Scala analysis: 577_M85
Miscellaneous tetrachord 256/243 * 729/640 * 10/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 256/243 90.2250 limma, Pythagorean minor second 2: 729/640 225.4163 acute major second 3: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 10/9 182.404 cents minor whole tone 1: 1 729/640 225.416 cents acute major second 2: 1 2560/2187 272.629 cents grave minor third 2: 1 6/5 315.641 cents minor third 2: 1 81/64 407.820 cents Pythagorean 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 : 90.2 315.6 498.0 90.2 : 225.4 407.8 498.0 315.6: 182.4 272.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 225.4163 cents 177147/163840, 135.1913 cents 256/243, 90.2250 cents 2: 272.6287 .. 407.8200 cents 177147/163840, 135.1913 cents 1638400/1594323, 47.2124 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 729/640, 225.4163 cents Average / Smallest step : 1.840011 Largest / Average step : 1.357807 Largest / Smallest step : 2.498380 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 158.26018 cents, oct.: 474.78055 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1540-tone equal temperament with octave 4/3 degrees: 279 976 1540 Least number of segments generator : 771 of 249.346 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1033 of 334.078 cents and inv. generated superset size: 38 = 35 more = 1266.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 47.21242 cents Scale diversity : 1.132147 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.457112 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 : 6561/6400, 43.0126 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 5 Odd number limit : 2187 (O: 729 U: 2187) Highest odd numerator or denominator: 243 Scale harmonicity : 0.032895 Average absolute harmonicity : 0.120166 Specific harmonicity : 0.168657 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 768, 9.5850 octaves, 200928.434 Hz. Exponens Consonantiae : 9.331200E+05, 19.83170 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 258.5, average 86.16667 Mersenne's string divisions : 38423 Sum of van Prooijen's expressibility: 3.56170, average 1.18723 Sum of Tenney's harmonic distance : 7.35015, average 2.45005 Vogel's harmonic complexity : 17.00000 Wille's k value : 364 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 32.33631, average 5.38939 Lattice compactness (without 2's) : 19.73304, average 3.28884 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 3.66667 11 3: -5 .. 1 -1.66667 7 2 5: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 16| Scale is weakly epimorphic with val: <7 11 19|
FIT/MODE
3: 1 1 1 SP B ME I SD: 44.7687 c. M:-75.7900 c. 5: 1 2 2 SP M ME S SD: 11.1173 c. M: 16.8143 c. 6: 1 3 2 P T3 SD: 10.3390 c. M:-16.3887 c. 11: 2 5 4 SP T3 SD: 0.7722 c. M:-1.2964 c. 49: 9 22 18 SP T3 SD: 0.7902 c. M:-1.2527 c. 60: 11 27 22 SP T3 SD: 0.6374 c. M:-1.0833 c. 71: 13 32 26 SP T3 SD: 0.5581 c. M:-0.9663 c. 82: 15 37 30 SP T3 SD: 0.5205 c. M:-0.8808 c. 93: 17 42 34 SP T3 SD: 0.5064 c. M:-0.8155 c. 104: 19 47 38 SP T3 SD: 0.5050 c. M:-0.7640 c. 115: 21 52 42 SP T3 SD: 0.5102 c. M:-0.7224 c. 126: 23 57 46 SP T3 SD: 0.5187 c. M:-0.6880 c. 128: 23 58 47 SP T3 SD: 0.5032 c. M: 0.7325 c. 137: 25 62 50 SP T3 SD: 0.5286 c. M:-0.6591 c. 139: 25 63 51 SP T3 SD: 0.4207 c. M: 0.6486 c. 150: 27 68 55 SP T3 SD: 0.3550 c. M: 0.5769 c. 161: 29 73 59 SP T3 SD: 0.3040 c. M: 0.5150 c. 172: 31 78 63 SP T3 SD: 0.2664 c. M: 0.4611 c. 177: 32 80 65 SP T3 SD: 0.3042 c. M: 0.4942 c. 183: 33 83 67 SP T3 SD: 0.2412 c. M: 0.4136 c. 188: 34 85 69 SP T3 SD: 0.2416 c. M: 0.3894 c. 194: 35 88 71 SP T3 SD: 0.2272 c. M: 0.3715 c. 199: 36 90 73 SP T3 SD: 0.1859 c. M: 0.2962 c. 210: 38 95 77 SP T3 SD: 0.1364 c. M: 0.2128 c. 221: 40 100 81 SP T3 SD: 0.0923 c. M: 0.1377 c. 232: 42 105 85 SP T3 SD: 0.0537 c. M: 0.0697 c. 243: 44 110 89 SP T3 SD: 0.0258 c. M: 0.0440 c. 497: 90 225 182 SP T3 SD: 0.0240 c. M: 0.0358 c. 740: 134 335 271 SP T3 SD: 0.0232 c. M: 0.0385 c. 751: 136 340 275 SP T3 SD: 0.0259 c. M: 0.0331 c. 983: 178 445 360 SP T3 SD: 0.0233 c. M: 0.0398 c. 1021: 185 462 374 SP T3 SD: 0.0222 c. M: 0.0339 c. 1032: 187 467 378 SP T3 SD: 0.0169 c. M:-0.0215 c. 1043: 189 472 382 SP T3 SD: 0.0147 c. M:-0.0248 c. 1054: 191 477 386 SP T3 SD: 0.0167 c. M:-0.0279 c. 1275: 231 577 467 SP T3 SD: 0.0114 c. M: 0.0175 c. 1286: 233 582 471 SP T3 SD: 0.0077 c. M:-0.0118 c. 1297: 235 587 475 SP T3 SD: 0.0088 c. M:-0.0145 c. 1529: 277 692 560 SP T3 SD: 0.0041 c. M: 0.0065 c. 1540: 279 697 564 SP T3 SD: 0.0034 c. M:-0.0052 c. 1783: 323 807 653 SP T3 SD: 0.0012 c. M: 0.0015 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 5 x S SD: 70.6724 cents 5 x 6:7 S SD: 42.2336 cents 6 x 7:8 S SD: 24.3852 cents 7 x 8:9 S SD: 52.6754 cents 8 x 10:11 S SD: 44.2510 cents 9:10:11:12 H SD: 32.4996 cents 10:11:12:13 H SD: 28.8927 cents 11:12:13:15 SD: 25.5210 cents 12:13:14:16 S SD: 22.8912 cents 13:14:16:17 S SD: 22.3628 cents 14:15:17:19 SD: 15.6787 cents 15:16:18:20 S SD: 7.1688 cents 21:22:25:28 SD: 5.6189 cents 35:37:42:47 SD: 4.5654 cents 36:38:43:48 SD: 2.9050 cents 39:41:47:52 SD: 2.7445 cents 54:57:65:72 SD: 2.1049 cents 60:63:72:80 S SD: 1.9193 cents 75:79:90:100 SD: 0.0902 cents