Scala analysis: 229_C14
Chromatic tetrachord 34/33 * 6/5 * 55/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 68/55 367.323753 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 55/51 130.7212 1: 34/33 51.6825 2: 6/5 315.6413 minor third 3: 55/51 130.7212
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 55/51 130.721 cents 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 68/55 367.324 cents 2: 1 22/17 446.363 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 : 51.7 367.3 498.0 51.7 : 315.6 446.4 498.0 367.3: 130.7 182.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 315.6413 cents 99/85, 263.9588 cents 34/33, 51.6825 cents 2: 182.4037 .. 446.3625 cents 99/85, 263.9588 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 3.212211 Largest / Average step : 1.901282 Largest / Smallest step : 6.107319 Median interval of one step : 55/51, 130.7212 cents, amount: 1 Least squares average step : 162.89036 cents, oct.: 488.67107 cents Scale is not proper Scale has trivalence property Scale is a mode of a 983-tone equal temperament with octave 4/3 degrees: 102 725 983 Least number of segments generator : 492 of 249.276 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 795 of 402.793 cents and inv. generated superset size: 31 = 28 more = 1033.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 51.68247 cents Scale diversity : 0.866972 Lumma stability : 0.207541 Lumma impropriety factor : 0.267521 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 : 34/33, 51.6825 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 : 17 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.016845 Average absolute harmonicity : 0.083722 Specific harmonicity : 0.069545 Fundamental : 1/165, -7.3663 octaves, 1.5856 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.122000E+04, 13.45379 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 98.5, average 32.83333 Mersenne's string divisions : 57687 Sum of van Prooijen's expressibility: 3.73600, average 1.24533 Sum of Tenney's harmonic distance : 7.70205, average 2.56735 Vogel's harmonic complexity : 21.00000 Wille's k value : 42 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.34592, average 2.05765 Lattice compactness (without 2's) : 9.29253, average 1.54875 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.66667 2 17: 0 .. 1 0.66667 2 2 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 23 30| Scale is weakly epimorphic with val: <6 10 15 24 31| Scale is weakly epimorphic with val: <6 10 15 25 32| Scale is weakly epimorphic with val: <6 10 15 26 33| Scale is weakly epimorphic with val: <6 10 17 23 31| Scale is weakly epimorphic with val: <6 10 17 24 32| Scale is weakly epimorphic with val: <6 10 17 25 33| Scale is weakly epimorphic with val: <6 10 18 23 30| Scale is weakly epimorphic with val: <6 10 18 24 31| Scale is weakly epimorphic with val: <6 10 18 25 32| Scale is weakly epimorphic with val: <6 10 18 26 33| Scale is weakly epimorphic with val: <6 11 15 23 31| Scale is weakly epimorphic with val: <6 11 15 24 32| Scale is weakly epimorphic with val: <6 11 15 25 33| Scale is weakly epimorphic with val: <6 11 16 23 30| Scale is weakly epimorphic with val: <6 11 16 24 31| Scale is weakly epimorphic with val: <6 11 16 25 32| Scale is weakly epimorphic with val: <6 11 16 26 33| Scale is weakly epimorphic with val: <6 11 18 23 31| Scale