Scala analysis: 172_C7
Chromatic tetrachord 264/257 * 257/243 * 27/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 264/257 46.523484 2: 88/81 143.497939 2nd undecimal neutral second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi 1: 264/257 46.5235 2: 257/243 96.9745 3: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 264/257 46.523 cents 1: 1 257/243 96.974 cents 1: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 88/81 143.498 cents 2nd undecimal neutral second 2: 1 324/257 401.071 cents 2: 1 257/198 451.522 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 : 46.5 143.5 498.0 46.5 : 97.0 451.5 498.0 143.5: 354.5 401.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 46.5235 .. 354.5471 cents 2313/1936, 308.0236 cents 264/257, 46.5235 cents 2: 143.4979 .. 451.5215 cents 2313/1936, 308.0236 cents 1936/2187,-211.0491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 264/257, 46.5235 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/22, 354.5471 cents Average / Smallest step : 3.568413 Largest / Average step : 2.135633 Largest / Smallest step : 7.620819 Median interval of one step : 257/243, 96.9745 cents, amount: 1 Least squares average step : 130.54674 cents, oct.: 391.64022 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1777-tone equal temperament with octave 4/3 degrees: 166 512 1777 Least number of segments generator : 889 of 249.163 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1293 of 362.393 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 46.52348 cents Scale diversity : 0.691346 Lumma stability : 0.186824 Lumma impropriety factor : 0.423755 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 : 264/257, 46.5235 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 : 257 Odd number limit : 257 (O: 257 U: 257) Highest odd numerator or denominator: 257 Scale harmonicity : 0.028973 Fundamental : 1/20817, -14.3455 octaves, 0.0126 Hz. Guide tone : 264, 8.0444 octaves, 69069.149 Hz. Exponens Consonantiae : 5.495688E+06, 22.38987 octaves Euler's gradus suavitatis : 280 Sum of Mann's harmonic distance : 348.5, average 116.16667 Mersenne's string divisions : 616343 Sum of van Prooijen's expressibility: 4.79554, average 1.59851 Sum of Tenney's harmonic distance : 9.76369, average 3.25456 Vogel's harmonic complexity : 189.33333 Wille's k value : 3469 Wilson's harmonic complexity : 283 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 21.41783, average 3.56964 Lattice compactness (without 2's) : 16.93566, average 2.82261 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.66667 8 3: -4 .. 1 -1.33333 6 1 11: 0 .. 1 0.66667 2 1 257: -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 25 58| Scale is weakly epimorphic with val: <7 11 24 57| Scale is weakly epimorphic with val: <7 11 25 59| Scale is weakly epimorphic with val: <7 11 27 57| Scale is weakly epimorphic with val: <8 11 23 57| Scale is weakly epimorphic with val: <8 11 27 59| Scale is weakly epimorphic with val: <8 12 26 59| Scale is weakly epimorphic with val: <8 12 27 58|
FIT/MODE
3: 0 1 2 N G T3 SD: 29.8410 c. M: 46.5235 c. 4: 0 1 3 N G T3 SD: 29.0111 c. M: 46.5235 c. 6: 1 1 4 N M DE S SD: 24.7528 c. M:-36.4840 c. 7: 1 1 5 N M DE S SD: 14.2346 c. M:-24.6258 c. 8: 1 1 6 N M DE S SD: 14.2360 c. M: 18.9867 c. 9: 1 2 6 N T3 SD: 13.9609 c. M:-22.5171 c. 10: 1 2 7 N T3 SD: 3.9055 c. M:-5.9156 c. 21: 2 4 15 N T3 SD: 0.8690 c. M: 1.1994 c. 52: 5 10 37 N T3 SD: 0.7944 c. M:-1.3655 c. 66: 6 13 47 N T3 SD: 0.7232 c. M: 1.2467 c. 76: 7 15 54 N T3 SD: 0.5406 c. M:-0.6730 c. 87: 8 17 62 N T3 SD: 0.4736 c. M: 0.7262 c. 97: 9 19 69 N T3 SD: 0.2378 c. M: 0.3131 c. 118: 11 23 84 N T3 SD: 0.0553 c. M: 0.0956 c. 257: 24 50 183 N T3 SD: 0.0537 c. M: 0.0920 c. 375: 35 73 267 N T3 SD: 0.0419 c. M: 0.0610 c. 493: 46 96 351 N T3 SD: 0.0400 c. M: 0.0528 c. 524: 49 102 373 N T3 SD: 0.0314 c. M:-0.0494 c. 642: 60 125 457 N T3 SD: 0.0174 c. M:-0.0228 c. 760: 71 148 541 N T3 SD: 0.0105 c. M:-0.0177 c. 878: 82 171 625 N T3 SD: 0.0107 c. M:-0.0162 c. 899: 84 175 640 N T3 SD: 0.0101 c. M:-0.0124 c. 1017: 95 198 724 N T3 SD: 0.0058 c. M: 0.0100 c. 1135: 106 221 808 N T3 SD: 0.0075 c. M: 0.0100 c. 1659: 155 323 1181 N T3 SD: 0.0051 c. M:-0.0087 c. 1777: 166 346 1265 N T3 SD: 0.0015 c. M:-0.0018 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: 95.8750 cents 6 x 7:8 S SD: 61.6865 cents 7 x 8:9 S SD: 53.9703 cents 8 x 9:11 SD: 40.2729 cents 9 x 10:12 S SD: 19.4529 cents 10 x 11:13 SD: 24.4115 cents 11 x 12:15 S SD: 19.7777 cents 12 x 13:16 SD: 2.4626 cents 13 x 14:17 SD: 18.4469 cents 14 x 15:19 SD: 19.4781 cents 15 x 16:20 S SD: 15.8833 cents 16 x 17:21 SD: 23.6054 cents 17 x 18:23 SD: 25.6070 cents 18:19:20:24 S SD: 20.3583 cents 19:20:21:25 SD: 18.8545 cents 20:21:22:27 SD: 16.2096 cents 21:22:23:28 SD: 12.2601 cents 23:24:25:31 SD: 10.9977 cents 24:25:26:32 SD: 8.2154 cents 30:31:33:40 SD: 7.9404 cents 31:32:34:41 SD: 7.7276 cents 32:33:35:43 SD: 6.3473 cents 33:34:36:44 SD: 2.9360 cents 36:37:39:48 SD: 1.6696 cents 69:71:75:92 SD: 1.0218 cents 105:108:114:140 SD: 0.8375 cents 150:154:163:200 SD: 0.3465 cents 186:191:202:248 SD: 0.2910 cents 219:225:238:292 SD: 0.2008 cents 255:262:277:340 SD: 0.1427 cents 405:416:440:540 SD: 0.0432 cents