Scala analysis: 003_H1
Hyperenharmonic tetrachord 120/119 * 119/117 * 13/10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 120/119 14.487399 2: 40/39 43.831051 tridecimal minor diesis 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/10 454.2139 tridecimal semi-diminished fourth 1: 120/119 14.4874 2: 119/117 29.3437 3: 13/10 454.2139 tridecimal semi-diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 120/119 14.487 cents 1: 1 119/117 29.344 cents 1: 1 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 40/39 43.831 cents tridecimal minor diesis 2: 1 156/119 468.701 cents 2: 1 119/90 483.558 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 : 14.5 43.8 498.0 14.5 : 29.3 483.6 498.0 43.8 : 454.2 468.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.4874 .. 454.2139 cents 1547/1200, 439.7265 cents 120/119, 14.4874 cents 2: 43.8311 .. 483.5576 cents 1547/1200, 439.7265 cents 400/507,-410.3829 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 120/119, 14.4874 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 13/10, 454.2139 cents Average / Smallest step : 11.459269 Largest / Average step : 2.735981 Largest / Smallest step : 31.352347 Median interval of one step : 119/117, 29.3437 cents, amount: 1 Least squares average step : 114.02032 cents, oct.: 342.06096 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1375-tone equal temperament with octave 4/3 degrees: 40 121 1375 Least number of segments generator : 688 of 249.204 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1011 of 366.199 cents and inv. generated superset size: 16 = 13 more = 533.333% 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 14.48740 cents Scale diversity : 0.007064 Lumma stability : 0.058177 Lumma impropriety factor : 0.823988 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 : 120/119, 14.4874 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 483.5576 cents Number of appreciable 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% Limited inverse transpositions with margin 424.8703 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 119 (O: 119 U: 119) Highest odd numerator or denominator: 119 Scale harmonicity : 0.012938 Average absolute harmonicity : 0.087522 Specific harmonicity : 0.066132 Fundamental : 1/4641, -12.1802 octaves, 0.0564 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 5.569200E+05, 19.08711 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 162.5, average 54.16667 Mersenne's string divisions : 132167 Sum of van Prooijen's expressibility: 4.14373, average 1.38124 Sum of Tenney's harmonic distance : 8.42703, average 2.80901 Vogel's harmonic complexity : 32.66667 Wille's k value : 773 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.51195, average 2.75199 Lattice compactness (without 2's) : 11.43777, average 1.90629 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -1 .. 