Scala analysis: 402_D6
Diatonic tetrachord 46/45 * 105/92 * 8/7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 46/45 38.0506 23rd-partial chroma 2: 105/92 228.8203 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 46/45 38.051 cents 23rd-partial chroma 1: 1 105/92 228.820 cents 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 368/315 269.225 cents 2: 1 30/23 459.994 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 : 38.1 266.9 498.0 38.1 : 228.8 460.0 498.0 266.9: 231.2 269.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 231.1741 cents 180/161, 193.1235 cents 46/45, 38.0506 cents 2: 266.8709 .. 459.9944 cents 180/161, 193.1235 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 4.363002 Largest / Average step : 1.392489 Largest / Smallest step : 6.075434 Median interval of one step : 105/92, 228.8203 cents, amount: 1 Least squares average step : 147.56625 cents, oct.: 442.69874 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1898-tone equal temperament with octave 4/3 degrees: 145 1017 1898 Least number of segments generator : 951 of 249.547 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1133 of 297.305 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 35.69681 cents Scale diversity : 0.522766 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.224474 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 : 736/735, 2.3538 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 190.7696 cents: 1 -- Rational properties -- Prime limit : 23 Odd number limit : 315 (O: 105 U: 315) Highest odd numerator or denominator: 45 Scale harmonicity : 0.014902 Average absolute harmonicity : 0.101399 Specific harmonicity : 0.079083 Fundamental : 1/90, -6.4919 octaves, 2.9070 Hz. Guide tone : 644, 9.3309 octaves, 168486.864 Hz. Exponens Consonantiae : 5.796000E+04, 15.82277 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 55.5, average 18.50000 Mersenne's string divisions : 91 Sum of van Prooijen's expressibility: 2.97543, average 0.99181 Sum of Tenney's harmonic distance : 6.01840, average 2.00613 Vogel's harmonic complexity : 17.00000 Wille's k value : 52 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.60457, average 2.43410 Lattice compactness (without 2's) : 9.59575, average 1.59929 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -2 ..-1 -1.33333 4 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.33333 1 1 23: 0 .. 1 0.33333 1 1 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 15 19 30| Scale is weakly epimorphic with val: <6 10 15 19 33| Scale is weakly epimorphic with val: <6 10 15 19 36| Scale is weakly epimorphic with val: <6 10 15 20 32| Scale is weakly epimorphic with val: <6 10 16 19 31| Scale is weakly epimorphic with val: <6 10 16 19 34| Scale is weakly epimorphic with val: <6 10 16 20 33| Scale is weakly epimorphic with val: <6 10 17 19 32| Scale is weakly epimorphic with val: <6 10 17 19 35| Scale is weakly epimorphic with val: <6 10 17 20 34| Scale is weakly epimorphic with val: <6 10 18 19 30| Scale is weakly epimorphic with val: <6 10 18 19 33| Scale is weakly epimorphic with val: <6 10 18 19 36| Scale is weakly epimorphic with val: <6 10 18 20 35| Scale is weakly epimorphic with val: <6 10 19 19 31| Scale is weakly epimorphic with val: <6 10 19 19 34| Scale is weakly epimorphic with val: <6 10 19 20 36| Scale is weakly epimorphic with val: <6 11 15 19 34| Scale is weakly epimorphic with val: <6 11 15 20 30| Scale is weakly epimorphic with val: <6 11 15 20 33| Scale is weakly epimorphic with val: <6 11 15 20 36| Scale is weakly epimorphic with val: <6 11 15 22 34| Scale is weakly epimorphic with val: <6 11 16 19 35| Scale is weakly epimorphic with val: <6 11 16 20 31| Scale is weakly epimorphic with val: <6 11 16 20 34| Scale is weakly epimorphic with val: <6 11 16 22 35| Scale is weakly epimorphic with val: <6 11 17 19 36| Scale