Scala analysis: 007_H2
Hyperenharmonic tetrachord 54/53 * 106/105 * 35/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 54/53 32.360457 2: 36/35 48.770381 septimal diesis, 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 35/27 449.2746 septimal semi-diminished fourth, 9/4-tone 1: 54/53 32.3605 2: 106/105 16.4099 3: 35/27 449.2746 septimal semi-diminished fourth, 9/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 106/105 16.410 cents 1: 1 54/53 32.360 cents 1: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 36/35 48.770 cents septimal diesis, 1/4-tone 2: 1 106/81 465.685 cents 2: 1 70/53 481.635 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 : 32.4 48.8 498.0 32.4 : 16.4 465.7 498.0 48.8 : 449.3 481.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.4099 .. 449.2746 cents 1225/954, 432.8647 cents 106/105, 16.4099 cents 2: 48.7704 .. 481.6351 cents 1225/954, 432.8647 cents 972/1225,-400.5042 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 106/105, 16.4099 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 35/27, 449.2746 cents Average / Smallest step : 10.116744 Largest / Average step : 2.706229 Largest / Smallest step : 27.378226 Median interval of one step : 54/53, 32.3605 cents, amount: 1 Least squares average step : 116.00259 cents, oct.: 348.00776 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1062-tone equal temperament with octave 4/3 degrees: 69 104 1062 Least number of segments generator : 533 of 249.960 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 925 of 433.796 cents and inv. generated superset size: 39 = 36 more = 1300.000% 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 16.40992 cents Scale diversity : 0.040303 Lumma stability : 0.065897 Lumma impropriety factor : 0.804153 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 : 2835/2809, 15.9505 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 481.6351 cents Number of appreciable 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 432.8647 cents: 2 -- Rational properties -- Prime limit : 53 Odd number limit : 105 (O: 53 U: 105) Highest odd numerator or denominator: 53 Scale harmonicity : 0.034069 Fundamental : 1/5565, -12.4422 octaves, 0.0470 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 6.010200E+05, 19.19705 octaves Euler's gradus suavitatis : 73 Sum of Mann's harmonic distance : 92.5, average 30.83333 Mersenne's string divisions : 53179 Sum of van Prooijen's expressibility: 3.74547, average 1.24849 Sum of Tenney's harmonic distance : 7.63622, average 2.54541 Vogel's harmonic complexity : 52.00000 Wille's k value : 1417 Wilson's harmonic complexity : 77 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 18.00035, average 3.00006 Lattice compactness (without 2's) : 15.49817, average 2.58303 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 3 1.33333 6 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 53: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <7 11 15 19 42| Scale is weakly