Scala analysis: 180_C8
Chromatic tetrachord 56/55 * 15/14 * 11/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/55 31.194250 undecimal diesis, konbini comma 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: 56/55 31.1943 undecimal diesis, konbini comma 2: 15/14 119.4428 major diatonic semitone 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 15/14 119.443 cents major 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 56/45 378.602 cents septimal narrow major third 2: 1 55/42 466.851 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 : 31.2 150.6 498.0 31.2 : 119.4 466.9 498.0 150.6: 347.4 378.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 347.4079 cents 605/504, 316.2137 cents 56/55, 31.1943 cents 2: 150.6371 .. 466.8507 cents 605/504, 316.2137 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 5.321974 Largest / Average step : 2.092630 Largest / Smallest step : 11.136922 Median interval of one step : 15/14, 119.4428 cents, amount: 1 Least squares average step : 130.47167 cents, oct.: 391.41501 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1501-tone equal temperament with octave 4/3 degrees: 94 454 1501 Least number of segments generator : 751 of 249.188 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1137 of 377.267 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 31.19425 cents Scale diversity : 0.624612 Lumma stability : 0.125267 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 : 56/55, 31.1943 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 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.023148 Average absolute harmonicity : 0.094820 Specific harmonicity : 0.108265 Fundamental : 1/165, -7.3663 octaves, 1.5856 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 2.772000E+04, 14.75864 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 70.5, average 23.50000 Mersenne's string divisions : 17871 Sum of van Prooijen's expressibility: 3.25888, average 1.08629 Sum of Tenney's harmonic distance : 6.68831, average 2.22944 Vogel's harmonic complexity : 14.66667 Wille's k value : 27 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.62180, average 2.43697 Lattice compactness (without 2's) : 10.11438, average 1.68573 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.00000 2 1 5: -1 .. 0 -0.33333 1 7: 0 .. 1 0.33333 1 11: -1 .. 0 -0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 15 22 25| Scale is JI-epimorphic with val: <7 11 15 18 23| Scale is weakly epimorphic with val: <7 11 15 18 26| Scale is weakly epimorphic with val: <7 11 15 20 24| Scale is weakly epimorphic with val: <7 11 15 20 27| Scale is weakly epimorphic with val: <7 11 15 21 23| Scale is weakly epimorphic with val: <7 11 15 21 26| Scale is weakly epimorphic with val: <7 11 16 18 24| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is JI-epimorphic with val: <7 11 16 19 23| Scale is weakly epimorphic with val: <7 11 16 19 26| Scale is weakly epimorphic with val: <7 11 16 21 24| Scale is weakly epimorphic with val: <7 11 16 21 27| Scale is weakly epimorphic with val: <7 11 16 22 23| Scale is weakly epimorphic with val: <7 11 16 22 26| Scale is weakly epimorphic with val: <7 11 17 19 24| Scale is weakly epimorphic with val: <7 11 17 19 27| Scale is JI-epimorphic with val: <7 11 17 20 23| Scale is weakly epimorphic with val: <7 11 17 20 26| Scale is weakly epimorphic with val: <7 11 17 22 24| Scale is weakly epimorphic with val: <7 11 17 22 27| Scale is weakly epimorphic with val: <7 11 18 18 23| Scale is weakly epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 20 24| Scale is weakly epimorphic with val: <7 11 18 20 27| Scale is JI-epimorphic with val: <7 11 18 21 23| Scale is weakly epimorphic with val: <7 11 18 21 26| Scale is weakly epimorphic with val: <7 11 19 19 23| Scale is weakly epimorphic with val: <7 11 19 19 