Scala analysis: 176_C8
Chromatic tetrachord 24/23 * 23/22 * 11/9, Winnington-Ingram
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 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: 24/23 73.6807 vicesimotertial minor semitone 2: 23/22 76.9564 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 23/22 76.956 cents 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 88/69 421.089 cents 2: 1 23/18 424.364 cents vicesimotertial major third 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 : 73.7 150.6 498.0 73.7 : 77.0 424.4 498.0 150.6: 347.4 421.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 347.4079 cents 253/216, 273.7273 cents 24/23, 73.6807 cents 2: 150.6371 .. 424.3643 cents 253/216, 273.7273 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 2.253169 Largest / Average step : 2.092630 Largest / Smallest step : 4.715050 Median interval of one step : 23/22, 76.9564 cents, amount: 1 Least squares average step : 133.50641 cents, oct.: 400.51924 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1825-tone equal temperament with octave 4/3 degrees: 270 552 1825 Least number of segments generator : 913 of 249.159 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 983 of 268.262 cents and inv. generated superset size: 36 = 33 more = 1200.000% 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 73.68065 cents Scale diversity : 0.805312 Lumma stability : 0.295880 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 : 529/528, 3.2758 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 : 2 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 Limited inverse transpositions with margin 270.4515 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 69 (O: 23 U: 69) Highest odd numerator or denominator: 23 Scale harmonicity : 0.014577 Average absolute harmonicity : 0.092997 Specific harmonicity : 0.076748 Fundamental : 1/759, -9.5680 octaves, 0.3447 Hz. Guide tone : 24, 4.5850 octaves, 6279.014 Hz. Exponens Consonantiae : 1.821600E+04, 14.15292 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 38.5, average 12.83333 Mersenne's string divisions : 7567 Sum of van Prooijen's expressibility: 2.88024, average 0.96008 Sum of Tenney's harmonic distance : 5.94169, average 1.98056 Vogel's harmonic complexity : 29.00000 Wille's k value : 126 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 14.41979, average 2.40330 Lattice compactness (without 2's) : 9.71478, average 1.61913 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.33333 3 1 11: -1 .. 0 -0.33333 1 1 23: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is JI-epimorphic with val: <7 11 23 31| Scale is weakly epimorphic with val: <7 11 23 34| Scale is weakly epimorphic with val: <7 11 24 30| Scale is weakly epimorphic with val: <7 11 24 33| Scale is weakly epimorphic with val: <7 11 24 36| Scale is weakly epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 34| Scale is weakly epimorphic with val: <7 11 27 30| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 11 27 36| Scale is weakly epimorphic with val: <7 12 23 32| Scale is weakly epimorphic with val: <7 12 23 35| Scale is weakly epimorphic with val: <7 12 25 30| Scale is weakly epimorphic with val: <8 11 23 32| Scale is weakly epimorphic with val: <8 11 24 31| Scale is weakly epimorphic with val: <8 11 24 34| Scale is weakly epimorphic with val: <8 11 26 32| Scale is weakly epimorphic with val: <8 12 23 33| Scale is weakly epimorphic with val: <8 12 25 31| Scale is weakly epimorphic with val: <8 12 25 34| Scale is weakly epimorphic with val: <8 12 26 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 43.4562 c. M: 73.6807 c. 4: 0 1 3 N G T3 SD: 45.1346 c. M: 73.6807 c. 6: 1 1 4 N M DE S SD: 10.3838 c. M:-15.3779 c. 7: 1 1 5 N M DE S SD: 5.0312 c. M: 8.3385 c. 13: 2 2 9 N M DE S SD: 2.2696 c. M:-2.9417 c. 20: 3 3 14 N M DE S SD: 0.9219 c. M: 1.2236 c. 33: 5 5 23 N M DE S SD: 1.0412 c. M:-1.7807 c. 53: 8 8 37 N M DE S SD: 0.8791 c. M:-1.4960 c. 73: 11 11 51 N M DE S SD: 0.8490 c. M:-1.3672 c. 76: 11 12 53 N T3 SD: 0.9224 c. M: 1.5952 c. 82: 12 13 57 N T3 SD: 0.8342 c. M:-1.2059 c. 89: 13 14 62 N T3 SD: 0.5991 c. M: 0.9325 c. 96: 14 15 67 N T3 SD: 0.6151 c. M: 1.0491 c. 102: 15 16 71 N T3 SD: 0.4915 c. M:-0.7296 c. 109: 16 17 76 N T3 SD: 0.3416 c. M: 0.5731 c. 122: 18 19 85 N T3 SD: 0.2627 c. M:-0.4094 c. 129: 19 20 90 N T3 SD: 0.1915 c. M: 0.3252 c. 142: 21 22 99 N T3 SD: 0.1047 c. M:-0.1794 c. 162: 24 25 113 N T3 SD: 0.0600 c. M:-0.1038 c. 291: 43 45 203 N T3 SD: 0.0520 c. M: 0.0864 c. 304: 45 47 212 N T3 SD: 0.0561 c. M:-0.0871 c. 433: 64 67 302 N T3 SD: 0.0454 c. M: 0.0666 c. 453: 67 70 316 N T3 SD: 0.0134 c. M: 0.0184 c. 615: 91 95 429 N T3 SD: 0.0095 c. M:-0.0138 c. 1068: 158 165 745 N T3 SD: 0.0064 c. M: 0.0111 c. 1372: 203 212 957 N T3 SD: 0.0083 c. M:-0.0107 c. 1521: 225 235 1061 N T3 SD: 0.0076 c. M: 0.0120 c. 1663: 246 257 1160 N T3 SD: 0.0048 c. M: 0.0071 c. 1825: 270 282 1273 N T3 SD: 0.0030 c. M:-0.0045 c. 2278: 337 352 1589 N T3 SD: 0.0010 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 15:16 x 20 S SD: 19.0253 cents 16:17 x 21 SD: 20.7451 cents 17:18:19:23 SD: 18.3632 cents 18:19:20:24 S SD: 12.4990 cents 19:20:21:25 SD: 11.8630 cents 20:21:22:27 SD: 9.3410 cents 21:22:23:28 SD: 3.2321 cents 45:47:49:60 SD: 1.1956 cents 66:69:72:88 SD: 1.0919 cents 111:116:121:148 SD: 0.9682 cents 141:147:154:188 SD: 0.8525 cents 165:172:180:220 SD: 0.5832 cents 186:194:203:248 SD: 0.3656 cents 231:241:252:308 SD: 0.1041 cents 483:504:527:644 SD: 0.0996 cents 528:551:576:704 SD: 0.0455 cents