Scala analysis: 438_D12
Diatonic tetrachord 66/61 * 61/56 * 112/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66/61 136.388138 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/99 213.5980 1: 66/61 136.3881 2: 61/56 148.0589 3: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 66/61 136.388 cents 1: 1 61/56 148.059 cents 1: 1 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 1 224/183 349.986 cents 2: 1 122/99 361.657 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 : 136.4 284.4 498.0 136.4: 148.1 361.7 498.0 284.4: 213.6 350.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 136.3881 .. 213.5980 cents 3416/3267, 77.2098 cents 66/61, 136.3881 cents 2: 284.4470 .. 361.6569 cents 3416/3267, 77.2098 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 66/61, 136.3881 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 1.217225 Largest / Average step : 1.286618 Largest / Smallest step : 1.566104 Median interval of one step : 61/56, 148.0589 cents, amount: 1 Least squares average step : 157.10123 cents, oct.: 471.30369 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1877-tone equal temperament with octave 4/3 degrees: 514 1072 1877 Least number of segments generator : 939 of 249.155 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1072 of 284.446 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 70.84907 cents Scale diversity : 1.346694 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.689948 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 : 3721/3696, 11.6708 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 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 65.5391 cents: 2 -- Rational properties -- Prime limit : 61 Odd number limit : 183 (O: 61 U: 183) Highest odd numerator or denominator: 61 Scale harmonicity : 0.026454 Fundamental : 1/5124, -12.3231 octaves, 0.0511 Hz. Guide tone : 132, 7.0444 octaves, 34534.575 Hz. Exponens Consonantiae : 6.763680E+05, 19.36745 octaves Euler's gradus suavitatis : 85 Sum of Mann's harmonic distance : 97.5, average 32.50000 Mersenne's string divisions : 54229 Sum of van Prooijen's expressibility: 3.78097, average 1.26032 Sum of Tenney's harmonic distance : 7.64973, average 2.54991 Vogel's harmonic complexity : 59.00000 Wille's k value : 3019 Wilson's harmonic complexity : 85 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.91605, average 2.81934 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 1 0.33333 3 1 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 61: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 23 44| Scale is weakly epimorphic with val: <6 10 19 24 42| Scale is weakly epimorphic with val: <6 10 20 25 43| Scale is weakly epimorphic with val: <6 10 21 26 44| Scale is weakly epimorphic with val: <6 10 22 27 42| Scale is weakly epimorphic with val: <6 11 19 23 44| Scale is weakly epimorphic with val: <6 11 20 24 42| Scale is weakly epimorphic with val: <6 11 21 25 43| Scale is weakly epimorphic with val: <6 11 22 26 44| Scale is weakly epimorphic with val: <7 10 18 25 43| Scale is weakly epimorphic with val: <7 10 19 26 44| Scale is weakly epimorphic with val: <7 10 20 27 42| Scale is weakly epimorphic with val: <7 11 18 23 43| Scale is weakly epimorphic with val: <7 11 18 25 44| Scale is weakly epimorphic with val: <7 11 18 26 43| Scale is weakly epimorphic with val: <7 11 19 23 42| Scale is weakly epimorphic with val: <7 11 19 24 44| Scale is weakly epimorphic with val: <7 11 19 26 42| Scale is weakly epimorphic with val: <7 11 19 27 44| Scale is weakly epimorphic with val: <7 11 20 24 43| Scale is JI-epimorphic with val: <7 11 20 25 