Scala analysis: 149_C4
Chromatic tetrachord 81/79 * 79/75 * 100/81
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/79 43.283106 2: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 100/81 364.8074 grave major third 1: 81/79 43.2831 2: 79/75 89.9545 3: 100/81 364.8074 grave major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 81/79 43.283 cents 1: 1 79/75 89.954 cents 1: 1 100/81 364.807 cents grave major third 2: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 1 100/79 408.091 cents 2: 1 316/243 454.762 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 : 43.3 133.2 498.0 43.3 : 90.0 454.8 498.0 133.2: 364.8 408.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.2831 .. 364.8074 cents 7900/6561, 321.5243 cents 81/79, 43.2831 cents 2: 133.2376 .. 454.7619 cents 7900/6561, 321.5243 cents 2187/2500,-231.5698 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 81/79, 43.2831 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 100/81, 364.8074 cents Average / Smallest step : 3.835561 Largest / Average step : 2.197437 Largest / Smallest step : 8.428402 Median interval of one step : 79/75, 89.9545 cents, amount: 1 Least squares average step : 128.84952 cents, oct.: 386.54855 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2198-tone equal temperament with octave 4/3 degrees: 191 588 2198 Least number of segments generator : 1101 of 249.476 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1235 of 279.839 cents and inv. generated superset size: 40 = 37 more = 1333.333% 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 43.28311 cents Scale diversity : 0.622834 Lumma stability : 0.173812 Lumma impropriety factor : 0.464958 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 : 81/79, 43.2831 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 79 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.035545 Fundamental : 1/5925, -12.5326 octaves, 0.0442 Hz. Guide tone : 324, 8.3399 octaves, 84766.683 Hz. Exponens Consonantiae : 1.919700E+06, 20.87245 octaves Euler's gradus suavitatis : 99 Sum of Mann's harmonic distance : 109.5, average 36.50000 Mersenne's string divisions : 14560 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.71460, average 2.57153 Vogel's harmonic complexity : 69.00000 Wille's k value : 3199 Wilson's harmonic complexity : 104 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 22.36183, average 3.72697 Lattice compactness (without 2's) : 20.31376, average 3.38563 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -1 .. 4 2.00000 8 1 5: -2 .. 0 -0.66667 2 1 79: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is weakly epimorphic with val: <6 11 15 45| Scale is weakly epimorphic with val: <7 11 16 45| Scale is weakly epimorphic with val: <7 11 17 46| = patent Scale is weakly epimorphic with val: <7 11 19 45| Scale is weakly epimorphic with val: <7 12 16 45| Scale is weakly epimorphic with val: <7 12 19 45| Scale is weakly epimorphic with val: <8 11 15 46| Scale is weakly epimorphic with val: <8 12 17 45|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.3464 c. M: 43.2831 c. 4: 0 1 3 N G T3 SD: 25.4923 c. M: 43.2831 c. 7: 1 1 5 N M DE S SD: 16.9177 c. M:-27.8662 c. 8: 1 1 6 N M DE S SD: 12.0569 c. M:-18.9725 c. 10: 1 2 7 N T3 SD: 10.0696 c. M:-16.1759 c. 11: 1 2 8 N T3 SD: 1.8884 c. M:-2.5929 c. 34: 3 6 25 N T3 SD: 0.8952 c. M: 1.4021 c. 45: 4 8 33 N T3 SD: 0.6209 c. M:-0.9876 c. 56: 5 10 41 N T3 SD: 0.6911 c. M:-1.1852 c. 71: 6 13 52 N T3 SD: 0.6902 c. M: 1.1948 c. 79: 7 14 58 N T3 SD: 0.6913 c. M:-0.8475 c. 82: 7 15 60 N T3 SD: 0.4953 c. M: 0.7671 c. 93: 8 17 68 N T3 SD: 0.4512 c. M:-0.6455 c. 105: 9 19 77 N T3 SD: 0.4217 c. M: 0.5935 c. 116: 10 21 85 N T3 SD: 0.2165 c. M: 0.3482 c. 127: 11 23 93 N T3 SD: 0.1010 c. M: 0.1453 c. 172: 15 31 126 N T3 SD: 0.0901 c. M:-0.1511 c. 288: 25 52 211 N T3 SD: 0.0543 c. M: 0.0797 c. 299: 26 54 219 N T3 SD: 0.0181 c. M:-0.0252 c. 886: 77 160 649 N T3 SD: 0.0077 c. M: 0.0133 c. 1185: 103 214 868 N T3 SD: 0.0050 c. M:-0.0069 c. 1611: 140 291 1180 N T3 SD: 0.0043 c. M:-0.0072 c. 2198: 191 397 1610 N T3 SD: 0.0030 c. M: 0.0044 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: 100.5060 cents 6 x 7:8 S SD: 66.8167 cents 7 x 8:9 S SD: 58.2143 cents 8 x 9:11 SD: 44.2510 cents 9 x 10:12 S SD: 24.5831 cents 10 x 11:13 SD: 27.0660 cents 11 x 12:15 S SD: 21.3096 cents 12 x 13:16 SD: 2.6675 cents 13 x 14:17 SD: 16.9891 cents 14 x 15:19 SD: 16.8020 cents 15 x 16:20 S SD: 10.7531 cents 16 x 17:21 SD: 19.6419 cents 17 x 18:23 SD: 21.2961 cents 18 x 19:24 SD: 19.8173 cents 19 x 21:25 SD: 23.0664 cents 20:21:22:27 SD: 18.7610 cents 21:22:23:28 SD: 14.8182 cents 22:23:24:29 SD: 14.2521 cents 23:24:25:31 SD: 12.4627 cents 24:25:26:32 SD: 9.3014 cents 27:28:29:36 SD: 7.2873 cents 33:34:36:44 SD: 6.4402 cents 35:36:38:47 SD: 5.4304 cents 36:37:39:48 SD: 2.2532 cents 39:40:42:52 SD: 1.6565 cents 75:77:81:100 SD: 0.7594 cents 162:166:175:216 SD: 0.3758 cents 201:206:217:268 SD: 0.3269 cents 237:243:256:316 SD: 0.0902 cents 513:526:554:684 SD: 0.0439 cents