epimorphic with val: <7 11 15 20 41| Scale is weakly epimorphic with val: <7 11 15 22 42| Scale is weakly epimorphic with val: <7 11 16 18 42| Scale is weakly epimorphic with val: <7 11 16 19 41| Scale is weakly epimorphic with val: <7 11 16 21 42| Scale is weakly epimorphic with val: <7 11 16 22 41| Scale is weakly epimorphic with val: <7 11 17 18 41| Scale is weakly epimorphic with val: <7 11 17 20 42| Scale is weakly epimorphic with val: <7 11 17 21 41| Scale is weakly epimorphic with val: <7 11 18 19 42| Scale is weakly epimorphic with val: <7 11 18 20 41| Scale is weakly epimorphic with val: <7 11 18 22 42| Scale is weakly epimorphic with val: <7 11 19 19 41| Scale is weakly epimorphic with val: <7 11 19 21 42| Scale is weakly epimorphic with val: <7 11 19 22 41| Scale is weakly epimorphic with val: <7 12 15 19 40| Scale is weakly epimorphic with val: <7 12 15 20 42| Scale is weakly epimorphic with val: <7 12 15 22 40| Scale is weakly epimorphic with val: <7 12 16 18 40| Scale is weakly epimorphic with val: <7 12 16 19 42| Scale is weakly epimorphic with val: <7 12 16 21 40| Scale is weakly epimorphic with val: <7 12 17 18 42| Scale is weakly epimorphic with val: <7 12 17 20 40| Scale is weakly epimorphic with val: <7 12 18 19 40| Scale is weakly epimorphic with val: <7 12 18 22 40| Scale is weakly epimorphic with val: <7 12 19 21 40| Scale is weakly epimorphic with val: <8 11 15 20 40| Scale is weakly epimorphic with val: <8 11 16 19 40| Scale is weakly epimorphic with val: <8 11 17 18 40| Scale is weakly epimorphic with val: <8 12 15 20 41| Scale is weakly epimorphic with val: <8 12 15 22 42| Scale is weakly epimorphic with val: <8 12 16 19 41| Scale is weakly epimorphic with val: <8 12 16 21 42| Scale is weakly epimorphic with val: <8 12 16 22 41| Scale is weakly epimorphic with val: <8 12 17 18 41| Scale is weakly epimorphic with val: <8 12 17 20 42| Scale is weakly epimorphic with val: <8 12 17 21 41| Scale is weakly epimorphic with val: <8 12 18 19 42| Scale is weakly epimorphic with val: <8 12 18 20 41| Scale is weakly epimorphic with val: <8 12 19 19 41| Scale is weakly epimorphic with val: <8 12 19 22 41|
FIT/MODE
3: 0 0 3 N M DE S SD: 33.7923 c. M: 48.7704 c. 7: 0 1 6 N G T3 SD: 22.7157 c. M: 32.3605 c. 8: 1 0 7 N G T3 SD: 18.9347 c. M:-29.8952 c. 9: 1 0 8 N G T3 SD: 13.7976 c. M:-22.9779 c. 10: 1 0 9 N G T3 SD: 10.0890 c. M:-17.4440 c. 11: 1 0 10 N G T3 SD: 7.7252 c. M:-12.9164 c. 12: 1 0 11 N G T3 SD: 6.7430 c. M:-9.1433 c. 16: 1 1 14 N M DE S SD: 7.8182 c. M:-13.4852 c. 17: 1 1 15 N M DE S SD: 5.9408 c. M:-9.8231 c. 18: 1 1 16 N M DE S SD: 4.6600 c. M:-6.5680 c. 19: 1 1 17 N M DE S SD: 4.1293 c. M: 6.1476 c. 20: 1 1 18 N M DE S SD: 4.3472 c. M: 7.4582 c. 27: 2 1 24 N T3 SD: 4.6071 c. M:-6.5680 c. 28: 2 1 25 N T3 SD: 3.2359 c. M:-4.5916 c. 29: 2 1 26 N T3 SD: 1.9597 c. M:-2.7515 c. 30: 2 1 27 N T3 SD: 0.7701 c. M:-1.0341 c. 31: 2 1 28 N T3 SD: 0.3559 c. M: 0.5725 c. 61: 4 2 55 N T3 SD: 0.2132 c. M:-0.2982 c. 92: 6 3 83 N T3 