Scala analysis: 354_C29
Chromatic tetrachord 55/52 * 12/11 * 52/45
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/52 97.103994 2: 15/13 247.741053 tridecimal 5/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/45 250.3039 1: 55/52 97.1040 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 52/45 250.3039
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/52 97.104 cents 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 52/45 250.304 cents 2: 1 15/13 247.741 cents tridecimal 5/4-tone 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 208/165 400.941 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 : 97.1 247.7 498.0 97.1 : 150.6 400.9 498.0 247.7: 250.3 347.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.1040 .. 250.3039 cents 2704/2475, 153.2000 cents 55/52, 97.1040 cents 2: 247.7411 .. 400.9410 cents 2704/2475, 153.2000 cents 675/676,-2.5629 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55/52, 97.1040 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 52/45, 250.3039 cents Average / Smallest step : 1.709662 Largest / Average step : 1.507719 Largest / Smallest step : 2.577689 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 149.05151 cents, oct.: 447.15452 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1554-tone equal temperament with octave 4/3 degrees: 303 773 1554 Least number of segments generator : 779 of 249.663 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1319 of 422.729 cents and inv. generated superset size: 46 = 43 more = 1533.333% 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 2.56289 cents Scale diversity : 1.129064 Lumma stability : 0.389941 Lumma impropriety factor : 0.005146 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 : 676/675, 2.5629 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 13 Odd number limit : 165 (O: 55 U: 165) Highest odd numerator or denominator: 55 Scale harmonicity : 0.017835 Average absolute harmonicity : 0.088944 Specific harmonicity : 0.081317 Fundamental : 1/156, -7.2854 octaves, 1.6771 Hz. Guide tone : 660, 9.3663 octaves, 172672.873 Hz. Exponens Consonantiae : 1.029600E+05, 16.65172 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 71.0, average 23.66667 Mersenne's string divisions : 2996 Sum of van Prooijen's expressibility: 3.39358, average 1.13119 Sum of Tenney's harmonic distance : 6.82558, average 2.27519 Vogel's harmonic complexity : 16.33333 Wille's k value : 82 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.69777, average 2.78296 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.66667 2 11: 0 .. 1 0.33333 1 13: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 15 27 27| Scale is weakly epimorphic with val: <6 10 16 24 25| Scale is weakly epimorphic with val: <6 10 16 27 28| Scale is weakly epimorphic with val: <6 10 17 24 26| Scale is weakly epimorphic with val: <6 10 17 27 29| Scale is weakly epimorphic with val: <6 10 18 23 25| Scale is weakly epimorphic with val: <6 10 18 24 27| Scale is weakly epimorphic with val: <6 10 18 27 30| Scale is weakly epimorphic with val: <6 10 19 23 26| Scale is weakly epimorphic with val: <6 10 19 24 28| Scale is weakly epimorphic with val: <6 10 19 26 26| Scale is weakly epimorphic with val: <6 11 15 27 27| Scale is weakly epimorphic with val: <6 11 16 24 25| Scale is weakly epimorphic with val: <6 11 16 27 28| Scale is weakly epimorphic with val: <6 11 17 24 26| Scale is weakly epimorphic with val: <6 11 17 25 25| Scale is weakly epimorphic with val: <6 11 17 27 29| Scale is weakly epimorphic with val: <6 11 18 24 27| Scale is weakly epimorphic with val: <6 11 18 25 26| Scale is weakly epimorphic with val: <6 11 18 27 30| Scale is weakly epimorphic with val: <6 11 19 24 28| Scale is weakly epimorphic with val: <6 11 19 25 27| Scale is weakly epimorphic with val: <7 10 17 25 25| Scale is weakly epimorphic with val: <7 10 18 23 25| Scale is weakly epimorphic with val: <7 10 18 25 26| Scale is weakly epimorphic with val: <7 10 19 23 26| Scale is weakly epimorphic with val: <7 10 19 25 27| Scale is weakly epimorphic with val: <7 10 19 26 26| Scale is weakly epimorphic with val: <7 11 15 23 25| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 