Scala analysis: 183_C8
Chromatic tetrachord 30/29 * 58/55 * 11/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 30/29 58.691521 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: 30/29 58.6915 2: 58/55 91.9455 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30/29 58.692 cents 1: 1 58/55 91.946 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: 1 110/87 406.099 cents 2: 1 58/45 439.353 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 : 58.7 150.6 498.0 58.7 : 91.9 439.4 498.0 150.6: 347.4 406.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 347.4079 cents 319/270, 288.7164 cents 30/29, 58.6915 cents 2: 150.6371 .. 439.3535 cents 319/270, 288.7164 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 2.828603 Largest / Average step : 2.092630 Largest / Smallest step : 5.919219 Median interval of one step : 58/55, 91.9455 cents, amount: 1 Least squares average step : 132.43576 cents, oct.: 397.30728 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1468-tone equal temperament with octave 4/3 degrees: 173 444 1468 Least number of segments generator : 735 of 249.362 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1069 of 362.677 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 58.69152 cents Scale diversity : 0.779137 Lumma stability : 0.235688 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 : 841/825, 33.2540 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% -- Rational properties -- Prime limit : 29 Odd number limit : 87 (O: 55 U: 87) Highest odd numerator or denominator: 29 Scale harmonicity : 0.011630 Average absolute harmonicity : 0.091214 Specific harmonicity : 0.061157 Fundamental : 1/957, -9.9024 octaves, 0.2734 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 5.742000E+04, 15.80927 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 44.5, average 14.83333 Mersenne's string divisions : 9499 Sum of van Prooijen's expressibility: 2.98091, average 0.99364 Sum of Tenney's harmonic distance : 6.13927, average 2.04642 Vogel's harmonic complexity : 34.00000 Wille's k value : 247 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.56738, average 2.26123 Lattice compactness (without 2's) : 10.56387, average 1.76065 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 19 24 32| Scale is weakly epimorphic with val: <6 10 19 27 32| Scale is weakly epimorphic with val: <6 11 18 24 32| Scale is weakly epimorphic with val: <6 11 18 27 32| Scale is weakly epimorphic with val: <6 11 19 24 33| Scale is weakly epimorphic with val: <6 11 19 27 33| Scale is weakly epimorphic with val: <7 10 18 25 32| Scale is weakly epimorphic with val: <7 10 19 25 33| Scale is JI-epimorphic with val: <7 11 15 23 32| Scale is weakly epimorphic with val: <7 11 15 23 35| Scale is weakly epimorphic with val: <7 11 15 23 38| Scale is weakly epimorphic with val: <7 11 15 24 34| Scale is weakly epimorphic with val: <7 11 15 24 37| Scale is weakly epimorphic with val: <7 11 15 26 32| Scale is weakly epimorphic with val: <7 11 15 26 35| Scale is weakly epimorphic with val: <7 11 15 26 38| Scale is weakly epimorphic with val: <7 11 15 27 34| Scale is weakly epimorphic with val: <7 11 15 27 37| Scale is JI-epimorphic with val: <7 11 16 23 33| Scale is weakly epimorphic