Scala analysis: 554_M62
Miscellaneous tetrachord 24/23 * 115/106 * 53/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 60/53 214.764169 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 53/45 283.2808 1: 24/23 73.6807 vicesimotertial minor semitone 2: 115/106 141.0835 3: 53/45 283.2808
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 115/106 141.084 cents 1: 1 53/45 283.281 cents 2: 1 60/53 214.764 cents 2: 1 424/345 356.961 cents 2: 1 23/18 424.364 cents vicesimotertial major third 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 : 73.7 214.8 498.0 73.7 : 141.1 424.4 498.0 214.8: 283.3 357.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 283.2808 cents 1219/1080, 209.6002 cents 24/23, 73.6807 cents 2: 214.7642 .. 424.3643 cents 1219/1080, 209.6002 cents 2700/2809,-68.5167 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 53/45, 283.2808 cents Average / Smallest step : 2.253169 Largest / Average step : 1.706357 Largest / Smallest step : 3.844711 Median interval of one step : 115/106, 141.0835 cents, amount: 1 Least squares average step : 142.66743 cents, oct.: 428.00228 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1352-tone equal temperament with octave 4/3 degrees: 200 583 1352 Least number of segments generator : 677 of 249.391 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1159 of 426.948 cents and inv. generated superset size: 49 = 46 more = 1633.333% 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 68.51666 cents Scale diversity : 1.059607 Lumma stability : 0.295880 Lumma impropriety factor : 0.137571 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 : 2645/2544, 67.4029 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% -- Rational properties -- Prime limit : 53 Odd number limit : 345 (O: 115 U: 345) Highest odd numerator or denominator: 53 Scale harmonicity : 0.017599 Fundamental : 1/3657, -11.8364 octaves, 0.0715 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 4.388400E+05, 18.74334 octaves Euler's gradus suavitatis : 86 Sum of Mann's harmonic distance : 83.5, average 27.83333 Mersenne's string divisions : 37177 Sum of van Prooijen's expressibility: 3.56312, average 1.18771 Sum of Tenney's harmonic distance : 7.32355, average 2.44118 Vogel's harmonic complexity : 58.66667 Wille's k value : 609 Wilson's harmonic complexity : 87 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.41979, average 2.40330 Lattice compactness (without 2's) : 9.71478, average 1.61913 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.33333 1 23: -1 .. 0 -0.33333 1 1 53: -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: <7 10 19 32 40| Scale is weakly epimorphic with val: <7 10 19 35 40| Scale is weakly epimorphic with val: <7 11 15 30 42| Scale is weakly epimorphic with val: <7 11 15 31 41| Scale is weakly epimorphic with val: <7 11 15 33 42| Scale is weakly epimorphic with val: <7 11 15 34 41| Scale is weakly epimorphic with val: <7 11 15 36 42| Scale is weakly epimorphic with val: <7 11 16 30 40| Scale is weakly epimorphic with val: <7 11 16 31 42| Scale is weakly epimorphic with val: <7 11 16 33 40| Scale is weakly epimorphic with val: <7 11 16 34 42| Scale is weakly epimorphic with val: <7 11 16 36 40| Scale is weakly epimorphic with val: <7 11 17 30 41| Scale is JI-epimorphic with val: <7 11 17 31 40| Scale is weakly epimorphic with val: <7 11 17 33 41| = patent Scale is weakly epimorphic with val: <7 11 17 34 40| Scale is weakly epimorphic with val: <7 11 17 36 41| Scale is weakly epimorphic with val: <7 11 18 30 42| Scale is JI-epimorphic with val: <7 11 18 31 41| Scale is weakly epimorphic with val: <7 11 18 33 42| Scale is weakly epimorphic with val: <7 11 18 34 41| Scale is weakly epimorphic with val: <7 11 18 36 42| Scale is weakly epimorphic with val: <7 11 19 30 40| Scale is JI-epimorphic with val: <7 11 19 31 42| Scale is weakly epimorphic with val: <7 11 19 33 40| Scale is weakly epimorphic with val: <7 11 19 34 42| Scale is weakly epimorphic with val: <7 11 19 36 40| Scale is weakly