Scala analysis: 006_H2
Hyperenharmonic tetrachord 108/107 * 107/105 * 35/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 108/107 16.104619 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: 108/107 16.1046 2: 107/105 32.6658 3: 35/27 449.2746 septimal semi-diminished fourth, 9/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 108/107 16.105 cents 1: 1 107/105 32.666 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: 1 140/107 465.379 cents 2: 1 107/81 481.940 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 : 16.1 48.8 498.0 16.1 : 32.7 481.9 498.0 48.8 : 449.3 465.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.1046 .. 449.2746 cents 3745/2916, 433.1700 cents 108/107, 16.1046 cents 2: 48.7704 .. 481.9404 cents 3745/2916, 433.1700 cents 972/1225,-400.5042 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 108/107, 16.1046 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 35/27, 449.2746 cents Average / Smallest step : 10.308533 Largest / Average step : 2.706229 Largest / Smallest step : 27.897252 Median interval of one step : 107/105, 32.6658 cents, amount: 1 Least squares average step : 114.84146 cents, oct.: 344.52437 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1113-tone equal temperament with octave 4/3 degrees: 36 109 1113 Least number of segments generator : 557 of 249.246 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1040 of 465.379 cents and inv. generated superset size: 31 = 28 more = 1033.333% 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 16.10462 cents Scale diversity : 0.039620 Lumma stability : 0.064671 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 : 108/107, 16.1046 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 481.9404 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 416.6089 cents: 2 -- Rational properties -- Prime limit : 107 Odd number limit : 107 (O: 107 U: 107) Highest odd numerator or denominator: 107 Scale harmonicity : 0.034069 Fundamental : 1/11235, -13.4557 octaves, 0.0233 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 1.213380E+06, 20.21060 octaves Euler's gradus suavitatis : 127 Sum of Mann's harmonic distance : 146.5, average 48.83333 Mersenne's string divisions : 106855 Sum of van Prooijen's expressibility: 4.05057, average 1.35019 Sum of Tenney's harmonic distance : 8.24236, average 2.74745 Vogel's harmonic complexity : 88.33333 Wille's k value : 1872 Wilson's harmonic complexity : 131 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 18.05257, average 3.00876 Lattice compactness (without 2's) : 15.49817, average 2.58303 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 3 1.33333 6 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 107: -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 49| Scale is weakly epimorphic with val: <7 11 15 20 48| Scale is weakly epimorphic with val: <7 11 15 22 49| Scale is weakly epimorphic with val: <7 11 16 18 49| Scale is weakly epimorphic with val: <7 11 16 19 48| Scale is weakly epimorphic with val: <7 11 16 21 49| Scale is weakly epimorphic with val: <7 11 16 22 48| Scale is weakly epimorphic with val: <7 11 17 18 48| Scale is weakly epimorphic with val: <7 11 17 20 49| = patent Scale is weakly epimorphic with val: <7 11 17 21 48| Scale is weakly epimorphic with val: <7 11 18 19 49| Scale is weakly epimorphic with val: <7 11 18 20 48| Scale is weakly epimorphic with val: <7 11 18 22 49| Scale is weakly epimorphic with val: <7 11 19 19 48| Scale is weakly epimorphic with val: <7 11 19 21 49| Scale is weakly epimorphic with val: <7 11 19 22 48| Scale is weakly epimorphic with val: <7 12 15 20 49| Scale is weakly epimorphic with val: <7 12 16 19 49| Scale is weakly epimorphic with val: <7 12 17 18 49| Scale is weakly epimorphic with val: <8 11 15 20 48| Scale is weakly epimorphic with val: <8 11 16 19 48| Scale is weakly epimorphic with val: <8 11 17 18 48| Scale is weakly epimorphic with val: <8 12 15 20 49| Scale is weakly epimorphic with val: <8 12 15 22 50| Scale is weakly epimorphic with val: <8 12 16 19 49| Scale is weakly epimorphic with val: <8 12 16 21 50| Scale is weakly epimorphic with val: <8 12 16 22 49| Scale is weakly epimorphic with val: <8 12 17 18 49| Scale is weakly epimorphic with val: <8 12 17 20 50| Scale is weakly epimorphic with val: <8 12 17 21 49| Scale is weakly epimorphic with val: <8 12 18 19 50| Scale is weakly epimorphic with val: <8 12 18 20 49| Scale is weakly epimorphic with val: <8 12 19 19 49| Scale is weakly epimorphic with val: <8 12 19 22 49|