with val: <7 11 16 23 36| Scale is weakly epimorphic with val: <7 11 16 24 32| Scale is weakly epimorphic with val: <7 11 16 24 35| Scale is weakly epimorphic with val: <7 11 16 24 38| Scale is weakly epimorphic with val: <7 11 16 26 33| Scale is weakly epimorphic with val: <7 11 16 26 36| Scale is weakly epimorphic with val: <7 11 16 27 32| Scale is weakly epimorphic with val: <7 11 16 27 35| Scale is weakly epimorphic with val: <7 11 16 27 38| Scale is JI-epimorphic with val: <7 11 17 23 34| Scale is weakly epimorphic with val: <7 11 17 23 37| Scale is weakly epimorphic with val: <7 11 17 24 33| Scale is weakly epimorphic with val: <7 11 17 24 36| Scale is weakly epimorphic with val: <7 11 17 26 34| Scale is weakly epimorphic with val: <7 11 17 26 37| Scale is weakly epimorphic with val: <7 11 17 27 33| Scale is weakly epimorphic with val: <7 11 17 27 36| Scale is weakly epimorphic with val: <7 11 18 23 32| Scale is JI-epimorphic with val: <7 11 18 23 35| Scale is weakly epimorphic with val: <7 11 18 23 38| Scale is weakly epimorphic with val: <7 11 18 24 34| Scale is weakly epimorphic with val: <7 11 18 24 37| Scale is weakly epimorphic with val: <7 11 18 26 32| Scale is weakly epimorphic with val: <7 11 18 26 35| Scale is weakly epimorphic with val: <7 11 18 26 38| Scale is weakly epimorphic with val: <7 11 18 27 34| Scale is weakly epimorphic with val: <7 11 18 27 37| Scale is weakly epimorphic with val: <7 11 19 23 33| Scale is JI-epimorphic with val: <7 11 19 23 36| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 24 35| Scale is weakly epimorphic with val: <7 11 19 24 38| Scale is weakly epimorphic with val: <7 11 19 26 33| Scale is weakly epimorphic with val: <7 11 19 26 36| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 27 35| Scale is weakly epimorphic with val: <7 11 19 27 38| Scale is weakly epimorphic with val: <7 12 15 23 33| Scale is weakly epimorphic with val: <7 12 15 23 36| Scale is weakly epimorphic with val: <7 12 16 23 34| Scale is weakly epimorphic with val: <7 12 16 23 37| Scale is weakly epimorphic with val: <7 12 16 25 32| Scale is weakly epimorphic with val: <7 12 17 23 32| Scale is weakly epimorphic with val: <7 12 17 23 35| Scale is weakly epimorphic with val: <7 12 17 23 38| Scale is weakly epimorphic with val: <7 12 17 25 33| Scale is weakly epimorphic with val: <7 12 18 23 33| Scale is weakly epimorphic with val: <7 12 18 23 36| Scale is weakly epimorphic with val: <7 12 18 25 34| Scale is weakly epimorphic with val: <7 12 19 23 34| Scale is weakly epimorphic with val: <7 12 19 23 37| Scale is weakly epimorphic with val: <7 12 19 25 35| Scale is weakly epimorphic with val: <8 11 15 24 33| Scale is weakly epimorphic with val: <8 11 15 24 36| Scale is weakly epimorphic with val: <8 11 16 23 32| Scale is weakly epimorphic with val: <8 11 16 24 34| Scale is weakly epimorphic with val: <8 11 16 24 37| Scale is weakly epimorphic with val: <8 11 16 26 32| Scale is weakly epimorphic with val: <8 11 17 23 33| Scale is weakly epimorphic with val: <8 11 17 24 32| Scale is weakly epimorphic with val: <8 11 17 24 35| Scale is weakly epimorphic with val: <8 11 17 24 38| Scale is weakly epimorphic with val: <8 11 17 26 33| Scale is weakly epimorphic