1 -0.33333 3 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 1 17: -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: <7 11 16 19 27 31| Scale is weakly epimorphic with val: <7 11 16 19 28 30| Scale is weakly epimorphic with val: <7 11 16 20 27 30| Scale is weakly epimorphic with val: <7 11 16 20 28 29| Scale is weakly epimorphic with val: <7 11 16 21 27 29| Scale is weakly epimorphic with val: <7 11 16 21 28 31| Scale is weakly epimorphic with val: <7 11 17 19 26 31| Scale is weakly epimorphic with val: <7 11 17 19 28 29| Scale is weakly epimorphic with val: <7 11 17 20 26 30| Scale is weakly epimorphic with val: <7 11 17 20 28 31| Scale is weakly epimorphic with val: <7 11 17 21 26 29| Scale is weakly epimorphic with val: <7 11 17 21 28 30| Scale is JI-epimorphic with val: <7 11 18 19 26 30| Scale is weakly epimorphic with val: <7 11 18 19 27 29| Scale is JI-epimorphic with val: <7 11 18 20 26 29| Scale is weakly epimorphic with val: <7 11 18 20 27 31| Scale is weakly epimorphic with val: <7 11 18 21 26 31| Scale is weakly epimorphic with val: <7 11 18 21 27 30| Scale is weakly epimorphic with val: <7 12 18 19 26 29|
FIT/MODE
3: 0 0 3 N M DE S SD: 26.6524 c. M: 43.8311 c. 7: 0 1 6 N G T3 SD: 17.8528 c. M:-27.3182 c. 8: 0 1 7 N G T3 SD: 13.5321 c. M:-18.4246 c. 9: 0 1 8 N G T3 SD: 10.6818 c. M: 14.4874 c. 10: 0 1 9 N G T3 SD: 9.0474 c. M: 14.4874 c. 11: 0 1 10 N G T3 SD: 8.4059 c. M: 14.4874 c. 12: 0 1 11 N G T3 SD: 8.4715 c. M: 14.4874 c. 13: 0 1 12 N G T3 SD: 8.9509 c. M: 14.4874 c. 14: 0 1 13 N G T3 SD: 9.6273 c. M: 14.4874 c. 20: 1 1 18 N M DE S SD: 6.9318 c. M:-10.4149 c. 21: 1 1 19 N M DE S SD: 5.7198 c. M:-9.2290 c. 22: 1 1 20 N M DE S SD: 4.7794 c. M:-8.1510 c. 23: 1 1 21 N M DE S SD: 4.1487 c. M:-7.1667 c. 24: 1 1 22 N M DE S SD: 3.8583 c. M:-6.2645 c. 25: 1 1 23 N M DE S SD: 3.8916 c. M:-5.4344 c. 30: 1 2 27 N T3 SD: 3.6584 c. M:-5.9734 c. 31: 1 2 28 N T3 SD: 2.6809 c. M:-4.3669 c. 32: 1 2 29 N T3 SD: 1.7647 c. M:-2.8607 c. 33: 1 2 30 N T3 SD: 0.9048 c. M:-1.4458 c. 34: 1 2 31 N T3 SD: 0.1139 c. M:-0.1610 c. 171: 5 10 156 N T3 SD: 0.0933 c. M: 0.1429 c. 205: 6 12 187 N T3 SD: 0.0776 c. M: 0.1003 c. 239: 7 14 218 N T3 SD: 0.0703 c. M:-0.0997 c. 273: 8 16 249 N T3 SD: 0.0676 c. M:-0.1073 c. 307: 9 18 280 N T3 SD: 0.0675 c. M:-0.1133 c. 341: 10 20 311 N T3 SD: 0.0687 c. M:-0.1180 c. 375: 11 22 342 N T3 SD: 0.0704 c. M:-0.1219 c. 409: 12 24 373 N T3 SD: 0.0724 c. M:-0.1252 c. 443: 13 26 404 N T3 SD: 0.0744 c. M:-0.1279 c. 444: 13 26 405 N T3 SD: 0.0732 c. M:-0.0950 c. 477: 14 28 435 N T3 SD: 0.0763 c. M:-0.1303 c. 511: 15 30 466 N T3 SD: 0.0781 c. M:-0.1323 c. 512: 15 30 467 N T3 SD: 0.0685 c. M:-0.1038 c. 580: 17 34 529 N T3 SD: 0.0673 c. M:-0.1105 c. 649: 19 38 592 N T3 SD: 0.0744 c. M:-0.0933 c. 658: 19 39 600 N T3 SD: 0.0733 c. M: 0.1062 c. 683: 20 40 623 N T3 SD: 0.0720 c. M:-0.0966 c. 692: 20 41 631 N T3 SD: 0.0678 c. M: 0.0930 c. 693: 20 41 632 N T3 SD: 0.0659 c. M: 0.1138 c. 726: 21 43 662 N T3 SD: 0.0633 c. M: 0.0811 c. 727: 21 43 663 N T3 SD: 0.0588 c. M: 0.1010 c. 760: 22 45 693 N T3 SD: 0.0596 c. M:-0.0755 c. 761: 22 45 694 N T3 SD: 0.0526 c. M: 0.0893 c. 795: 23 47 725 N T3 SD: 0.0471 c. M: 0.0785 c. 829: 24 49 756 N T3 SD: 0.0424 c. M: 0.0687 c. 863: 25 51 787 N T3 SD: 0.0384 c. M: 0.0597 