Scala analysis: 179_C8
Chromatic tetrachord 45/44 * 16/15 * 11/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/44 38.905773 1/5-tone 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 45/44 38.9058 1/5-tone 2: 16/15 111.7313 minor diatonic semitone 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 45/44 38.906 cents 1/5-tone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 5/4 386.314 cents major third 2: 1 176/135 459.139 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 : 38.9 150.6 498.0 38.9 : 111.7 459.1 498.0 150.6: 347.4 386.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.9058 .. 347.4079 cents 484/405, 308.5022 cents 45/44, 38.9058 cents 2: 150.6371 .. 459.1392 cents 484/405, 308.5022 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 45/44, 38.9058 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 4.267104 Largest / Average step : 2.092630 Largest / Smallest step : 8.929470 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 131.02249 cents, oct.: 393.06748 cents Scale is not proper Scale has trivalence property Scale is a mode of a 896-tone equal temperament with octave 4/3 degrees: 70 271 896 Least number of segments generator : 449 of 249.578 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 507 of 281.818 cents and inv. generated superset size: 15 = 12 more = 500.000% 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 38.90577 cents Scale diversity : 0.679432 Lumma stability : 0.156234 Lumma impropriety factor : 0.395087 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 : 45/44, 38.9058 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% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 11 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.027336 Average absolute harmonicity : 0.096461 Specific harmonicity : 0.120669 Fundamental : 1/132, -7.0444 octaves, 1.9820 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 2.376000E+04, 14.53625 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 59.5, average 19.83333 Mersenne's string divisions : 14329 Sum of van Prooijen's expressibility: 3.17173, average 1.05724 Sum of Tenney's harmonic distance : 6.49642, average 2.16547 Vogel's harmonic complexity : 13.00000 Wille's k value : 67 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 19.52270, average 3.25378 Lattice compactness (without 2's) : 11.83061, average 1.97177 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.66667 6 3: -1 .. 2 0.66667 4 1 5: 0 .. 1 0.33333 1 11: -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 19 24| Scale is weakly epimorphic with val: <6 11 17 24| Scale is weakly epimorphic with val: <7 11 15 24| Scale is weakly epimorphic with val: <7 11 15 27| Scale is JI-epimorphic with val: <7 11 16 23| Scale is weakly epimorphic with val: <7 11 16 26| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 19 23| Scale is weakly epimorphic with val: <7 11 19 26| Scale is weakly epimorphic with val: <7 12 17 23| Scale is weakly epimorphic with val: <7 12 18 25| Scale is weakly epimorphic with val: <8 11 16 24| Scale is weakly epimorphic with val: <8 11 19 24| Scale is weakly epimorphic with val: <8 12 16 25| Scale is weakly epimorphic with val: <8 12 18 23| Scale is weakly epimorphic with val: <8 12 19 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 24.1533 c. M: 38.9058 c. 4: 0 1 3 N G T3 SD: 27.0568 c. M: 38.9058 c. 6: 0 2 4 N G T3 SD: 24.1533 c. M: 38.9058 c. 7: 0 2 5 N G T3 SD: 22.9724 c. M: 38.9058 c. 8: 1 1 6 N M DE S SD: 20.2301 c. M: 26.1258 c. 9: 1 2 6 N T3 SD: 12.9937 c. M:-16.4326 c. 10: 1 2 7 N T3 SD: 6.3319 c. M:-10.8987 c. 13: 1 3 9 N T3 SD: 1.5441 c. M:-2.6076 c. 36: 3 8 25 N T3 SD: 1.7447 c. M:-2.5980 c. 37: 3 8 26 N T3 SD: 1.7110 c. M: 2.5696 c. 40: 3 9 28 N T3 SD: 1.1412 c. M: 1.5524 c. 50: 4 11 35 N T3 SD: 0.8901 c. M: 1.2236 c. 53: 4 12 37 N T3 SD: 0.7781 c. M: 1.3175 c. 63: 5 14 44 N T3 SD: 0.4374 c. M:-0.6216 c. 76: 6 17 53 N T3 SD: 0.2440 c. M:-0.4136 c. 116: 9 26 81 N T3 SD: 0.2601 c. M: 0.3649 c. 129: 10 29 90 N T3 SD: 0.1759 c. M: 0.2976 c. 192: 15 43 134 N T3 SD: 0.1074 c. M: 0.1860 c. 205: 16 46 143 N T3 SD: 0.0203 c. M: 0.0340 c. 691: 54 155 482 N T3 SD: 0.0089 c. M:-0.0153 c. 896: 70 201 625 N T3 SD: 0.0023 c. M:-0.0040 c. 1101: 86 247 768 N T3 SD: 0.0022 c. M: 0.0031 c. 1997: 156 448 1393 N T3 SD: 0.0009 c. M: 0.0015 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: 92.6837 cents 6 x 7:8 S SD: 58.1169 cents 7 x 8:9 S SD: 51.1133 cents 8 x 9:11 SD: 37.6697 cents 9 x 10:12 S SD: 15.8833 cents 10 x 11:13 SD: 23.0628 cents 11 x 12:15 S SD: 19.4529 cents 12 x 13:16 SD: 6.0322 cents 13 x 14:17 SD: 20.1813 cents 14 x 15:19 SD: 21.8633 cents 15 x 16:20 S SD: 19.4529 cents 16 x 17:21 SD: 26.5995 cents 17 x 19:23 SD: 24.4750 cents 18:19:20:24 S SD: 21.0842 cents 19:20:21:25 SD: 19.7975 cents 20:21:22:27 SD: 17.4635 cents 21:22:23:28 SD: 14.0640 cents 23:24:25:31 SD: 13.3295 cents 24:25:26:32 SD: 11.3268 cents 29:30:32:39 SD: 10.5609 cents 30:31:33:40 SD: 7.6408 cents 32:33:35:43 SD: 6.7347 cents 33:34:36:44 SD: 4.2589 cents 42:43:46:56 SD: 2.3656 cents 45:46:49:60 SD: 1.1070 cents 87:89:95:116 SD: 0.5718 cents 132:135:144:176 SD: 0.0000 cents