Scala analysis: 042_H11
Hyperenharmonic tetrachord 75/73 * 73/72 * 32/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75/73 46.792958 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: 75/73 46.7930 2: 73/72 23.8795 3: 32/25 427.3726 classic diminished fourth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 73/72 23.879 cents 1: 1 75/73 46.793 cents 1: 1 32/25 427.373 cents classic diminished fourth 2: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 292/225 451.252 cents 2: 1 96/73 474.166 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 : 46.8 70.7 498.0 46.8 : 23.9 451.3 498.0 70.7 : 427.4 474.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 23.8795 .. 427.3726 cents 2304/1825, 403.4931 cents 73/72, 23.8795 cents 2: 70.6724 .. 474.1655 cents 2304/1825, 403.4931 cents 625/768,-356.7001 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 73/72, 23.8795 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/25, 427.3726 cents Average / Smallest step : 6.952207 Largest / Average step : 2.574301 Largest / Smallest step : 17.897072 Median interval of one step : 75/73, 46.7930 cents, amount: 1 Least squares average step : 120.16234 cents, oct.: 360.48703 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1043-tone equal temperament with octave 4/3 degrees: 98 148 1043 Least number of segments generator : 522 of 249.261 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 908 of 433.581 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 23.87947 cents Scale diversity : 0.189047 Lumma stability : 0.095893 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 : 5400/5329, 22.9135 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 403.4931 cents: 2 -- Rational properties -- Prime limit : 73 Odd number limit : 225 (O: 75 U: 225) Highest odd numerator or denominator: 75 Scale harmonicity : 0.043228 Fundamental : 1/1752, -10.7748 octaves, 0.1493 Hz. Guide tone : 300, 8.2288 octaves, 78487.670 Hz. Exponens Consonantiae : 5.256000E+05, 19.00361 octaves Euler's gradus suavitatis : 90 Sum of Mann's harmonic distance : 102.0, average 34.00000 Mersenne's string divisions : 7252 Sum of van Prooijen's expressibility: 3.75012, average 1.25004 Sum of Tenney's harmonic distance : 7.59572, average 2.53191 Vogel's harmonic complexity : 60.00000 Wille's k value : 912 Wilson's harmonic complexity : 89 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 20.66861, average 3.44477 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 -0.33333 5 3: -1 .. 1 -0.33333 3 1 5: 0 .. 2 1.33333 4 1 73: -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 45| Scale is weakly epimorphic with val: <6 11 16 44| Scale is weakly epimorphic with val: <7 10 17 45| Scale is weakly epimorphic with val: <7 11 15 45| Scale is JI-epimorphic with val: <7 11 17 44| Scale is weakly epimorphic with val: <7 11 18 45| Scale is weakly epimorphic with val: <7 12 18 44| Scale is weakly epimorphic with val: <8 11 18 44| Scale is weakly epimorphic with val: <8 11 19 45|
FIT/MODE
3: 0 0 3 N M DE S SD: 48.9359 c. M: 70.6724 c. 5: 1 0 4 N G T3 SD: 34.7700 c. M:-52.8160 c. 6: 1 0 5 N G T3 SD: 22.0881 c. M:-36.2145 c. 7: 1 0 6 N G T3 SD: 14.0648 c. M:-24.3563 c. 8: 1 0 7 N G T3 SD: 10.1643 c. M:-15.4627 c. 9: 1 0 8 N G T3 SD: 10.1351 c. M: 15.3341 c. 11: 1 1 9 N M DE S SD: 11.5118 c. M:-19.8812 c. 12: 1 1 10 N M DE S SD: 7.7488 c. M:-12.3351 c. 13: 1 1 11 N M DE S SD: 5.9817 c. M: 8.4818 c. 14: 1 1 12 N M DE S SD: 6.4827 c. M: 11.2183 c. 19: 2 1 16 N T3 SD: 5.6329 c. M:-7.9663 c. 20: 2 1 17 N T3 SD: 2.9066 c. M:-4.0343 c. 21: 2 1 18 N T3 SD: 0.4607 c. M:-0.6399 c. 64: 6 3 55 N T3 SD: 0.3712 c. M: 0.6348 c. 85: 8 4 73 N T3 SD: 0.2133 c. M: 0.3602 c. 106: 10 5 91 N T3 SD: 0.1579 c. M: 0.1944 c. 127: 12 6 109 N T3 SD: 0.1612 c. M:-0.2664 c. 233: 22 11 200 N T3 SD: 0.1550 c. M:-0.2328 c. 267: 25 13 229 N T3 SD: 0.1524 c. M:-0.2104 c. 288: 27 14 247 N T3 SD: 0.1450 c. M:-0.2298 c. 289: 27 14 248 N T3 SD: 0.1520 c. M: 0.2628 c. 309: 29 15 265 N T3 SD: 0.1454 c. M:-0.2466 c. 310: 29 15 266 N T3 SD: 0.1169 c. M: 0.2017 c. 331: 31 16 284 N T3 SD: 0.0898 c. M: 0.1483 c. 352: 33 17 302 N T3 SD: 0.0719 c. M: 0.1012 c. 373: 35 18 320 N T3 SD: 0.0649 c. M:-0.0954 c. 394: 37 19 338 N T3 SD: 0.0680 c. M:-0.1157 c. 416: 39 20 357 N T3 SD: 0.0621 c. M: 0.1012 c. 437: 41 21 375 N T3 SD: 0.0385 c. M: 0.0656 c. 458: 43 22 393 N T3 SD: 0.0202 c. M: 0.0333 c. 479: 45 23 411 N T3 SD: 0.0182 c. M:-0.0312 c. 564: 53 27 484 N T3 SD: 0.0169 c. M: 0.0277 c. 937: 88 45 804 N T3 SD: 0.0162 c. M:-0.0213 c. 1001: 94 48 859 N T3 SD: 0.0181 c. M: 0.0235 c. 1022: 96 49 877 N T3 SD: 0.0083 c. M: 0.0105 c. 1043: 98 50 895 N T3 SD: 0.0019 c. M:-0.0032 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 29:30 x 39 SD: 9.5185 cents 30:31 x 40 SD: 4.9869 cents 31:32 x 41 SD: 8.1130 cents 32:33 x 43 SD: 7.4750 cents 33:34 x 44 SD: 2.4448 cents 34:35 x 45 SD: 6.6095 cents 35:36 x 47 SD: 6.2398 cents 39:40:41:52 SD: 5.3936 cents 42:43:44:56 SD: 3.8584 cents 45:46:47:60 SD: 3.2945 cents 55 x 57:73 SD: 5.9221 cents 56 x 58:75 SD: 6.2828 cents 57 x 59:76 SD: 5.4844 cents 58:60 x 77 SD: 7.0268 cents 59:61 x 79 SD: 6.5734 cents 60:62:63:80 SD: 5.6743 cents 61:63:64:81 SD: 5.6512 cents 62:64:65:83 SD: 5.1560 cents 63:65:66:84 SD: 4.0931 cents 65:67:68:87 SD: 3.8257 cents 66:68:69:88 SD: 2.6540 cents 69:71:72:92 SD: 1.3417 cents 72:74:75:96 SD: 0.2137 cents 363:373:378:484 SD: 0.2088 cents 435:447:453:580 SD: 0.1913 cents 477:490:497:636 SD: 0.1661 cents 549:564:572:732 SD: 0.1329 cents 552:567:575:736 SD: 0.1255 cents