epimorphic with val: <7 12 15 30 40| Scale is weakly epimorphic with val: <7 12 16 30 41| Scale is weakly epimorphic with val: <7 12 17 30 42| Scale is weakly epimorphic with val: <7 12 17 32 40| Scale is weakly epimorphic with val: <7 12 17 35 40| Scale is weakly epimorphic with val: <7 12 18 30 40| Scale is weakly epimorphic with val: <7 12 18 32 41| Scale is weakly epimorphic with val: <7 12 18 35 41| Scale is weakly epimorphic with val: <7 12 19 30 41| Scale is weakly epimorphic with val: <7 12 19 32 42| Scale is weakly epimorphic with val: <7 12 19 35 42| Scale is weakly epimorphic with val: <8 11 15 32 41| Scale is weakly epimorphic with val: <8 11 16 31 40| Scale is weakly epimorphic with val: <8 11 16 32 42| Scale is weakly epimorphic with val: <8 11 16 34 40| Scale is weakly epimorphic with val: <8 11 17 31 41| Scale is weakly epimorphic with val: <8 11 17 32 40| Scale is weakly epimorphic with val: <8 11 17 34 41| Scale is weakly epimorphic with val: <8 11 18 31 42| Scale is weakly epimorphic with val: <8 11 18 32 41| Scale is weakly epimorphic with val: <8 11 18 34 42| Scale is weakly epimorphic with val: <8 11 19 32 42| Scale is weakly epimorphic with val: <8 12 15 31 40| Scale is weakly epimorphic with val: <8 12 15 33 41| Scale is weakly epimorphic with val: <8 12 15 34 40| Scale is weakly epimorphic with val: <8 12 16 31 41| Scale is weakly epimorphic with val: <8 12 16 33 42| Scale is weakly epimorphic with val: <8 12 16 34 41| Scale is weakly epimorphic with val: <8 12 17 31 42| Scale is weakly epimorphic with val: <8 12 17 33 40| Scale is weakly epimorphic with val: <8 12 17 34 42| Scale is weakly epimorphic with val: <8 12 18 33 41| Scale is weakly epimorphic with val: <8 12 19 33 42|
FIT/MODE
3: 0 1 2 N G T3 SD: 51.0076 c. M: 73.6807 c. 4: 1 1 2 P M ME S SD: 35.3901 c. M:-50.8306 c. 5: 1 1 3 N M DE S SD: 17.4543 c. M:-25.9283 c. 6: 1 2 3 P T3 SD: 20.4990 c. M:-34.2583 c. 7: 1 2 4 N T3 SD: 1.6473 c. M: 2.5314 c. 46: 7 13 26 N T3 SD: 1.5922 c. M:-2.1088 c. 53: 8 15 30 N T3 SD: 1.1706 c. M:-1.4960 c. 60: 9 17 34 N T3 SD: 0.8498 c. M:-1.0553 c. 67: 10 19 38 N T3 SD: 0.6001 c. M:-0.8075 c. 74: 11 21 42 N T3 SD: 0.4052 c. M:-0.6066 c. 81: 12 23 46 N T3 SD: 0.2613 c. M:-0.4405 c. 88: 13 25 50 N T3 SD: 0.1841 c. M:-0.3007 c. 95: 14 27 54 N T3 SD: 0.1949 c. M: 0.2845 c. 183: 27 52 104 N T3 SD: 0.1794 c. M:-0.2389 c. 271: 40 77 154 N T3 SD: 0.1784 c. M:-0.2589 c. 276: 41 78 157 N T3 SD: 0.1764 c. M:-0.3043 c. 278: 41 79 158 N T3 SD: 0.1826 c. M: 0.2280 c. 283: 42 80 161 N T3 SD: 0.1394 c. M:-0.2342 c. 290: 43 82 165 N T3 SD: 0.1096 c. M:-0.1674 c. 297: 44 84 169 N T3 SD: 0.0910 c. M: 0.1185 c. 304: 45 86 173 N T3 SD: 0.0879 c. M: 0.1461 c. 311: 46 88 177 N T3 SD: 0.0999 c. M: 0.1724 c. 371: 55 105 211 N T3 SD: 0.0899 c. M:-0.1535 c. 378: 56 107 215 N T3 SD: 0.0599 c. M:-0.1038 c. 385: 57 109 219 N T3 SD: 0.0348 c. M:-0.0559 c. 392: 58 111 223 N T3 SD: 0.0270 c. M: 0.0458 c. 473: 70 134 269 N T3 SD: 0.0263 c. M:-0.0375 c. 480: 71 136 273 N T3 SD: 0.0122 c. M:-0.0177 c. 865: 128 245 492 N T3 SD: 0.0107 c. M:-0.0185 c. 872: 129 247 496 N T3 SD: 0.0064 c. M: 0.0108 c. 1345: 199 381 765 N T3 SD: 0.0057 c. M:-0.0078 c. 1352: 200 383 769 N T3 SD: 0.0031 c. M: 0.0054 c. 2217: 328 628 1261 N T3 SD: 0.0023 c. M:-0.0039 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: 65.7854 cents 6 x 7:8 S SD: 26.0534 cents 7 x 8:9 S SD: 32.5321 cents 8 x 9:11 SD: 27.1837 cents 9 x 10:12 S SD: 16.1802 cents 10 x 11:13 SD: 33.1557 cents 11 x 12:15 S SD: 37.5032 cents 12:13:14:16 S SD: 27.7410 cents 13:14:15:17 SD: 24.0386 cents 14:15:16:19 SD: 19.1555 cents 15:16:17:20 SD: 12.6997 cents 18:19:20:24 S SD: 12.6671 cents 20:21:23:27 SD: 12.1038 cents 21:22:24:28 S SD: 5.9282 cents 24:25:27:32 SD: 3.7544 cents 45:47:51:60 SD: 0.8342 cents 114:119:129:152 SD: 0.3295 cents 159:166:180:212 SD: 0.3024 cents 273:285:309:364 SD: 0.2845 cents 348:363:394:464 SD: 0.2146 cents 393:410:445:524 SD: 0.1731 cents 462:482:523:616 SD: 0.1062 cents 507:529:574:676 SD: 0.0607 cents