Scala analysis: 573_M81
Miscellaneous tetrachord 30/29 * 116/103 * 103/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 2: 120/103 264.468082 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 103/90 233.5769 1: 30/29 58.6915 2: 116/103 205.7766 3: 103/90 233.5769
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30/29 58.692 cents 1: 1 116/103 205.777 cents 1: 1 103/90 233.577 cents 2: 1 120/103 264.468 cents 2: 1 103/87 292.268 cents 2: 1 58/45 439.353 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 : 58.7 264.5 498.0 58.7 : 205.8 439.4 498.0 264.5: 233.6 292.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 233.5769 cents 2987/2700, 174.8854 cents 30/29, 58.6915 cents 2: 264.4681 .. 439.3535 cents 2987/2700, 174.8854 cents 10800/10609, 30.8912 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 103/90, 233.5769 cents Average / Smallest step : 2.828603 Largest / Average step : 1.406963 Largest / Smallest step : 3.979739 Median interval of one step : 116/103, 205.7766 cents, amount: 1 Least squares average step : 148.69733 cents, oct.: 446.09200 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2096-tone equal temperament with octave 4/3 degrees: 247 1113 2096 Least number of segments generator : 1049 of 249.260 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1233 of 292.982 cents and inv. generated superset size: 58 = 55 more = 1933.333% 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 30.89117 cents Scale diversity : 0.797034 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.297712 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 : 10609/10440, 27.8004 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 : 103 Odd number limit : 103 (O: 103 U: 103) Highest odd numerator or denominator: 103 Scale harmonicity : 0.014534 Fundamental : 1/8961, -13.1294 octaves, 0.0292 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 1.075320E+06, 20.03633 octaves Euler's gradus suavitatis : 142 Sum of Mann's harmonic distance : 144.5, average 48.16667 Mersenne's string divisions : 92099 Sum of van Prooijen's expressibility: 3.95236, average 1.31745 Sum of Tenney's harmonic distance : 8.11072, average 2.70357 Vogel's harmonic complexity : 97.33333 Wille's k value : 2317 Wilson's harmonic complexity : 143 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.88400, average 2.48067 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.00000 6 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 29: -1 .. 0 -0.33333 1 1 103: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 19 32 49| Scale is weakly epimorphic with val: <6 11 18 32 48| Scale is weakly epimorphic with val: <6 11 19 33 49| Scale is weakly epimorphic with val: <7 10 18 32 47| Scale is weakly epimorphic with val: <7 10 19 33 48| Scale is weakly epimorphic with val: <7 10 19 34 47| Scale is weakly epimorphic with val: <7 10 19 37 47| Scale is weakly epimorphic with val: <7 11 15 32 48| Scale is weakly epimorphic with val: <7 11 15 34 49| Scale is weakly epimorphic with val: <7 11 15 35 48| Scale is weakly epimorphic with val: <7 11 15 37 49| Scale is weakly epimorphic with val: <7 11 15 38 48| Scale is weakly epimorphic with val: <7 11 16 32 47| Scale is weakly epimorphic with val: <7 11 16 33 49| Scale is weakly epimorphic with val: <7 11 16 35 47| Scale is weakly epimorphic with val: <7 11 16 36 49| Scale is weakly epimorphic with val: <7 11 16 38 47| Scale is weakly epimorphic with val: <7 11 17 33 48| Scale is JI-epimorphic with val: <7 11 17 34 47| Scale is weakly epimorphic with val: <7 11 17 36 48| Scale is weakly epimorphic with val: <7 11 17 37 47| Scale is weakly epimorphic with val: <7 11 18 32 48| Scale is weakly epimorphic with val: <7 11 18 34 49| Scale is JI-epimorphic with val: <7 11 18 35 48| Scale is weakly epimorphic with val: <7 11 18 37 49| Scale is weakly epimorphic with val: <7 11 18 38 48| Scale is weakly epimorphic with val: <7 11 19 32 47| Scale is weakly epimorphic with val: <7 11 19 33 49| Scale is weakly epimorphic with val: <7 11 19 35 47| Scale is JI-epimorphic with val: <7 11 19 36 49| Scale is weakly epimorphic with val: <7 11 19 38 