Scala analysis: 379_D3
Diatonic tetrachord 40/39 * 26/23 * 23/20
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 80/69 256.084366 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/20 241.9606 1: 40/39 43.8311 tridecimal minor diesis 2: 26/23 212.2533 3: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 26/23 212.253 cents 1: 1 23/20 241.961 cents 2: 1 80/69 256.084 cents 2: 1 46/39 285.792 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 256.1 498.0 43.8 : 212.3 454.2 498.0 256.1: 242.0 285.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 241.9606 cents 897/800, 198.1296 cents 40/39, 43.8311 cents 2: 256.0844 .. 454.2139 cents 897/800, 198.1296 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 3.787612 Largest / Average step : 1.457462 Largest / Smallest step : 5.520302 Median interval of one step : 26/23, 212.2533 cents, amount: 1 Least squares average step : 146.43820 cents, oct.: 439.31460 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1375-tone equal temperament with octave 4/3 degrees: 121 707 1375 Least number of segments generator : 688 of 249.204 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 886 of 320.922 cents and inv. generated superset size: 50 = 47 more = 1666.667% 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 14.12373 cents Scale diversity : 0.646826 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.204371 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 : 1600/1587, 14.1237 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% -- Rational properties -- Prime limit : 23 Odd number limit : 69 (O: 23 U: 69) Highest odd numerator or denominator: 69 Scale harmonicity : 0.012935 Average absolute harmonicity : 0.087213 Specific harmonicity : 0.066855 Fundamental : 1/897, -9.8090 octaves, 0.2917 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 7.176000E+04, 16.13089 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 117.5, average 39.16667 Mersenne's string divisions : 82397 Sum of van Prooijen's expressibility: 3.90703, average 1.30234 Sum of Tenney's harmonic distance : 8.01424, average 2.67141 Vogel's harmonic complexity : 30.33333 Wille's k value : 149 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 1 Lattice compactness : 15.97266, average 2.66211 Lattice compactness (without 2's) : 8.70674, average 1.45112 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.66667 2 13: -1 .. 0 -0.33333 1 1 23: -1 .. 0 -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 19 26 30| Scale is weakly epimorphic with val: <6 10 19 29 30| Scale is weakly epimorphic with val: <7 10 15 27 30| Scale is weakly epimorphic with val: <7 10 15 30 30| Scale is weakly epimorphic with val: <7 10 16 25 31| Scale is weakly epimorphic with val: <7 10 16 28 31| Scale is weakly epimorphic with val: <7 10 17 25 30| Scale is weakly epimorphic with val: <7 10 17 25 33| Scale is weakly epimorphic with val: <7 10 17 25 36| Scale is weakly epimorphic with val: <7 10 17 26 32| Scale is weakly epimorphic with val: <7 10 17 29 32| Scale is weakly epimorphic with val: <7 10 18 26 31| Scale is weakly epimorphic with val: <7 10 18 26 34| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 18 30 33| Scale is weakly epimorphic with val: <7 10 19 25 34| Scale is weakly epimorphic with val: <7 