Scala analysis: 432_D11
Diatonic tetrachord 80/77 * 77/68 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80/77 66.169865 2: 20/17 281.358304 septendecimal augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/15 216.6867 septendecimal whole tone 1: 80/77 66.1699 2: 77/68 215.1884 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 80/77 66.170 cents 1: 1 77/68 215.188 cents 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 272/231 282.857 cents 2: 1 77/60 431.875 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 : 66.2 281.4 498.0 66.2 : 215.2 431.9 498.0 281.4: 216.7 282.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.1699 .. 216.6867 cents 1309/1200, 150.5168 cents 80/77, 66.1699 cents 2: 281.3583 .. 431.8751 cents 1309/1200, 150.5168 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 80/77, 66.1699 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 2.508922 Largest / Average step : 1.305224 Largest / Smallest step : 3.274704 Median interval of one step : 77/68, 215.1884 cents, amount: 1 Least squares average step : 151.64439 cents, oct.: 454.93317 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1671-tone equal temperament with octave 4/3 degrees: 222 944 1671 Least number of segments generator : 836 of 249.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1358 of 404.755 cents and inv. generated superset size: 43 = 40 more = 1433.333% 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 64.67161 cents Scale diversity : 0.794026 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.395569 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 : 1156/1155, 1.4983 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 149.0186 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 231 (O: 77 U: 231) Highest odd numerator or denominator: 77 Scale harmonicity : 0.013956 Average absolute harmonicity : 0.088658 Specific harmonicity : 0.072281 Fundamental : 1/3927, -11.9392 octaves, 0.0666 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 3.141600E+05, 18.26114 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 100.5, average 33.50000 Mersenne's string divisions : 40663 Sum of van Prooijen's expressibility: 3.59406, average 1.19802 Sum of Tenney's harmonic distance : 7.40024, average 2.46675 Vogel's harmonic complexity : 31.33333 Wille's k value : 654 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 16.25069, average 2.70845 Lattice compactness (without 2's) : 9.61037, average 1.60173 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.66667 2 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 16 19 24 31| Scale is weakly epimorphic with val: <7 11 16 19 26 29| Scale is weakly epimorphic with val: <7 11 16 20 25 29| Scale is weakly epimorphic with val: <7 11 16 20 26 31| Scale is weakly epimorphic with val: <7 11 16 21 24 29| Scale is weakly epimorphic with val: <7 11 16 21 25 31| Scale is weakly epimorphic with val: <7 11 17 19 24 30| Scale is JI-epimorphic with val: <7 11 17 19 25 29| Scale is JI-epimorphic with val: <7 11 17 20 24 29| Scale is weakly