Scala analysis: 589_M97
Miscellaneous tetrachord 533/483 * 575/533 * 28/25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 533/483 170.534813 2: 25/21 301.846520 BP second, quasi-equal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/25 196.1985 middle second 1: 533/483 170.5348 2: 575/533 131.3117 3: 28/25 196.1985 middle second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 575/533 131.312 cents 1: 1 533/483 170.535 cents 1: 1 28/25 196.198 cents middle second 2: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 1 644/533 327.510 cents 2: 1 2132/1725 366.733 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 : 170.5 301.8 498.0 170.5: 131.3 327.5 498.0 301.8: 196.2 366.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 131.3117 .. 196.1985 cents 14924/14375, 64.8868 cents 575/533, 131.3117 cents 2: 301.8465 .. 366.7333 cents 14924/14375, 64.8868 cents 625/588, 105.6480 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 575/533, 131.3117 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 1.264282 Largest / Average step : 1.181812 Largest / Smallest step : 1.494143 Median interval of one step : 533/483, 170.5348 cents, amount: 1 Least squares average step : 162.02592 cents, oct.: 486.07775 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 105.64804 cents Scale diversity : 1.316383 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.739434 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 : 13524/13325, 25.6637 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 41 Odd number limit : 1725 (O: 575 U: 1725) Highest odd numerator or denominator: 533 Scale harmonicity : 0.010870 Fundamental : 1/483, -8.9159 octaves, 0.5417 Hz. Guide tone : 53300, 15.7018 octaves, 13944642.631 Hz. Exponens Consonantiae : 2.574390E+07, 24.61773 octaves Euler's gradus suavitatis : 93 Sum of Mann's harmonic distance : 534.5, average 178.16667 Mersenne's string divisions : 163576 Sum of van Prooijen's expressibility: 4.60179, average 1.53393 Sum of Tenney's harmonic distance : 9.21001, average 3.07000 Vogel's harmonic complexity : 39.66667 Wille's k value : 287 Wilson's harmonic complexity : 97 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 14.78080, average 2.46347 Lattice compactness (without 2's) : 11.86710, average 1.97785 Number of different primes : 7 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 ..-1 -1.00000 3 1 5: 0 .. 2 0.66667 2 7: -1 .. 0 -0.66667 2 1 13: 0 .. 1 0.33333 1 23: -1 .. 0 -0.33333 1 41: 0 .. 1 0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is JI-epimorphic with val: <7 11 16 19 26 32 37| Scale is weakly epimorphic with val: <7 11 16 19 26 32 40| Scale is JI-epimorphic with val: <7 11 16 19 26 33 38| Scale is weakly epimorphic with val: <7 11 16 19 26 33 41| Scale is JI-epimorphic with val: <7 11 16 19 26 34 39| Scale is weakly epimorphic with val: <7 11 16 19 26 35 37| Scale is JI-epimorphic with val: <7 11 16 19 26 35 40| Scale is weakly epimorphic with val: <7 11 16 19 27 32 39| Scale is JI-epimorphic with val: <7 11 16 19 27 33 37| Scale is weakly epimorphic with val: <7 11 16 19 27 33 40| Scale is JI-epimorphic with val: <7 11 16 19 27 34 38| Scale is weakly epimorphic with val: <7 11 16 19 27 34 41| Scale is JI-epimorphic with val: <7 11 16 19 27 35 39| Scale is weakly epimorphic with val: <7 11 16 19 28 32 38| Scale is weakly epimorphic with val: <7 11 16 19 28 32 41| Scale is weakly epimorphic with val: <7 11 16 19 28 33 39| Scale is JI-epimorphic with val: <7 11 16 19 28 34 37| Scale is weakly epimorphic with val: <7 11 16 19 28 34 40| Scale is JI-epimorphic with val: <7 11 16 19 28 35 38| Scale is weakly epimorphic with val: <7 11 16 19 28 35 41| Scale