Scala analysis: 299_C22
Chromatic tetrachord 138/127 * 254/243 * 27/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 138/127 143.807724 2: 92/81 220.454344 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 138/127 143.8077 2: 254/243 76.6466 3: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 254/243 76.647 cents 1: 1 138/127 143.808 cents 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 92/81 220.454 cents 2: 1 254/207 354.237 cents 2: 1 162/127 421.398 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 : 143.8 220.5 498.0 143.8: 76.6 354.2 498.0 220.5: 277.6 421.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.6466 .. 277.5907 cents 6561/5842, 200.9440 cents 254/243, 76.6466 cents 2: 220.4543 .. 421.3984 cents 6561/5842, 200.9440 cents 2116/2187,-57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 254/243, 76.6466 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/23, 277.5907 cents Average / Smallest step : 2.165979 Largest / Average step : 1.672082 Largest / Smallest step : 3.621695 Median interval of one step : 138/127, 143.8077 cents, amount: 1 Least squares average step : 148.48939 cents, oct.: 445.46816 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1787-tone equal temperament with octave 4/3 degrees: 516 791 1787 Least number of segments generator : 894 of 249.162 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1409 of 392.695 cents and inv. generated superset size: 32 = 29 more = 1066.667% Number of contiguous 1-step segments: 0 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 57.13631 cents Scale diversity : 1.076689 Lumma stability : 0.307790 Lumma impropriety factor : 0.114721 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 : 2187/2116, 57.1363 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 : 127 Odd number limit : 243 (O: 127 U: 243) Highest odd numerator or denominator: 127 Scale harmonicity : 0.017415 Fundamental : 1/10287, -13.3285 octaves, 0.0254 Hz. Guide tone : 276, 8.1085 octaves, 72208.656 Hz. Exponens Consonantiae : 2.839212E+06, 21.43706 octaves Euler's gradus suavitatis : 161 Sum of Mann's harmonic distance : 222.5, average 74.16667 Mersenne's string divisions : 320915 Sum of van Prooijen's expressibility: 4.48941, average 1.49647 Sum of Tenney's harmonic distance : 9.19514, average 3.06505 Vogel's harmonic complexity : 109.66667 Wille's k value : 2794 Wilson's harmonic complexity : 165 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.26148, average 3.21025 Lattice compactness (without 2's) : 16.93566, average 2.82261 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -4 .. 1 -1.33333 6 1 23: 0 .. 1 0.66667 2 1 127: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 31 52| Scale is weakly epimorphic with val: <6 11 35 50| Scale is weakly epimorphic with val: <7 11 31 50| Scale is weakly epimorphic with val: <7 11 32 52| Scale is weakly epimorphic with val: <7 11 34 50| Scale is weakly epimorphic with val: <7 11 35 52| Scale is weakly epimorphic with val: <7 12 35 51| Scale is weakly epimorphic with val: <8 11 31 52| Scale is weakly epimorphic with val: <8 11 35 51| Scale is weakly epimorphic with val: <8 12 34 51| Scale is weakly epimorphic with val: <8 12 35 50|
FIT/MODE
3: 1 0 2 N G T3 SD: 33.9451 c. M: 54.4393 c. 4: 1 1 2 P M ME S SD: 19.9039 c. M:-28.5682 c. 6: 2 1 3 P T3 SD: 20.8910 c. M:-28.5682 c. 7: 2 1 4 N T3 SD: 4.1380 c. M: 7.0065 c. 18: 5 3 10 N T3 SD: 3.1959 c. M: 5.4619 c. 25: 7 4 14 N T3 SD: 2.6265 c. M: 4.3551 c. 27: 8 4 15 N T3 SD: 2.2327 c. M:-3.7612 c. 32: 9 5 18 N T3 SD: 2.6130 c. M: 3.7326 c. 34: 10 5 19 N T3 SD: 1.6013 c. M:-2.6761 c. 38: 11 6 21 N T3 SD: 1.3759 c. M:-2.3553 c. 41: 12 6 23 N T3 SD: 1.5372 c. M:-1.9615 c. 45: 13 7 25 N T3 SD: 0.5207 c. M:-0.8990 c. 52: 15 8 29 N T3 SD: 0.1254 c. M: 0.1652 c. 149: 43 23 83 N T3 SD: 0.1004 c. M:-0.1562 c. 201: 58 31 112 N T3 SD: 0.0684 c. M: 0.0932 c. 253: 73 39 141 N T3 SD: 0.0611 c. M: 0.1030 c. 305: 88 47 170 N T3 SD: 0.0634 c. M: 0.1095 c. 357: 103 55 199 N T3 SD: 0.0683 c. M: 0.1141 c. 454: 131 70 253 N T3 SD: 0.0628 c. M: 0.0987 c. 488: 141 75 272 N T3 SD: 0.0548 c. M:-0.0946 c. 533: 154 82 297 N T3 SD: 0.0665 c. M:-0.0927 c. 540: 156 83 301 N T3 SD: 0.0437 c. M:-0.0719 c. 585: 169 90 326 N T3 SD: 0.0498 c. M:-0.0719 c. 592: 171 91 330 N T3 SD: 0.0370 c. M:-0.0532 c. 637: 184 98 355 N T3 SD: 0.0360 c. M:-0.0546 c. 644: 186 99 359 N T3 SD: 0.0344 c. M: 0.0462 c. 689: 199 106 384 N T3 SD: 0.0247 c. M:-0.0398 c. 741: 214 114 413 N T3 SD: 0.0158 c. M:-0.0271 c. 793: 229 122 442 N T3 SD: 0.0104 c. M:-0.0161 c. 942: 272 145 525 N T3 SD: 0.0103 c. M:-0.0178 c. 994: 287 153 554 N T3 SD: 0.0059 c. M:-0.0082 c. 1735: 501 267 967 N T3 SD: 0.0058 c. M:-0.0082 c. 1787: 516 275 996 N T3 SD: 0.0023 c. M:-0.0038 c. 1839: 531 283 1025 N T3 SD: 0.0022 c. M: 0.0038 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: 63.6303 cents 6 x 7:8 S SD: 23.2083 cents 7 x 8:9 S SD: 31.9335 cents 8 x 9:11 SD: 27.8914 cents 9 x 10:12 S SD: 19.0253 cents 10:11 x 13 SD: 24.3436 cents 12:13:14:16 S SD: 15.5703 cents 13:14:15:17 SD: 15.3305 cents 14:15:16:19 SD: 13.5298 cents 15:16:17:20 SD: 10.7657 cents 18 x 20:24 S SD: 19.0253 cents 19:21:22:25 SD: 16.6866 cents 20:22:23:27 SD: 12.3573 cents 21:23:24:28 SD: 5.7947 cents 24:26:27:32 SD: 5.7843 cents 35:38:40:47 SD: 5.4651 cents 36:39:41:48 SD: 2.3447 cents 45:49:51:60 SD: 1.7417 cents 81:88:92:108 SD: 0.1033 cents