Scala analysis: 388_D5
Diatonic tetrachord 204/185 * 370/351 * 39/34
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 204/185 169.252658 2: 136/117 260.517746 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/34 237.5273 1: 204/185 169.2527 2: 370/351 91.2651 3: 39/34 237.5273
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 370/351 91.265 cents 1: 1 204/185 169.253 cents 1: 1 39/34 237.527 cents 2: 1 136/117 260.518 cents 2: 1 185/153 328.792 cents 2: 1 234/185 406.780 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 : 169.3 260.5 498.0 169.3: 91.3 328.8 498.0 260.5: 237.5 406.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 91.2651 .. 237.5273 cents 13689/12580, 146.2622 cents 370/351, 91.2651 cents 2: 260.5177 .. 406.7799 cents 13689/12580, 146.2622 cents 4624/4563, 22.9905 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 370/351, 91.2651 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 39/34, 237.5273 cents Average / Smallest step : 1.819042 Largest / Average step : 1.430758 Largest / Smallest step : 2.602608 Median interval of one step : 204/185, 169.2527 cents, amount: 1 Least squares average step : 156.03022 cents, oct.: 468.09067 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1386-tone equal temperament with octave 4/3 degrees: 471 725 1386 Least number of segments generator : 695 of 249.741 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1297 of 466.064 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 22.99049 cents Scale diversity : 1.146723 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.412655 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 fifths form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 37 Odd number limit : 351 (O: 185 U: 351) Highest odd numerator or denominator: 185 Scale harmonicity : 0.014353 Fundamental : 1/21645, -14.4017 octaves, 0.0121 Hz. Guide tone : 408, 8.6724 octaves, 106743.231 Hz. Exponens Consonantiae : 8.831160E+06, 23.07417 octaves Euler's gradus suavitatis : 78 Sum of Mann's harmonic distance : 324.5, average 108.16667 Mersenne's string divisions : 688919 Sum of van Prooijen's expressibility: 4.81248, average 1.60416 Sum of Tenney's harmonic distance : 9.85771, average 3.28590 Vogel's harmonic complexity : 54.33333 Wille's k value : 3607 Wilson's harmonic complexity : 81 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 16.66839, average 2.77807 Lattice compactness (without 2's) : 12.67971, average 2.11328 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 .. 1 -0.66667 4 1 5: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 37: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is JI-epimorphic with val: <7 11 16 26 29 37| Scale is weakly epimorphic with val: <7 11 16 26 29 40| Scale is weakly epimorphic with val: <7 11 16 26 31 38| Scale is weakly epimorphic with val: <7 11 16 27 29 36| Scale is weakly epimorphic with val: <7 11 16 27 29 39| Scale is JI-epimorphic with val: <7 11 16 27 30 38| Scale is weakly epimorphic with val: <7 11 16 28 30 37| Scale is weakly epimorphic with val: <7 11 16 28 30 40| Scale is weakly epimorphic with val: <7 11 16 28 31 36| Scale is JI-epimorphic with val: <7 11 16 28 31 39| Scale is JI-epimorphic with val: <7 11 17 26 29 36| Scale is weakly epimorphic with val: <7 11 17 26 29 39| Scale is weakly epimorphic with val: <7 11 17 26 31 37| Scale is weakly epimorphic with val: <7 11 17 26 31 40| Scale is weakly epimorphic with val: <7 11 17 27 29 38| Scale is JI-epimorphic with val: <7 11 17 27 30 37| Scale is weakly epimorphic with val: <7 11 17 27 30 40| Scale is weakly epimorphic with val: <7 11 17 28 30 36| Scale is weakly epimorphic with val: <7 11 17 28 30 39| Scale is JI-epimorphic with val: <7 11 17 28 31 38| Scale is weakly epimorphic with val: <7 11 18 26 29 38| Scale is weakly epimorphic with val: <7 11 18 26 31 36| Scale is weakly epimorphic with val: <7 11 18 26 31 39| Scale is weakly epimorphic with val: <7 11 18 27 29 37| Scale is weakly epimorphic with val: <7 11 18 27 29 40| Scale is JI-epimorphic with val: <7 11 18 27 30 36| Scale is weakly epimorphic with val: <7 11 18 27 30 39| Scale is weakly epimorphic with val: <7 11 18 28 30 38| Scale is JI-epimorphic with val: <7 11 18 28 31 37| Scale is weakly epimorphic with val: <7 11 18 28 31 40| Scale is weakly epimorphic with val: <7 12 16 26 30 37| Scale is weakly epimorphic with val: <7 12 16 27 31 38| Scale is weakly epimorphic with val: <7 12 16 28 29 36| Scale is weakly epimorphic with val: <7 12 17 26 30 36| Scale is weakly epimorphic with val: <7 12 17 27 31 37| Scale is weakly epimorphic with val: <7 12 18 27 31 36|
FIT/MODE
3: 1 1 1 SP B ME I SD: 41.3299 c. M:-71.5123 c. 4: 1 1 2 P M ME S SD: 26.6704 c. M: 44.7414 c. 5: 2 1 2 SP M ME I SD: 28.0804 c. M:-38.3093 c. 6: 2 1 3 P T3 SD: 6.8950 c. M: 11.4952 c. 15: 5 3 7 SP T3 SD: 3.4908 c. M:-5.1063 c. 17: 6 3 8 SP T3 SD: 4.1855 c. M:-6.5279 c. 21: 7 4 10 SP T3 SD: 1.8810 c. M: 3.2377 c. 29: 10 5 14 SP T3 SD: 2.2093 c. M: 2.9083 c. 38: 13 7 18 SP T3 SD: 1.1366 c. M:-1.6112 c. 44: 15 8 21 SP T3 SD: 0.3254 c. M:-0.5354 c. 103: 35 19 49 SP T3 SD: 0.3426 c. M:-0.5932 c. 109: 37 20 52 SP T3 SD: 0.1182 c. M: 0.1915 c. 153: 52 28 73 SP T3 SD: 0.0598 c. M: 0.1021 c. 262: 89 48 125 SP T3 SD: 0.0655 c. M: 0.0896 c. 409: 139 75 195 SP T3 SD: 0.0425 c. M:-0.0730 c. 453: 154 83 216 SP T3 SD: 0.0450 c. M:-0.0607 c. 518: 176 95 247 SP T3 SD: 0.0310 c. M:-0.0425 c. 562: 191 103 268 SP T3 SD: 0.0161 c. M:-0.0254 c. 671: 228 123 320 SP T3 SD: 0.0135 c. M: 0.0213 c. 715: 243 131 341 SP T3 SD: 0.0076 c. M:-0.0130 c. 1277: 434 234 609 SP T3 SD: 0.0093 c. M:-0.0124 c. 1386: 471 254 661 SP T3 SD: 0.0030 c. M:-0.0036 c. 2101: 714 385 1002 SP T3 SD: 0.0016 c. M:-0.0020 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 8:9 x 11 SD: 31.7771 cents 9:10 x 12 S SD: 6.5755 cents 15 x 17:20 SD: 21.9155 cents 16:18:19:21 SD: 19.1865 cents 17:19:20:23 SD: 13.4008 cents 18:20:21:24 S SD: 4.8684 cents 30:33:35:40 SD: 2.5476 cents 48:53:56:64 SD: 2.2519 cents 68:75:79:91 SD: 2.1442 cents 69:76:80:92 SD: 1.6170 cents 87:96:101:116 SD: 0.8295 cents 117:129:136:156 SD: 0.0725 cents