Scala analysis: 017_H5
Hyperenharmonic tetrachord 96/95 * 95/93 * 31/24
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96/95 18.128271 19th-partial chroma 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: 96/95 18.1283 19th-partial chroma 2: 95/93 36.8362 3: 31/24 443.0806
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 96/95 18.128 cents 19th-partial chroma 1: 1 95/93 36.836 cents 1: 1 31/24 443.081 cents 2: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 2: 1 124/95 461.209 cents 2: 1 95/72 479.917 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 : 18.1 55.0 498.0 18.1 : 36.8 479.9 498.0 55.0 : 443.1 461.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.1283 .. 443.0806 cents 2945/2304, 424.9523 cents 96/95, 18.1283 cents 2: 54.9644 .. 479.9167 cents 2945/2304, 424.9523 cents 768/961,-388.1161 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 96/95, 18.1283 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 31/24, 443.0806 cents Average / Smallest step : 9.157796 Largest / Average step : 2.668919 Largest / Smallest step : 24.441414 Median interval of one step : 95/93, 36.8362 cents, amount: 1 Least squares average step : 115.87087 cents, oct.: 347.61260 cents Scale is not proper Scale has trivalence property Scale is a mode of a 879-tone equal temperament with octave 4/3 degrees: 32 97 879 Least number of segments generator : 440 of 249.306 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 614 of 347.895 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 18.12827 cents Scale diversity : 0.080863 Lumma stability : 0.072798 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 : 96/95, 18.1283 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% Limited inverse transpositions with margin 406.2444 cents: 2 -- Rational properties -- Prime limit : 31 Odd number limit : 95 (O: 95 U: 95) Highest odd numerator or denominator: 95 Scale harmonicity : 0.019670 Fundamental : 1/8835, -13.1090 octaves, 0.0296 Hz. Guide tone : 96, 6.5850 octaves, 25116.054 Hz. Exponens Consonantiae : 8.481600E+05, 19.69398 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 130.5, average 43.50000 Mersenne's string divisions : 12033 Sum of van Prooijen's expressibility: 3.94621, average 1.31540 Sum of Tenney's harmonic distance : 8.03569, average 2.67856 Vogel's harmonic complexity : 43.66667 Wille's k value : 1472 Wilson's harmonic complexity : 61 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 21.29488, average 3.54915 Lattice compactness (without 2's) : 7.91359, average 1.31893 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 4.00000 12 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.33333 1 19: -1 .. 0 -0.33333 1 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 11 15 29 34| Scale is weakly epimorphic with val: <7 11 15 29 37| Scale is JI-epimorphic with val: <7 11 15 30 33| Scale is weakly epimorphic with val: <7 11 15 30 36| Scale is weakly epimorphic with val: <7 11 15 30 39| Scale is weakly epimorphic with val: <7 11 15 32 34| Scale is weakly epimorphic with val: <7 11 15 32 37| Scale is weakly epimorphic with val: <7 11 15 33 33| Scale is weakly epimorphic with val: <7 11 15 33 36| Scale is weakly epimorphic with val: <7 11 15 33 39| Scale is weakly epimorphic with val: <7 11 16 28 34| Scale is weakly epimorphic with val: <7 11 16 28 37| Scale is JI-epimorphic with val: <7 11 16 29 33| Scale is weakly epimorphic with val: <7 11 16 29 36| Scale is weakly epimorphic with val: <7 11 16 29 39| Scale is weakly epimorphic with val: <7 11 16 31 34| Scale is weakly epimorphic with val: <7 11 16 31 37| Scale is weakly epimorphic with val: <7 11 16 32 33| Scale is weakly epimorphic with val: <7 11 16 32 36| Scale is weakly epimorphic with val: <7 11 16 32 39| Scale is weakly epimorphic with val: <7 11 16 34 34| Scale is weakly epimorphic with val: <7 11 16 34 37| Scale is JI-epimorphic with val: <7 11 17 28 33| Scale is weakly epimorphic with val: <7 11 17 28 36| Scale is weakly epimorphic with val: <7 11 17 28 39| Scale is weakly epimorphic with val: <7 11 17 30 34| Scale is weakly epimorphic with val: <7 11 17 30 37| Scale is weakly epimorphic with val: <7 11 17 31 33| Scale is weakly epimorphic with val: <7 11 17 31 36| = patent Scale is weakly epimorphic with val: <7 11 17 31 39| Scale is weakly epimorphic with val: <7 11 17 33 34| Scale is weakly epimorphic with val: <7 11 17 33 37| Scale is weakly epimorphic with val: <7 11 17 34 36| Scale is weakly epimorphic with val: <7 11 17 34 39| Scale is weakly 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 30 39| 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 18 33 39| 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 29 33| Scale is weakly epimorphic with val: <7 11 19 29 36| Scale is weakly epimorphic with val: <7 11 19 29 39| 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 32 33| Scale is weakly epimorphic with val: <7 11 19 32 36| Scale is weakly epimorphic with val: <7 11 19 32 39| 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 12 15 29 34| Scale is weakly epimorphic with val: <7 12 15 29 37| Scale is weakly epimorphic with val: <7 12 16 28 34| Scale is weakly epimorphic with val: <7 12 16 28 37| Scale is weakly epimorphic with val: <8 11 15 29 37| Scale is weakly epimorphic with val: <8 11 15 32 37| Scale is weakly epimorphic with val: <8 11 15 33 33| Scale is weakly epimorphic with val: <8 11 15 33 36| Scale is weakly epimorphic with val: <8 11 15 33 39| Scale is weakly epimorphic with val: <8 11 16 28 37| Scale is weakly epimorphic with val: <8 11 16 31 37| Scale is weakly epimorphic with val: <8 11 16 32 33| Scale is weakly epimorphic with val: <8 11 16 32 36| Scale is weakly epimorphic with val: <8 11 16 32 39| Scale is weakly epimorphic with val: <8 11 16 34 37| Scale is weakly epimorphic with val: <8 11 17 30 37| Scale is weakly epimorphic with val: <8 11 17 31 33| Scale is weakly epimorphic with val: <8 11 17 31 36| Scale is weakly epimorphic with val: <8 11 17 31 39| Scale is weakly epimorphic with val: <8 11 17 33 37| Scale is weakly epimorphic with val: <8 11 18 29 37| Scale is weakly epimorphic with val: <8 11 18 30 33| Scale is weakly epimorphic with val: <8 11 18 30 36| Scale is weakly epimorphic with val: <8 11 18 30 39| Scale is weakly epimorphic with val: <8 11 18 32 37| Scale is weakly epimorphic with val: <8 11 19 28 37| Scale is weakly epimorphic with val: <8 11 19 29 33| Scale is weakly epimorphic with val: <8 11 19 29 36| Scale is weakly epimorphic with val: <8 11 19 29 39| Scale is weakly epimorphic with val: <8 11 19 31 37| Scale is weakly epimorphic with val: <8 11 19 34 37| Scale is weakly epimorphic with val: <8 12 15 29 37| Scale is weakly epimorphic with val: <8 12 15 32 37| Scale is weakly epimorphic with val: <8 12 15 34 35| Scale is weakly epimorphic with val: <8 12 15 34 38| Scale is weakly epimorphic with val: <8 12 16 28 37| Scale is weakly epimorphic with val: <8 12 16 31 37| Scale