10 19 27 32| Scale is weakly epimorphic with val: <7 10 19 27 35| Scale is weakly epimorphic with val: <7 10 19 28 34| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 26 34| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is weakly epimorphic with val: <7 11 15 27 36| Scale is weakly epimorphic with val: <7 11 15 29 31| Scale is weakly epimorphic with val: <7 11 15 29 34| Scale is weakly epimorphic with val: <7 11 15 30 30| Scale is weakly epimorphic with val: <7 11 15 30 33| Scale is weakly epimorphic with val: <7 11 15 30 36| Scale is JI-epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 25 34| Scale is weakly epimorphic with val: <7 11 16 27 32| Scale is weakly epimorphic with val: <7 11 16 27 35| Scale is weakly epimorphic with val: <7 11 16 28 31| Scale is weakly epimorphic with val: <7 11 16 28 34| Scale is weakly epimorphic with val: <7 11 16 30 32| Scale is weakly epimorphic with val: <7 11 16 30 35| Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is weakly epimorphic with val: <7 11 17 25 36| Scale is JI-epimorphic with val: <7 11 17 26 32| Scale is weakly epimorphic with val: <7 11 17 26 35| Scale is weakly epimorphic with val: <7 11 17 28 30| Scale is weakly epimorphic with val: <7 11 17 28 33| Scale is weakly epimorphic with val: <7 11 17 28 36| Scale is weakly epimorphic with val: <7 11 17 29 32| Scale is weakly epimorphic with val: <7 11 17 29 35| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 26 34| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is JI-epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 27 36| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 29 34| Scale is weakly epimorphic with val: <7 11 18 30 30| Scale is weakly epimorphic with val: <7 11 18 30 33| Scale is weakly epimorphic with val: <7 11 18 30 36| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 27 35| Scale is weakly epimorphic with val: <7 11 19 28 31| Scale is JI-epimorphic with val: <7 11 19 28 34| Scale is weakly epimorphic with val: <7 11 19 30 32| Scale is weakly epimorphic with val: <7 11 19 30 35| Scale is weakly epimorphic with val: <7 12 17 25 30| Scale is weakly epimorphic with val: <7 12 17 28 30| Scale is weakly epimorphic with val: <7 12 18 26 31| Scale is weakly epimorphic with val: <7 12 18 29 31| Scale is weakly epimorphic with val: <7 12 19 25 31| Scale is weakly epimorphic with val: <7 12 19 25 34| Scale is weakly epimorphic with val: <7 12 19 27 32| Scale is weakly epimorphic with val: <7 12 19 30 32| Scale is weakly epimorphic with val: <8 11 15 25 32| Scale is weakly epimorphic with val: <8 11 15 25 35| Scale is weakly epimorphic with val: <8 11 15 27 33| Scale is weakly epimorphic with val: <8 11 15 30 33| Scale is weakly epimorphic with val: <8 11 16 25 34| Scale is weakly epimorphic with val: <8 11 16 26 30| Scale is weakly epimorphic with val: <8 11 16 26 33| Scale is weakly epimorphic with val: <8 11 16 26 36| Scale is weakly epimorphic with val: <8 11 16 28 34| Scale is weakly epimorphic with val: <8 11 17 26 35| Scale is weakly epimorphic with val: <8 11 17 27 31| Scale is weakly epimorphic with val: <8 11 17 27 34| Scale is weakly epimorphic with val: <8 11 17 29 35| Scale is weakly epimorphic with val: <8 11 18 27 36| Scale is weakly epimorphic with val: <8 11 18 28 