is weakly epimorphic with val: <7 11 16 20 26 32 39| Scale is weakly epimorphic with val: <7 11 16 20 26 33 37| Scale is weakly epimorphic with val: <7 11 16 20 26 33 40| Scale is weakly epimorphic with val: <7 11 16 20 26 34 38| Scale is weakly epimorphic with val: <7 11 16 20 26 34 41| Scale is weakly epimorphic with val: <7 11 16 20 26 35 39| Scale is weakly epimorphic with val: <7 11 16 20 27 32 38| Scale is weakly epimorphic with val: <7 11 16 20 27 32 41| Scale is weakly epimorphic with val: <7 11 16 20 27 33 39| Scale is weakly epimorphic with val: <7 11 16 20 27 34 37| Scale is weakly epimorphic with val: <7 11 16 20 27 34 40| Scale is weakly epimorphic with val: <7 11 16 20 27 35 38| Scale is weakly epimorphic with val: <7 11 16 20 27 35 41| Scale is weakly epimorphic with val: <7 11 16 20 28 32 37| Scale is weakly epimorphic with val: <7 11 16 20 28 32 40| Scale is weakly epimorphic with val: <7 11 16 20 28 33 38| Scale is weakly epimorphic with val: <7 11 16 20 28 33 41| Scale is weakly epimorphic with val: <7 11 16 20 28 34 39| Scale is weakly epimorphic with val: <7 11 16 20 28 35 37| Scale is weakly epimorphic with val: <7 11 16 20 28 35 40| Scale is weakly epimorphic with val: <7 11 17 19 26 32 38| Scale is weakly epimorphic with val: <7 11 17 19 26 32 41| Scale is weakly epimorphic with val: <7 11 17 19 26 33 39| Scale is weakly epimorphic with val: <7 11 17 19 26 34 37| Scale is weakly epimorphic with val: <7 11 17 19 26 34 40| Scale is weakly epimorphic with val: <7 11 17 19 26 35 38| Scale is weakly epimorphic with val: <7 11 17 19 26 35 41| Scale is weakly epimorphic with val: <7 11 17 19 27 32 37| Scale is weakly epimorphic with val: <7 11 17 19 27 32 40| Scale is weakly epimorphic with val: <7 11 17 19 27 33 38| Scale is weakly epimorphic with val: <7 11 17 19 27 33 41| Scale is weakly epimorphic with val: <7 11 17 19 27 34 39| Scale is weakly epimorphic with val: <7 11 17 19 27 35 37| Scale is weakly epimorphic with val: <7 11 17 19 27 35 40| Scale is weakly epimorphic with val: <7 11 17 19 28 32 39| Scale is weakly epimorphic with val: <7 11 17 19 28 33 37| Scale is weakly epimorphic with val: <7 11 17 19 28 33 40| Scale is weakly epimorphic with val: <7 11 17 19 28 34 38| Scale is weakly epimorphic with val: <7 11 17 19 28 34 41| Scale is weakly epimorphic with val: <7 11 17 19 28 35 39| Scale is JI-epimorphic with val: <7 11 17 21 26 32 39| Scale is weakly epimorphic with val: <7 11 17 21 26 33 37| Scale is JI-epimorphic with val: <7 11 17 21 26 33 40| Scale is weakly epimorphic with val: <7 11 17 21 26 34 38| Scale is JI-epimorphic with val: <7 11 17 21 26 34 41| Scale is weakly epimorphic with val: <7 11 17 21 26 35 39| Scale is JI-epimorphic with val: <7 11 17 21 27 32 38| Scale is weakly epimorphic with val: <7 11 17 21 27 32 41| Scale is JI-epimorphic with val: <7 11 17 21 27 33 39| Scale is weakly epimorphic with val: <7 11 17 21 27 34 37| Scale is JI-epimorphic with val: <7 11 17 21 27 34 40| Scale is weakly epimorphic with val: <7 11 17 21 27 35 38| Scale is JI-epimorphic with val: <7 11 17 21 27 35 41| Scale is JI-epimorphic with val: <7 11 17 21 28 32 37| Scale is weakly epimorphic with val: <7 11 17 21 28 32 40| Scale is JI-epimorphic with val: <7 11 17 21 28 33 38| Scale is weakly epimorphic with val: <7 11 17 21 28 33 41| Scale is JI-epimorphic with val: <7 11 17 21 28 34 39| Scale is weakly epimorphic with val: <7 11 17 21 28 35 37| Scale is JI-epimorphic with val: <7 11 17 21 28 35 40| Scale is weakly epimorphic with val: <7 11 18 20 26 32 38| Scale is weakly epimorphic with val: <7 11 18 20 26 32 41| Scale is weakly epimorphic with val: <7 11 18 20 26 33 39| Scale is weakly