42| Scale is weakly epimorphic with val: <7 11 20 27 43| Scale is weakly epimorphic with val: <7 11 21 23 43| Scale is weakly epimorphic with val: <7 11 21 25 44| Scale is JI-epimorphic with val: <7 11 21 26 43| Scale is weakly epimorphic with val: <7 11 22 23 42| Scale is weakly epimorphic with val: <7 11 22 24 44| Scale is weakly epimorphic with val: <7 11 22 26 42| Scale is JI-epimorphic with val: <7 11 22 27 44| Scale is weakly epimorphic with val: <7 12 18 23 44| Scale is weakly epimorphic with val: <7 12 18 27 43| Scale is weakly epimorphic with val: <7 12 19 24 42| Scale is weakly epimorphic with val: <7 12 20 25 43| Scale is weakly epimorphic with val: <7 12 20 26 42| Scale is weakly epimorphic with val: <7 12 21 26 44| Scale is weakly epimorphic with val: <7 12 21 27 43| Scale is weakly epimorphic with val: <7 12 22 27 42| Scale is weakly epimorphic with val: <8 11 18 26 44| Scale is weakly epimorphic with val: <8 11 18 27 43| Scale is weakly epimorphic with val: <8 11 19 27 42| Scale is weakly epimorphic with val: <8 11 20 26 42| Scale is weakly epimorphic with val: <8 11 21 27 43| Scale is weakly epimorphic with val: <8 12 18 25 43| Scale is weakly epimorphic with val: <8 12 18 27 44| Scale is weakly epimorphic with val: <8 12 19 25 42| Scale is weakly epimorphic with val: <8 12 19 26 44| Scale is weakly epimorphic with val: <8 12 20 26 43| Scale is weakly epimorphic with val: <8 12 20 27 42| Scale is weakly epimorphic with val: <8 12 21 27 44| Scale is weakly epimorphic with val: <8 12 22 25 42|
FIT/MODE
3: 1 1 1 SP B ME I SD: 32.3620 c. M:-47.5830 c. 4: 1 1 2 P M ME S SD: 21.5713 c. M: 35.4245 c. 6: 2 1 3 P T3 SD: 26.6624 c. M: 35.4245 c. 7: 2 2 3 SP M ME S SD: 3.4135 c. M:-5.9104 c. 19: 5 6 8 SP T3 SD: 3.8084 c. M: 5.3237 c. 23: 6 7 10 SP T3 SD: 4.1003 c. M: 6.4634 c. 25: 7 7 11 SP M DE S SD: 3.6562 c. M: 5.5418 c. 26: 7 8 11 SP T3 SD: 2.1306 c. M:-2.8866 c. 30: 8 9 13 SP T3 SD: 2.4306 c. M: 3.5761 c. 33: 9 10 14 SP T3 SD: 1.3698 c. M:-2.3061 c. 37: 10 11 16 SP T3 SD: 1.4510 c. M: 1.7814 c. 40: 11 12 17 SP T3 SD: 1.1619 c. M:-1.9288 c. 44: 12 13 19 SP T3 SD: 0.9061 c. M: 1.4669 c. 51: 14 15 22 SP T3 SD: 0.7436 c. M: 1.2450 c. 58: 16 17 25 SP T3 SD: 0.8498 c. M: 1.0766 c. 70: 19 21 30 SP T3 SD: 0.7008 c. M: 1.2045 c. 77: 21 23 33 SP T3 SD: 0.3334 c. M: 0.5577 c. 84: 23 25 36 SP T3 SD: 0.0873 c. M:-0.1501 c. 259: 71 77 111 SP T3 SD: 0.1191 c. M:-0.1501 c. 296: 81 88 127 SP T3 SD: 0.0773 c. M: 0.0988 c. 303: 83 90 130 SP T3 SD: 0.0541 c. M: 0.0847 c. 380: 104 113 163 SP T3 SD: 0.0515 c. M: 0.0811 c. 387: 106 115 166 SP T3 SD: 0.0251 c. M: 0.0337 c. 471: 129 140 202 SP T3 SD: 0.0110 c. M:-0.0191 c. 1026: 281 305 440 SP T3 SD: 0.0113 c. M:-0.0160 c. 1322: 362 393 567 SP T3 SD: 0.0086 c. M: 0.0114 c. 1406: 385 418 603 SP T3 SD: 0.0060 c. M: 0.0102 c. 1793: 491 533 769 SP T3 SD: 0.0051 c. M: 0.0086 c. 1877: 514 558 805 SP T3 SD: 0.0019 c. M: 0.0029 c. 2348: 643 698 1007 SP T3 SD: 0.0012 c. M:-0.0015 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: 101.8667 cents 5 x 6:7 S SD: 45.0216 cents 6 x 7:8 S SD: 8.7881 cents 7 x 8:9 S SD: 41.2374 cents 8:9 x 11 SD: 43.0035 cents 9:10:11:12 H SD: 25.9947 cents 10:11:12:13 H SD: 20.3118 cents 11:12:13:15 SD: 13.9019 cents 12:13:14:16 S SD: 5.9038 cents 27:29:32:36 SD: 5.3181 cents 33:36:39:44 SD: 5.0079 cents 38:41:45:51 SD: 4.9506 cents 39:42:46:52 SD: 2.7336 cents 51:55:60:68 SD: 2.1513 cents 72:78:85:96 SD: 1.2135 cents 84:91:99:112 SD: 0.7282 cents 123:133:145:164 SD: 0.3829 cents 207:224:244:276 SD: 0.1195 cents 342:370:403:456 SD: 0.1143 cents 537:581:633:716 SD: 0.0990 cents 549:594:647:732 SD: 0.0319 cents