Scala analysis: 244_C16
Chromatic tetrachord 40/39 * 104/95 * 19/16
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: 64/57 200.531983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 40/39 43.8311 tridecimal minor diesis 2: 104/95 156.7009 3: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 104/95 156.701 cents 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 95/78 341.344 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 : 43.8 200.5 498.0 43.8 : 156.7 454.2 498.0 200.5: 297.5 341.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 297.5130 cents 741/640, 253.6820 cents 40/39, 43.8311 cents 2: 200.5320 .. 454.2139 cents 741/640, 253.6820 cents 1024/1083,-96.9810 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 : 19/16, 297.5130 cents Average / Smallest step : 3.787612 Largest / Average step : 1.792085 Largest / Smallest step : 6.787723 Median interval of one step : 104/95, 156.7009 cents, amount: 1 Least squares average step : 138.50214 cents, oct.: 415.50643 cents Scale is not proper Scale has trivalence property Scale is a mode of a 909-tone equal temperament with octave 4/3 degrees: 80 366 909 Least number of segments generator : 455 of 249.296 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 623 of 341.344 cents and inv. generated superset size: 77 = 74 more = 2566.667% 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 43.83105 cents Scale diversity : 0.809712 Lumma stability : 0.176012 Lumma impropriety factor : 0.194723 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 : 40/39, 43.8311 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 : 19 Odd number limit : 95 (O: 95 U: 95) Highest odd numerator or denominator: 57 Scale harmonicity : 0.014020 Average absolute harmonicity : 0.088962 Specific harmonicity : 0.074426 Fundamental : 1/741, -9.5333 octaves, 0.3531 Hz. Guide tone : 320, 8.3219 octaves, 83720.181 Hz. Exponens Consonantiae : 2.371200E+05, 17.85526 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 103.5, average 34.50000 Mersenne's string divisions : 66913 Sum of van Prooijen's expressibility: 3.82406, average 1.27469 Sum of Tenney's harmonic distance : 7.83436, average 2.61145 Vogel's harmonic complexity : 26.66667 Wille's k value : 123 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 21.18384, average 3.53064 Lattice compactness (without 2's) : 8.29253, average 1.38209 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 3.66667 11 3: -1 ..-1 -1.00000 3 1 5: 0 .. 1 0.33333 1 13: -1 .. 0 -0.33333 1 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 15 27 29| Scale is weakly epimorphic with val: <7 10 16 25 29| Scale is weakly epimorphic with val: <7 10 16 28 29| 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 26 29| Scale is weakly epimorphic with val: <7 10 17 29 29| Scale is weakly epimorphic with val: <7 10 18 26 30| Scale is weakly epimorphic with val: <7 10 18 26 33| Scale is weakly epimorphic with val: <7 10 18 27 29| Scale is weakly epimorphic with val: <7 10 19 25 29| Scale is weakly epimorphic with val: <7 10 19 27 30| Scale is weakly epimorphic with val: <7 10 19 27 33| Scale is weakly epimorphic with val: <7 10 19 28 29| Scale is weakly epimorphic with val: <7 11 15 26 30| Scale is weakly epimorphic with val: <7 11 15 26 33| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 29 30| Scale is weakly epimorphic with val: <7 11 15 29 33| Scale is weakly epimorphic with val: <7 11 15 30 32| Scale is JI-epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 25 32| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is weakly epimorphic with val: <7 11 16 28 29| Scale is weakly epimorphic with val: <7 11 16 28 32| Scale is weakly epimorphic with val: <7 11 16 30 30| Scale is weakly epimorphic with val: <7 11 16 30 33| Scale is weakly epimorphic with val: <7 11 17 25 30| Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is JI-epimorphic with val: <7 11 17 26 29| Scale is weakly epimorphic with val: <7 11 17 26 32| 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 