epimorphic with val: <7 11 18 20 26 34 37| Scale is weakly epimorphic with val: <7 11 18 20 26 34 40| Scale is weakly epimorphic with val: <7 11 18 20 26 35 38| Scale is weakly epimorphic with val: <7 11 18 20 26 35 41| Scale is weakly epimorphic with val: <7 11 18 20 27 32 37| Scale is weakly epimorphic with val: <7 11 18 20 27 32 40| Scale is weakly epimorphic with val: <7 11 18 20 27 33 38| Scale is weakly epimorphic with val: <7 11 18 20 27 33 41| Scale is weakly epimorphic with val: <7 11 18 20 27 34 39| Scale is weakly epimorphic with val: <7 11 18 20 27 35 37| Scale is weakly epimorphic with val: <7 11 18 20 27 35 40| Scale is weakly epimorphic with val: <7 11 18 20 28 32 39| Scale is weakly epimorphic with val: <7 11 18 20 28 33 37| Scale is weakly epimorphic with val: <7 11 18 20 28 33 40| Scale is weakly epimorphic with val: <7 11 18 20 28 34 38| Scale is weakly epimorphic with val: <7 11 18 20 28 34 41| Scale is weakly epimorphic with val: <7 11 18 20 28 35 39| Scale is weakly epimorphic with val: <7 11 18 21 26 32 37| Scale is weakly epimorphic with val: <7 11 18 21 26 32 40| Scale is weakly epimorphic with val: <7 11 18 21 26 33 38| Scale is weakly epimorphic with val: <7 11 18 21 26 33 41| Scale is weakly epimorphic with val: <7 11 18 21 26 34 39| Scale is weakly epimorphic with val: <7 11 18 21 26 35 37| Scale is weakly epimorphic with val: <7 11 18 21 26 35 40| Scale is weakly epimorphic with val: <7 11 18 21 27 32 39| Scale is weakly epimorphic with val: <7 11 18 21 27 33 37| Scale is weakly epimorphic with val: <7 11 18 21 27 33 40| Scale is weakly epimorphic with val: <7 11 18 21 27 34 38| Scale is weakly epimorphic with val: <7 11 18 21 27 34 41| Scale is weakly epimorphic with val: <7 11 18 21 27 35 39| Scale is weakly epimorphic with val: <7 11 18 21 28 32 38| Scale is weakly epimorphic with val: <7 11 18 21 28 32 41| Scale is weakly epimorphic with val: <7 11 18 21 28 33 39| Scale is weakly epimorphic with val: <7 11 18 21 28 34 37| Scale is weakly epimorphic with val: <7 11 18 21 28 34 40| Scale is weakly epimorphic with val: <7 11 18 21 28 35 38| Scale is weakly epimorphic with val: <7 11 18 21 28 35 41| Scale is weakly epimorphic with val: <7 12 16 19 26 32 40| Scale is weakly epimorphic with val: <7 12 16 19 26 33 41| Scale is weakly epimorphic with val: <7 12 16 19 27 32 39| Scale is weakly epimorphic with val: <7 12 16 19 27 33 40| Scale is weakly epimorphic with val: <7 12 16 19 27 34 41| Scale is weakly epimorphic with val: <7 12 16 19 28 32 38| Scale is weakly epimorphic with val: <7 12 16 19 28 33 39| Scale is weakly epimorphic with val: <7 12 16 19 28 34 40| Scale is weakly epimorphic with val: <7 12 16 19 28 35 41| Scale is weakly epimorphic with val: <7 12 17 19 26 32 38| Scale is weakly epimorphic with val: <7 12 17 19 26 32 41| Scale is weakly epimorphic with val: <7 12 17 19 26 33 39| Scale is weakly epimorphic with val: <7 12 17 19 26 34 37| Scale is weakly epimorphic with val: <7 12 17 19 26 34 40| Scale is weakly epimorphic with val: <7 12 17 19 26 35 38| Scale is weakly epimorphic with val: <7 12 17 19 26 35 41| Scale is weakly epimorphic with val: <7 12 17 19 27 32 37| Scale is weakly epimorphic with val: <7 12 17 19 27 32 40| Scale is weakly epimorphic with val: <7 12 17 19 27 33 38| Scale is weakly epimorphic with val: <7 12 17 19 27 33 41| Scale is weakly epimorphic with val: <7 12 17 19 27 34 39| Scale is weakly epimorphic with val: <7 12 17 19 27 35 37| Scale is weakly epimorphic with val: <7 12 17 19 27 35 40| Scale is weakly epimorphic with val: <7 12 17 19 28 32 39| Scale is weakly epimorphic with val: <7 12 17 19 28 33 37| Scale is weakly epimorphic with val: <7 12 17 19 28 