Scala analysis: 513_M21
Miscellaneous tetrachord 87/86 * 43/42 * 112/87
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 87/86 20.014489 2: 29/28 60.751288 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/87 437.2937 1: 87/86 20.0145 2: 43/42 40.7368 3: 112/87 437.2937
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 87/86 20.014 cents 1: 1 43/42 40.737 cents 1: 1 112/87 437.294 cents 2: 1 29/28 60.751 cents 2: 1 56/43 457.308 cents 2: 1 344/261 478.031 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 : 20.0 60.8 498.0 20.0 : 40.7 478.0 498.0 60.8 : 437.3 457.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.0145 .. 437.2937 cents 9632/7569, 417.2792 cents 87/86, 20.0145 cents 2: 60.7513 .. 478.0305 cents 9632/7569, 417.2792 cents 2523/3136,-376.5424 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 87/86, 20.0145 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/87, 437.2937 cents Average / Smallest step : 8.294741 Largest / Average step : 2.634061 Largest / Smallest step : 21.848857 Median interval of one step : 43/42, 40.7368 cents, amount: 1 Least squares average step : 116.83229 cents, oct.: 350.49687 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1369-tone equal temperament with octave 4/3 degrees: 55 167 1369 Least number of segments generator : 685 of 249.204 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 931 of 338.700 cents and inv. generated superset size: 35 = 32 more = 1166.667% 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 20.01449 cents Scale diversity : 0.119793 Lumma stability : 0.080372 Lumma impropriety factor : 0.756041 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 : 87/86, 20.0145 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 396.5569 cents: 2 -- Rational properties -- Prime limit : 43 Odd number limit : 261 (O: 87 U: 261) Highest odd numerator or denominator: 87 Scale harmonicity : 0.013571 Fundamental : 1/3612, -11.8186 octaves, 0.0724 Hz. Guide tone : 348, 8.4429 octaves, 91045.697 Hz. Exponens Consonantiae : 1.256976E+06, 20.26153 octaves Euler's gradus suavitatis : 85 Sum of Mann's harmonic distance : 118.5, average 39.50000 Mersenne's string divisions : 69027 Sum of van Prooijen's expressibility: 3.87904, average 1.29301 Sum of Tenney's harmonic distance : 7.86275, average 2.62092 Vogel's harmonic complexity : 57.33333 Wille's k value : 1870 Wilson's harmonic complexity : 85 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.25022, average 2.70837 Lattice compactness (without 2's) : 9.21076, average 1.53513 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 -0.33333 5 3: -1 .. 1 0.00000 2 1 7: -1 .. 0 -0.33333 1 29: 0 .. 1 0.66667 2 1 43: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 33 36| Scale is weakly epimorphic with val: <6 10 18 33 39| Scale is weakly epimorphic with val: <6 10 18 33 42| Scale is weakly epimorphic with val: <6 10 18 37 38| Scale is weakly epimorphic with val: <6 10 19 34 37| Scale is weakly epimorphic with val: <6 10 19 34 40| Scale is weakly epimorphic with val: <6 10 19 35 36| Scale is weakly epimorphic with val: <6 10 19 38 39| Scale is weakly epimorphic with val: <6 10 20 35 38| Scale is weakly epimorphic with val: <6 10 20 35 41| Scale is weakly epimorphic with val: <6 10 20 36 37| Scale is weakly epimorphic with val: <6 10 