Scala analysis: 221_C14
Chromatic tetrachord 256/243 * 6/5 * 135/128, Xenakis
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 512/405 405.866283 narrow diminished fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 135/128 92.1787 major chroma, major limma 1: 256/243 90.2250 limma, Pythagorean minor second 2: 6/5 315.6413 minor third 3: 135/128 92.1787 major chroma, major limma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 135/128 92.179 cents major chroma, major limma 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 512/405 405.866 cents narrow diminished fourth 2: 1 81/64 407.820 cents Pythagorean major third 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 : 90.2 405.9 498.0 90.2 : 315.6 407.8 498.0 405.9: 92.2 182.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 315.6413 cents 729/640, 225.4163 cents 256/243, 90.2250 cents 2: 182.4037 .. 407.8200 cents 729/640, 225.4163 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 1.840011 Largest / Average step : 1.901282 Largest / Smallest step : 3.498380 Median interval of one step : 135/128, 92.1787 cents, amount: 1 Least squares average step : 171.14947 cents, oct.: 513.44841 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1529-tone equal temperament with octave 4/3 degrees: 277 1246 1529 Least number of segments generator : 765 of 249.185 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 969 of 315.635 cents and inv. generated superset size: 37 = 34 more = 1233.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.000607 Lumma stability : 0.362317 Lumma impropriety factor : 0.267521 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 : 32805/32768, 1.9537 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% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 5 Odd number limit : 405 (O: 135 U: 405) Highest odd numerator or denominator: 405 Scale harmonicity : 0.034803 Average absolute harmonicity : 0.099841 Specific harmonicity : 0.159680 Fundamental : 1/1215, -10.2467 octaves, 0.2153 Hz. Guide tone : 512, 9.0000 octaves, 133952.289 Hz. Exponens Consonantiae : 6.220800E+05, 19.24674 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 711.5, average 237.16667 Mersenne's string divisions : 457583 Sum of van Prooijen's expressibility: 5.47018, average 1.82339 Sum of Tenney's harmonic distance : 11.18975, average 3.72992 Vogel's harmonic complexity : 14.66667 Wille's k value : 202 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 38.19384, average 6.36564 Lattice compactness (without 2's) : 18.69960, average 3.11660 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 9 6.33333 19 3: -5 ..-1 -3.33333 10 2 5: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-11 / 3 =-3.66667 Average absolute exponent except 2's: 11 / 3 = 3.66667 Scale is JI-epimorphic with val: <7 11 17| = patent
FIT/MODE
3: 0 2 1 N G T3 SD: 67.3111 c. M: 90.2250 c. 4: 1 2 1 P M ME I SD: 27.2087 c. M:-34.2863 c. 5: 1 3 1 N M DE I SD: 6.9106 c. M:-9.3840 c. 6: 1 4 1 N M DE I SD: 6.7380 c. M:-9.1712 c. 11: 2 7 2 N M DE I SD: 0.9572 c. M:-1.6251 c. 38: 7 24 7 N M DE I SD: 0.9127 c. M:-1.5201 c. 49: 9 31 9 N M DE I SD: 0.8288 c. M:-1.2527 c. 60: 11 38 11 N M DE I SD: 0.8023 c. M:-1.0833 c. 71: 13 45 13 N M DE I SD: 0.7976 c. M:-0.9874 c. 134: 24 85 25 N T3 SD: 0.7290 c. M: 1.0229 c. 139: 25 88 26 N T3 SD: 0.6789 c. M: 0.9808 c. 145: 26 92 27 N T3 SD: 0.6222 c. M: 0.9204 c. 150: 27 95 28 N T3 SD: 0.5646 c. M: 0.7897 c. 156: 28 99 29 N T3 SD: 0.5348 c. M: 0.8323 c. 161: 29 102 30 N T3 SD: 0.4674 c. M: 0.6247 c. 167: 30 106 31 N T3 SD: 0.4639 c. M: 0.7558 c. 172: 31 109 32 N T3 SD: 0.3846 c. M: 0.4808 c. 183: 33 116 34 N T3 SD: 0.3144 c. M: 0.4136 c. 194: 35 123 36 N T3 SD: 0.2560 c. M: 0.3715 c. 199: 36 126 37 N T3 SD: 0.2547 c. M: 0.4226 c. 205: 37 130 38 N T3 SD: 0.2095 c. M: 0.3339 c. 210: 38 133 39 N T3 SD: 0.1915 c. M: 0.3154 c. 216: 39 137 40 N T3 SD: 0.1759 c. M: 0.3002 c. 221: 40 140 41 N T3 SD: 0.1347 c. M: 0.2188 c. 232: 42 147 43 N T3 SD: 0.0838 c. M: 0.1313 c. 243: 44 154 45 N T3 SD: 0.0393 c. M: 0.0518 c. 254: 46 161 47 N T3 SD: 0.0201 c. M: 0.0279 c. 497: 90 315 92 N T3 SD: 0.0223 c. M: 0.0358 c. 751: 136 476 139 N T3 SD: 0.0192 c. M: 0.0331 c. 1005: 182 637 186 N T3 SD: 0.0184 c. M: 0.0318 c. 1021: 185 647 189 N T3 SD: 0.0139 c. M:-0.0182 c. 1032: 187 654 191 N T3 SD: 0.0125 c. M:-0.0215 c. 1275: 231 808 236 N T3 SD: 0.0071 c. M:-0.0090 c. 1286: 233 815 238 N T3 SD: 0.0075 c. M:-0.0118 c. 1529: 277 969 283 N T3 SD: 0.0027 c. M: 0.0036 c. 1783: 323 1130 330 N T3 SD: 0.0009 c. M: 0.0015 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 5 x S SD: 19.5526 cents 5 x 6:7 S SD: 61.7966 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 71.9728 cents 8:9:10:11 H SD: 42.3538 cents 9:10:11:12 H SD: 36.3842 cents 10:11 x 13 SD: 43.3391 cents 11:12:14:15 S SD: 24.2643 cents 12:13:15:16 SD: 17.3839 cents 14:15:18:19 S SD: 17.1474 cents 15:16:19:20 SD: 7.2567 cents 18:19:23:24 SD: 6.2680 cents 33:35:42:44 SD: 5.4879 cents 34:36:43:45 SD: 5.1633 cents 37:39:47:49 SD: 4.8008 cents 38:40:48:51 S SD: 3.8432 cents 39:41:49:52 SD: 3.7671 cents 42:44:53:56 SD: 3.3950 cents 53:56:67:71 SD: 3.2033 cents 54:57:68:72 SD: 2.5237 cents 57:60:72:76 S SD: 0.6714 cents 129:136:163:172 SD: 0.5089 cents 132:139:167:176 SD: 0.5051 cents 186:196:235:248 SD: 0.3749 cents 189:199:239:252 SD: 0.3601 cents 204:215:258:272 SD: 0.3281 cents 261:275:330:348 SD: 0.1099 cents 318:335:402:424 SD: 0.0301 cents