74 * 37/36 * 32/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75/74 23.238390 2: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/25 427.3726 classic diminished fourth 1: 75/74 23.2384 2: 37/36 47.4340 3: 32/25 427.3726 classic diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 75/74 23.238 cents 1: 1 37/36 47.434 cents 1: 1 32/25 427.373 cents classic diminished fourth 2: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 48/37 450.611 cents 2: 1 296/225 474.807 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 : 23.2 70.7 498.0 23.2 : 47.4 474.8 498.0 70.7 : 427.4 450.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 23.2384 .. 427.3726 cents 2368/1875, 404.1342 cents 75/74, 23.2384 cents 2: 70.6724 .. 474.8066 cents 2368/1875, 404.1342 cents 625/768,-356.7001 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 75/74, 23.2384 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/25, 427.3726 cents Average / Smallest step : 7.143998 Largest / Average step : 2.574301 Largest / Smallest step : 18.390800 Median interval of one step : 37/36, 47.4340 cents, amount: 1 Least squares average step : 118.47987 cents, oct.: 355.43962 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1050-tone equal temperament with octave 4/3 degrees: 49 149 1050 Least number of segments generator : 527 of 249.971 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 607 of 287.917 cents and inv. generated superset size: 51 = 48 more = 1700.000% 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 23.23839 cents Scale diversity : 0.187361 Lumma stability : 0.093318 Lumma impropriety factor : 0.716201 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 : 75/74, 23.2384 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 : 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 379.9385 cents: 2 -- Rational properties -- Prime limit : 37 Odd number limit : 225 (O: 75 U: 225) Highest odd numerator or denominator: 75 Scale harmonicity : 0.043228 Fundamental : 1/888, -9.7944 octaves, 0.2946 Hz. Guide tone : 300, 8.2288 octaves, 78487.670 Hz. Exponens Consonantiae : 2.664000E+05, 18.02323 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 102.5, average 34.16667 Mersenne's string divisions : 7301 Sum of van Prooijen's expressibility: 3.75012, average 1.25004 Sum of Tenney's harmonic distance : 7.60163, average 2.53388 Vogel's harmonic complexity : 35.66667 Wille's k value : 462 Wilson's harmonic complexity : 53 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 20.76391, average 3.46065 Lattice compactness (without 2's) : 12.30056, average 2.05009 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.66667 6 3: -1 .. 1 -0.33333 3 1 5: 0 .. 2 1.33333 4 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 19 39| Scale is weakly epimorphic with val: <6 11 16 35| Scale is weakly epimorphic with val: <6 11 16 38| Scale is weakly epimorphic with val: <6 11 16 41| Scale is weakly epimorphic with val: <6 11 17 36| Scale is weakly epimorphic with val: <7 10 17 35| Scale is weakly epimorphic with val: <7 10 17 38| Scale is weakly epimorphic with val: <7 10 17 41| Scale is weakly epimorphic with val: <7 10 18 36| Scale is weakly epimorphic with val: <7 11 15 35| Scale is weakly epimorphic with val: <7 11 15 38| Scale is weakly epimorphic with val: <7 11 15 41| Scale is JI-epimorphic with val: <7 11 17 37| Scale is weakly epimorphic with val: <7 11 17 40| Scale is weakly epimorphic with val: <7 11 18 35| Scale is weakly epimorphic with val: <7 11 18 38| Scale is weakly epimorphic with val: <7 11 18 41| Scale is weakly epimorphic with val: <7 12 17 36| Scale is weakly epimorphic with val: <7 12 18 37| Scale is weakly epimorphic with val: <7 12 18 40| Scale is weakly epimorphic with val: <8 11 18 36| Scale is weakly epimorphic with val: <8 11 19 37| Scale is weakly epimorphic with val: <8 11 19 40| Scale is weakly epimorphic with val: <8 12 19 39|
