Scala analysis: 523_M31
Miscellaneous tetrachord 68/65 * 65/63 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/65 78.114034 Valentine semitone 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 68/65 78.1140 Valentine semitone 2: 65/63 54.1055 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 65/63 54.105 cents 1: 1 68/65 78.114 cents Valentine semitone 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 65/51 419.931 cents 2: 1 84/65 443.940 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 : 78.1 132.2 498.0 78.1 : 54.1 419.9 498.0 132.2: 365.8 443.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.1055 .. 365.8255 cents 1323/1105, 311.7200 cents 65/63, 54.1055 cents 2: 132.2195 .. 443.9395 cents 1323/1105, 311.7200 cents 1156/1323,-233.6060 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 65/63, 54.1055 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 21/17, 365.8255 cents Average / Smallest step : 3.068359 Largest / Average step : 2.203569 Largest / Smallest step : 6.761341 Median interval of one step : 68/65, 78.1140 cents, amount: 1 Least squares average step : 131.19200 cents, oct.: 393.57601 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1390-tone equal temperament with octave 4/3 degrees: 218 369 1390 Least number of segments generator : 697 of 249.739 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 847 of 303.485 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 54.10547 cents Scale diversity : 0.655014 Lumma stability : 0.217271 Lumma impropriety factor : 0.469046 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 : 4284/4225, 24.0086 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% Limited inverse transpositions with margin 311.7200 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 65 (O: 65 U: 65) Highest odd numerator or denominator: 65 Scale harmonicity : 0.013108 Average absolute harmonicity : 0.083905 Specific harmonicity : 0.061149 Fundamental : 1/4095, -11.9996 octaves, 0.0639 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 2.784600E+05, 18.08711 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 135.5, average 45.16667 Mersenne's string divisions : 17423 Sum of van Prooijen's expressibility: 4.08938, average 1.36313 Sum of Tenney's harmonic distance : 8.35645, average 2.78548 Vogel's harmonic complexity : 33.00000 Wille's k value : 682 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 14.42190, average 2.40365 Lattice compactness (without 2's) : 11.55934, average 1.92656 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -2 .. 0 -1.00000 3 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 16 19 26 29| Scale is weakly epimorphic with val: <7 11 16 19 27 31| Scale is JI-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 26 30| Scale is JI-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 JI-epimorphic with val: <7 11 17 20 26 30| Scale is weakly epimorphic with val: <7 11 17 20 27 29| Scale is JI-epimorphic with val: <7 11 17 21 27 31| Scale is weakly epimorphic with val: <7 11 17 21 28 30| Scale is weakly epimorphic with val: <7 11 18 19 27 29| Scale is weakly epimorphic with val: <7 11 18 19 28 31| Scale is weakly epimorphic with val: <7 11 18 20 26 29| Scale is weakly epimorphic with val: <7 11 18 20 28 30| Scale is JI-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 16 20 26 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 49.1390 c. M: 78.1140 c. 4: 1 0 3 N G T3 SD: 27.1546 c. M:-46.3972 c. 5: 1 0 4 N G T3 SD: 22.5498 c. M: 32.6105 c. 6: 1 1 4 N M DE S SD: 19.7153 c. M:-33.7955 c. 7: 1 1 5 N M DE S SD: 7.0733 c. M:-10.0791 c. 11: 2 1 8 N T3 SD: 7.4785 c. M:-12.4396 c. 12: 2 1 9 N T3 SD: 5.2714 c. M: 7.7083 c. 18: 3 2 13 N T3 SD: 4.5269 c. M:-6.1263 c. 19: 3 2 14 N T3 SD: 0.7324 c. M: 1.1550 c. 45: 7 5 33 N T3 SD: 0.5037 c. M: 0.6404 c. 64: 10 7 47 N T3 SD: 0.1753 c. M: 0.2945 c. 83: 13 9 61 N T3 SD: 0.1348 c. M: 0.2076 c. 147: 23 16 108 N T3 SD: 0.1195 c. M: 0.1886 c. 230: 36 25 169 N T3 SD: 0.1184 c. M: 0.1592 c. 313: 49 34 230 N T3 SD: 0.1206 c. M: 0.1501 c. 350: 55 38 257 N T3 SD: 0.1103 c. M:-0.1502 c. 369: 58 40 271 N T3 SD: 0.1024 c. M:-0.1695 c. 414: 65 45 304 N T3 SD: 0.0796 c. M:-0.1113 c. 433: 68 47 318 N T3 SD: 0.0665 c. M:-0.1009 c. 478: 75 52 351 N T3 SD: 0.0639 c. M:-0.1063 c. 497: 78 54 365 N T3 SD: 0.0442 c. M:-0.0580 c. 516: 81 56 379 N T3 SD: 0.0397 c. M:-0.0674 c. 561: 88 61 412 N T3 SD: 0.0351 c. M:-0.0598 c. 580: 91 63 426 N T3 SD: 0.0196 c. M:-0.0275 c. 644: 101 70 473 N T3 SD: 0.0149 c. M:-0.0254 c. 663: 104 72 487 N T3 SD: 0.0079 c. M:-0.0107 c. 727: 114 79 534 N T3 SD: 0.0094 c. M: 0.0162 c. 1307: 205 142 960 N T3 SD: 0.0051 c. M:-0.0082 c. 1390: 218 151 1021 N T3 SD: 0.0033 c. M: 0.0047 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: 67.3257 cents 7 x 8:9 S SD: 58.6432 cents 8 x 9:11 SD: 44.6585 cents 9 x 10:12 S SD: 25.0921 cents 10 x 11:13 SD: 27.3679 cents 11 x 12:15 S SD: 21.5225 cents 12 x 13:16 SD: 3.1766 cents 13 x 14:17 SD: 16.9226 cents 14 x 15:19 SD: 16.5996 cents 15 x 16:20 S SD: 10.2441 cents 16:17 x 21 SD: 19.1298 cents 17:18 x 23 SD: 16.3791 cents 18:19 x 24 SD: 7.7445 cents 23:24:25:31 SD: 7.5805 cents 24:25:26:32 SD: 3.2616 cents 39:41:42:52 SD: 3.1099 cents 60:63:65:80 SD: 2.9949 cents 62:65:67:83 SD: 2.7157 cents 63:66:68:84 SD: 0.8077 cents 87:91:94:116 SD: 0.5931 cents 150:157:162:200 SD: 0.4418 cents 216:226:233:288 SD: 0.3623 cents 240:251:259:320 SD: 0.2062 cents 303:317:327:404 SD: 0.0886 cents 390:408:421:520 SD: 0.0653 cents