47| Scale is weakly epimorphic with val: <7 12 16 32 48| Scale is weakly epimorphic with val: <7 12 17 32 47| Scale is weakly epimorphic with val: <7 12 17 33 49| Scale is weakly epimorphic with val: <7 12 17 35 47| Scale is weakly epimorphic with val: <7 12 17 38 47| Scale is weakly epimorphic with val: <7 12 18 33 48| Scale is weakly epimorphic with val: <7 12 18 34 47| Scale is weakly epimorphic with val: <7 12 18 36 48| Scale is weakly epimorphic with val: <7 12 19 34 49| Scale is weakly epimorphic with val: <7 12 19 35 48| Scale is weakly epimorphic with val: <7 12 19 37 49| Scale is weakly epimorphic with val: <8 11 15 33 47| Scale is weakly epimorphic with val: <8 11 15 36 47| Scale is weakly epimorphic with val: <8 11 16 32 47| Scale is weakly epimorphic with val: <8 11 16 34 48| Scale is weakly epimorphic with val: <8 11 16 37 48| Scale is weakly epimorphic with val: <8 11 17 32 49| Scale is weakly epimorphic with val: <8 11 17 33 48| Scale is weakly epimorphic with val: <8 11 17 35 49| Scale is weakly epimorphic with val: <8 11 17 38 49| Scale is weakly epimorphic with val: <8 11 18 34 49| Scale is weakly epimorphic with val: <8 11 19 35 47| Scale is weakly epimorphic with val: <8 12 15 32 49| Scale is weakly epimorphic with val: <8 12 15 33 48| Scale is weakly epimorphic with val: <8 12 15 36 48| Scale is weakly epimorphic with val: <8 12 16 33 47| Scale is weakly epimorphic with val: <8 12 16 34 49| Scale is weakly epimorphic with val: <8 12 16 37 49| Scale is weakly epimorphic with val: <8 12 17 34 48| Scale is weakly epimorphic with val: <8 12 18 35 49| Scale is weakly epimorphic with val: <8 12 19 36 47|
FIT/MODE
3: 0 1 2 N G T3 SD: 66.1758 c. M: 98.4531 c. 4: 0 2 2 P M DE S SD: 35.0393 c. M: 58.6915 c. 6: 1 2 3 P T3 SD: 16.6316 c. M:-24.3160 c. 7: 1 3 3 SP M DE S SD: 13.6672 c. M:-20.1291 c. 8: 1 3 4 P T3 SD: 9.1518 c. M: 15.4456 c. 9: 1 4 4 SP M DE S SD: 7.3180 c. M:-12.2236 c. 15: 2 6 7 SP T3 SD: 4.5037 c. M:-7.7145 c. 17: 2 7 8 SP T3 SD: 0.4637 c. M: 0.7972 c. 77: 9 32 36 SP T3 SD: 0.5014 c. M:-0.7247 c. 94: 11 39 44 SP T3 SD: 0.3511 c. M:-0.4495 c. 111: 13 46 52 SP T3 SD: 0.2568 c. M: 0.3619 c. 128: 15 53 60 SP T3 SD: 0.2007 c. M: 0.3269 c. 145: 17 60 68 SP T3 SD: 0.1733 c. M: 0.3000 c. 162: 19 67 76 SP T3 SD: 0.1665 c. M: 0.2788 c. 179: 21 74 84 SP T3 SD: 0.1720 c. M: 0.2617 c. 196: 23 81 92 SP T3 SD: 0.1835 c. M: 0.2475 c. 213: 25 88 100 SP T3 SD: 0.1971 c. M: 0.2470 c. 228: 27 94 107 SP T3 SD: 0.1885 c. M:-0.2875 c. 254: 30 105 119 SP T3 SD: 0.1588 c. M:-0.2409 c. 262: 31 108 123 SP T3 SD: 0.1942 c. M: 0.2381 c. 271: 32 112 127 SP T3 SD: 0.1223 c. M:-0.1758 c. 288: 34 119 135 SP T3 SD: 0.0915 c. M:-0.1183 c. 305: 36 126 143 SP T3 SD: 0.0668 c. M:-0.0941 c. 322: 38 133 151 SP T3 SD: 0.0501 c. M:-0.0840 c. 339: 40 140 159 SP T3 SD: 0.0446 c. M:-0.0749 c. 356: 42 147 167 SP T3 SD: 0.0504 c. M:-0.0666 c. 450: 53 186 211 SP T3 SD: 0.0341 c. M:-0.0492 c. 467: 55 193 219 SP T3 SD: 0.0229 c. M: 0.0353 c. 484: 57 200 227 SP T3 SD: 0.0224 c. M: 0.0375 c. 772: 91 319 362 SP T3 SD: 0.0236 c. M:-0.0377 c. 789: 93 326 370 SP T3 SD: 0.0138 c. M:-0.0197 c. 806: 95 333 378 SP T3 SD: 0.0065 c. M:-0.0111 c. 1273: 150 526 597 SP T3 SD: 0.0059 c. M:-0.0083 c. 1290: 152 533 605 SP T3 SD: 0.0043 c. M: 0.0071 c. 2079: 245 859 975 SP T3 SD: 0.0035 c. M:-0.0060 c. 2096: 247 866 983 SP T3 SD: 0.0003 c. M: 0.0005 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: 49.3797 cents 6 x 7:8 S SD: 1.2014 cents 7 x 8:9 S SD: 35.6110 cents 8 x 9:11 SD: 40.3277 cents 9 x 10:12 S SD: 41.0322 cents 10 x 12:13 S SD: 33.6892 cents 12:13:14:16 S SD: 26.6391 cents 13:14:15:17 SD: 26.3629 cents 14:15:16:19 SD: 25.2502 cents 15:16:17:20 SD: 23.7961 cents 16:17:19:21 SD: 21.0176 cents 17:18:20:23 SD: 16.8165 cents 18:19:21:24 SD: 11.6647 cents 23:24:27:31 SD: 9.1115 cents 24:25:28:32 SD: 4.0732 cents 30:31:35:40 SD: 1.0262 cents 114:118:133:152 SD: 0.8691 cents 144:149:168:192 SD: 0.8120 cents 171:177:199:228 SD: 0.7298 cents 177:183:206:236 SD: 0.6812 cents 201:208:234:268 SD: 0.4714 cents 231:239:269:308 SD: 0.2832 cents 261:270:304:348 SD: 0.1474 cents 291:301:339:388 SD: 0.0826 cents