Scala analysis: 187_C9
Chromatic tetrachord 384/373 * 373/351 * 39/32
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 384/373 50.316817 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: 384/373 50.3168 2: 373/351 105.2455 3: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 384/373 50.317 cents 1: 1 373/351 105.246 cents 1: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 128/117 155.562 cents 2: 1 468/373 392.799 cents 2: 1 373/288 447.728 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 : 50.3 155.6 498.0 50.3 : 105.2 447.7 498.0 155.6: 342.5 392.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.3168 .. 342.4827 cents 4849/4096, 292.1658 cents 384/373, 50.3168 cents 2: 155.5623 .. 447.7282 cents 4849/4096, 292.1658 cents 4096/4563,-186.9203 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 384/373, 50.3168 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 39/32, 342.4827 cents Average / Smallest step : 3.299394 Largest / Average step : 2.062962 Largest / Smallest step : 6.806525 Median interval of one step : 373/351, 105.2455 cents, amount: 1 Least squares average step : 132.54118 cents, oct.: 397.62353 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1732-tone equal temperament with octave 4/3 degrees: 175 541 1732 Least number of segments generator : 867 of 249.310 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1355 of 389.637 cents and inv. generated superset size: 52 = 49 more = 1733.333% 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 50.31682 cents Scale diversity : 0.768224 Lumma stability : 0.202057 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 : 384/373, 50.3168 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 : 373 Odd number limit : 373 (O: 373 U: 373) Highest odd numerator or denominator: 373 Scale harmonicity : 0.026915 Fundamental : 1/43641, -15.4134 octaves, 0.0060 Hz. Guide tone : 384, 8.5850 octaves, 100464.217 Hz. Exponens Consonantiae : 1.675814E+07, 23.99836 octaves Euler's gradus suavitatis : 398 Sum of Mann's harmonic distance : 504.5, average 168.16667 Mersenne's string divisions : 185465 Sum of van Prooijen's expressibility: 5.11702, average 1.70567 Sum of Tenney's harmonic distance : 10.41062, average 3.47021 Vogel's harmonic complexity : 266.66667 Wille's k value : 7273 Wilson's harmonic complexity : 395 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 30.39920, average 5.06653 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 5.33333 16 3: -2 .. 1 -0.66667 4 1 13: -1 .. 0 -0.33333 1 1 373: -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 63| Scale is weakly epimorphic with val: <7 11 25 62| Scale is weakly epimorphic with val: <7 11 26 61| Scale is weakly epimorphic with val: <7 11 28 62| Scale is weakly epimorphic with val: <7 11 29 61| Scale is weakly epimorphic with val: <8 12 29 63|
FIT/MODE
3: 0 1 2 N G T3 SD: 29.6706 c. M: 50.3168 c. 4: 0 1 3 N G T3 SD: 34.1367 c. M: 50.3168 c. 6: 1 1 4 N M DE S SD: 19.8153 c. M:-32.6907 c. 7: 1 1 5 N M DE S SD: 14.2586 c. M:-20.8325 c. 9: 1 2 6 N T3 SD: 6.6951 c. M:-10.4527 c. 10: 1 2 7 N T3 SD: 3.5623 c. M: 6.1488 c. 19: 2 4 13 N T3 SD: 1.5694 c. M:-2.1090 c. 29: 3 6 20 N T3 SD: 0.9029 c. M:-1.2051 c. 48: 5 10 33 N T3 SD: 0.9034 c. M:-1.5629 c. 61: 6 13 42 N T3 SD: 0.8070 c. M: 1.3288 c. 70: 7 15 48 N T3 SD: 0.6313 c. M:-0.9661 c. 80: 8 17 55 N T3 SD: 0.2991 c. M: 0.5123 c. 99: 10 21 68 N T3 SD: 0.2259 c. M:-0.3911 c. 109: 11 23 75 N T3 SD: 0.1247 c. M: 0.2089 c. 208: 21 44 143 N T3 SD: 0.0483 c. M:-0.0767 c. 317: 32 67 218 N T3 SD: 0.0267 c. M: 0.0410 c. 525: 53 111 361 N T3 SD: 0.0241 c. M: 0.0380 c. 554: 56 117 381 N T3 SD: 0.0258 c. M: 0.0356 c. 653: 66 138 449 N T3 SD: 0.0209 c. M:-0.0291 c. 762: 77 161 524 N T3 SD: 0.0067 c. M:-0.0106 c. 970: 98 205 667 N T3 SD: 0.0073 c. M:-0.0125 c. 1079: 109 228 742 N T3 SD: 0.0063 c. M: 0.0098 c. 1287: 130 272 885 N T3 SD: 0.0059 c. M: 0.0092 c. 1732: 175 366 1191 N T3 SD: 0.0041 c. M:-0.0053 c. 2049: 207 433 1409 N T3 SD: 0.0012 c. M: 0.0019 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 x 14:17 SD: 21.6417 cents 14 x 15:19 SD: 23.6831 cents 15 x 16:20 S SD: 21.9155 cents 16 x 18:21 S SD: 27.7526 cents 17:18:19:23 SD: 22.0430 cents 18:19:20:24 S SD: 16.9776 cents 19:20:21:25 SD: 16.0565 cents 20:21:22:27 SD: 13.8159 cents 21:22:23:28 SD: 10.0940 cents 24:25:26:32 SD: 8.8380 cents 29:30:32:39 SD: 7.5410 cents 30:31:33:40 SD: 3.8116 cents 33:34:36:44 SD: 1.7037 cents 63:65:69:84 SD: 1.4175 cents 96:99:105:128 SD: 0.9954 cents 105:108:115:140 SD: 0.8247 cents 138:142:151:184 SD: 0.2997 cents 171:176:187:228 SD: 0.2759 cents 234:241:256:312 SD: 0.2376 cents 309:318:338:412 SD: 0.2223 cents 339:349:371:452 SD: 0.1995 cents 372:383:407:496 SD: 0.0574 cents 543:559:594:724 SD: 0.0517 cents