Scala analysis: 387_D5
Diatonic tetrachord 408/389 * 389/351 * 39/34
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 408/389 82.558796 2: 136/117 260.517746 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/34 237.5273 1: 408/389 82.5588 2: 389/351 177.9589 3: 39/34 237.5273
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 408/389 82.559 cents 1: 1 389/351 177.959 cents 1: 1 39/34 237.527 cents 2: 1 136/117 260.518 cents 2: 1 468/389 320.086 cents 2: 1 389/306 415.486 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 : 82.6 260.5 498.0 82.6 : 178.0 415.5 498.0 260.5: 237.5 320.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.5588 .. 237.5273 cents 5057/4624, 154.9685 cents 408/389, 82.5588 cents 2: 260.5177 .. 415.4862 cents 5057/4624, 154.9685 cents 4624/4563, 22.9905 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 408/389, 82.5588 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 39/34, 237.5273 cents Average / Smallest step : 2.010870 Largest / Average step : 1.430758 Largest / Smallest step : 2.877068 Median interval of one step : 389/351, 177.9589 cents, amount: 1 Least squares average step : 149.83781 cents, oct.: 449.51342 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2015-tone equal temperament with octave 4/3 degrees: 334 1054 2015 Least number of segments generator : 1008 of 249.146 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1399 of 345.789 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 22.99049 cents Scale diversity : 1.073937 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.377693 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 : 4624/4563, 22.9905 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 389 Odd number limit : 389 (O: 389 U: 389) Highest odd numerator or denominator: 389 Scale harmonicity : 0.015805 Fundamental : 1/45513, -15.4740 octaves, 0.0057 Hz. Guide tone : 408, 8.6724 octaves, 106743.231 Hz. Exponens Consonantiae : 1.856930E+07, 24.14642 octaves Euler's gradus suavitatis : 426 Sum of Mann's harmonic distance : 528.5, average 176.16667 Mersenne's string divisions : 1411487 Sum of van Prooijen's expressibility: 5.13526, average 1.71175 Sum of Tenney's harmonic distance : 10.48152, average 3.49384 Vogel's harmonic complexity : 286.00000 Wille's k value : 7585 Wilson's harmonic complexity : 428 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 17.03744, average 2.83957 Lattice compactness (without 2's) : 11.99410, average 1.99902 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -2 .. 1 -0.66667 4 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 389: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 25 30 63| Scale is weakly epimorphic with val: <6 10 26 31 61| Scale is weakly epimorphic with val: <6 10 27 32 62| Scale is weakly epimorphic with val: <6 10 28 33 63| Scale is weakly epimorphic with val: <6 11 25 32 62| Scale is weakly epimorphic with val: <6 11 26 33 63| Scale is weakly epimorphic with val: <7 10 25 27 62| Scale is weakly epimorphic with val: <7 10 26 28 63| Scale is weakly epimorphic with val: <7 10 26 33 61| Scale is weakly epimorphic with val: <7 10 27 29 61| Scale is weakly epimorphic with val: <7 10 28 30 62| Scale is weakly epimorphic with val: <7 10 29 31 63| Scale is weakly epimorphic with val: <7 10 29 33 61| Scale is weakly epimorphic with val: <7 10 30 32 61| Scale is weakly epimorphic with val: <7 11 25 27 63| Scale is weakly epimorphic with val: <7 11 25 28 62| Scale is weakly epimorphic with val: <7 11 25 30 63| Scale is weakly epimorphic with val: <7 11 25 31 62| Scale is weakly epimorphic with val: <7 11 25 33 63| Scale is weakly epimorphic with val: <7 11 26 28 61| Scale is weakly epimorphic with val: <7 11 26 29 63| Scale is weakly epimorphic with val: <7 11 26 31 61| Scale is weakly epimorphic with val: <7 11 26 32 63| Scale is weakly epimorphic with val: <7 11 27 27 61| Scale is weakly epimorphic with val: <7 11 27 29 62| Scale is JI-epimorphic with val: <7 11 27 30 61| Scale is weakly epimorphic