21 36 36| Scale is weakly epimorphic with val: <6 10 21 36 39| Scale is weakly epimorphic with val: <6 10 21 36 42| Scale is weakly epimorphic with val: <6 10 21 37 38| Scale is weakly epimorphic with val: <6 10 22 35 36| Scale is weakly epimorphic with val: <6 10 22 37 37| Scale is weakly epimorphic with val: <6 10 22 37 40| Scale is weakly epimorphic with val: <6 10 22 38 39| Scale is weakly epimorphic with val: <6 11 18 33 36| Scale is weakly epimorphic with val: <6 11 18 33 39| Scale is weakly epimorphic with val: <6 11 18 33 42| Scale is weakly epimorphic with val: <6 11 18 35 37| Scale is weakly epimorphic with val: <6 11 18 38 40| Scale is weakly epimorphic with val: <6 11 19 34 37| Scale is weakly epimorphic with val: <6 11 19 34 40| Scale is weakly epimorphic with val: <6 11 19 36 38| Scale is weakly epimorphic with val: <6 11 20 34 36| Scale is weakly epimorphic with val: <6 11 20 35 38| Scale is weakly epimorphic with val: <6 11 20 35 41| Scale is weakly epimorphic with val: <6 11 20 37 39| Scale is weakly epimorphic with val: <6 11 21 35 37| Scale is weakly epimorphic with val: <6 11 21 36 36| Scale is weakly epimorphic with val: <6 11 21 36 39| Scale is weakly epimorphic with val: <6 11 21 36 42| Scale is weakly epimorphic with val: <6 11 21 38 40| Scale is weakly epimorphic with val: <6 11 22 36 38| Scale is weakly epimorphic with val: <6 11 22 37 37| Scale is weakly epimorphic with val: <6 11 22 37 40| Scale is weakly epimorphic with val: <7 10 18 35 36| Scale is weakly epimorphic with val: <7 10 18 35 39| Scale is weakly epimorphic with val: <7 10 18 35 42| Scale is weakly epimorphic with val: <7 10 18 37 37| Scale is weakly epimorphic with val: <7 10 19 36 37| Scale is weakly epimorphic with val: <7 10 19 36 40| Scale is weakly epimorphic with val: <7 10 19 38 38| Scale is weakly epimorphic with val: <7 10 20 36 36| Scale is weakly epimorphic with val: <7 10 20 37 38| Scale is weakly epimorphic with val: <7 10 20 37 41| Scale is weakly epimorphic with val: <7 10 21 37 37| Scale is weakly epimorphic with val: <7 10 21 38 39| Scale is weakly epimorphic with val: <7 10 21 38 42| Scale is weakly epimorphic with val: <7 10 22 38 38| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 18 33 41| Scale is JI-epimorphic with val: <7 11 18 34 37| Scale is weakly epimorphic with val: <7 11 18 34 40| Scale is weakly epimorphic with val: <7 11 18 36 38| Scale is weakly epimorphic with val: <7 11 18 36 41| Scale is weakly epimorphic with val: <7 11 18 37 37| Scale is weakly epimorphic with val: <7 11 18 37 40| Scale is weakly epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 11 19 32 41| Scale is weakly epimorphic with val: <7 11 19 34 36| Scale is weakly epimorphic with val: <7 11 19 34 39| Scale is weakly epimorphic with val: <7 11 19 34 42| Scale is JI-epimorphic with val: <7 11 19 35 38| Scale is weakly epimorphic with val: <7 11 19 35 41| Scale is weakly epimorphic with val: <7 11 19 37 39| Scale is weakly epimorphic with val: <7 11 19 37 42| Scale is weakly epimorphic with val: <7 11 19 38 38| Scale is weakly epimorphic with val: <7 11 19 38 41| Scale is weakly epimorphic with val: <7 11 20 32 37| Scale is weakly epimorphic with val: <7 11 20 32 40| Scale is weakly epimorphic with val: <7 11 20 33 36| Scale is weakly epimorphic with val: <7 11 