26| Scale is weakly epimorphic with val: <7 11 19 21 24| Scale is weakly epimorphic with val: <7 11 19 21 27| Scale is JI-epimorphic with val: <7 11 19 22 23| Scale is weakly epimorphic with val: <7 11 19 22 26| Scale is weakly epimorphic with val: <7 12 15 18 23| Scale is weakly epimorphic with val: <7 12 15 21 23| Scale is weakly epimorphic with val: <7 12 15 22 25| Scale is weakly epimorphic with val: <7 12 16 19 23| Scale is weakly epimorphic with val: <7 12 16 22 23| Scale is weakly epimorphic with val: <7 12 17 20 23| Scale is weakly epimorphic with val: <7 12 18 18 23| Scale is weakly epimorphic with val: <7 12 18 21 23| Scale is weakly epimorphic with val: <7 12 19 19 23| Scale is weakly epimorphic with val: <7 12 19 22 23| Scale is weakly epimorphic with val: <8 11 15 19 24| Scale is weakly epimorphic with val: <8 11 15 20 26| Scale is weakly epimorphic with val: <8 11 15 22 24| Scale is weakly epimorphic with val: <8 11 16 18 23| Scale is weakly epimorphic with val: <8 11 16 20 24| Scale is weakly epimorphic with val: <8 11 16 21 26| Scale is weakly epimorphic with val: <8 11 17 18 24| Scale is weakly epimorphic with val: <8 11 17 19 23| Scale is weakly epimorphic with val: <8 11 17 21 24| Scale is weakly epimorphic with val: <8 11 17 22 26| Scale is weakly epimorphic with val: <8 11 18 19 24| Scale is weakly epimorphic with val: <8 11 18 20 23| Scale is weakly epimorphic with val: <8 11 18 22 24| Scale is weakly epimorphic with val: <8 11 19 20 24| Scale is weakly epimorphic with val: <8 11 19 21 23| Scale is weakly epimorphic with val: <8 12 15 18 25| Scale is weakly epimorphic with val: <8 12 15 20 26| Scale is weakly epimorphic with val: <8 12 15 21 25| Scale is weakly epimorphic with val: <8 12 16 18 23| Scale is weakly epimorphic with val: <8 12 16 19 25| Scale is weakly epimorphic with val: <8 12 16 21 26| Scale is weakly epimorphic with val: <8 12 16 22 25| Scale is weakly epimorphic with val: <8 12 17 19 23| Scale is weakly epimorphic with val: <8 12 17 20 25| Scale is weakly epimorphic with val: <8 12 17 22 26| Scale is weakly epimorphic with val: <8 12 18 18 25| Scale is weakly epimorphic with val: <8 12 18 20 23| Scale is weakly epimorphic with val: <8 12 18 21 25| Scale is weakly epimorphic with val: <8 12 19 19 25| Scale is weakly epimorphic with val: <8 12 19 21 23| Scale is weakly epimorphic with val: <8 12 19 22 25|
FIT/MODE
3: 0 1 2 N G T3 SD: 20.0795 c. M: 31.1943 c. 4: 0 1 3 N G T3 SD: 23.4921 c. M: 31.1943 c. 6: 0 2 4 N G T3 SD: 20.0795 c. M: 31.1943 c. 7: 0 2 5 N G T3 SD: 18.6423 c. M: 31.1943 c. 9: 1 2 6 N T3 SD: 16.5269 c. M:-24.1441 c. 10: 1 2 7 N T3 SD: 10.7678 c. M:-18.6102 c. 11: 1 2 8 N T3 SD: 11.7977 c. M: 14.8066 c. 12: 1 3 8 N T3 SD: 10.6890 c. M:-15.3779 c. 13: 1 3 9 N T3 SD: 4.3761 c. M:-7.1169 c. 16: 1 4 11 N T3 SD: 2.8882 c. M:-5.0020 c. 17: 1 4 12 N T3 SD: 2.6363 c. M: 4.1532 c. 29: 2 7 20 N T3 SD: 2.9086 c. M:-3.9286 c. 30: 2 7 21 N T3 SD: 1.3580 c. M:-2.0087 c. 33: 2 8 23 N T3 SD: 0.6058 c. M: 1.0097 c. 63: 4 15 44 N T3 SD: 0.3514 c. M: 0.4330 c. 96: 6 23 67 N T3 SD: 0.1140 c. M: 0.1860 c. 271: 17 65 189 N T3 SD: 0.0458 c. M:-0.0629 c. 367: 23 88 256 N T3 SD: 0.0107 c. M:-0.0184 c. 1134: 71 272 791 N T3 SD: 0.0076 c. M: 0.0115 c. 1501: 94 360 1047 N T3 SD: 0.0034 c. M: 0.0042 c. 1868: 117 448 1303 N T3 SD: 0.0017 c. M:-0.0029 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 x 20:24 S SD: 15.8833 cents 23:24:25:31 SD: 15.6165 cents 24:25:26:32 SD: 13.7602 cents 29:30:32:39 SD: 12.3307 cents 30:31:33:40 SD: 9.7774 cents 31:32:34:41 SD: 9.7051 cents 32:33:35:43 SD: 8.7512 cents 33:34:36:44 SD: 6.8294 cents 36:37:39:48 SD: 6.7436 cents 41:42:45:55 SD: 6.0762 cents 42:43:46:56 SD: 3.9168 cents 45:46:49:60 SD: 2.5234 cents 54:55:59:72 SD: 0.9101 cents 111:113:121:148 SD: 0.4432 cents 165:168:180:220 SD: 0.0000 cents