Scala analysis: 238_C16
Chromatic tetrachord 96/89 * 178/171 * 19/16
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96/89 131.074884 2: 64/57 200.531983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 96/89 131.0749 2: 178/171 69.4571 3: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 178/171 69.457 cents 1: 1 96/89 131.075 cents 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 89/72 366.970 cents 2: 1 114/89 428.588 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 : 131.1 200.5 498.0 131.1: 69.5 367.0 498.0 200.5: 297.5 428.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.4571 .. 297.5130 cents 3249/2848, 228.0559 cents 178/171, 69.4571 cents 2: 200.5320 .. 428.5879 cents 3249/2848, 228.0559 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 178/171, 69.4571 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 2.390180 Largest / Average step : 1.792085 Largest / Smallest step : 4.283407 Median interval of one step : 96/89, 131.0749 cents, amount: 1 Least squares average step : 144.73385 cents, oct.: 434.20154 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1972-tone equal temperament with octave 4/3 degrees: 519 794 1972 Least number of segments generator : 987 of 249.275 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1799 of 454.352 cents and inv. generated superset size: 102 = 99 more = 3400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 69.45710 cents Scale diversity : 1.022066 Lumma stability : 0.278919 Lumma impropriety factor : 0.194723 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 : 8208/7921, 61.6178 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 89 Odd number limit : 171 (O: 89 U: 171) Highest odd numerator or denominator: 89 Scale harmonicity : 0.022008 Fundamental : 1/5073, -12.3086 octaves, 0.0516 Hz. Guide tone : 192, 7.5850 octaves, 50232.109 Hz. Exponens Consonantiae : 9.740160E+05, 19.89359 octaves Euler's gradus suavitatis : 117 Sum of Mann's harmonic distance : 156.5, average 52.16667 Mersenne's string divisions : 156695 Sum of van Prooijen's expressibility: 4.18239, average 1.39413 Sum of Tenney's harmonic distance : 8.57290, average 2.85763 Vogel's harmonic complexity : 78.33333 Wille's k value : 845 Wilson's harmonic complexity : 114 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 23.67765, average 3.94627 Lattice compactness (without 2's) : 8.65028, average 1.44171 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 4.33333 13 3: -1 .. 1 -0.33333 3 1 19: -1 .. 0 -0.33333 1 1 89: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 29 46| Scale is weakly epimorphic with val: <7 11 29 48| Scale is weakly epimorphic with val: <7 11 30 47| Scale is weakly epimorphic with val: <7 11 32 48| Scale is weakly epimorphic with val: <7 11 33 47| Scale is weakly epimorphic with val: <8 11 30 48| Scale is weakly epimorphic with val: <8 11 33 48| Scale is weakly epimorphic with val: <8 11 34 47| Scale is weakly epimorphic with val: <8 12 33 47|
FIT/MODE
3: 1 0 2 N G T3 SD: 28.3563 c. M:-34.9401 c. 4: 1 1 2 P M ME S SD: 28.2513 c. M:-48.4905 c. 5: 1 1 3 N M DE S SD: 18.1827 c. M: 31.4659 c. 7: 2 1 4 N T3 SD: 9.8791 c. M:-12.9159 c. 8: 2 1 5 N T3 SD: 8.8045 c. M: 13.7651 c. 12: 3 2 7 N T3 SD: 5.5346 c. M:-6.9868 c. Vietnamese tritonic 15: 4 2 9 N T3 SD: 1.2575 c. M:-1.7371 c. 42: 11 6 25 N T3 SD: 0.7121 c. M:-1.0577 c. 57: 15 8 34 N T3 SD: 0.2504 c. M:-0.4335 c. 72: 19 10 43 N T3 SD: 0.2081 c. M:-0.3537 c. 129: 34 18 77 N T3 SD: 0.1734 c. M:-0.2303 c. 236: 62 33 141 N T3 SD: 0.1371 c. M: 0.2326 c. 251: 66 35 150 N T3 SD: 0.0973 c. M: 0.1234 c. 308: 81 43 184 N T3 SD: 0.0564 c. M: 0.0955 c. 323: 85 45 193 N T3 SD: 0.0468 c. M: 0.0804 c. 380: 100 53 227 N T3 SD: 0.0063 c. M: 0.0104 c. 1592: 419 222 951 N T3 SD: 0.0035 c. M:-0.0061 c. 1972: 519 275 1178 N T3 SD: 0.0017 c. M:-0.0029 c. 2352: 619 328 1405 N T3 SD: 0.0008 c. M: 0.0011 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: 71.3878 cents 6 x 7:8 S SD: 33.1695 cents 7 x 8:9 S SD: 35.0108 cents 8 x 9:11 SD: 26.6900 cents 9 x 10:12 S SD: 9.0641 cents 10:11 x 13 SD: 27.7144 cents 11:12 x 15 S SD: 21.7735 cents 12:13 x 16 SD: 3.7489 cents 19 x 21:25 SD: 17.8125 cents 20:22 x 27 SD: 20.0856 cents 21:23:24:28 SD: 13.4861 cents 22:24:25:29 SD: 11.5752 cents 23:25:26:31 SD: 8.5894 cents 24:26:27:32 SD: 2.7412 cents 51:55:57:68 SD: 2.6607 cents 63:68:71:84 SD: 2.1766 cents 66:71:74:88 SD: 1.7541 cents 75:81:84:100 SD: 1.6144 cents 90:97:101:120 SD: 0.5560 cents 114:123:128:152 SD: 0.1582 cents 318:343:357:424 SD: 0.0871 cents 432:466:485:576 SD: 0.0685 cents