29 29| Scale is weakly epimorphic with val: <7 11 17 29 32| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 26 33| Scale is JI-epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 29 30| Scale is weakly epimorphic with val: <7 11 18 29 33| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is weakly epimorphic with val: <7 11 19 25 32| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is JI-epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 30 30| Scale is weakly epimorphic with val: <7 11 19 30 33| Scale is weakly epimorphic with val: <7 12 19 25 29| Scale is weakly epimorphic with val: <7 12 19 25 32| Scale is weakly epimorphic with val: <8 11 15 25 30| Scale is weakly epimorphic with val: <8 11 15 25 33| Scale is weakly epimorphic with val: <8 11 15 27 34| Scale is weakly epimorphic with val: <8 11 15 30 34| 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 28 34| Scale is weakly epimorphic with val: <8 11 17 26 34| Scale is weakly epimorphic with val: <8 11 17 27 30| Scale is weakly epimorphic with val: <8 11 17 27 33| Scale is weakly epimorphic with val: <8 11 17 29 34| Scale is weakly epimorphic with val: <8 11 18 27 34| Scale is weakly epimorphic with val: <8 11 18 28 30| Scale is weakly epimorphic with val: <8 11 18 28 33| Scale is weakly epimorphic with val: <8 11 18 30 34| Scale is weakly epimorphic with val: <8 11 19 25 34| Scale is weakly epimorphic with val: <8 11 19 28 34| 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 12 15 25 33| Scale is weakly epimorphic with val: <8 12 15 28 33| Scale is weakly epimorphic with val: <8 12 16 25 28| 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 28| Scale is weakly epimorphic with val: <8 12 17 26 31| Scale is weakly epimorphic with val: <8 12 17 26 34| Scale is weakly epimorphic with val: <8 12 17 27 33| Scale is weakly epimorphic with val: <8 12 17 30 33| Scale is weakly epimorphic with val: <8 12 18 25 33| Scale is weakly epimorphic with val: <8 12 18 27 28| Scale is weakly epimorphic with val: <8 12 18 27 31| Scale is weakly epimorphic with val: <8 12 18 27 34| Scale is weakly epimorphic with val: <8 12 18 28 33| Scale is weakly epimorphic with val: <8 12 19 26 33| Scale is weakly epimorphic with val: <8 12 19 28 28| 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 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 32.2107 c. M: 43.8311 c. 5: 0 2 3 N G T3 SD: 25.3172 c. M: 43.8311 c. 7: 1 2 4 N T3 SD: 17.4462 c. M:-27.3182 c. 8: 1 2 5 N T3 SD: 13.2783 c. M:-18.4246 c. 9: 1 3 5 N T3 SD: 13.7349 c. M:-20.8213 c. 10: 1 3 6 N T3 SD: 3.5312 c. M:-5.9734 c. 22: 2 7 13 N T3 SD: 2.0345 c. M:-3.2137 c. 32: 3 10 19 N T3 SD: 1.9510 c. M:-2.8607 c. 35: 3 11 21 N T3 SD: 1.0049 c. M: 1.3140 c. 45: 4 14 27 N T3 SD: 0.8000 c. M: 1.3140 c. 57: 5 18 34 N T3 SD: 0.2636 c. M:-0.4335 c. 102: 9 32 61 N T3 SD: 0.2056 c. M: 0.3374 c. 159: 14 50 95 N T3 SD: 0.0375 c. M: 0.0610 c. 375: 33 118 224 N T3 SD: 0.0084 c. M:-0.0141 c. 534: 47 168 319 N T3 SD: 0.0054 c. M: 0.0082 c. 909: 80 286 543 N T3 SD: 0.0009 c. M:-0.0013 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: 71.3878 cents 6 x 7:8 S SD: 33.1695 cents 7 x 8:9 S SD: 35.0108 cents 8 x 9:11 SD: 26.6900 cents 9 x 10:12 S SD: 9.0641 cents 10 x 11:13 SD: 28.2107 cents 11 x 12:15 S SD: 31.6353 cents 12 x 13:16 SD: 30.9797 cents 13 x 15:17 SD: 28.9776 cents 15:16:17:20 SD: 23.2652 cents 16:17:18:21 S SD: 22.3381 cents 17:18:19:23 SD: 20.3878 cents 18:19:20:24 S SD: 17.6569 cents 21:22:24:28 S SD: 15.9383 cents 22:23:25:29 SD: 14.6077 cents 23:24:26:31 SD: 12.3769 cents 24:25:27:32 SD: 9.0177 cents 27:28:30:36 S SD: 8.7850 cents 30:31:34:40 SD: 6.8985 cents 31:32:35:41 SD: 6.7666 cents 32:33:36:43 SD: 5.5984 cents 33:34:37:44 SD: 2.7427 cents 42:43:47:56 SD: 2.1931 cents 72:74:81:96 SD: 1.6463 cents 75:77:84:100 SD: 1.5554 cents 81:83:91:108 SD: 0.6303 cents 114:117:128:152 SD: 0.3795 cents 195:200:219:260 SD: 0.1387 cents 432:443:485:576 SD: 0.1182 cents 546:560:613:728 SD: 0.0495 cents