24 27| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 16 23 26| Scale is weakly epimorphic with val: <7 11 16 23 29| Scale is JI-epimorphic with val: <7 11 16 24 25| Scale is weakly epimorphic with val: <7 11 16 24 28| Scale is weakly epimorphic with val: <7 11 16 26 26| Scale is weakly epimorphic with val: <7 11 16 26 29| Scale is weakly epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 17 23 27| Scale is weakly epimorphic with val: <7 11 17 23 30| Scale is JI-epimorphic with val: <7 11 17 24 26| Scale is weakly epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 18 23 25| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is JI-epimorphic with val: <7 11 18 24 27| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 19 23 26| Scale is weakly epimorphic with val: <7 11 19 23 29| Scale is weakly epimorphic with val: <7 11 19 24 25| Scale is JI-epimorphic with val: <7 11 19 24 28| Scale is weakly epimorphic with val: <7 11 19 26 26| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 12 16 24 25| Scale is weakly epimorphic with val: <7 12 17 24 26| Scale is weakly epimorphic with val: <7 12 17 25 25| Scale is weakly epimorphic with val: <7 12 18 24 27| Scale is weakly epimorphic with val: <7 12 18 25 26| Scale is weakly epimorphic with val: <7 12 18 27 27| Scale is weakly epimorphic with val: <7 12 19 24 28| Scale is weakly epimorphic with val: <7 12 19 25 27| Scale is weakly epimorphic with val: <7 12 19 27 28| Scale is weakly epimorphic with val: <8 11 17 25 25| Scale is weakly epimorphic with val: <8 11 18 25 26| Scale is weakly epimorphic with val: <8 11 19 25 27| Scale is weakly epimorphic with val: <8 11 19 26 26| Scale is weakly epimorphic with val: <8 12 16 24 25| Scale is weakly epimorphic with val: <8 12 17 24 26| Scale is weakly epimorphic with val: <8 12 18 24 27| Scale is weakly epimorphic with val: <8 12 18 27 27| Scale is weakly epimorphic with val: <8 12 19 24 28| Scale is weakly epimorphic with val: <8 12 19 26 26| Scale is weakly epimorphic with val: <8 12 19 27 28|
FIT/MODE
3: 0 1 2 N G T3 SD: 73.2765 c. M: 97.1040 c. 4: 1 1 2 P M ME S SD: 15.8409 c. M:-27.4073 c. 6: 1 2 3 P T3 SD: 8.1722 c. M: 14.0965 c. 10: 2 3 5 P T3 SD: 1.6245 c. M:-2.5050 c. 26: 5 8 13 P T3 SD: 1.0647 c. M: 1.3261 c. 36: 7 11 18 P T3 SD: 0.7551 c. M:-1.2814 c. 46: 9 14 23 P T3 SD: 0.7654 c. M:-1.2814 c. 56: 11 17 28 P T3 SD: 0.8504 c. M:-1.2814 c. 62: 12 19 31 P T3 SD: 0.8453 c. M:-1.2814 c. 82: 16 25 41 P T3 SD: 0.7411 c. M:-1.2814 c. 98: 19 30 49 P T3 SD: 0.8038 c. M:-1.2814 c. 103: 20 31 52 N T3 SD: 0.6948 c. M: 1.1362 c. 107: 21 32 54 N T3 SD: 0.7089 c. M: 1.0459 c. 113: 22 34 57 N T3 SD: 0.5385 c. M: 0.9223 c. 117: 23 35 59 N T3 SD: 0.6735 c. M: 0.8470 c. 119: 23 36 60 N T3 SD: 0.6755 c. M: 0.8432 c. 123: 24 37 62 N T3 SD: 0.4313 c. M: 0.7431 c. 129: 25 39 65 N T3 SD: 0.5039 c. M: 0.6490 c. 133: 26 40 67 N T3 SD: 0.3723 c. M: 0.5909 c. 139: 27 42 70 N T3 SD: 0.3609 c. M: 0.5101 c. 143: 28 43 72 N T3 SD: 0.3578 c. M: 0.4600 c. 149: 29 45 75 N T3 SD: 0.2453 c. M: 0.3898 c. 159: 31 48 80 N T3 SD: 0.1644 c. M: 0.2847 c. 169: 33 51 85 N T3 SD: 0.1398 c. M: 0.1921 c. 185: 36 56 93 N T3 SD: 0.1143 c. M: 0.1871 c. 195: 38 59 98 N T3 SD: 0.0284 c. M: 0.0491 c. 400: 78 121 201 N T3 SD: 0.0226 c. M:-0.0363 c. 595: 116 180 299 N T3 SD: 0.0154 c. M:-0.0259 c. 790: 154 239 397 N T3 SD: 0.0153 c. M:-0.0206 c. 959: 187 290 482 N T3 SD: 0.0120 c. M: 0.0169 c. 1154: 225 349 580 N T3 SD: 0.0078 c. M: 0.0133 c. 1349: 263 408 678 N T3 SD: 0.0070 c. M: 0.0107 c. 1554: 303 470 781 N T3 SD: 0.0030 c. M:-0.0052 c. 1749: 341 529 879 N T3 SD: 0.0005 c. M: 0.0009 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: 54.1875 cents 6 x 7:8 S SD: 9.5649 cents 7 x 8:9 S SD: 32.5520 cents 8 x 9:11 SD: 34.4934 cents 9 x 10:12 S SD: 32.6687 cents 11:12:13:15 SD: 26.0322 cents 12:13:14:16 S SD: 15.2228 cents 14:15:16:19 SD: 13.7938 cents 15:16:17:20 SD: 11.4423 cents 18:19:21:24 SD: 6.4825 cents 32:34:37:43 SD: 5.3348 cents 33:35:38:44 SD: 1.9703 cents 51:54:59:68 SD: 1.6281 cents 72:76:83:96 SD: 1.2836 cents 84:89:97:112 SD: 1.0984 cents 105:111:121:140 SD: 0.7922 cents 123:130:142:164 SD: 0.5290 cents 156:165:180:208 SD: 0.0000 cents