33 40| Scale is weakly epimorphic with val: <7 12 17 19 28 34 38| Scale is weakly epimorphic with val: <7 12 17 19 28 34 41| Scale is weakly epimorphic with val: <7 12 17 19 28 35 39| Scale is weakly epimorphic with val: <7 12 17 21 27 32 41| Scale is weakly epimorphic with val: <7 12 17 21 28 32 40| Scale is weakly epimorphic with val: <7 12 17 21 28 33 41| Scale is weakly epimorphic with val: <7 12 18 20 26 32 41| Scale is weakly epimorphic with val: <7 12 18 20 27 32 40| Scale is weakly epimorphic with val: <7 12 18 20 27 33 41| Scale is weakly epimorphic with val: <7 12 18 20 28 32 39| Scale is weakly epimorphic with val: <7 12 18 20 28 33 40| Scale is weakly epimorphic with val: <7 12 18 20 28 34 41| Scale is weakly epimorphic with val: <7 12 18 21 26 32 37| Scale is weakly epimorphic with val: <7 12 18 21 26 32 40| Scale is weakly epimorphic with val: <7 12 18 21 26 33 38| Scale is weakly epimorphic with val: <7 12 18 21 26 33 41| Scale is weakly epimorphic with val: <7 12 18 21 26 34 39| Scale is weakly epimorphic with val: <7 12 18 21 26 35 37| Scale is weakly epimorphic with val: <7 12 18 21 26 35 40| Scale is weakly epimorphic with val: <7 12 18 21 27 32 39| Scale is weakly epimorphic with val: <7 12 18 21 27 33 37| Scale is weakly epimorphic with val: <7 12 18 21 27 33 40| Scale is weakly epimorphic with val: <7 12 18 21 27 34 38| Scale is weakly epimorphic with val: <7 12 18 21 27 34 41| Scale is weakly epimorphic with val: <7 12 18 21 27 35 39| Scale is weakly epimorphic with val: <7 12 18 21 28 32 38| Scale is weakly epimorphic with val: <7 12 18 21 28 32 41| Scale is weakly epimorphic with val: <7 12 18 21 28 33 39| Scale is weakly epimorphic with val: <7 12 18 21 28 34 37| Scale is weakly epimorphic with val: <7 12 18 21 28 34 40| Scale is weakly epimorphic with val: <7 12 18 21 28 35 38| Scale is weakly epimorphic with val: <7 12 18 21 28 35 41|
FIT/MODE
3: 1 1 1 SP B ME I SD: 17.6207 c. M:-30.1835 c. 5: 2 1 2 SP M ME I SD: 16.6518 c. M:-28.6832 c. 7: 2 2 3 SP M ME S SD: 19.1035 c. M: 28.2362 c. 8: 3 2 3 SP M ME I SD: 10.8387 c. M:-16.2321 c. 11: 4 3 4 SP M ME I SD: 10.6383 c. M:-15.0912 c. 12: 4 3 5 SP T3 SD: 7.0375 c. M: 11.3203 c. Raga Malasri, Peruvian tritonic 1 15: 5 4 6 SP T3 SD: 3.1383 c. M: 4.5198 c. 18: 6 5 7 SP T3 SD: 2.9861 c. M: 4.5198 c. 20: 7 5 8 SP T3 SD: 2.7936 c. M:-3.7809 c. 23: 8 6 9 SP T3 SD: 1.7320 c. M:-2.6982 c. 38: 13 10 15 SP T3 SD: 0.2459 c. M: 0.3982 c. 117: 40 31 46 SP T3 SD: 0.2696 c. M:-0.3859 c. 137: 47 36 54 SP T3 SD: 0.1996 c. M:-0.3273 c. 155: 53 41 61 SP T3 SD: 0.1761 c. M: 0.2356 c. 175: 60 46 69 SP T3 SD: 0.1634 c. M:-0.2235 c. 193: 66 51 76 SP T3 SD: 0.1340 c. M: 0.2189 c. 213: 73 56 84 SP T3 SD: 0.1530 c. M: 0.2136 c. 216: 74 57 85 SP T3 SD: 0.1315 c. M:-0.2085 c. 231: 79 61 91 SP T3 SD: 0.1199 c. M: 0.2077 c. 254: 87 67 100 SP T3 SD: 0.0751 c. M:-0.1178 c. 292: 100 77 115 SP T3 SD: 0.0336 c. M:-0.0506 c. 330: 113 87 130 SP T3 SD: 0.0046 c. M:-0.0079 c. 2348: 804 619 925 SP T3 SD: 0.0053 c. M: 0.0075 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: 84.4672 cents 5 x 6:7 S SD: 42.7931 cents 6 x 7:8 S SD: 17.4878 cents 7:8 x 9 S SD: 43.7070 cents 8:9:10:11 H SD: 35.0977 cents 9:10:11:12 H SD: 15.6940 cents 10:11:12:13 H SD: 15.4274 cents 11:12:13:15 SD: 15.1631 cents 16:18:19:21 SD: 14.4377 cents 17:19:20:23 SD: 13.0960 cents 18:20:21:24 S SD: 12.3115 cents 20:22:24:27 S SD: 8.7140 cents 21:23:25:28 SD: 4.3471 cents 47:52:56:63 SD: 3.4423 cents 48:53:57:64 SD: 1.4836 cents 69:76:82:92 SD: 1.4776 cents 78:86:93:104 SD: 1.0183 cents 105:116:125:140 SD: 0.6493 cents 126:139:150:168 SD: 0.1805 cents 357:394:425:476 SD: 0.0637 cents 483:533:575:644 SD: 0.0000 cents