Scala analysis: 378_D3
Diatonic tetrachord 8/7 * 70/69 * 23/20
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 80/69 256.084366 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/20 241.9606 1: 8/7 231.1741 septimal whole tone 2: 70/69 24.9103 3: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 70/69 24.910 cents 1: 1 8/7 231.174 cents septimal whole tone 1: 1 23/20 241.961 cents 2: 1 80/69 256.084 cents 2: 1 7/6 266.871 cents septimal minor third 2: 1 46/35 473.135 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 : 231.2 256.1 498.0 231.2: 24.9 266.9 498.0 256.1: 242.0 473.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.9103 .. 241.9606 cents 1587/1400, 217.0504 cents 70/69, 24.9103 cents 2: 256.0844 .. 473.1347 cents 1587/1400, 217.0504 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 70/69, 24.9103 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 6.664520 Largest / Average step : 1.457462 Largest / Smallest step : 9.713287 Median interval of one step : 8/7, 231.1741 cents, amount: 1 Least squares average step : 159.81984 cents, oct.: 479.45953 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1939-tone equal temperament with octave 4/3 degrees: 900 997 1939 Least number of segments generator : 970 of 249.151 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1388 of 356.517 cents and inv. generated superset size: 61 = 58 more = 2033.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 14.12373 cents Scale diversity : 0.415596 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.128391 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 : 161/160, 10.7865 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 -- Rational properties -- Prime limit : 23 Odd number limit : 69 (O: 35 U: 69) Highest odd numerator or denominator: 69 Scale harmonicity : 0.015281 Average absolute harmonicity : 0.102561 Specific harmonicity : 0.080006 Fundamental : 1/483, -8.9159 octaves, 0.5417 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 3.864000E+04, 15.23781 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 85.5, average 28.50000 Mersenne's string divisions : 15645 Sum of van Prooijen's expressibility: 3.16107, average 1.05369 Sum of Tenney's harmonic distance : 6.56931, average 2.18977 Vogel's harmonic complexity : 25.66667 Wille's k value : 80 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.17485, average 2.69581 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 0 -0.66667 2 1 5: 0 .. 1 0.33333 1 7: -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: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 19 20 30| Scale is weakly epimorphic with val: <7 10 15 18 31| Scale is weakly epimorphic with val: <7 10 15 18 34| Scale is weakly epimorphic with val: <7 10 15 19 30| Scale is weakly epimorphic with val: <7 10 15 22 30| Scale is weakly epimorphic with val: <7 10 16 18 32| Scale is weakly epimorphic with val: <7 10 16 18 35| Scale is weakly epimorphic with val: <7 10 16 19 31| Scale is weakly epimorphic with val: <7 10 16 22 31| Scale is weakly epimorphic with val: <7 10 17 18 30| Scale is weakly epimorphic with val: <7 10 17 18 33| Scale is weakly epimorphic with val: <7 10 17 18 36| Scale is weakly epimorphic with val: <7 10 17 19 32| Scale is weakly epimorphic with val: <7 10 17 22 32| Scale is weakly epimorphic with val: <7 10 18 18 31| Scale is weakly epimorphic with val: <7 10 18 18 34| Scale is weakly epimorphic with val: <7 10 18 19 33| Scale is weakly epimorphic with val: <7 10 18 22 33| Scale is weakly epimorphic with val: <7 10 19 19 34| Scale is weakly epimorphic with val: <7 10 19 22 34| Scale is weakly epimorphic with val: <7 11 15 19 31| Scale is weakly epimorphic with val: <7 11 15 19 34| Scale is JI-epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 20 36| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 15 22 34| Scale is weakly epimorphic with val: <7 11 16 19 32| Scale is weakly epimorphic with val: <7 11 16 19 35| Scale is JI-epimorphic with val: <7 11 16 20 31| Scale is weakly epimorphic with val: <7 11 16 20 34| Scale is weakly epimorphic with val: <7 11 16 22 32| Scale is weakly epimorphic with val: <7 11 16 22 35| Scale is weakly epimorphic with val: <7 11 17 19 30| Scale is weakly epimorphic with val: <7 11 17 19 33| Scale is weakly epimorphic with val: <7 11 17 19 36| Scale is JI-epimorphic with val: <7 11 17 20 32| Scale is weakly epimorphic with val: <7 11 17 20 35| Scale is weakly epimorphic with val: <7 11 17 22 30| Scale is weakly epimorphic with val: <7 11 17 22 33| Scale is weakly epimorphic with val: <7 11 17 22 36| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 19 34| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is JI-epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 20 36| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 18 22 34| Scale is weakly epimorphic with val: <7 11 19 19 32| Scale is weakly epimorphic with val: <7 11 19 19 35| Scale is weakly epimorphic with val: <7 11 19 20 31| Scale is JI-epimorphic with val: <7 11 19 20 34| Scale is weakly epimorphic with val: <7 11 19 22 32| Scale is weakly epimorphic with val: <7 11 19 22 35| Scale is weakly epimorphic with val: <7 12 15 18 30| Scale is weakly epimorphic with val: <7 12 15 18 33| Scale is weakly epimorphic with val: <7 12 15 18 36| Scale is weakly epimorphic with val: <7 12 16 18 31| Scale is weakly epimorphic with val: <7 12 16 18 34| Scale is weakly epimorphic with val: <7 12 17 18 32| Scale is weakly epimorphic with val: <7 12 17 18 35| Scale is weakly epimorphic with val: <7 12 17 20 30| Scale is weakly epimorphic with val: <7 12 18 18 30| Scale is weakly epimorphic with val: <7 12 18 18 33| Scale is weakly epimorphic with val: <7 12 18 18 36| Scale is weakly epimorphic with val: <7 12 18 20 31| Scale is weakly epimorphic with val: <7 12 19 20 32| Scale is weakly epimorphic with val: <8 11 15 20 33| Scale is weakly epimorphic with val: <8 11 15 21 32| Scale is weakly epimorphic with val: <8 11 15 21 35| Scale is weakly epimorphic with val: <8 11 16 20 34| Scale is weakly epimorphic with val: <8 11 16 21 30| Scale is weakly epimorphic with val: <8 11 16 21 33| Scale is weakly epimorphic with val: <8 11 16 21 36| Scale is weakly epimorphic with val: <8 11 17 20 35| Scale is weakly epimorphic with val: <8 11 17 21 31| Scale is weakly epimorphic with val: <8 11 17 21 34| Scale is weakly epimorphic with val: <8 11 18 20 36| Scale is weakly epimorphic with val: <8 11 18 21 32| Scale is weakly epimorphic with val: <8 11 18 21 35| Scale is weakly epimorphic with val: <8 11 19 21 30| Scale is weakly epimorphic with val: <8 11 19 21 33| Scale is weakly epimorphic with val: <8 11 19 21 36| Scale is weakly epimorphic with val: <8 12 15 19 32| Scale is weakly epimorphic with val: <8 12 15 21 30| Scale is weakly epimorphic with val: <8 12 15 21 33| Scale is weakly epimorphic with val: <8 12 15 21 36| Scale is weakly epimorphic with val: <8 12 15 22 32| Scale is weakly epimorphic with val: <8 12 16 19 33| Scale is weakly epimorphic with val: <8 12 16 21 31| Scale is weakly epimorphic with val: <8 12 16 21 34| Scale is weakly epimorphic with val: <8 12 16 22 33| Scale is weakly epimorphic with