with val: <8 11 18 23 34| Scale is weakly epimorphic with val: <8 11 18 24 33| Scale is weakly epimorphic with val: <8 11 18 24 36| Scale is weakly epimorphic with val: <8 11 18 26 34| Scale is weakly epimorphic with val: <8 11 19 23 35| Scale is weakly epimorphic with val: <8 11 19 24 34| Scale is weakly epimorphic with val: <8 11 19 24 37| Scale is weakly epimorphic with val: <8 11 19 26 35| Scale is weakly epimorphic with val: <8 12 15 23 32| Scale is weakly epimorphic with val: <8 12 15 25 33| Scale is weakly epimorphic with val: <8 12 15 25 36| Scale is weakly epimorphic with val: <8 12 15 26 32| Scale is weakly epimorphic with val: <8 12 16 23 33| Scale is weakly epimorphic with val: <8 12 16 25 34| Scale is weakly epimorphic with val: <8 12 16 25 37| Scale is weakly epimorphic with val: <8 12 16 26 33| Scale is weakly epimorphic with val: <8 12 17 23 34| Scale is weakly epimorphic with val: <8 12 17 25 32| Scale is weakly epimorphic with val: <8 12 17 25 35| Scale is weakly epimorphic with val: <8 12 17 25 38| Scale is weakly epimorphic with val: <8 12 17 26 34| Scale is weakly epimorphic with val: <8 12 18 23 35| Scale is weakly epimorphic with val: <8 12 18 25 33| Scale is weakly epimorphic with val: <8 12 18 25 36| Scale is weakly epimorphic with val: <8 12 18 26 35| Scale is weakly epimorphic with val: <8 12 19 23 36| Scale is weakly epimorphic with val: <8 12 19 25 34| Scale is weakly epimorphic with val: <8 12 19 25 37| Scale is weakly epimorphic with val: <8 12 19 26 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 35.0294 c. M: 58.6915 c. 4: 0 1 3 N G T3 SD: 37.0911 c. M: 58.6915 c. 6: 1 1 4 N M DE S SD: 16.6107 c. M:-24.3160 c. 7: 1 1 5 N M DE S SD: 8.6550 c. M:-12.4578 c. 9: 1 2 6 N T3 SD: 9.0871 c. M:-15.3779 c. 10: 1 2 7 N T3 SD: 5.1793 c. M: 8.8870 c. 16: 2 3 11 N T3 SD: 3.5460 c. M:-5.0020 c. 17: 2 3 12 N T3 SD: 2.3985 c. M: 4.1532 c. 26: 3 5 18 N T3 SD: 1.6633 c. M:-2.6076 c. 33: 4 6 23 N T3 SD: 0.9825 c. M:-1.6776 c. 43: 5 8 30 N T3 SD: 0.4515 c. M: 0.7793 c. 76: 9 14 53 N T3 SD: 0.1734 c. M:-0.2875 c. 119: 14 22 83 N T3 SD: 0.0595 c. M: 0.0980 c. 195: 23 36 136 N T3 SD: 0.0432 c. M:-0.0535 c. 314: 37 58 219 N T3 SD: 0.0263 c. M:-0.0453 c. 433: 51 80 302 N T3 SD: 0.0298 c. M:-0.0417 c. 509: 60 94 355 N T3 SD: 0.0297 c. M:-0.0485 c. 747: 88 138 521 N T3 SD: 0.0274 c. M:-0.0432 c. 840: 99 155 586 N T3 SD: 0.0221 c. M: 0.0377 c. 916: 108 169 639 N T3 SD: 0.0234 c. M:-0.0299 c. 959: 113 177 669 N T3 SD: 0.0172 c. M: 0.0291 c. 1035: 122 191 722 N T3 SD: 0.0148 c. M: 0.0206 c. 1078: 127 199 752 N T3 SD: 0.0160 c. M: 0.0223 c. 1154: 136 213 805 N T3 SD: 0.0090 c. M: 0.0151 c. 1273: 150 235 888 N T3 SD: 0.0071 c. M: 0.0107 c. 1349: 159 249 941 N T3 SD: 0.0068 c. M:-0.0106 c. 1468: 173 271 1024 N T3 SD: 0.0016 c. M: 0.0022 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 17:18:19:23 SD: 21.1272 cents 18:19:20:24 S SD: 15.7337 cents 19:20:21:25 SD: 14.6989 cents 20:21:22:27 SD: 12.1716 cents 21:22:23:28 SD: 7.6321 cents 24:25:26:32 SD: 5.6676 cents 30:31:33:40 SD: 4.8318 cents 33:34:36:44 SD: 2.3364 cents 54:56:59:72 SD: 1.6784 cents 87:90:95:116 SD: 0.5525 cents 144:149:157:192 SD: 0.3598 cents 231:239:252:308 SD: 0.0833 cents 495:512:540:660 SD: 0.0777 cents