Scala analysis: 386_D5
Diatonic tetrachord 272/253 * 253/234 * 39/34
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 272/253 125.363120 2: 136/117 260.517746 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/34 237.5273 1: 272/253 125.3631 2: 253/234 135.1546 3: 39/34 237.5273
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 272/253 125.363 cents 1: 1 253/234 135.155 cents 1: 1 39/34 237.527 cents 2: 1 136/117 260.518 cents 2: 1 312/253 362.890 cents 2: 1 253/204 372.682 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 : 125.4 260.5 498.0 125.4: 135.2 372.7 498.0 260.5: 237.5 362.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 125.3631 .. 237.5273 cents 9867/9248, 112.1641 cents 272/253, 125.3631 cents 2: 260.5177 .. 372.6819 cents 9867/9248, 112.1641 cents 4624/4563, 22.9905 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 272/253, 125.3631 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 39/34, 237.5273 cents Average / Smallest step : 1.324273 Largest / Average step : 1.430758 Largest / Smallest step : 1.894714 Median interval of one step : 253/234, 135.1546 cents, amount: 1 Least squares average step : 152.89526 cents, oct.: 458.68577 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2189-tone equal temperament with octave 4/3 degrees: 551 1145 2189 Least number of segments generator : 1095 of 249.136 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1140 of 259.375 cents and inv. generated superset size: 48 = 45 more = 1600.000% 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 : 1.219811 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.549582 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 : 64009/63648, 9.7915 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% Limited inverse transpositions with margin 102.3726 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 253 (O: 253 U: 253) Highest odd numerator or denominator: 253 Scale harmonicity : 0.008205 Average absolute harmonicity : 0.080460 Specific harmonicity : 0.040059 Fundamental : 1/29601, -14.8534 octaves, 0.0088 Hz. Guide tone : 272, 8.0875 octaves, 71162.154 Hz. Exponens Consonantiae : 8.051472E+06, 22.94082 octaves Euler's gradus suavitatis : 69 Sum of Mann's harmonic distance : 392.5, average 130.83333 Mersenne's string divisions : 132825 Sum of van Prooijen's expressibility: 4.94843, average 1.64948 Sum of Tenney's harmonic distance : 10.11860, average 3.37287 Vogel's harmonic complexity : 48.66667 Wille's k value : 4933 Wilson's harmonic complexity : 70 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 18.12480, average 3.02080 Lattice compactness (without 2's) : 11.55934, average 1.92656 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -2 .. 0 -1.00000 3 1 11: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 24 26 29 32| Scale is weakly epimorphic with val: <7 11 24 26 29 35| Scale is weakly epimorphic with val: <7 11 24 26 31 33| Scale is weakly epimorphic with val: <7 11 24 27 29 34| Scale is JI-epimorphic with val: <7 11 24 27 30 33| Scale is weakly epimorphic with val: <7 11 24 28 30 32| Scale is weakly epimorphic with val: <7 11 24 28 30 35| Scale is JI-epimorphic with val: <7 11 24 28 31 34| Scale is weakly epimorphic with val: <7 11 25 26 29 34| Scale is weakly epimorphic with val: <7 11 25 26 31 32| Scale is weakly epimorphic with val: <7 11 25 26 31 35| Scale is weakly epimorphic with val: <7 11 25 27 29 33| Scale is JI-epimorphic with val: <7 11 25 27 30 32| Scale is weakly epimorphic with val: <7 11 25 27 30 35| Scale is weakly epimorphic with val: <7 11 25 28 30 34| Scale is JI-epimorphic with val: <7 11 25 28 31 33| Scale is weakly epimorphic with val: <7 11 26 26 29 33| Scale is weakly epimorphic with val: <7 11 26 26 31 34| Scale is weakly epimorphic with val: <7 11 26 27 29 32| Scale is weakly epimorphic with val: <7 11 26 27 29 35| Scale is weakly epimorphic with val: <7 11 26 27 30 34| Scale is weakly epimorphic with val: <7 11 26 28 30 33| Scale is JI-epimorphic with val: <7 11 26 28 31 32| Scale is weakly epimorphic with val: <7 11 26 28 31 35| Scale is weakly epimorphic with val: <7 12 24 27 31 32|
FIT/MODE
3: 1 1 1 SP B ME I SD: 47.4924 c. M:-71.5123 c. 4: 1 1 2 P M ME S SD: 6.6550 c. M: 11.4952 c. 11: 3 3 5 SP M DE S SD: 8.8268 c. M:-11.1432 c. 13: 3 4 6 SP T3 SD: 7.4712 c. M: 10.4297 c. 15: 4 4 7 SP M DE S SD: 5.2141 c. M:-7.4489 c. 17: 4 5 8 SP T3 SD: 5.0593 c. M: 8.1761 c. 19: 5 5 9 SP M DE S SD: 3.4206 c. M:-5.7014 c. 23: 6 6 11 SP M DE S SD: 2.6618 c. M:-4.5617 c. 27: 7 7 13 SP M DE S SD: 2.5363 c. M:-3.7597 c. 31: 8 8 15 SP M DE S SD: 2.7081 c. M: 3.4623 c. 32: 8 9 15 SP T3 SD: 2.4000 c. M:-4.0687 c. 36: 9 10 17 SP T3 SD: 1.4374 c. M:-2.3393 c. 40: 10 11 19 SP T3 SD: 0.7392 c. M:-0.9559 c. 44: 11 12 21 SP T3 SD: 0.5022 c. M: 0.8519 c. 103: 26 28 49 SP T3 SD: 0.3997 c. M:-0.5932 c. 107: 27 29 51 SP T3 SD: 0.1976 c. M:-0.3118 c. 111: 28 30 53 SP T3 SD: 0.2237 c. M: 0.2780 c. 147: 37 40 70 SP T3 SD: 0.2096 c. M:-0.3630 c. 151: 38 41 72 SP T3 SD: 0.0323 c. M:-0.0488 c. 457: 115 124 218 SP T3 SD: 0.0361 c. M: 0.0522 c. 564: 142 153 269 SP T3 SD: 0.0201 c. M:-0.0312 c. 715: 180 194 341 SP T3 SD: 0.0109 c. M:-0.0188 c. 866: 218 235 413 SP T3 SD: 0.0074 c. M:-0.0108 c. 1474: 371 400 703 SP T3 SD: 0.0058 c. M: 0.0072 c. 1625: 409 441 775 SP T3 SD: 0.0053 c. M: 0.0090 c. 2189: 551 594 1044 SP T3 SD: 0.0032 c. M: 0.0054 c. 2340: 589 635 1116 SP T3 SD: 0.0011 c. M: 0.0019 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 9:10 x 12 S SD: 28.5203 cents 10:11:12:13 H SD: 26.9386 cents 11:12:13:15 SD: 18.1832 cents 12:13:14:16 S SD: 4.8860 cents 38:41:44:51 SD: 4.8558 cents 39:42:45:52 SD: 4.3698 cents 42:45:49:56 SD: 2.8947 cents 54:58:63:72 SD: 2.1881 cents 66:71:77:88 SD: 2.1470 cents 69:74:80:92 SD: 2.0468 cents 80:86:93:107 SD: 1.8021 cents 81:87:94:108 SD: 1.0924 cents 93:100:108:124 SD: 0.5553 cents 147:158:171:196 SD: 0.4563 cents 228:245:265:304 SD: 0.2939 cents 240:258:279:320 SD: 0.0750 cents 573:616:666:764 SD: 0.0534 cents