32| Scale is weakly epimorphic with val: <8 11 18 28 35| Scale is weakly epimorphic with val: <8 11 18 30 36| Scale is weakly epimorphic with val: <8 11 19 29 30| Scale is weakly epimorphic with val: <8 11 19 29 33| Scale is weakly epimorphic with val: <8 11 19 29 36| Scale is weakly epimorphic with val: <8 12 15 25 32| Scale is weakly epimorphic with val: <8 12 15 28 32| Scale is weakly epimorphic with val: <8 12 16 25 31| Scale is weakly epimorphic with val: <8 12 16 25 34| Scale is weakly epimorphic with val: <8 12 16 26 33| Scale is weakly epimorphic with val: <8 12 16 29 33| Scale is weakly epimorphic with val: <8 12 17 26 32| Scale is weakly epimorphic with val: <8 12 17 26 35| Scale is weakly epimorphic with val: <8 12 17 27 34| Scale is weakly epimorphic with val: <8 12 17 30 34| Scale is weakly epimorphic with val: <8 12 18 25 35| Scale is weakly epimorphic with val: <8 12 18 27 30| Scale is weakly epimorphic with val: <8 12 18 27 33| Scale is weakly epimorphic with val: <8 12 18 27 36| Scale is weakly epimorphic with val: <8 12 18 28 35| Scale is weakly epimorphic with val: <8 12 19 26 36| Scale is weakly epimorphic with val: <8 12 19 28 31| Scale is weakly epimorphic with val: <8 12 19 28 34| Scale is weakly epimorphic with val: <8 12 19 29 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 57.8321 c. M: 90.0694 c. 4: 0 2 2 P M DE S SD: 25.6322 c. M: 43.8311 c. 8: 1 3 4 P T3 SD: 11.3920 c. M:-18.4246 c. 9: 1 4 4 SP M DE S SD: 13.6269 c. M:-20.6073 c. 10: 1 4 5 P T3 SD: 5.3402 c. M: 7.0619 c. 12: 1 5 6 P T3 SD: 4.2929 c. M: 7.0619 c. 21: 2 9 10 SP T3 SD: 3.4630 c. M:-4.7963 c. 23: 2 10 11 SP T3 SD: 2.1947 c. M:-3.7652 c. 31: 3 13 15 SP T3 SD: 2.5828 c. M:-4.3669 c. 33: 3 14 16 SP T3 SD: 0.8803 c. M:-1.4458 c. 35: 3 15 17 SP T3 SD: 0.6597 c. M: 1.1415 c. 68: 6 29 33 SP T3 SD: 0.1652 c. M:-0.2623 c. 171: 15 73 83 SP T3 SD: 0.1512 c. M:-0.2195 c. 181: 16 77 88 SP T3 SD: 0.1543 c. M:-0.1950 c. 216: 19 92 105 SP T3 SD: 0.0844 c. M: 0.1446 c. 284: 25 121 138 SP T3 SD: 0.0279 c. M: 0.0471 c. 352: 31 150 171 SP T3 SD: 0.0193 c. M:-0.0309 c. 636: 56 271 309 SP T3 SD: 0.0151 c. M:-0.0220 c. 988: 87 421 480 SP T3 SD: 0.0147 c. M:-0.0251 c. 1023: 90 436 497 SP T3 SD: 0.0087 c. M: 0.0148 c. 1091: 96 465 530 SP T3 SD: 0.0089 c. M:-0.0139 c. 1307: 115 557 635 SP T3 SD: 0.0088 c. M: 0.0123 c. 1375: 121 586 668 SP T3 SD: 0.0019 c. M: 0.0031 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: 51.6762 cents 6 x 7:8 S SD: 5.3933 cents 7 x 8:9 S SD: 33.8548 cents 8 x 9:11 SD: 37.2833 cents 9 x 10:12 S SD: 36.8403 cents 10 x 12:13 S SD: 36.9736 cents 11 x 13:15 SD: 25.5487 cents 17:18:20:23 SD: 21.8991 cents 18:19:21:24 SD: 16.9758 cents 19:20:22:25 SD: 16.8433 cents 20:21:23:27 SD: 16.0322 cents 21:22:24:28 S SD: 14.7868 cents 23:24:27:31 SD: 13.7591 cents 24:25:28:32 SD: 9.6425 cents 26:27:30:35 S SD: 9.4669 cents 27:28:31:36 SD: 8.5116 cents 30:31:35:40 SD: 5.6143 cents 33:34:38:44 SD: 4.7368 cents 36:37:42:48 SD: 3.7908 cents 39:40:45:52 SD: 2.7811 cents 45:46:52:60 SD: 2.7249 cents 69:71:80:92 SD: 1.8787 cents 75:77:87:100 SD: 0.6449 cents 156:160:181:208 SD: 0.4160 cents 195:200:226:260 SD: 0.2220 cents 270:277:313:360 SD: 0.1792 cents 276:283:320:368 SD: 0.1568 cents 351:360:407:468 SD: 0.0617 cents 546:560:633:728 SD: 0.0396 cents