SD: 0.0751 c. M:-0.1207 c. 307: 20 10 277 N T3 SD: 0.0766 c. M: 0.1015 c. 399: 26 13 360 N T3 SD: 0.0747 c. M:-0.0936 c. 491: 32 16 443 N T3 SD: 0.0740 c. M:-0.0987 c. 521: 34 17 470 N T3 SD: 0.0823 c. M:-0.1415 c. 522: 34 17 471 N T3 SD: 0.0787 c. M: 0.1108 c. 571: 37 19 515 N T3 SD: 0.0666 c. M: 0.0878 c. 602: 39 20 543 N T3 SD: 0.0599 c. M: 0.0951 c. 632: 41 21 570 N T3 SD: 0.0588 c. M:-0.0885 c. 633: 41 21 571 N T3 SD: 0.0590 c. M: 0.1016 c. 663: 43 22 598 N T3 SD: 0.0475 c. M: 0.0589 c. 694: 45 23 626 N T3 SD: 0.0420 c. M: 0.0665 c. 725: 47 24 654 N T3 SD: 0.0424 c. M: 0.0734 c. 755: 49 25 681 N T3 SD: 0.0335 c. M:-0.0446 c. 786: 51 26 709 N T3 SD: 0.0283 c. M: 0.0446 c. 817: 53 27 737 N T3 SD: 0.0298 c. M: 0.0515 c. 847: 55 28 764 N T3 SD: 0.0230 c. M:-0.0345 c. 878: 57 29 792 N T3 SD: 0.0174 c. M: 0.0272 c. 909: 59 30 820 N T3 SD: 0.0201 c. M: 0.0341 c. 939: 61 31 847 N T3 SD: 0.0156 c. M:-0.0264 c. 970: 63 32 875 N T3 SD: 0.0087 c. M: 0.0132 c. 1062: 69 35 958 N T3 SD: 0.0017 c. M:-0.0024 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: 109.0503 cents 7 x 8:9 S SD: 96.4821 cents 8 x 9:11 SD: 82.0157 cents 9 x 10:12 S SD: 66.8167 cents 10 x 11:13 SD: 62.1117 cents 11 x 12:15 S SD: 54.5217 cents 12 x 13:16 SD: 44.9011 cents 13 x 14:17 SD: 43.1706 cents 14 x 15:19 SD: 38.5147 cents 15 x 16:20 S SD: 31.4805 cents 16 x 17:21 SD: 31.2253 cents 17 x 18:23 SD: 28.0946 cents 18 x 19:24 SD: 22.4163 cents 19 x 20:25 S SD: 23.0664 cents 20 x 21:27 SD: 20.8374 cents 21 x 22:28 SD: 15.8833 cents 22 x 23:29 SD: 17.2187 cents 23 x 24:31 SD: 15.5790 cents 24 x 25:32 SD: 10.9510 cents 25 x 26:33 SD: 12.9296 cents 26 x 27:35 SD: 11.7146 cents 27 x 28:36 SD: 7.0953 cents 28 x 29:37 SD: 9.8059 cents 29 x 30:39 SD: 8.9340 cents 30 x 31:40 SD: 3.9982 cents 31 x 32:41 SD: 7.6628 cents 32 x 33:43 SD: 7.1026 cents 33 x 34:44 SD: 1.4560 cents 34 x 35:45 SD: 6.4273 cents 35 x 36:47 SD: 6.1610 cents 36 x 37:48 SD: 0.6682 cents 37 x 38:49 SD: 6.0110 cents 38 x 39:51 SD: 5.9859 cents 39 x 40:52 SD: 2.4697 cents 40 x 41:53 SD: 6.2063 cents 41 x 42:55 SD: 6.3342 cents 42 x 43:56 SD: 4.0168 cents 43:44 x 57 SD: 6.2700 cents 44:45 x 59 SD: 5.8960 cents 45:46 x 60 SD: 2.8451 cents 46:47 x 61 SD: 5.3091 cents 47:48 x 63 SD: 5.0265 cents 48:49 x 64 SD: 1.6682 cents 49:50 x 65 SD: 4.6168 cents 50:51 x 67 SD: 4.4230 cents 51:52 x 68 SD: 0.6284 cents 52:53 x 69 SD: 4.1830 cents 57:58:59:76 SD: 3.7209 cents 60:61:62:80 SD: 2.9432 cents 63:64:65:84 SD: 2.4594 cents 66:67:68:88 SD: 2.3215 cents 80 x 82:107 SD: 4.0447 cents 81 x 83:108 SD: 3.2715 cents 82 x 84:109 SD: 4.4066 cents 83 x 85:111 SD: 4.5851 cents 84 x 86:112 SD: 4.0168 cents 85:87 x 113 SD: 4.7025 cents 86:88 x 115 SD: 4.4890 cents 87:89 x 116 SD: 3.4937 cents 90:92:93:120 SD: 3.2715 cents 92:94:95:123 SD: 3.1938 cents 93:95:96:124 SD: 2.5473 cents 96:98:99:128 SD: 1.8680 cents 99:101:102:132 SD: 1.2298 cents 102:104:105:136 SD: 0.6306 cents 105:107:108:140 SD: 0.1018 cents 528:538:543:704 SD: 0.0997 cents