Scala analysis: 467_D15
Diatonic tetrachord 184/171 * 9/8 * 76/69
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 184/171 126.851329 2: 23/19 330.761331 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 76/69 167.2837 1: 184/171 126.8513 2: 9/8 203.9100 major whole tone 3: 76/69 167.2837
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 184/171 126.851 cents 1: 1 76/69 167.284 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 23/19 330.761 cents 2: 1 57/46 371.194 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 : 126.9 330.8 498.0 126.9: 203.9 371.2 498.0 330.8: 167.3 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.8513 .. 203.9100 cents 1539/1472, 77.0587 cents 184/171, 126.8513 cents 2: 294.1350 .. 371.1937 cents 1539/1472, 77.0587 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 184/171, 126.8513 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.308737 Largest / Average step : 1.228263 Largest / Smallest step : 1.607472 Median interval of one step : 76/69, 167.2837 cents, amount: 1 Least squares average step : 163.03636 cents, oct.: 489.10907 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1700-tone equal temperament with octave 4/3 degrees: 433 1129 1700 Least number of segments generator : 851 of 249.315 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1491 of 436.815 cents and inv. generated superset size: 64 = 61 more = 2133.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.334749 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.690555 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 : 621/608, 36.6263 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 : 23 Odd number limit : 171 (O: 57 U: 171) Highest odd numerator or denominator: 171 Scale harmonicity : 0.011831 Average absolute harmonicity : 0.079747 Specific harmonicity : 0.047841 Fundamental : 1/171, -7.4179 octaves, 1.5300 Hz. Guide tone : 184, 7.5236 octaves, 48139.104 Hz. Exponens Consonantiae : 3.146400E+04, 14.94141 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 202.0, average 67.33333 Mersenne's string divisions : 14910 Sum of van Prooijen's expressibility: 4.07185, average 1.35728 Sum of Tenney's harmonic distance : 8.21748, average 2.73916 Vogel's harmonic complexity : 26.33333 Wille's k value : 103 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 15.77457, average 2.62909 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.66667 5 3: -2 .. 0 -1.00000 3 1 19: -1 .. 0 -0.66667 2 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 28 31| Scale is weakly epimorphic with val: <6 10 29 32| Scale is weakly epimorphic with val: <6 10 30 33| Scale is weakly epimorphic with val: <6 10 31 34| Scale is weakly epimorphic with val: <6 10 32 35| Scale is weakly epimorphic with val: <6 10 33 36| Scale is weakly epimorphic with val: <6 11 28 31| Scale is weakly epimorphic with val: <6 11 29 32| Scale is weakly epimorphic with val: <6 11 30 33| Scale is weakly epimorphic with val: <6 11 31 34| Scale is weakly epimorphic with val: <6 11 32 35| Scale is weakly epimorphic with val: <6 11 33 36| Scale is weakly epimorphic with val: <7 10 28 30| Scale is weakly epimorphic with val: <7 10 29 31| Scale is weakly epimorphic with val: <7 10 30 32| Scale is weakly epimorphic with val: <7 10 31 33| Scale is weakly epimorphic with val: <7 10 32 34| Scale is weakly epimorphic with val: <7 10 33 35| Scale is weakly epimorphic with val: <7 10 34 36| Scale is JI-epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 28 36| Scale is JI-epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 11 29 34| Scale is JI-epimorphic with val: <7 11 30 32| Scale is weakly epimorphic with val: <7 11 30 35| Scale is JI-epimorphic with val: <7 11 31 33| = patent Scale is weakly epimorphic with val: <7 11 31 36| Scale is JI-epimorphic with val: <7 11 32 34| Scale is JI-epimorphic with val: <7 11 33 35| Scale is JI-epimorphic with val: <7 11 34 36| Scale is weakly epimorphic with val: <8 11 29 30| Scale is weakly epimorphic with val: <8 11 30 31| Scale is weakly epimorphic with val: <8 11 31 32| Scale is weakly epimorphic with val: <8 11 32 33| Scale is weakly epimorphic with val: <8 11 33 34| Scale is weakly epimorphic with val: <8 11 34 35|
FIT/MODE
3: 1 1 1 SP B ME I SD: 22.6230 c. M:-39.1637 c. 5: 1 2 2 SP M ME S SD: 24.2346 c. M: 31.9343 c. 7: 2 3 2 SP M ME I SD: 16.9595 c. M:-24.9851 c. 8: 2 3 3 SP M ME S SD: 11.3295 c. M: 19.4832 c. 9: 2 4 3 SP T3 SD: 9.3671 c. M: 16.1747 c. 11: 3 4 4 SP M ME S SD: 9.5169 c. M: 13.8236 c. 12: 3 5 4 SP T3 SD: 1.5368 c. M: 2.3401 c. 27: 7 11 9 SP T3 SD: 1.5021 c. M:-2.2714 c. 39: 10 16 13 SP T3 SD: 0.8825 c. M:-1.2687 c. 51: 13 21 17 SP T3 SD: 0.7348 c. M:-1.2687 c. 71: 18 29 24 SP T3 SD: 0.7042 c. M: 1.0696 c. 74: 19 30 25 SP T3 SD: 0.8167 c. M:-1.0251 c. 83: 21 34 28 SP T3 SD: 0.6431 c. M: 0.8399 c. 86: 22 35 29 SP T3 SD: 0.4988 c. M: 0.6617 c. 98: 25 40 33 SP T3 SD: 0.2716 c. M: 0.4254 c. 110: 28 45 37 SP T3 SD: 0.1457 c. M: 0.2406 c. 149: 38 61 50 SP T3 SD: 0.1313 c. M:-0.1669 c. 247: 63 101 83 SP T3 SD: 0.1129 c. M:-0.1804 c. 259: 66 106 87 SP T3 SD: 0.0375 c. M:-0.0636 c. 271: 69 111 91 SP T3 SD: 0.0352 c. M:-0.0435 c. 381: 97 156 128 SP T3 SD: 0.0376 c. M: 0.0525 c. 530: 135 217 178 SP T3 SD: 0.0105 c. M:-0.0157 c. 911: 232 373 306 SP T3 SD: 0.0104 c. M: 0.0166 c. 1170: 298 479 393 SP T3 SD: 0.0049 c. M: 0.0084 c. 1441: 367 590 484 SP T3 SD: 0.0042 c. M: 0.0071 c. 1700: 433 696 571 SP T3 SD: 0.0022 c. M:-0.0037 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: 55.5524 cents 5 x 6:7 S SD: 42.9049 cents 6 x 7:8 S SD: 31.9452 cents 7 x 8:9 S SD: 58.9103 cents 8:9:10:11 H SD: 36.3044 cents 9:10:11:12 H SD: 19.3310 cents 12:13:15:16 SD: 18.9252 cents 13:14:16:17 S SD: 14.7442 cents 14:15:17:19 SD: 10.6596 cents 15:16:18:20 S SD: 7.1277 cents 24:26:29:32 SD: 4.0448 cents 39:42:47:52 SD: 2.6238 cents 66:71:80:88 SD: 0.7731 cents 105:113:127:140 SD: 0.4864 cents 171:184:207:228 SD: 0.0000 cents