is weakly epimorphic with val: <6 11 17 20 32| Scale is weakly epimorphic with val: <6 11 17 20 35| Scale is weakly epimorphic with val: <6 11 17 22 36| Scale is weakly epimorphic with val: <6 11 18 20 30| Scale is weakly epimorphic with val: <6 11 18 20 33| Scale is weakly epimorphic with val: <6 11 18 20 36| Scale is weakly epimorphic with val: <6 11 19 20 31| Scale is weakly epimorphic with val: <6 11 19 20 34| Scale is weakly epimorphic with val: <7 10 15 19 31| Scale is weakly epimorphic with val: <7 10 15 20 30| Scale is weakly epimorphic with val: <7 10 15 20 33| Scale is weakly epimorphic with val: <7 10 15 20 36| Scale is weakly epimorphic with val: <7 10 15 22 31| Scale is weakly epimorphic with val: <7 10 16 19 32| Scale is weakly epimorphic with val: <7 10 16 20 31| Scale is weakly epimorphic with val: <7 10 16 20 34| Scale is weakly epimorphic with val: <7 10 16 22 32| Scale is weakly epimorphic with val: <7 10 17 19 33| Scale is weakly epimorphic with val: <7 10 17 20 32| Scale is weakly epimorphic with val: <7 10 17 20 35| Scale is weakly epimorphic with val: <7 10 17 22 33| Scale is weakly epimorphic with val: <7 10 18 19 34| Scale is weakly epimorphic with val: <7 10 18 20 30| Scale is weakly epimorphic with val: <7 10 18 20 33| Scale is weakly epimorphic with val: <7 10 18 20 36| Scale is weakly epimorphic with val: <7 10 18 22 34| Scale is weakly epimorphic with val: <7 10 19 19 35| Scale is weakly epimorphic with val: <7 10 19 20 31| Scale is weakly epimorphic with val: <7 10 19 20 34| Scale is weakly epimorphic with val: <7 10 19 22 35| Scale is weakly epimorphic with val: <7 11 15 19 32| Scale is weakly epimorphic with val: <7 11 15 19 35| Scale is JI-epimorphic with val: <7 11 15 20 31| Scale is weakly epimorphic with val: <7 11 15 20 34| Scale is weakly epimorphic with val: <7 11 15 22 32| Scale is weakly epimorphic with val: <7 11 15 22 35| Scale is weakly epimorphic with val: <7 11 16 19 30| Scale is weakly epimorphic with val: <7 11 16 19 33| Scale is weakly epimorphic with val: <7 11 16 19 36| Scale is JI-epimorphic with val: <7 11 16 20 32| Scale is weakly epimorphic with val: <7 11 16 20 35| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 16 22 33| Scale is weakly epimorphic with val: <7 11 16 22 36| Scale is weakly epimorphic with val: <7 11 17 19 31| Scale is weakly epimorphic with val: <7 11 17 19 34| Scale is weakly epimorphic with val: <7 11 17 20 30| Scale is JI-epimorphic with val: <7 11 17 20 33| = patent Scale is weakly epimorphic with val: <7 11 17 20 36| Scale is weakly epimorphic with val: <7 11 17 22 31| Scale is weakly epimorphic with val: <7 11 17 22 34| Scale is weakly epimorphic with val: <7 11 18 19 32| Scale is weakly epimorphic with val: <7 11 18 19 35| Scale is weakly epimorphic with val: <7 11 18 20 31| Scale is JI-epimorphic with val: <7 11 18 20 34| Scale is weakly epimorphic with val: <7 11 18 22 32| Scale is weakly epimorphic with val: <7 11 18 22 35| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 19 33| Scale is weakly epimorphic with val: <7 11 19 19 36| Scale is weakly epimorphic with val: <7 11 19 20 32| Scale is JI-epimorphic with val: <7 11 19 20 35| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 11 19 22 33| Scale is weakly epimorphic with val: <7 11 19 22 36| Scale is weakly epimorphic with val: <7 12 15 20 35| Scale is weakly epimorphic with val: <7 12 15 22 30| Scale is weakly epimorphic with val: <7 12 15 22 33| Scale is weakly epimorphic with val: <7 12 15 22 36| Scale is weakly epimorphic with val: <7 12 16 20 36| Scale is weakly epimorphic with val: <7 12 16 22 31| Scale is weakly epimorphic with val: <7 12 16 22 34| Scale is weakly epimorphic with val: <7 12 17 22 32| Scale is weakly epimorphic with val: <7 12 17 22 35| Scale is weakly epimorphic with val: <7 12 18 22 30| Scale is weakly epimorphic with val: <7 12 18 22 33| Scale is weakly epimorphic with val: <7 12 18 22 36| Scale is weakly epimorphic with val: <7 12 19 22 31| Scale is weakly epimorphic with val: <7 12 19 22 34| Scale is weakly epimorphic with val: <8 11 15 20 32| Scale is weakly epimorphic with val: <8 11 15 22 30| Scale is weakly epimorphic with val: <8 11 15 22 33| Scale is weakly epimorphic with val: <8 11 15 22 36| Scale is weakly epimorphic with val: <8 11 16 20 33| Scale is weakly epimorphic with val: <8 11 16 22 31| Scale is weakly epimorphic with val: <8 11 16 22 34| Scale is weakly epimorphic with val: <8 11 17 20 34| Scale is weakly epimorphic with val: <8 11 17 22 32| Scale is weakly epimorphic with val: <8 11 17 22 35| Scale is weakly epimorphic with val: <8 11 18 20 35| Scale is weakly epimorphic with val: <8 11 18 22 30| Scale is weakly epimorphic with val: <8 11 18 22 33| Scale is weakly epimorphic with val: <8 11 18 22 36| Scale is weakly epimorphic with val: <8 11 19 20 36| Scale is weakly epimorphic with val: <8 11 19 22 31| Scale is weakly epimorphic with val: <8 11 19 22 34| Scale is weakly epimorphic with val: <8 12 15 19 34| Scale is weakly epimorphic with val: <8 12 15 22 34| Scale is weakly epimorphic with val: <8 12 16 19 35| Scale is weakly epimorphic with val: <8 12 16 22 35| Scale is weakly epimorphic with val: <8 12 17 19 36| Scale is weakly epimorphic with val: <8 12 17 22 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 62.2355 c. M: 100.8559 c. 4: 0 2 2 P M DE S SD: 24.2653 c. M: 38.0506 c. 6: 0 3 3 P M DE S SD: 24.2653 c. M: 38.0506 c. 7: 1 3 3 SP M DE S SD: 21.6775 c. M:-33.0987 c. 9: 1 4 4 SP M DE S SD: 11.4791 c. M:-17.2877 c. 11: 1 5 5 SP M DE S SD: 5.0054 c. M:-7.2262 c. 13: 1 6 6 SP M DE S SD: 0.7695 c. M:-1.3072 c. 54: 4 25 25 SP M DE S SD: 0.7526 c. M: 1.1584 c. 67: 5 31 31 SP M DE S SD: 0.6635 c. M: 0.8831 c. 80: 6 37 37 SP M DE S SD: 0.6251 c. M:-0.8283 c. 93: 7 43 43 SP M DE S SD: 0.6107 c. M:-0.8952 c. 105: 8 48 49 SP T3 SD: 0.7224 c. M: 1.2469 c. 106: 8 49 49 SP M DE S SD: 0.6078 c. M:-0.9457 c. 116: 9 53 54 SP T3 SD: 0.5177 c. M: 0.6744 c. 118: 9 54 55 SP T3 SD: 0.5587 c. M: 0.9655 c. 129: 10 59 60 SP T3 SD: 0.4228 c. M:-0.5575 c. 131: 10 60 61 SP T3 SD: 0.4276 c. M: 0.7400 c. 142: 11 65 66 SP T3 SD: 0.3551 c. M:-0.5303 c. 144: 11 66 67 SP T3 SD: 0.3205 c. M: 0.5552 c. 155: 12 71 72 SP T3 SD: 0.3102 c. M:-0.5077 c. 157: 12 72 73 SP T3 SD: 0.2317 c. M: 0.4010 c. 170: 13 78 79 SP T3 SD: 0.1574 c. M: 0.2703 c. 183: 14 84 85 SP T3 SD: 0.0960 c. M: 0.1583 c. 196: 15 90 91 SP T3 SD: 0.0515 c. M:-0.0651 c. 209: 16 96 97 SP T3 SD: 0.0467 c. M:-0.0772 c. 405: 31 186 188 SP T3 SD: 0.0424 c. M:-0.0713 c. 616: 47 283 286 SP T3 SD: 0.0457 c. M: 0.0611 c. 629: 48 289 292 SP T3 SD: 0.0317 c. M: 0.0440 c. 642: 49 295 298 SP T3 SD: 0.0221 c. M: 0.0379 c. 655: 50 301 304 SP T3 SD: 0.0219 c. M: 0.0319 c. 825: 63 379 383 SP T3 SD: 0.0251 c. M: 0.0395 c. 838: 64 385 389 SP T3 SD: 0.0134 c. M: 0.0186 c. 851: 65 391 395 SP T3 SD: 0.0056 c. M: 0.0096 c. 1060: 81 487 492 SP T3 SD: 0.0056 c. M:-0.0075 c. 1898: 145 872 881 SP T3 SD: 0.0030 c. M: 0.0049 c. 1911: 146 878 887 SP T3 SD: 0.0024 c. M:-0.0041 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: 48.7680 cents 6 x 7:8 S SD: 0.0000 cents 7 x 8:9 S SD: 36.1882 cents 8 x 9:11 SD: 41.2374 cents 9 x 11:12 SD: 40.2685 cents 10 x 12:13 S SD: 32.7861 cents 13:14:15:17 SD: 32.7290 cents 14:15:16:19 SD: 31.3367 cents 15:16:18:20 S SD: 29.4531 cents 16:17:19:21 SD: 26.1587 cents 17:18:20:23 SD: 22.5042 cents 18:19:21:24 SD: 18.5175 cents 21:22:25:28 SD: 18.3436 cents 22:23:26:29 SD: 16.3441 cents 23:24:27:31 SD: 13.8833 cents 24:25:28:32 SD: 10.8739 cents 29:30:34:39 SD: 8.9396 cents 30:31:35:40 SD: 6.2387 cents 35:36:41:47 SD: 5.9299 cents 36:37:42:48 SD: 3.1278 cents 42:43:49:56 SD: 0.8954 cents 48:49:56:64 S SD: 0.7846 cents 90:92:105:120 SD: 0.0000 cents