Scala analysis: 383_D4
Diatonic tetrachord 108/103 * 103/93 * 31/27
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 108/103 82.064370 2: 36/31 258.874429 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 31/27 239.1706 1: 108/103 82.0644 2: 103/93 176.8101 3: 31/27 239.1706
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 108/103 82.064 cents 1: 1 103/93 176.810 cents 1: 1 31/27 239.171 cents 2: 1 36/31 258.874 cents 2: 1 124/103 321.235 cents 2: 1 103/81 415.981 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 : 82.1 258.9 498.0 82.1 : 176.8 416.0 498.0 258.9: 239.2 321.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 82.0644 .. 239.1706 cents 3193/2916, 157.1062 cents 108/103, 82.0644 cents 2: 258.8744 .. 415.9806 cents 3193/2916, 157.1062 cents 972/961, 19.7039 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 108/103, 82.0644 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 31/27, 239.1706 cents Average / Smallest step : 2.022985 Largest / Average step : 1.440656 Largest / Smallest step : 2.914426 Median interval of one step : 103/93, 176.8101 cents, amount: 1 Least squares average step : 149.56773 cents, oct.: 448.70319 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1062-tone equal temperament with octave 4/3 degrees: 175 552 1062 Least number of segments generator : 533 of 249.960 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 685 of 321.244 cents and inv. generated superset size: 25 = 22 more = 833.333% 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 19.70386 cents Scale diversity : 1.068972 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.369108 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 : 972/961, 19.7039 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 : 103 Odd number limit : 103 (O: 103 U: 103) Highest odd numerator or denominator: 103 Scale harmonicity : 0.078947 Fundamental : 1/9579, -13.2257 octaves, 0.0273 Hz. Guide tone : 108, 6.7549 octaves, 28255.561 Hz. Exponens Consonantiae : 1.034532E+06, 19.98055 octaves Euler's gradus suavitatis : 143 Sum of Mann's harmonic distance : 142.5, average 47.50000 Mersenne's string divisions : 98959 Sum of van Prooijen's expressibility: 3.98132, average 1.32711 Sum of Tenney's harmonic distance : 8.17311, average 2.72437 Vogel's harmonic complexity : 98.33333 Wille's k value : 1596 Wilson's harmonic complexity : 146 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.67005, average 2.77834 Lattice compactness (without 2's) : 14.00000, average 2.33333 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 3 1.33333 6 1 31: -1 .. 0 -0.33333 1 1 103: -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: <7 11 34 49| Scale is weakly epimorphic with val: <7 11 35 48| Scale is weakly epimorphic with val: <7 11 37 49| Scale is weakly epimorphic with val: <7 11 38 48| Scale is weakly epimorphic with val: <7 12 34 47| Scale is weakly epimorphic with val: <7 12 35 49| Scale is weakly epimorphic with val: <7 12 37 47| Scale is weakly epimorphic with val: <8 11 35 48| Scale is weakly epimorphic with val: <8 12 35 49| Scale is weakly epimorphic with val: <8 12 37 47| Scale is weakly epimorphic with val: <8 12 38 49|
FIT/MODE
3: 0 1 2 N G T3 SD: 71.5482 c. M: 92.8594 c. 4: 1 1 2 P M ME S SD: 25.1582 c. M:-42.4469 c. 5: 1 2 2 SP M ME S SD: 25.1927 c. M:-39.9526 c. 6: 1 2 3 P T3 SD: 5.7140 c. M: 9.8519 c. 13: 2 5 6 SP T3 SD: 6.2229 c. M:-9.3036 c. 17: 3 6 8 SP T3 SD: 4.3569 c. M:-5.8259 c. 19: 3 7 9 SP T3 SD: 2.7281 c. M: 3.4257 c. 23: 4 8 11 SP T3 SD: 2.6878 c. M:-4.5522 c. 25: 4 9 12 SP T3 SD: 1.3739 c. M: 2.3772 c. 31: 5 11 15 SP T3 SD: 1.4511 c. M: 1.8189 c. 42: 7 15 20 SP T3 SD: 1.2799 c. M:-2.0063 c. 48: 8 17 23 SP T3 SD: 0.6229 c. M:-0.9431 c. 54: 9 19 26 SP T3 SD: 0.6545 c. M:-0.9431 c. 73: 12 26 35 SP T3 SD: 0.2473 c. M:-0.3819 c. 79: 13 28 38 SP T3 SD: 0.2366 c. M: 0.3954 c. 127: 21 45 61 SP T3 SD: 0.1694 c. M:-0.2895 c. 152: 25 54 73 SP T3 SD: 0.0870 c. M: 0.1491 c. 200: 33 71 96 SP T3 SD: 0.0907 c. M:-0.1131 c. 279: 46 99 134 SP T3 SD: 0.0351 c. M:-0.0506 c. 352: 58 125 169 SP T3 SD: 0.0302 c. M:-0.0524 c. 431: 71 153 207 SP T3 SD: 0.0206 c. M: 0.0297 c. 631: 104 224 303 SP T3 SD: 0.0153 c. M:-0.0223 c. 783: 129 278 376 SP T3 SD: 0.0076 c. M: 0.0110 c. 1062: 175 377 510 SP T3 SD: 0.0036 c. M:-0.0052 c. 1845: 304 655 886 SP T3 SD: 0.0011 c. M: 0.0017 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: 50.8851 cents 6 x 7:8 S SD: 3.9982 cents 7 x 8:9 S SD: 34.3925 cents 8 x 9:11 SD: 38.2724 cents 9 x 10:12 S SD: 38.2354 cents 10:11:12:13 H SD: 36.5493 cents 11:12:13:15 SD: 28.1585 cents 12:13:14:16 S SD: 19.0238 cents 14:15:16:19 SD: 18.5694 cents 15:16:17:20 SD: 17.1915 cents 17:18:20:23 SD: 12.6032 cents 18:19:21:24 SD: 4.6796 cents 24:25:28:32 SD: 4.6394 cents 39:41:45:52 SD: 4.0047 cents 42:44:49:56 SD: 2.7137 cents 62:65:72:83 SD: 2.3238 cents 63:66:73:84 SD: 1.3716 cents 81:85:94:108 SD: 0.6081 cents 105:110:122:140 SD: 0.5936 cents 168:176:195:224 SD: 0.5841 cents 186:195:216:248 SD: 0.0862 cents 453:475:526:604 SD: 0.0718 cents