FIT/MODE
3: 0 0 3 N M DE S SD: 42.9520 c. M: 70.6724 c. 4: 0 0 4 N M DE S SD: 42.9520 c. M: 70.6724 c. 5: 0 1 4 N G T3 SD: 21.4270 c. M:-28.9366 c. 6: 0 1 5 N G T3 SD: 15.1897 c. M: 23.2384 c. 7: 0 1 6 N G T3 SD: 13.4195 c. M: 23.2384 c. 8: 0 1 7 N G T3 SD: 14.2696 c. M: 23.2384 c. 13: 1 1 11 N M DE S SD: 9.3557 c. M:-15.0728 c. 14: 1 1 12 N M DE S SD: 7.1277 c. M:-12.3363 c. 15: 1 1 13 N M DE S SD: 6.2582 c. M:-9.9646 c. 16: 1 1 14 N M DE S SD: 6.6605 c. M: 8.4168 c. 18: 1 2 15 N T3 SD: 7.5672 c. M:-12.3351 c. 19: 1 2 16 N T3 SD: 4.9095 c. M:-7.9663 c. 20: 1 2 17 N T3 SD: 2.5195 c. M:-4.0343 c. 21: 1 2 18 N T3 SD: 0.3898 c. M:-0.4780 c. 64: 3 6 55 N T3 SD: 0.3717 c. M: 0.6348 c. 85: 4 8 73 N T3 SD: 0.2376 c. M: 0.3602 c. 106: 5 10 91 N T3 SD: 0.1848 c. M:-0.2543 c. 127: 6 12 109 N T3 SD: 0.1749 c. M:-0.2913 c. 148: 7 14 127 N T3 SD: 0.1835 c. M:-0.3178 c. 169: 8 16 145 N T3 SD: 0.1976 c. M:-0.3377 c. 233: 11 22 200 N T3 SD: 0.1763 c. M:-0.2745 c. 260: 12 25 223 N T3 SD: 0.1868 c. M: 0.2517 c. 261: 12 25 224 N T3 SD: 0.2001 c. M: 0.3398 c. 275: 13 26 236 N T3 SD: 0.1780 c. M:-0.3056 c. 281: 13 27 241 N T3 SD: 0.1721 c. M:-0.2237 c. 282: 13 27 242 N T3 SD: 0.1618 c. M: 0.2789 c. 303: 14 29 260 N T3 SD: 0.1308 c. M: 0.2264 c. 324: 15 31 278 N T3 SD: 0.1066 c. M: 0.1808 c. 345: 16 33 296 N T3 SD: 0.0893 c. M: 0.1407 c. 366: 17 35 314 N T3 SD: 0.0792 c. M: 0.1052 c. 387: 18 37 332 N T3 SD: 0.0760 c. M:-0.1092 c. 388: 18 37 333 N T3 SD: 0.0878 c. M: 0.1332 c. 408: 19 39 350 N T3 SD: 0.0784 c. M:-0.1281 c. 409: 19 39 351 N T3 SD: 0.0643 c. M: 0.1018 c. 430: 20 41 369 N T3 SD: 0.0439 c. M: 0.0735 c. 451: 21 43 387 N T3 SD: 0.0277 c. M: 0.0478 c. 472: 22 45 405 N T3 SD: 0.0200 c. M:-0.0246 c. 557: 26 53 478 N T3 SD: 0.0205 c. M: 0.0341 c. 578: 27 55 496 N T3 SD: 0.0178 c. M:-0.0267 c. 1008: 47 96 865 N T3 SD: 0.0136 c. M: 0.0172 c. 1029: 48 98 883 N T3 SD: 0.0054 c. M: 0.0072 c. 1050: 49 100 901 N T3 SD: 0.0026 c. M:-0.0037 c. 2079: 97 198 1784 N T3 SD: 0.0014 c. M: 0.0023 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: 98.0992 cents 7 x 8:9 S SD: 86.2045 cents 8 x 9:11 SD: 71.7465 cents 9 x 10:12 S SD: 55.8656 cents 10 x 11:13 SD: 52.0088 cents 11 x 12:15 S SD: 44.4635 cents 12 x 13:16 SD: 33.9501 cents 13 x 14:17 SD: 33.3574 cents 14 x 15:19 SD: 28.7988 cents 15 x 16:20 S SD: 20.5294 cents 16 x 17:21 SD: 21.9012 cents 17 x 18:23 SD: 18.9648 cents 18 x 19:24 SD: 11.4653 cents 19 x 20:25 S SD: 14.6155 cents 20 x 21:27 SD: 12.7751 cents 21 x 22:28 SD: 4.9323 cents 22 x 23:29 SD: 10.3798 cents 23 x 24:31 SD: 9.4782 cents 24 x 25:32 SD: 0.0000 cents 25 x 26:33 SD: 8.8095 cents 26 x 27:35 SD: 8.7024 cents 27 x 28:36 SD: 3.8558 cents 28 x 29:37 SD: 9.2129 cents 29 x 30:39 SD: 9.5443 cents 30 x 31:40 SD: 6.9528 cents 31 x 32:41 SD: 10.5268 cents 32 x 33:43 SD: 11.0029 cents 33 x 34:44 SD: 9.4950 cents 34 x 35:45 SD: 12.0728 cents 35 x 36:47 SD: 12.5651 cents 36 x 38:48 SD: 11.4653 cents 37:38:39:49 SD: 10.9668 cents 38:39:40:51 SD: 10.1640 cents 39:40:41:52 SD: 8.6737 cents 41:42:43:55 SD: 8.1043 cents 42:43:44:56 SD: 6.6958 cents 44:45:46:59 SD: 6.5078 cents 45:46:47:60 SD: 5.1711 cents 48:49:50:64 SD: 4.1528 cents 51:52:53:68 SD: 3.7171 cents 63:64:66:84 SD: 3.5515 cents 65:66:68:87 SD: 3.4919 cents 66:67:69:88 SD: 2.2926 cents 69:70:72:92 SD: 1.1472 cents 72:73:75:96 SD: 0.2137 cents 456:462:475:608 SD: 0.2025 cents 525:532:547:700 SD: 0.1671 cents 528:535:550:704 SD: 0.1457 cents 597:605:622:796 SD: 0.1327 cents 600:608:625:800 SD: 0.1026 cents