val: <8 12 17 19 34| Scale is weakly epimorphic with val: <8 12 17 21 32| Scale is weakly epimorphic with val: <8 12 17 21 35| Scale is weakly epimorphic with val: <8 12 17 22 34| Scale is weakly epimorphic with val: <8 12 18 19 35| Scale is weakly epimorphic with val: <8 12 18 21 30| Scale is weakly epimorphic with val: <8 12 18 21 33| Scale is weakly epimorphic with val: <8 12 18 21 36| Scale is weakly epimorphic with val: <8 12 18 22 35| Scale is weakly epimorphic with val: <8 12 19 19 36| Scale is weakly epimorphic with val: <8 12 19 21 31| Scale is weakly epimorphic with val: <8 12 19 21 34| Scale is weakly epimorphic with val: <8 12 19 22 36|
FIT/MODE
3: 1 0 2 N G T3 SD: 64.1825 c. M: 90.0694 c. 4: 2 0 2 P M DE I SD: 11.0821 c. M:-17.8484 c. 10: 5 0 5 P M DE I SD: 11.0821 c. M:-17.8484 c. 11: 5 1 5 SP M DE I SD: 9.4087 c. M:-15.5765 c. 13: 6 1 6 SP M DE I SD: 7.0230 c. M:-12.0937 c. 15: 7 1 7 SP M DE I SD: 5.5546 c. M:-9.5396 c. 17: 8 1 8 SP M DE I SD: 4.7538 c. M:-7.5865 c. 19: 9 1 9 SP M DE I SD: 4.4356 c. M:-6.0446 c. 21: 10 1 10 SP M DE I SD: 4.4305 c. M:-5.9902 c. 24: 11 1 12 P T3 SD: 4.4083 c. M: 7.0619 c. 26: 12 1 13 P T3 SD: 4.1464 c. M: 7.0619 c. 28: 13 1 14 P T3 SD: 4.0773 c. M: 7.0619 c. 31: 14 2 15 SP T3 SD: 3.6520 c. M: 6.2505 c. 33: 15 2 16 SP T3 SD: 2.7796 c. M: 4.7900 c. 35: 16 2 17 SP T3 SD: 2.0189 c. M: 3.4964 c. 37: 17 2 18 SP T3 SD: 1.3660 c. M: 2.3426 c. 39: 18 2 19 SP T3 SD: 0.8498 c. M: 1.3072 c. 41: 19 2 20 SP T3 SD: 0.6097 c. M: 0.9881 c. 80: 37 4 39 SP T3 SD: 0.6796 c. M: 0.8363 c. 84: 39 4 41 SP T3 SD: 0.6549 c. M: 1.1328 c. 95: 44 5 46 SP T3 SD: 0.5458 c. M:-0.8020 c. 97: 45 5 47 SP T3 SD: 0.3761 c. M:-0.6399 c. 99: 46 5 48 SP T3 SD: 0.3122 c. M:-0.4843 c. 136: 63 7 66 SP T3 SD: 0.3068 c. M: 0.4621 c. 138: 64 7 67 SP T3 SD: 0.1450 c. M: 0.1967 c. 140: 65 7 68 SP T3 SD: 0.0467 c. M:-0.0611 c. 321: 149 16 156 SP T3 SD: 0.0463 c. M: 0.0799 c. 459: 213 23 223 SP T3 SD: 0.0323 c. M: 0.0552 c. 461: 214 23 224 SP T3 SD: 0.0263 c. M: 0.0395 c. 599: 278 30 291 SP T3 SD: 0.0165 c. M: 0.0280 c. 739: 343 37 359 SP T3 SD: 0.0106 c. M:-0.0146 c. 879: 408 44 427 SP T3 SD: 0.0119 c. M:-0.0207 c. 1060: 492 53 515 SP T3 SD: 0.0088 c. M: 0.0141 c. 1200: 557 60 583 SP T3 SD: 0.0037 c. M: 0.0062 c. 1939: 900 97 942 SP T3 SD: 0.0021 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 7:8 x 9 S SD: 31.4805 cents 8:9 x 11 SD: 29.9221 cents 9:10 x 12 S SD: 24.3852 cents 11 x 13:15 SD: 25.5487 cents 12 x 14:16 S SD: 5.3933 cents 13 x 15:17 SD: 17.3186 cents 14:16 x 19 SD: 15.3211 cents 15:17 x 20 SD: 7.2437 cents 18 x 21:24 S SD: 5.3933 cents 19 x 22:25 SD: 11.5218 cents 20:23 x 27 SD: 12.0299 cents 21:24 x 28 S SD: 0.0000 cents 25 x 29:33 SD: 8.7105 cents 26 x 30:35 SD: 9.2746 cents 27:31 x 36 SD: 3.9982 cents 28:32 x 37 SD: 7.7634 cents 30:34:35:40 SD: 6.0207 cents 32 x 37:43 SD: 7.1412 cents 33 x 38:44 SD: 5.9221 cents 34:39 x 45 SD: 7.1345 cents 36:41:42:48 SD: 4.1178 cents 39 x 45:52 SD: 4.1717 cents 40:46 x 53 SD: 7.6512 cents 41:47:48:55 SD: 6.8398 cents 42:48:49:56 S SD: 3.5955 cents 46 x 53:61 SD: 7.1907 cents 47:54 x 63 SD: 6.4943 cents 48:55:56:64 SD: 3.8962 cents 49:56:57:65 SD: 3.5162 cents 50:57:58:67 SD: 3.2332 cents 51:58:59:68 SD: 3.1090 cents 53:61 x 71 SD: 7.3376 cents 54:62:63:72 SD: 4.4758 cents 55:63:64:73 SD: 3.6077 cents 56:64:65:75 SD: 2.6499 cents 57:65:66:76 SD: 1.4773 cents 63:72:73:84 SD: 0.3436 cents 288:329:334:384 SD: 0.2921 cents 294:336:341:392 SD: 0.2208 cents 351:401:407:468 SD: 0.2146 cents 357:408:414:476 SD: 0.1212 cents 420:480:487:560 SD: 0.0515 cents 483:552:560:644 SD: 0.0000 cents