20 33 39| Scale is weakly epimorphic with val: <7 11 20 33 42| Scale is weakly epimorphic with val: <7 11 20 35 37| Scale is weakly epimorphic with val: <7 11 20 35 40| Scale is weakly epimorphic with val: <7 11 20 36 36| Scale is JI-epimorphic with val: <7 11 20 36 39| Scale is weakly epimorphic with val: <7 11 20 36 42| Scale is weakly epimorphic with val: <7 11 20 38 40| Scale is weakly epimorphic with val: <7 11 21 33 38| Scale is weakly epimorphic with val: <7 11 21 33 41| Scale is weakly epimorphic with val: <7 11 21 34 37| Scale is weakly epimorphic with val: <7 11 21 34 40| Scale is weakly epimorphic with val: <7 11 21 36 38| Scale is weakly epimorphic with val: <7 11 21 36 41| Scale is weakly epimorphic with val: <7 11 21 37 37| Scale is JI-epimorphic with val: <7 11 21 37 40| Scale is weakly epimorphic with val: <7 11 22 32 38| Scale is weakly epimorphic with val: <7 11 22 32 41| Scale is weakly epimorphic with val: <7 11 22 34 36| Scale is weakly epimorphic with val: <7 11 22 34 39| Scale is weakly epimorphic with val: <7 11 22 34 42| Scale is weakly epimorphic with val: <7 11 22 35 38| Scale is weakly epimorphic with val: <7 11 22 35 41| Scale is weakly epimorphic with val: <7 11 22 37 39| Scale is weakly epimorphic with val: <7 11 22 37 42| Scale is weakly epimorphic with val: <7 11 22 38 38| Scale is JI-epimorphic with val: <7 11 22 38 41| Scale is weakly epimorphic with val: <7 12 18 35 36| Scale is weakly epimorphic with val: <7 12 18 35 39| Scale is weakly epimorphic with val: <7 12 18 35 42| Scale is weakly epimorphic with val: <7 12 18 36 38| Scale is weakly epimorphic with val: <7 12 19 34 36| Scale is weakly epimorphic with val: <7 12 19 36 37| Scale is weakly epimorphic with val: <7 12 19 36 40| Scale is weakly epimorphic with val: <7 12 19 37 39| Scale is weakly epimorphic with val: <7 12 20 35 37| Scale is weakly epimorphic with val: <7 12 20 37 38| Scale is weakly epimorphic with val: <7 12 20 37 41| Scale is weakly epimorphic with val: <7 12 20 38 40| Scale is weakly epimorphic with val: <7 12 21 36 38| Scale is weakly epimorphic with val: <7 12 21 38 39| Scale is weakly epimorphic with val: <7 12 21 38 42| Scale is weakly epimorphic with val: <7 12 22 34 36| Scale is weakly epimorphic with val: <7 12 22 37 39| Scale is weakly epimorphic with val: <8 11 18 37 39| Scale is weakly epimorphic with val: <8 11 18 37 42| Scale is weakly epimorphic with val: <8 11 18 38 38| Scale is weakly epimorphic with val: <8 11 19 36 36| Scale is weakly epimorphic with val: <8 11 19 38 40| Scale is weakly epimorphic with val: <8 11 20 37 37| Scale is weakly epimorphic with val: <8 11 21 38 38| Scale is weakly epimorphic with val: <8 11 22 36 36| Scale is weakly epimorphic with val: <8 12 18 36 37| Scale is weakly epimorphic with val: <8 12 18 37 39| Scale is weakly epimorphic with val: <8 12 18 37 42| Scale is weakly epimorphic with val: <8 12 19 37 38| Scale is weakly epimorphic with val: <8 12 19 38 40| Scale is weakly epimorphic with val: <8 12 20 35 36| Scale is weakly epimorphic with val: <8 12 20 38 39| Scale is weakly epimorphic with val: <8 12 21 36 37| Scale is weakly epimorphic with val: <8 12 22 37 38|
FIT/MODE