FIT/MODE
3: 0 0 3 N M DE S SD: 29.6530 c. M: 48.7704 c. 7: 0 1 6 N G T3 SD: 15.9183 c. M:-22.3789 c. 8: 0 1 7 N G T3 SD: 12.1272 c. M: 16.1046 c. 9: 0 1 8 N G T3 SD: 10.0415 c. M: 16.1046 c. 10: 0 1 9 N G T3 SD: 9.3172 c. M: 16.1046 c. 11: 0 1 10 N G T3 SD: 9.5143 c. M: 16.1046 c. 12: 0 1 11 N G T3 SD: 10.2007 c. M: 16.1046 c. 18: 1 1 16 N M DE S SD: 7.6785 c. M:-11.5645 c. 19: 1 1 17 N M DE S SD: 6.2059 c. M:-10.1083 c. 20: 1 1 18 N M DE S SD: 5.1143 c. M:-8.7976 c. 21: 1 1 19 N M DE S SD: 4.4620 c. M:-7.6118 c. 22: 1 1 20 N M DE S SD: 4.2777 c. M:-6.5338 c. 23: 1 1 21 N M DE S SD: 4.4956 c. M:-5.5495 c. 26: 1 2 23 N T3 SD: 5.3209 c. M:-8.6963 c. 27: 1 2 24 N T3 SD: 4.0258 c. M:-6.5680 c. 28: 1 2 25 N T3 SD: 2.8234 c. M:-4.5916 c. 29: 1 2 26 N T3 SD: 1.7043 c. M:-2.7515 c. 30: 1 2 27 N T3 SD: 0.6624 c. M:-1.0341 c. 31: 1 2 28 N T3 SD: 0.3313 c. M: 0.5725 c. 61: 2 4 55 N T3 SD: 0.1806 c. M:-0.2247 c. 92: 3 6 83 N T3 SD: 0.0834 c. M:-0.1360 c. 215: 7 14 194 N T3 SD: 0.0961 c. M: 0.1241 c. 245: 8 16 221 N T3 SD: 0.0918 c. M:-0.1581 c. 307: 10 20 277 N T3 SD: 0.0900 c. M:-0.1183 c. 337: 11 22 304 N T3 SD: 0.0878 c. M:-0.1520 c. 398: 13 26 359 N T3 SD: 0.0961 c. M:-0.1632 c. 399: 13 26 360 N T3 SD: 0.0875 c. M:-0.1224 c. 429: 14 28 387 N T3 SD: 0.0860 c. M:-0.1486 c. 521: 17 34 470 N T3 SD: 0.0851 c. M:-0.1464 c. 522: 17 34 471 N T3 SD: 0.0923 c. M:-0.1152 c. 531: 17 35 479 N T3 SD: 0.0922 c. M: 0.1597 c. 561: 18 37 506 N T3 SD: 0.0792 c. M: 0.1246 c. 562: 18 37 507 N T3 SD: 0.0899 c. M: 0.1530 c. 582: 19 38 525 N T3 SD: 0.0893 c. M:-0.1546 c. 583: 19 38 526 N T3 SD: 0.0854 c. M:-0.1267 c. 591: 19 39 533 N T3 SD: 0.0819 c. M:-0.1071 c. 592: 19 39 534 N T3 SD: 0.0708 c. M: 0.1201 c. 622: 20 41 561 N T3 SD: 0.0671 c. M: 0.0903 c. 623: 20 41 562 N T3 SD: 0.0670 c. M: 0.1160 c. 653: 21 43 589 N T3 SD: 0.0564 c. M: 0.0879 c. 654: 21 43 590 N T3 SD: 0.0674 c. M: 0.1123 c. 683: 22 45 616 N T3 SD: 0.0613 c. M:-0.0862 c. 684: 22 45 617 N T3 SD: 0.0502 c. M: 0.0856 c. 714: 23 47 644 N T3 SD: 0.0485 c. M: 0.0612 c. 715: 23 47 645 N T3 SD: 0.0487 c. M: 0.0836 c. 745: 24 49 672 N T3 SD: 0.0392 c. M: 0.0602 c. 776: 25 51 700 N T3 SD: 0.0345 c. M: 0.0594 c. 806: 26 53 727 N T3 SD: 0.0344 c. M:-0.0454 c. 807: 26 53 728 N T3 SD: 0.0349 c. M: 0.0586 c. 837: 27 55 755 N T3 SD: 0.0258 c. M: 0.0387 c. 868: 28 57 783 N T3 SD: 0.0223 c. M: 0.0387 c. 898: 29 59 810 N T3 SD: 0.0239 c. M:-0.0358 c. 899: 29 59 811 N T3 SD: 0.0247 c. M: 0.0387 c. 929: 30 61 838 N T3 SD: 0.0152 c. M: 0.0214 c. 960: 31 63 866 N T3 SD: 0.0128 c. M: 0.0219 c. 1021: 33 67 921 N T3 SD: 0.0070 c. M:-0.0097 c. 1052: 34 69 949 N T3 SD: 0.0063 c. M: 0.0081 c. 1113: 36 73 1004 N T3 SD: 0.0039 c. M:-0.0049 c. 2165: 70 142 1953 N T3 SD: 0.0011 c. M: 0.0015 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 x 44:57 SD: 6.7522 cents 44 x 45:59 SD: 6.9556 cents 45 x 46:60 SD: 5.3599 cents 46 x 47:61 SD: 7.4522 cents 47 x 48:63 SD: 7.6841 cents 48 x 49:64 SD: 6.5368 cents 49 x 50:65 SD: 8.1963 cents 50 x 51:67 SD: 8.4327 cents 51 x 52:68 SD: 7.5766 cents 52 x 53:69 SD: 8.9309 cents 53:54:55:71 SD: 7.9334 cents 54:55:56:72 SD: 7.0449 cents 56:57:58:75 SD: 6.7852 cents 57:58:59:76 SD: 5.9223 cents 59:60:61:79 SD: 5.7962 cents 60:61:62:80 SD: 4.9495 cents 63:64:65:84 SD: 4.1231 cents 66:67:68:88 SD: 3.4492 cents 69:70:71:92 SD: 2.9444 cents 72:73:74:96 SD: 2.6296 cents 75:76:77:100 SD: 2.5142 cents 93:94:96:124 SD: 2.2156 cents 96:97:99:128 SD: 1.6208 cents 99:100:102:132 SD: 1.0623 cents 102:103:105:136 SD: 0.5391 cents 105:106:108:140 SD: 0.1018 cents