with val: <7 11 27 32 62| Scale is weakly epimorphic with val: <7 11 27 33 61| Scale is weakly epimorphic with val: <7 11 28 28 62| Scale is weakly epimorphic with val: <7 11 28 30 63| Scale is JI-epimorphic with val: <7 11 28 31 62| Scale is weakly epimorphic with val: <7 11 28 33 63| Scale is weakly epimorphic with val: <7 11 29 29 63| Scale is weakly epimorphic with val: <7 11 29 31 61| Scale is JI-epimorphic with val: <7 11 29 32 63| Scale is weakly epimorphic with val: <7 11 30 30 61| Scale is weakly epimorphic with val: <7 11 30 32 62| Scale is weakly epimorphic with val: <7 11 30 33 61| Scale is weakly epimorphic with val: <7 12 25 31 63| Scale is weakly epimorphic with val: <7 12 25 32 62| Scale is weakly epimorphic with val: <7 12 26 32 61| Scale is weakly epimorphic with val: <7 12 26 33 63| Scale is weakly epimorphic with val: <7 12 27 31 61| Scale is weakly epimorphic with val: <7 12 27 33 62| Scale is weakly epimorphic with val: <7 12 28 32 62| Scale is weakly epimorphic with val: <7 12 29 33 63| Scale is weakly epimorphic with val: <7 12 30 31 61| Scale is weakly epimorphic with val: <8 11 25 30 62| Scale is weakly epimorphic with val: <8 11 26 27 61| Scale is weakly epimorphic with val: <8 11 26 31 63| Scale is weakly epimorphic with val: <8 11 27 28 62| Scale is weakly epimorphic with val: <8 11 27 29 61| Scale is weakly epimorphic with val: <8 11 28 29 63| Scale is weakly epimorphic with val: <8 11 28 30 62| Scale is weakly epimorphic with val: <8 11 29 30 61| Scale is weakly epimorphic with val: <8 11 29 31 63| Scale is weakly epimorphic with val: <8 11 30 31 62| Scale is weakly epimorphic with val: <8 12 25 28 62| Scale is weakly epimorphic with val: <8 12 25 30 63| Scale is weakly epimorphic with val: <8 12 26 28 61| Scale is weakly epimorphic with val: <8 12 26 29 63| Scale is weakly epimorphic with val: <8 12 27 29 62| Scale is weakly epimorphic with val: <8 12 27 30 61| Scale is weakly epimorphic with val: <8 12 28 30 63| Scale is weakly epimorphic with val: <8 12 28 31 62| Scale is weakly epimorphic with val: <8 12 29 32 63| Scale is weakly epimorphic with val: <8 12 30 33 61|
FIT/MODE
3: 0 1 2 N G T3 SD: 72.4493 c. M: 94.5027 c. 4: 1 1 2 P M ME S SD: 25.1141 c. M:-41.9525 c. 5: 1 2 2 SP M ME S SD: 24.2096 c. M:-38.3093 c. 6: 1 2 3 P T3 SD: 6.6418 c. M: 11.4952 c. 11: 2 4 5 SP T3 SD: 7.9181 c. M:-11.1432 c. 13: 2 5 6 SP T3 SD: 5.5953 c. M:-7.6603 c. 17: 3 6 8 SP T3 SD: 3.5762 c. M:-5.3315 c. 19: 3 7 9 SP T3 SD: 2.4470 c. M: 3.9201 c. 23: 4 8 11 SP T3 SD: 2.3743 c. M:-4.0577 c. 25: 4 9 12 SP T3 SD: 1.8797 c. M: 2.8716 c. 36: 6 13 17 SP T3 SD: 1.3752 c. M:-2.3393 c. 42: 7 15 20 SP T3 SD: 0.3332 c. M:-0.4487 c. 90: 15 32 43 SP T3 SD: 0.3578 c. M:-0.4487 c. 109: 18 39 52 SP T3 SD: 0.1854 c. M: 0.3128 c. 151: 25 54 72 SP T3 SD: 0.0648 c. M: 0.1010 c. 193: 32 69 92 SP T3 SD: 0.0685 c. M:-0.1172 c. 344: 57 123 164 SP T3 SD: 0.0540 c. M:-0.0872 c. 392: 65 140 187 SP T3 SD: 0.0379 c. M: 0.0605 c. 543: 90 194 259 SP T3 SD: 0.0183 c. M: 0.0301 c. 585: 97 209 279 SP T3 SD: 0.0133 c. M:-0.0230 c. 736: 122 263 351 SP T3 SD: 0.0051 c. M:-0.0085 c. 1279: 212 457 610 SP T3 SD: 0.0056 c. M: 0.0079 c. 1321: 219 472 630 SP T3 SD: 0.0056 c. M:-0.0088 c. 1864: 309 666 889 SP T3 SD: 0.0040 c. M: 0.0060 c. 2015: 334 720 961 SP T3 SD: 0.0028 c. M: 0.0044 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: 50.4314 cents 6 x 7:8 S SD: 3.1766 cents 7 x 8:9 S SD: 34.7316 cents 8 x 9:11 SD: 38.8666 cents 9 x 10:12 S SD: 39.0570 cents 10:11:12:13 H SD: 36.1433 cents 11:12:13:15 SD: 27.8319 cents 12:13:14:16 S SD: 18.7910 cents 14:15:16:19 SD: 18.7392 cents 15:16:17:20 SD: 17.5505 cents 16:17:19:21 SD: 17.0411 cents 17:18:20:23 SD: 12.2108 cents 18:19:21:24 SD: 4.2471 cents 42:44:49:56 SD: 2.2224 cents 60:63:70:80 S SD: 2.2112 cents 63:66:73:84 SD: 1.9421 cents 80:84:93:107 SD: 1.9104 cents 81:85:94:108 SD: 0.9893 cents 105:110:122:140 SD: 0.7162 cents 123:129:143:164 SD: 0.1091 cents 450:472:523:600 SD: 0.0885 cents 573:601:666:764 SD: 0.0461 cents