3: 0 0 3 N M DE S SD: 36.9292 c. M: 60.7513 c. 5: 0 1 4 N G T3 SD: 25.2356 c. M:-38.8577 c. 6: 0 1 5 N G T3 SD: 17.2812 c. M:-22.2562 c. 7: 0 1 6 N G T3 SD: 13.0218 c. M: 20.0145 c. 8: 0 1 7 N G T3 SD: 11.5880 c. M: 20.0145 c. 9: 0 1 8 N G T3 SD: 11.9705 c. M: 20.0145 c. 10: 0 1 9 N G T3 SD: 13.1708 c. M: 20.0145 c. 14: 1 1 12 N M DE S SD: 10.8049 c. M:-15.5602 c. 15: 1 1 13 N M DE S SD: 8.2848 c. M:-13.1885 c. 16: 1 1 14 N M DE S SD: 6.4748 c. M:-11.1133 c. 17: 1 1 15 N M DE S SD: 5.5020 c. M:-9.2823 c. 18: 1 1 16 N M DE S SD: 5.4128 c. M:-7.6547 c. 21: 1 2 18 N T3 SD: 6.3724 c. M:-10.3980 c. 22: 1 2 19 N T3 SD: 4.4048 c. M:-7.1639 c. 23: 1 2 20 N T3 SD: 2.6091 c. M:-4.2111 c. 24: 1 2 21 N T3 SD: 0.9673 c. M:-1.5043 c. 25: 1 2 22 N T3 SD: 0.5717 c. M: 0.9859 c. 49: 2 4 43 N T3 SD: 0.2260 c. M:-0.3139 c. 74: 3 6 65 N T3 SD: 0.1448 c. M: 0.1782 c. 123: 5 10 108 N T3 SD: 0.1338 c. M:-0.2312 c. 172: 7 14 151 N T3 SD: 0.1507 c. M:-0.2548 c. 197: 8 16 173 N T3 SD: 0.1293 c. M:-0.2107 c. 377: 15 31 331 N T3 SD: 0.1150 c. M: 0.1984 c. 401: 16 33 352 N T3 SD: 0.1029 c. M: 0.1424 c. 402: 16 33 353 N T3 SD: 0.1137 c. M: 0.1918 c. 426: 17 35 374 N T3 SD: 0.0842 c. M: 0.1395 c. 450: 18 37 395 N T3 SD: 0.0879 c. M:-0.1209 c. 451: 18 37 396 N T3 SD: 0.0794 c. M: 0.1369 c. 475: 19 39 417 N T3 SD: 0.0646 c. M: 0.0927 c. 500: 20 41 439 N T3 SD: 0.0538 c. M: 0.0927 c. 524: 21 43 460 N T3 SD: 0.0553 c. M:-0.0786 c. 525: 21 43 461 N T3 SD: 0.0577 c. M: 0.0927 c. 549: 22 45 482 N T3 SD: 0.0369 c. M: 0.0564 c. 574: 23 47 504 N T3 SD: 0.0345 c. M: 0.0580 c. 598: 24 49 525 N T3 SD: 0.0310 c. M:-0.0468 c. 623: 25 51 547 N T3 SD: 0.0169 c. M: 0.0287 c. 672: 27 55 590 N T3 SD: 0.0129 c. M:-0.0221 c. 697: 28 57 612 N T3 SD: 0.0091 c. M: 0.0141 c. 746: 30 61 655 N T3 SD: 0.0083 c. M:-0.0141 c. 1369: 55 112 1202 N T3 SD: 0.0038 c. M: 0.0054 c. 2066: 83 169 1814 N T3 SD: 0.0037 c. M: 0.0059 c. 2115: 85 173 1857 N T3 SD: 0.0020 c. M:-0.0031 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: 103.0598 cents 7 x 8:9 S SD: 90.8405 cents 8 x 9:11 SD: 76.3748 cents 9 x 10:12 S SD: 60.8262 cents 10 x 11:13 SD: 56.5461 cents 11 x 12:15 S SD: 48.9722 cents 12 x 13:16 SD: 38.9107 cents 13 x 14:17 SD: 37.7250 cents 14 x 15:19 SD: 33.1045 cents 15 x 16:20 S SD: 25.4900 cents 16 x 17:21 SD: 25.9679 cents 17 x 18:23 SD: 22.9034 cents 18 x 19:24 SD: 16.4259 cents 19 x 20:25 S SD: 18.1148 cents 20 x 21:27 SD: 16.0075 cents 21 x 22:28 SD: 9.8929 cents 22 x 23:29 SD: 12.7875 cents 23 x 24:31 SD: 11.3739 cents 24 x 25:32 SD: 4.9606 cents 25 x 26:33 SD: 9.4054 cents 26 x 27:35 SD: 8.5950 cents 27 x 28:36 SD: 1.1048 cents 28 x 29:37 SD: 7.7634 cents 29 x 30:39 SD: 7.5013 cents 30 x 31:40 SD: 1.9922 cents 31 x 32:41 SD: 7.5828 cents 32 x 33:43 SD: 7.7045 cents 33 x 34:44 SD: 4.5344 cents 34 x 35:45 SD: 8.2902 cents 35 x 36:47 SD: 8.5932 cents 36 x 37:48 SD: 6.6586 cents 37 x 38:49 SD: 9.3596 cents 38 x 39:51 SD: 9.7203 cents 39 x 40:52 SD: 8.4601 cents 40 x 41:53 SD: 10.5108 cents 41 x 42:55 SD: 10.8744 cents 42 x 44:56 SD: 9.8929 cents 43:44:45:57 SD: 9.5204 cents 44:45:46:59 SD: 8.9175 cents 45:46:47:60 SD: 7.7206 cents 47:48:49:63 SD: 7.3352 cents 48:49:50:64 SD: 6.1857 cents 50:51:52:67 SD: 6.0484 cents 51:52:53:68 SD: 4.9348 cents 54:55:56:72 SD: 3.9860 cents 57:58:59:76 SD: 3.3830 cents 60:61:62:80 SD: 3.1599 cents 75:76:78:100 SD: 2.5736 cents 78:79:81:104 SD: 1.6731 cents 81:82:84:108 SD: 0.8426 cents 84:85:87:112 SD: 0.1579 cents