Scala analysis: 545_M53
Miscellaneous tetrachord 32/31 * 13/12 * 31/26
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/31 54.964428 Greek enharmonic 1/4-tone 2: 104/93 193.537088 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 31/26 304.5079 1: 32/31 54.9644 Greek enharmonic 1/4-tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 31/26 304.5079
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 1 31/26 304.508 cents 2: 1 104/93 193.537 cents 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 31/24 443.081 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 : 55.0 193.5 498.0 55.0 : 138.6 443.1 498.0 193.5: 304.5 359.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.9644 .. 304.5079 cents 961/832, 249.5435 cents 32/31, 54.9644 cents 2: 193.5371 .. 443.0806 cents 961/832, 249.5435 cents 2704/2883,-110.9708 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 32/31, 54.9644 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 31/26, 304.5079 cents Average / Smallest step : 3.020408 Largest / Average step : 1.834219 Largest / Smallest step : 5.540091 Median interval of one step : 13/12, 138.5727 cents, amount: 1 Least squares average step : 138.29811 cents, oct.: 414.89434 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1894-tone equal temperament with octave 4/3 degrees: 209 736 1894 Least number of segments generator : 949 of 249.548 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1193 of 313.710 cents and inv. generated superset size: 75 = 72 more = 2500.000% 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 54.96443 cents Scale diversity : 0.910452 Lumma stability : 0.220721 Lumma impropriety factor : 0.222813 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 : 32/31, 54.9644 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 -- Rational properties -- Prime limit : 31 Odd number limit : 93 (O: 31 U: 93) Highest odd numerator or denominator: 93 Scale harmonicity : 0.033534 Fundamental : 1/93, -6.5392 octaves, 2.8132 Hz. Guide tone : 416, 8.7004 octaves, 108836.235 Hz. Exponens Consonantiae : 3.868800E+04, 15.23960 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 133.5, average 44.50000 Mersenne's string divisions : 12411 Sum of van Prooijen's expressibility: 3.93697, average 1.31232 Sum of Tenney's harmonic distance : 8.06121, average 2.68707 Vogel's harmonic complexity : 19.00000 Wille's k value : 15 Wilson's harmonic complexity : 47 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 17.57867, average 2.92978 Lattice compactness (without 2's) : 5.82843, average 0.97140 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.33333 10 3: -1 .. 0 -0.66667 2 1 13: 0 .. 1 0.33333 1 31: -1 .. 0 -0.66667 2 2 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: <6 10 30 35| Scale is weakly epimorphic with val: <6 11 30 34| Scale is weakly epimorphic with val: <7 10 25 33| Scale is weakly epimorphic with val: <7 10 28 36| Scale is JI-epimorphic with val: <7 11 26 34| Scale is weakly epimorphic with val: <7 11 26 37| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 11 27 36| = patent Scale is weakly epimorphic with val: <7 11 27 39| Scale is weakly epimorphic with val: <7 11 29 34| Scale is weakly epimorphic with val: <7 11 29 37| Scale is weakly