is weakly epimorphic with val: <8 12 16 33 35| Scale is weakly epimorphic with val: <8 12 16 33 38| Scale is weakly epimorphic with val: <8 12 16 34 37| Scale is weakly epimorphic with val: <8 12 17 30 37| Scale is weakly epimorphic with val: <8 12 17 32 35| Scale is weakly epimorphic with val: <8 12 17 32 38| Scale is weakly epimorphic with val: <8 12 17 33 37| Scale is weakly epimorphic with val: <8 12 18 29 37| Scale is weakly epimorphic with val: <8 12 18 31 35| Scale is weakly epimorphic with val: <8 12 18 31 38| Scale is weakly epimorphic with val: <8 12 18 32 37| Scale is weakly epimorphic with val: <8 12 19 28 37| Scale is weakly epimorphic with val: <8 12 19 30 35| Scale is weakly epimorphic with val: <8 12 19 30 38| Scale is weakly epimorphic with val: <8 12 19 31 37| Scale is weakly epimorphic with val: <8 12 19 34 37|
FIT/MODE
3: 0 0 3 N M DE S SD: 33.4152 c. M: 54.9644 c. 6: 0 1 5 N G T3 SD: 19.2791 c. M:-28.0431 c. 7: 0 1 6 N G T3 SD: 14.0307 c. M: 18.1283 c. 8: 0 1 7 N G T3 SD: 11.2812 c. M: 18.1283 c. 9: 0 1 8 N G T3 SD: 10.4686 c. M: 18.1283 c. 10: 0 1 9 N G T3 SD: 10.8821 c. M: 18.1283 c. 11: 0 1 10 N G T3 SD: 11.8671 c. M: 18.1283 c. 16: 1 1 14 N M DE S SD: 8.6052 c. M:-12.9995 c. 17: 1 1 15 N M DE S SD: 6.7800 c. M:-11.1685 c. 18: 1 1 16 N M DE S SD: 5.5127 c. M:-9.5409 c. 19: 1 1 17 N M DE S SD: 4.8924 c. M:-8.0846 c. 20: 1 1 18 N M DE S SD: 4.9164 c. M:-6.7740 c. 24: 1 2 21 N T3 SD: 4.4738 c. M:-7.2912 c. 25: 1 2 22 N T3 SD: 2.9589 c. M:-4.8010 c. 26: 1 2 23 N T3 SD: 1.5617 c. M:-2.5023 c. 27: 1 2 24 N T3 SD: 0.2833 c. M:-0.3739 c. 82: 3 6 73 N T3 SD: 0.1818 c. M: 0.3010 c. 109: 4 8 97 N T3 SD: 0.1154 c. M:-0.1486 c. 136: 5 10 121 N T3 SD: 0.1069 c. M:-0.1822 c. 163: 6 12 145 N T3 SD: 0.1198 c. M:-0.2047 c. 245: 9 18 218 N T3 SD: 0.1065 c. M:-0.1673 c. 381: 14 28 339 N T3 SD: 0.1058 c. M:-0.1726 c. 443: 16 33 394 N T3 SD: 0.1081 c. M: 0.1402 c. 444: 16 33 395 N T3 SD: 0.1043 c. M: 0.1807 c. 470: 17 35 418 N T3 SD: 0.1035 c. M:-0.1384 c. 471: 17 35 419 N T3 SD: 0.0887 c. M: 0.1521 c. 498: 18 37 443 N T3 SD: 0.0768 c. M: 0.1266 c. 525: 19 39 467 N T3 SD: 0.0686 c. M: 0.1038 c. 552: 20 41 491 N T3 SD: 0.0639 c. M: 0.0832 c. 553: 20 41 492 N T3 SD: 0.0686 c. M: 0.1158 c. 579: 21 43 515 N T3 SD: 0.0626 c. M:-0.0872 c. 580: 21 43 516 N T3 SD: 0.0554 c. M: 0.0956 c. 607: 22 45 540 N T3 SD: 0.0449 c. M: 0.0772 c. 634: 23 47 564 N T3 SD: 0.0377 c. M: 0.0604 c. 661: 24 49 588 N T3 SD: 0.0344 c. M: 0.0449 c. 689: 25 51 613 N T3 SD: 0.0366 c. M: 0.0570 c. 716: 26 53 637 N T3 SD: 0.0258 c. M: 0.0428 c. 743: 27 55 661 N T3 SD: 0.0172 c. M: 0.0297 c. 770: 28 57 685 N T3 SD: 0.0132 c. M: 0.0175 c. 852: 31 63 758 N T3 SD: 0.0100 c. M: 0.0158 c. 879: 32 65 782 N T3 SD: 0.0028 c. M: 0.0038 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 x 39:51 SD: 7.5626 cents 39 x 40:52 SD: 5.5667 cents 40 x 41:53 SD: 8.1706 cents 41 x 42:55 SD: 8.4589 cents 42 x 43:56 SD: 7.1138 cents 43 x 44:57 SD: 9.1084 cents 44 x 45:59 SD: 9.4087 cents 45 x 46:60 SD: 8.4569 cents 46 x 47:61 SD: 10.0429 cents 47:48:49:63 SD: 8.9141 cents 48:49:50:64 SD: 7.8556 cents 50:51:52:67 SD: 7.4749 cents 51:52:53:68 SD: 6.4563 cents 53:54:55:71 SD: 6.2617 cents 54:55:56:72 SD: 5.2699 cents 56:57:58:75 SD: 5.2657 cents 57:58:59:76 SD: 4.2947 cents 60:61:62:80 SD: 3.5472 cents 63:64:65:84 SD: 3.0587 cents 66:67:68:88 SD: 2.8533 cents 84:85:87:112 SD: 2.0832 cents 87:88:90:116 SD: 1.3597 cents 90:91:93:120 SD: 0.6873 cents 93:94:96:124 SD: 0.1293 cents