Scala analysis: 188_C9
Chromatic tetrachord 192/181 * 362/351 * 39/32
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 192/181 102.139936 2: 128/117 155.562336 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina 1: 192/181 102.1399 2: 362/351 53.4224 3: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 362/351 53.422 cents 1: 1 192/181 102.140 cents 1: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 128/117 155.562 cents 2: 1 181/144 395.905 cents 2: 1 234/181 444.623 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 : 102.1 155.6 498.0 102.1: 53.4 395.9 498.0 155.6: 342.5 444.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.4224 .. 342.4827 cents 13689/11584, 289.0603 cents 362/351, 53.4224 cents 2: 155.5623 .. 444.6226 cents 13689/11584, 289.0603 cents 4096/4563,-186.9203 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 362/351, 53.4224 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 39/32, 342.4827 cents Average / Smallest step : 3.107592 Largest / Average step : 2.062962 Largest / Smallest step : 6.410844 Median interval of one step : 192/181, 102.1399 cents, amount: 1 Least squares average step : 136.24283 cents, oct.: 408.72849 cents Scale is not proper Scale has trivalence property 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 53.42240 cents Scale diversity : 0.783789 Lumma stability : 0.214528 Lumma impropriety factor : 0.375308 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 : 33696/32761, 48.7175 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 : 181 Odd number limit : 351 (O: 181 U: 351) Highest odd numerator or denominator: 181 Scale harmonicity : 0.026915 Fundamental : 1/21177, -14.3702 octaves, 0.0124 Hz. Guide tone : 384, 8.5850 octaves, 100464.217 Hz. Exponens Consonantiae : 8.131968E+06, 22.95517 octaves Euler's gradus suavitatis : 206 Sum of Mann's harmonic distance : 312.5, average 104.16667 Mersenne's string divisions : 91385 Sum of van Prooijen's expressibility: 4.80299, average 1.60100 Sum of Tenney's harmonic distance : 9.79556, average 3.26519 Vogel's harmonic complexity : 138.33333 Wille's k value : 3529 Wilson's harmonic complexity : 203 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 28.65221, average 4.77537 Lattice compactness (without 2's) : 10.81256, average 1.80209 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 7 5.00000 15 3: -2 .. 1 -0.66667 4 1 13: -1 .. 0 -0.33333 1 1 181: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 26 53| Scale is weakly epimorphic with val: <7 11 25 55| Scale is weakly epimorphic with val: <7 11 26 54| Scale is weakly epimorphic with val: <7 11 28 55| Scale is weakly epimorphic with val: <7 11 29 54| Scale is weakly epimorphic with val: <8 12 29 55|
FIT/MODE
3: 1 0 2 N G T3 SD: 37.3688 c. M:-63.8751 c. 4: 1 0 3 N G T3 SD: 22.0956 c. M: 31.0511 c. 5: 1 1 3 N M DE S SD: 25.2469 c. M:-43.6557 c. 6: 1 1 4 N M DE S SD: 12.5871 c. M: 19.1324 c. 9: 2 1 6 N T3 SD: 7.7917 c. M:-10.4527 c. 10: 2 1 7 N T3 SD: 3.8390 c. M: 6.1488 c. 19: 4 2 13 N T3 SD: 1.8524 c. M:-2.7116 c. 29: 6 3 20 N T3 SD: 0.7768 c. M: 0.9966 c. 64: 13 7 44 N T3 SD: 0.5644 c. M: 0.9745 c. 83: 17 9 57 N T3 SD: 0.2715 c. M:-0.4518 c. 93: 19 10 64 N T3 SD: 0.2694 c. M: 0.3888 c. 112: 23 12 77 N T3 SD: 0.0907 c. M:-0.1372 c. 205: 42 22 141 N T3 SD: 0.0729 c. M: 0.1014 c. 317: 65 34 218 N T3 SD: 0.0159 c. M: 0.0215 c. 429: 88 46 295 N T3 SD: 0.0136 c. M:-0.0231 c. 746: 153 80 513 N T3 SD: 0.0052 c. M: 0.0067 c. 1809: 371 194 1244 N T3 SD: 0.0055 c. M: 0.0093 c. 2209: 453 237 1519 N T3 SD: 0.0049 c. M:-0.0063 c. 2321: 476 249 1596 N T3 SD: 0.0056 c. M:-0.0097 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: 90.4986 cents 6 x 7:8 S SD: 55.6543 cents 7 x 8:9 S SD: 49.1966 cents 8 x 9:11 SD: 35.9705 cents 9 x 10:12 S SD: 13.4207 cents 10 x 11:13 SD: 22.4182 cents 11 x 12:15 S SD: 19.6081 cents 12 x 13:16 SD: 8.4948 cents 13:14 x 17 SD: 21.2978 cents 14:15 x 19 SD: 17.5949 cents 15:16 x 20 S SD: 4.7957 cents 25 x 27:33 SD: 14.1522 cents 26:28 x 35 S SD: 15.4816 cents 27:29:30:36 SD: 11.4786 cents 28:30:31:37 SD: 10.3644 cents 29:31:32:39 SD: 8.2936 cents 30:32:33:40 SD: 4.4863 cents 33:35:36:44 SD: 1.6443 cents 63:67:69:84 SD: 1.6112 cents 84:89:92:112 SD: 0.9365 cents 117:124:128:156 SD: 0.5140 cents 180:191:197:240 SD: 0.2907 cents 213:226:233:284 SD: 0.1547 cents 330:350:361:440 SD: 0.0999 cents 510:541:558:680 SD: 0.0534 cents 543:576:594:724 SD: 0.0498 cents