is weakly epimorphic with val: <6 11 18 24 32| Scale is weakly epimorphic with val: <6 11 18 25 33| Scale is weakly epimorphic with val: <6 11 19 23 33| Scale is weakly epimorphic with val: <7 10 15 23 29| Scale is weakly epimorphic with val: <7 10 15 24 30| Scale is weakly epimorphic with val: <7 10 15 25 31| Scale is weakly epimorphic with val: <7 10 15 26 32| Scale is weakly epimorphic with val: <7 10 15 27 33| Scale is weakly epimorphic with val: <7 10 16 23 28| Scale is weakly epimorphic with val: <7 10 16 24 29| Scale is weakly epimorphic with val: <7 10 16 25 30| Scale is weakly epimorphic with val: <7 10 16 26 31| Scale is weakly epimorphic with val: <7 10 16 27 32| Scale is weakly epimorphic with val: <7 10 18 23 29| Scale is weakly epimorphic with val: <7 10 18 24 30| Scale is weakly epimorphic with val: <7 10 18 25 31| Scale is weakly epimorphic with val: <7 10 18 26 32| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 19 23 31| Scale is weakly epimorphic with val: <7 10 19 24 32| Scale is weakly epimorphic with val: <7 10 19 25 33| Scale is weakly epimorphic with val: <7 11 16 23 29| Scale is weakly epimorphic with val: <7 11 16 23 32| Scale is weakly epimorphic with val: <7 11 16 24 27| Scale is weakly epimorphic with val: <7 11 16 24 30| Scale is weakly epimorphic with val: <7 11 16 24 33| Scale is weakly epimorphic with val: <7 11 16 25 28| Scale is weakly epimorphic with val: <7 11 16 25 31| Scale is weakly epimorphic with val: <7 11 16 26 29| Scale is weakly epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 16 27 27| Scale is weakly epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is JI-epimorphic with val: <7 11 17 23 28| Scale is weakly epimorphic with val: <7 11 17 23 31| Scale is JI-epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 24 32| Scale is weakly epimorphic with val: <7 11 17 25 27| Scale is JI-epimorphic with val: <7 11 17 25 30| = patent Scale is weakly epimorphic with val: <7 11 17 25 33| Scale is weakly epimorphic with val: <7 11 17 26 28| Scale is JI-epimorphic with val: <7 11 17 26 31| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is JI-epimorphic with val: <7 11 17 27 32| Scale is weakly epimorphic with val: <7 11 19 23 29| Scale is weakly epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 24 27| Scale is weakly epimorphic with val: <7 11 19 24 30| Scale is weakly epimorphic with val: <7 11 19 24 33| Scale is weakly epimorphic with val: <7 11 19 25 28| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 12 15 23 31| Scale is weakly epimorphic with val: <7 12 15 24 32| Scale is weakly epimorphic with val: <7 12 15 25 33| Scale is weakly epimorphic with val: <7 12 17 23 29| Scale is weakly epimorphic with val: <7 12 17 24 30| Scale is weakly epimorphic with val: <7 12 17 25 31| Scale is weakly epimorphic with val: <7 12 17 26 32| Scale is weakly epimorphic with val: <7 12 17 27 33| Scale is weakly epimorphic with val: <7 12 18 23 31| Scale is weakly epimorphic with val: <7 12 18 24 32| Scale is weakly epimorphic with val: <7 12 18 25 33| Scale is weakly epimorphic with val: <8 11 15 23 29| Scale is weakly epimorphic with val: <8 11 15 24 30| Scale is weakly epimorphic with val: <8 11 15 25 31| Scale is weakly epimorphic with val: <8 11 15 26 32| Scale is weakly epimorphic with val: <8 11 15 27 33| Scale is weakly epimorphic with val: <8 11 17 23 27| Scale is weakly epimorphic with val: <8 11 17 24 28| Scale is weakly epimorphic with val: <8 11 17 25 29| Scale is weakly epimorphic with val: <8 11 17 26 30| Scale is weakly epimorphic with val: <8 11 17 27 31| Scale is weakly epimorphic with val: <8 11 18 23 29| Scale is weakly epimorphic with val: <8 11 18 24 30| Scale is weakly epimorphic with val: <8 11 18 25 31| Scale is weakly epimorphic with val: <8 11 18 26 32| Scale is weakly epimorphic with val: <8 11 18 27 33| Scale is weakly epimorphic with val: <8 12 15 23 30| Scale is weakly epimorphic with val: <8 12 15 24 31| Scale is weakly epimorphic with val: <8 12 15 25 32| Scale is weakly epimorphic with val: <8 12 15 26 33| Scale is weakly epimorphic with val: <8 12 16 24 27| Scale is weakly epimorphic with val: <8 12 16 25 28| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 16 27 30| Scale is weakly epimorphic with val: <8 12 18 23 30| Scale is weakly epimorphic with val: <8 12 18 24 31| Scale is weakly epimorphic with val: <8 12 18 25 32| Scale is weakly epimorphic with val: <8 12 18 26 33| Scale is weakly epimorphic with val: <8 12 19 23 29| Scale is weakly epimorphic with val: <8 12 19 24 30| Scale is weakly epimorphic with val: <8 12 19 25 31| Scale is weakly epimorphic with val: <8 12 19 26 32| Scale is weakly epimorphic with val: <8 12 19 27 33|
FIT/MODE
3: 0 2 1 N G T3 SD: 36.1327 c. M: 51.6825 c. 4: 0 3 1 N G T3 SD: 30.0535 c. M: 51.6825 c. 6: 1 3 2 P T3 SD: 27.2452 c. M: 35.2938 c. 7: 1 4 2 N T3 SD: 13.0766 c. M:-19.4668 c. 8: 1 5 2 N T3 SD: 7.0794 c. M:-10.5732 c. 11: 1 7 3 N T3 SD: 4.7306 c. M: 6.4056 c. 19: 2 12 5 N T3 SD: 0.4727 c. M:-0.7433 c. 87: 9 55 23 N T3 SD: 0.5539 c. M: 0.9458 c. 88: 9 56 23 N T3 SD: 0.5353 c. M: 0.7460 c. 106: 11 67 28 N T3 SD: 0.4837 c. M: 0.8378 c. 107: 11 68 28 N T3 SD: 0.3584 c. M: 0.4816 c. 126: 13 80 33 N T3 SD: 0.2360 c. M: 0.2969 c. 145: 15 92 38 N T3 SD: 0.1477 c. M:-0.1991 c. 164: 17 104 43 N T3 SD: 0.0850 c. M:-0.1363 c. 183: 19 116 48 N T3 SD: 0.0523 c. M:-0.0865 c. 385: 40 244 101 N T3 SD: 0.0522 c. M:-0.0653 c. 568: 59 360 149 N T3 SD: 0.0510 c. M:-0.0721 c. 579: 60 367 152 N T3 SD: 0.0440 c. M: 0.0716 c. 598: 62 379 157 N T3 SD: 0.0337 c. M: 0.0457 c. 617: 64 391 162 N T3 SD: 0.0292 c. M: 0.0458 c. 762: 79 483 200 N T3 SD: 0.0276 c. M: 0.0479 c. 781: 81 495 205 N T3 SD: 0.0171 c. M: 0.0286 c. 800: 83 507 210 N T3 SD: 0.0108 c. M: 0.0156 c. 983: 102 623 258 N T3 SD: 0.0028 c. M:-0.0034 c. 1985: 206 1258 521 N T3 SD: 0.0022 c. M:-0.0038 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: 18.9900 cents 5 x 6:7 S SD: 49.5121 cents 6 x 7:8 S SD: 50.2264 cents 7 x x 9 SD: 62.9609 cents 8:9:10:11 H SD: 54.1314 cents 9:10:11:12 H SD: 44.0766 cents 10:11:12:13 H SD: 44.0127 cents 11:12:14:15 S SD: 39.1920 cents 12:13:15:16 SD: 29.6470 cents 13:14:16:17 S SD: 28.0114 cents 14:15:17:19 SD: 26.8814 cents 15:16:19:20 SD: 24.4113 cents 16:17:20:21 SD: 20.9283 cents 17:18:21:23 SD: 17.8751 cents 18:19:22:24 SD: 15.4703 cents 20:21:25:27 SD: 14.5219 cents 21:22:26:28 SD: 9.6520 cents 24:25:30:32 S SD: 8.9520 cents 25:26:31:33 SD: 8.1077 cents 26:27:32:35 SD: 7.6199 cents 29:30:36:39 S SD: 5.9543 cents 30:31:37:40 SD: 2.2086 cents 63:65:78:84 SD: 1.1422 cents 93:96:115:124 SD: 1.0978 cents 102:105:126:136 SD: 0.7063 cents 135:139:167:180 SD: 0.4910 cents 165:170:204:220 SD: 0.0000 cents