Scala analysis: 268_C18
Chromatic tetrachord 76/75 * 10/9 * 45/38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76/75 22.930588 2: 152/135 205.334300 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 45/38 292.7107 1: 76/75 22.9306 2: 10/9 182.4037 minor whole tone 3: 45/38 292.7107
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 76/75 22.931 cents 1: 1 10/9 182.404 cents minor whole tone 1: 1 45/38 292.711 cents 2: 1 152/135 205.334 cents 2: 1 6/5 315.641 cents minor third 2: 1 25/19 475.114 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 : 22.9 205.3 498.0 22.9 : 182.4 475.1 498.0 205.3: 292.7 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.9306 .. 292.7107 cents 3375/2888, 269.7801 cents 76/75, 22.9306 cents 2: 205.3343 .. 475.1144 cents 3375/2888, 269.7801 cents 5776/6075,-87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 76/75, 22.9306 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 45/38, 292.7107 cents Average / Smallest step : 7.239893 Largest / Average step : 1.763158 Largest / Smallest step : 12.765076 Median interval of one step : 10/9, 182.4037 cents, amount: 1 Least squares average step : 137.69530 cents, oct.: 413.08590 cents Scale is not proper Scale has trivalence property Scale is a mode of a 456-tone equal temperament with octave 4/3 degrees: 21 188 456 Least number of segments generator : 229 of 250.115 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 275 of 300.356 cents and inv. generated superset size: 16 = 13 more = 533.333% 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 22.93059 cents Scale diversity : 0.573389 Lumma stability : 0.092082 Lumma impropriety factor : 0.175439 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 : 76/75, 22.9306 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 : 135 (O: 45 U: 135) Highest odd numerator or denominator: 135 Scale harmonicity : 0.017270 Average absolute harmonicity : 0.084363 Specific harmonicity : 0.074689 Fundamental : 1/675, -9.3987 octaves, 0.3876 Hz. Guide tone : 152, 7.2479 octaves, 39767.086 Hz. Exponens Consonantiae : 1.026000E+05, 16.64667 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 222.5, average 74.16667 Mersenne's string divisions : 43337 Sum of van Prooijen's expressibility: 4.48252, average 1.49417 Sum of Tenney's harmonic distance : 9.14723, average 3.04908 Vogel's harmonic complexity : 24.00000 Wille's k value : 112 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.20179, average 2.86697 Lattice compactness (without 2's) : 13.68774, average 2.28129 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -3 ..-1 -1.66667 5 1 5: -2 .. 0 -1.00000 3 19: 0 .. 1 0.66667 2 2 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 15 31| Scale is weakly epimorphic with val: <6 10 16 31| Scale is weakly epimorphic with val: <6 10 19 34| Scale is weakly epimorphic with val: <6 11 15 32| Scale is weakly epimorphic with val: <7 10 15 29| Scale is weakly epimorphic with val: <7 10 17 29| Scale is JI-epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| 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 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 12 15 31| Scale is weakly epimorphic with val: <7 12 16 34| Scale is weakly epimorphic with val: <8 11 15 28| Scale is weakly epimorphic with val: <8 11 16 28| Scale is weakly epimorphic with val: <8 11 18 34| Scale is weakly epimorphic with val: <8 11 19 31| Scale is weakly epimorphic with val: <8 12 15 29| Scale is weakly epimorphic with val: <8 12 17 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 26.2794 c. M: 39.3193 c. 5: 0 2 3 N G T3 SD: 13.7018 c. M: 22.9306 c. 12: 1 4 7 N T3 SD: 10.7971 c. M:-18.5732 c. 14: 1 5 8 N T3 SD: 8.6738 c. M:-12.6441 c. 15: 1 5 9 N T3 SD: 6.9025 c. M:-10.2724 c. 17: 1 6 10 N T3 SD: 3.6785 c. M:-6.3662 c. 19: 1 7 11 N T3 SD: 3.1549 c. M:-4.3689 c. 22: 1 8 13 N T3 SD: 0.9326 c. M: 1.5886 c. 41: 2 15 24 N T3 SD: 1.0385 c. M:-1.3643 c. 46: 2 17 27 N T3 SD: 0.7689 c. M: 1.2765 c. 63: 3 23 37 N T3 SD: 0.4693 c. M:-0.7858 c. 85: 4 31 50 N T3 SD: 0.3281 c. M:-0.5068 c. 109: 5 40 64 N T3 SD: 0.1692 c. M:-0.2806 c. 131: 6 48 77 N T3 SD: 0.0715 c. M: 0.1194 c. 240: 11 88 141 N T3 SD: 0.0869 c. M:-0.1093 c. 325: 15 119 191 N T3 SD: 0.0333 c. M:-0.0561 c. 456: 21 167 268 N T3 SD: 0.0033 c. M:-0.0057 c. 1499: 69 549 881 N T3 SD: 0.0034 c. M: 0.0052 c. 1955: 90 716 1149 N T3 SD: 0.0020 c. M: 0.0027 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: 69.4664 cents 6 x 7:8 S SD: 30.7683 cents 7 x 8:9 S SD: 34.0286 cents 8 x 9:11 SD: 26.6460 cents 9 x 10:12 S SD: 11.4653 cents 10 x 11:13 SD: 29.7812 cents 11 x 12:15 S SD: 33.5613 cents 12 x 14:16 S SD: 30.7683 cents 13 x 15:17 SD: 27.0576 cents 14 x 16:19 SD: 20.0414 cents 22:23:25:29 SD: 19.9039 cents 23:24:26:31 SD: 18.1773 cents 24:25:27:32 SD: 15.9210 cents 27:28:30:36 S SD: 15.3776 cents 29:30:33:39 SD: 14.2860 cents 30:31:34:40 SD: 11.8966 cents 31:32:35:41 SD: 11.7635 cents 32:33:36:43 SD: 11.0765 cents 33:34:37:44 SD: 9.8850 cents 37:38:42:49 SD: 9.8695 cents 38:39:43:51 SD: 8.7545 cents 39:40:44:52 SD: 7.0639 cents 42:43:47:56 SD: 6.9090 cents 45:46:51:60 SD: 6.3025 cents 46:47:52:61 SD: 6.1592 cents 47:48:53:63 SD: 5.5194 cents 48:49:54:64 SD: 4.2818 cents 54:55:61:72 SD: 3.5024 cents 57:58:64:76 SD: 2.8789 cents 63:64:71:84 SD: 1.5429 cents 72:73:81:96 SD: 0.5705 cents 150:152:169:200 SD: 0.3795 cents 222:225:250:296 SD: 0.1451 cents 381:386:429:508 SD: 0.1233 cents 453:459:510:604 SD: 0.0711 cents