epimorphic with val: <7 11 30 33| Scale is weakly epimorphic with val: <7 11 30 36| Scale is weakly epimorphic with val: <7 11 30 39| Scale is weakly epimorphic with val: <7 12 28 34| Scale is weakly epimorphic with val: <8 11 25 37| Scale is weakly epimorphic with val: <8 11 26 36| Scale is weakly epimorphic with val: <8 11 28 37| Scale is weakly epimorphic with val: <8 11 29 39| Scale is weakly epimorphic with val: <8 12 26 35| Scale is weakly epimorphic with val: <8 12 27 37| Scale is weakly epimorphic with val: <8 12 29 38| Scale is weakly epimorphic with val: <8 12 30 37|
FIT/MODE
3: 0 1 2 N G T3 SD: 35.4897 c. M: 54.9644 c. 5: 1 1 3 N M DE S SD: 25.9834 c. M:-44.6446 c. 7: 1 2 4 N T3 SD: 14.8143 c. M:-19.9108 c. 8: 1 2 5 N T3 SD: 5.7445 c. M:-7.2912 c. 10: 1 3 6 N T3 SD: 4.4309 c. M:-5.6809 c. 18: 2 5 11 N T3 SD: 0.2320 c. M:-0.3739 c. 237: 26 66 145 N T3 SD: 0.2221 c. M: 0.3266 c. 255: 28 71 156 N T3 SD: 0.1903 c. M: 0.2771 c. 273: 30 76 167 N T3 SD: 0.1628 c. M: 0.2342 c. 291: 32 81 178 N T3 SD: 0.1387 c. M: 0.1966 c. 309: 34 86 189 N T3 SD: 0.1176 c. M: 0.1634 c. 327: 36 91 200 N T3 SD: 0.0988 c. M: 0.1338 c. 345: 38 96 211 N T3 SD: 0.0822 c. M: 0.1073 c. 363: 40 101 222 N T3 SD: 0.0674 c. M: 0.0834 c. 381: 42 106 233 N T3 SD: 0.0543 c. M: 0.0708 c. 399: 44 111 244 N T3 SD: 0.0428 c. M: 0.0610 c. 417: 46 116 255 N T3 SD: 0.0331 c. M: 0.0520 c. 435: 48 121 266 N T3 SD: 0.0256 c. M: 0.0437 c. 453: 50 126 277 N T3 SD: 0.0213 c. M: 0.0362 c. 471: 52 131 288 N T3 SD: 0.0209 c. M: 0.0292 c. 888: 98 247 543 N T3 SD: 0.0230 c. M: 0.0399 c. 924: 102 257 565 N T3 SD: 0.0206 c. M: 0.0326 c. 960: 106 267 587 N T3 SD: 0.0220 c. M:-0.0280 c. 1042: 115 290 637 N T3 SD: 0.0236 c. M:-0.0409 c. 1060: 117 295 648 N T3 SD: 0.0251 c. M:-0.0427 c. 1323: 146 368 809 N T3 SD: 0.0238 c. M: 0.0411 c. 1341: 148 373 820 N T3 SD: 0.0223 c. M: 0.0386 c. 1351: 149 376 826 N T3 SD: 0.0207 c. M: 0.0357 c. 1369: 151 381 837 N T3 SD: 0.0178 c. M: 0.0303 c. 1387: 153 386 848 N T3 SD: 0.0151 c. M: 0.0251 c. 1405: 155 391 859 N T3 SD: 0.0127 c. M: 0.0200 c. 1423: 157 396 870 N T3 SD: 0.0107 c. M: 0.0150 c. 1441: 159 401 881 N T3 SD: 0.0094 c. M:-0.0127 c. 1459: 161 406 892 N T3 SD: 0.0088 c. M:-0.0143 c. 1477: 163 411 903 N T3 SD: 0.0092 c. M:-0.0159 c. 1495: 165 416 914 N T3 SD: 0.0103 c. M:-0.0175 c. 1840: 203 512 1125 N T3 SD: 0.0100 c. M: 0.0171 c. 1858: 205 517 1136 N T3 SD: 0.0077 c. M: 0.0133 c. 1876: 207 522 1147 N T3 SD: 0.0055 c. M: 0.0096 c. 1894: 209 527 1158 N T3 SD: 0.0035 c. M: 0.0059 c. 1912: 211 532 1169 N T3 SD: 0.0019 c. M:-0.0024 c. 1930: 213 537 1180 N T3 SD: 0.0022 c. M:-0.0037 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 6:7 S SD: 74.2363 cents 6 x 7:8 S SD: 36.6669 cents 7 x 8:9 S SD: 36.6764 cents 8 x 9:11 SD: 27.1367 cents 9 x 10:12 S SD: 5.5667 cents 10 x 11:13 SD: 26.1500 cents 11 x 12:15 S SD: 28.9572 cents 12 x 13:16 SD: 27.4822 cents 13 x 15:17 SD: 31.8912 cents 14:15:16:19 SD: 26.9009 cents 15:16:17:20 SD: 20.4352 cents 16:17:18:21 S SD: 19.2931 cents 17:18:19:23 SD: 16.9144 cents 18:19:20:24 S SD: 13.4035 cents 23:24:26:31 SD: 10.8058 cents 24:25:27:32 SD: 6.2746 cents 27:28:30:36 S SD: 4.5692 cents 33:34:37:44 SD: 1.8657 cents 60:62:67:80 SD: 1.0270 cents 93:96:104:124 SD: 0.0000 cents