epimorphic with val: <7 11 17 20 26 30| Scale is weakly epimorphic with val: <7 11 17 21 25 30| Scale is weakly epimorphic with val: <7 11 17 21 26 29| Scale is weakly epimorphic with val: <7 11 18 19 25 31| Scale is JI-epimorphic with val: <7 11 18 19 26 30| Scale is weakly epimorphic with val: <7 11 18 20 24 31| Scale is JI-epimorphic with val: <7 11 18 20 25 30| Scale is JI-epimorphic with val: <7 11 18 21 24 30| Scale is weakly epimorphic with val: <7 11 18 21 26 31| Scale is weakly epimorphic with val: <7 12 18 19 24 31| Scale is weakly epimorphic with val: <7 12 18 19 26 29| Scale is weakly epimorphic with val: <7 12 18 20 25 29| Scale is weakly epimorphic with val: <7 12 18 21 24 29|
FIT/MODE
3: 0 2 1 N G T3 SD: 48.1182 c. M: 66.1699 c. 4: 0 2 2 P M DE S SD: 42.5208 c. M: 66.1699 c. 5: 1 2 2 SP M ME S SD: 21.7817 c. M:-33.4391 c. 6: 1 2 3 P T3 SD: 21.0484 c. M: 32.3358 c. 7: 1 3 3 SP M DE S SD: 3.4295 c. M:-4.9794 c. 16: 2 7 7 SP M DE S SD: 2.3651 c. M: 3.9142 c. 23: 3 10 10 SP M DE S SD: 0.7022 c. M: 1.2075 c. 30: 4 13 13 SP M DE S SD: 0.5189 c. M:-0.8672 c. 53: 7 23 23 SP M DE S SD: 0.3913 c. M:-0.5540 c. 83: 11 36 36 SP M DE S SD: 0.3966 c. M:-0.6672 c. 113: 15 49 49 SP M DE S SD: 0.4172 c. M:-0.7203 c. 129: 17 56 56 SP M DE S SD: 0.4159 c. M: 0.5360 c. 136: 18 59 59 SP M DE S SD: 0.3881 c. M:-0.6231 c. 143: 19 62 62 SP M DE S SD: 0.4337 c. M:-0.7511 c. 165: 22 71 72 SP T3 SD: 0.3950 c. M: 0.6420 c. 172: 23 74 75 SP T3 SD: 0.3735 c. M: 0.4841 c. 181: 24 78 79 SP T3 SD: 0.4066 c. M: 0.6921 c. 182: 24 79 79 SP M DE S SD: 0.4066 c. M:-0.5023 c. 188: 25 81 82 SP T3 SD: 0.3169 c. M: 0.5457 c. 195: 26 84 85 SP T3 SD: 0.2731 c. M: 0.4098 c. 202: 27 87 88 SP T3 SD: 0.2833 c. M:-0.4005 c. 211: 28 91 92 SP T3 SD: 0.2753 c. M: 0.4704 c. 218: 29 94 95 SP T3 SD: 0.2085 c. M: 0.3513 c. 225: 30 97 98 SP T3 SD: 0.1942 c. M: 0.2396 c. 241: 32 104 105 SP T3 SD: 0.1769 c. M: 0.3039 c. 248: 33 107 108 SP T3 SD: 0.1317 c. M: 0.2039 c. 271: 36 117 118 SP T3 SD: 0.1007 c. M: 0.1742 c. 278: 37 120 121 SP T3 SD: 0.0845 c. M:-0.1167 c. 301: 40 130 131 SP T3 SD: 0.0416 c. M: 0.0704 c. 331: 44 143 144 SP T3 SD: 0.0222 c. M:-0.0355 c. 632: 84 273 275 SP T3 SD: 0.0212 c. M:-0.0260 c. 655: 87 283 285 SP T3 SD: 0.0152 c. M: 0.0199 c. 685: 91 296 298 SP T3 SD: 0.0115 c. M:-0.0189 c. 986: 131 426 429 SP T3 SD: 0.0048 c. M: 0.0083 c. 1671: 222 722 727 SP T3 SD: 0.0021 c. M:-0.0028 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: 104.9554 cents 5 x 6:7 S SD: 45.5797 cents 6 x 7:8 S SD: 7.2437 cents 7 x 8:9 S SD: 40.2571 cents 8 x 9:11 SD: 47.0007 cents 9 x 11:12 SD: 33.0248 cents 11:12:13:15 SD: 31.1091 cents 12:13:14:16 S SD: 24.6127 cents 15:16:18:20 S SD: 19.0063 cents 16:17:19:21 SD: 16.6954 cents 17:18:20:23 SD: 13.7986 cents 18:19:21:24 SD: 10.3412 cents 21:22:25:28 SD: 8.3412 cents 22:23:26:29 SD: 7.9545 cents 23:24:27:31 SD: 6.8387 cents 24:25:28:32 SD: 5.0570 cents 27:28:32:36 S SD: 4.3912 cents 45:47:53:60 SD: 3.1045 cents 51:53:60:68 SD: 0.1414 cents 516:536:607:688 SD: 0.1250 cents 567:589:667:756 SD: 0.1026 cents