Scala analysis: 242_C16
Chromatic tetrachord 96/95 * 10/9 * 19/16, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96/95 18.128271 19th-partial chroma 2: 64/57 200.531983 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 96/95 18.1283 19th-partial chroma 2: 10/9 182.4037 minor whole tone 3: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 96/95 18.128 cents 19th-partial chroma 1: 1 10/9 182.404 cents minor whole tone 1: 1 19/16 297.513 cents 19th harmonic 2: 1 64/57 200.532 cents 2: 1 6/5 315.641 cents minor third 2: 1 95/72 479.917 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 : 18.1 200.5 498.0 18.1 : 182.4 479.9 498.0 200.5: 297.5 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.1283 .. 297.5130 cents 1805/1536, 279.3847 cents 96/95, 18.1283 cents 2: 200.5320 .. 479.9167 cents 1805/1536, 279.3847 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 96/95, 18.1283 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 9.157796 Largest / Average step : 1.792085 Largest / Smallest step : 16.411550 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 136.66623 cents, oct.: 409.99869 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1813-tone equal temperament with octave 4/3 degrees: 66 730 1813 Least number of segments generator : 907 of 249.160 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1089 of 299.157 cents and inv. generated superset size: 56 = 53 more = 1866.667% 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 18.12827 cents Scale diversity : 0.527118 Lumma stability : 0.072798 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 : 96/95, 18.1283 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 19 Odd number limit : 95 (O: 95 U: 95) Highest odd numerator or denominator: 95 Scale harmonicity : 0.019291 Average absolute harmonicity : 0.086141 Specific harmonicity : 0.081930 Fundamental : 1/285, -8.1548 octaves, 0.9180 Hz. Guide tone : 192, 7.5850 octaves, 50232.109 Hz. Exponens Consonantiae : 5.472000E+04, 15.73978 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 159.5, average 53.16667 Mersenne's string divisions : 161777 Sum of van Prooijen's expressibility: 4.21072, average 1.40357 Sum of Tenney's harmonic distance : 8.60123, average 2.86708 Vogel's harmonic complexity : 16.00000 Wille's k value : 47 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 24.13756, average 4.02293 Lattice compactness (without 2's) : 9.83182, average 1.63864 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 5: -1 .. 0 -0.33333 1 19: -1 .. 0 -0.66667 2 2 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 17 29| Scale is JI-epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 33| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 12 15 29| Scale is weakly epimorphic with val: <8 11 15 33| Scale is weakly epimorphic with val: <8 11 16 34| Scale is weakly epimorphic with val: <8 11 18 30| Scale is weakly epimorphic with val: <8 11 19 34| Scale is weakly epimorphic with val: <8 12 15 34| Scale is weakly epimorphic with val: <8 12 17 33| Scale is weakly epimorphic with val: <8 12 18 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 22.5097 c. M: 34.5170 c. 5: 0 2 3 N G T3 SD: 10.4938 c. M: 18.1283 c. 13: 0 5 8 N G T3 SD: 11.6791 c. M: 18.1283 c. 15: 0 6 9 N G T3 SD: 10.4938 c. M: 18.1283 c. 16: 1 5 10 N T3 SD: 10.9311 c. M: 13.7651 c. 17: 1 6 10 N T3 SD: 6.9617 c. M:-11.1685 c. 18: 1 6 11 N T3 SD: 6.7804 c. M:-9.5409 c. 19: 1 7 11 N T3 SD: 7.0586 c. M:-9.1712 c. 20: 1 7 12 N T3 SD: 3.9839 c. M:-6.7740 c. 22: 1 8 13 N T3 SD: 3.1974 c. M:-4.5101 c. 25: 1 9 15 N T3 SD: 1.2837 c. M:-1.7935 c. 27: 1 10 16 N T3 SD: 1.3836 c. M:-2.3752 c. 30: 1 11 18 N T3 SD: 1.1630 c. M: 1.5268 c. 52: 2 19 31 N T3 SD: 0.6873 c. M:-1.0273 c. 57: 2 21 34 N T3 SD: 0.4525 c. M: 0.6530 c. 82: 3 30 49 N T3 SD: 0.0785 c. M: 0.0992 c. 221: 8 81 132 N T3 SD: 0.0615 c. M: 0.0995 c. 303: 11 111 181 N T3 SD: 0.0274 c. M: 0.0474 c. 385: 14 141 230 N T3 SD: 0.0155 c. M: 0.0204 c. 1125: 41 412 672 N T3 SD: 0.0154 c. M:-0.0227 c. 1264: 46 463 755 N T3 SD: 0.0150 c. M:-0.0257 c. 1346: 49 493 804 N T3 SD: 0.0106 c. M:-0.0181 c. 1428: 52 523 853 N T3 SD: 0.0080 c. M:-0.0113 c. 1510: 55 553 902 N T3 SD: 0.0078 c. M:-0.0124 c. 1731: 63 634 1034 N T3 SD: 0.0056 c. M:-0.0095 c. 1813: 66 664 1083 N T3 SD: 0.0030 c. M:-0.0046 c. 2198: 80 805 1313 N T3 SD: 0.0006 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 x 11:13 SD: 28.2107 cents 11 x 12:15 S SD: 31.6353 cents 12 x 13:16 SD: 30.9797 cents 13 x 15:17 SD: 28.9776 cents 14 x 16:19 SD: 21.6672 cents 15 x 17:20 SD: 8.0774 cents 42:43:47:56 SD: 7.7807 cents 47:48:53:63 SD: 7.2703 cents 48:49:54:64 SD: 5.9635 cents 51:52:57:68 SD: 5.8071 cents 54:55:61:72 SD: 5.7349 cents 55:56:62:73 SD: 5.5792 cents 56:57:63:75 SD: 5.0274 cents 57:58:64:76 SD: 3.9936 cents 63:64:71:84 SD: 3.7237 cents 65:66:73:87 SD: 3.5478 cents 66:67:74:88 SD: 2.7600 cents 72:73:81:96 SD: 2.2233 cents 75:76:84:100 SD: 2.1562 cents 81:82:91:108 SD: 1.0904 cents 90:91:101:120 SD: 0.4493 cents 195:197:219:260 SD: 0.2074 cents 285:288:320:380 SD: 0.0000 cents