c. 864: 25 51 788 N T3 SD: 0.0458 c. M: 0.0764 c. 897: 26 53 818 N T3 SD: 0.0350 c. M: 0.0513 c. 898: 26 53 819 N T3 SD: 0.0400 c. M: 0.0674 c. 931: 27 55 849 N T3 SD: 0.0324 c. M: 0.0436 c. 932: 27 55 850 N T3 SD: 0.0348 c. M: 0.0591 c. 965: 28 57 880 N T3 SD: 0.0304 c. M:-0.0382 c. 966: 28 57 881 N T3 SD: 0.0299 c. M: 0.0513 c. 999: 29 59 911 N T3 SD: 0.0291 c. M:-0.0408 c. 1000: 29 59 912 N T3 SD: 0.0255 c. M: 0.0441 c. 1034: 30 61 943 N T3 SD: 0.0216 c. M: 0.0374 c. 1068: 31 63 974 N T3 SD: 0.0181 c. M: 0.0310 c. 1102: 32 65 1005 N T3 SD: 0.0152 c. M: 0.0251 c. 1136: 33 67 1036 N T3 SD: 0.0129 c. M: 0.0195 c. 1170: 34 69 1067 N T3 SD: 0.0115 c. M: 0.0143 c. 1204: 35 71 1098 N T3 SD: 0.0111 c. M:-0.0168 c. 1239: 36 73 1130 N T3 SD: 0.0132 c. M: 0.0164 c. 1272: 37 75 1160 N T3 SD: 0.0127 c. M:-0.0220 c. 1273: 37 75 1161 N T3 SD: 0.0098 c. M: 0.0125 c. 1307: 38 77 1192 N T3 SD: 0.0067 c. M: 0.0092 c. 1341: 39 79 1223 N T3 SD: 0.0039 c. M: 0.0061 c. 1375: 40 81 1254 N T3 SD: 0.0019 c. M: 0.0031 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: 111.5199 cents 7 x 8:9 S SD: 98.8199 cents 8 x 9:11 SD: 84.3553 cents 9 x 10:12 S SD: 69.2863 cents 10 x 11:13 SD: 64.4284 cents 11 x 12:15 S SD: 56.8357 cents 12 x 13:16 SD: 47.3708 cents 13 x 14:17 SD: 45.4555 cents 14 x 15:19 SD: 40.7924 cents 15 x 16:20 S SD: 33.9501 cents 16 x 17:21 SD: 33.4646 cents 17 x 18:23 SD: 30.3207 cents 18 x 19:24 SD: 24.8860 cents 19 x 20:25 S SD: 25.2393 cents 20 x 21:27 SD: 22.9881 cents 21 x 22:28 SD: 18.3530 cents 22 x 23:29 SD: 19.2923 cents 23 x 24:31 SD: 17.6160 cents 24 x 25:32 SD: 13.4207 cents 25 x 26:33 SD: 14.8498 cents 26 x 27:35 SD: 13.5737 cents 27 x 28:36 SD: 9.5649 cents 28 x 29:37 SD: 11.4824 cents 29 x 30:39 SD: 10.5079 cents 30 x 31:40 SD: 6.4679 cents 31 x 32:41 SD: 8.9507 cents 32 x 33:43 SD: 8.2259 cents 33 x 34:44 SD: 3.9257 cents 34 x 35:45 SD: 7.1345 cents 35 x 36:47 SD: 6.6376 cents 36 x 37:48 SD: 1.8015 cents 37 x 38:49 SD: 5.9839 cents 38 x 39:51 SD: 5.7047 cents 39 x 40:52 SD: 0.0000 cents 40 x 41:53 SD: 5.4540 cents 41 x 42:55 SD: 5.3671 cents 42 x 43:56 SD: 1.5471 cents 43 x 44:57 SD: 5.4348 cents 44 x 45:59 SD: 5.4879 cents 45 x 46:60 SD: 2.8902 cents 46 x 47:61 SD: 5.7566 cents 47 x 48:63 SD: 5.8918 cents 48 x 49:64 SD: 4.0671 cents 49 x 50:65 SD: 6.2617 cents 50 x 51:67 SD: 6.4367 cents 51 x 52:68 SD: 5.1069 cents 52 x 53:69 SD: 6.8451 cents 53 x 54:71 SD: 7.0347 cents 54 x 55:72 SD: 6.0322 cents 55 x 56:73 SD: 7.4481 cents 56 x 57:75 SD: 7.6390 cents 57 x 58:76 SD: 6.8609 cents 58 x 59:77 SD: 8.0406 cents 59:60:61:79 SD: 7.1472 cents 60:61:62:80 SD: 6.3854 cents 62:63:64:83 SD: 6.2099 cents 63:64:65:84 SD: 5.4651 cents 65:66:67:87 SD: 5.3892 cents 66:67:68:88 SD: 4.6544 cents 69:70:71:92 SD: 3.9497 cents 72:73:74:96 SD: 3.3531 cents 75:76:77:100 SD: 2.8729 cents 78:79:80:104 SD: 2.5223 cents 81:82:83:108 SD: 2.3143 cents 84:85:86:112 SD: 2.2505 cents 105:106:108:140 SD: 1.7668 cents 108:109:111:144 SD: 1.2970 cents 111:112:114:148 SD: 0.8529 cents 114:115:117:152 SD: 0.4342 cents 117:118:120:156 SD: 0.0822 cents