Scala analysis: 301_C22
Chromatic tetrachord 23/22 * 88/81 * 27/23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/22 76.956405 2: 92/81 220.454344 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 23/22 76.9564 2: 88/81 143.4979 2nd undecimal neutral second 3: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 23/22 76.956 cents 1: 1 88/81 143.498 cents 2nd undecimal neutral second 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 92/81 220.454 cents 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 88/69 421.089 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 : 77.0 220.5 498.0 77.0 : 143.5 421.1 498.0 220.5: 277.6 354.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.9564 .. 277.5907 cents 594/529, 200.6343 cents 23/22, 76.9564 cents 2: 220.4543 .. 421.0886 cents 594/529, 200.6343 cents 2116/2187,-57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 23/22, 76.9564 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/23, 277.5907 cents Average / Smallest step : 2.157260 Largest / Average step : 1.672082 Largest / Smallest step : 3.607116 Median interval of one step : 88/81, 143.4979 cents, amount: 1 Least squares average step : 143.71429 cents, oct.: 431.14288 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1482-tone equal temperament with octave 4/3 degrees: 229 656 1482 Least number of segments generator : 743 of 249.695 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1021 of 343.120 cents and inv. generated superset size: 41 = 38 more = 1366.667% 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 57.13631 cents Scale diversity : 1.078558 Lumma stability : 0.309034 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 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% -- Rational properties -- Prime limit : 23 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.013525 Average absolute harmonicity : 0.082957 Specific harmonicity : 0.059577 Fundamental : 1/1782, -10.7993 octaves, 0.1468 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 1.639440E+05, 17.32284 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 112.5, average 37.50000 Mersenne's string divisions : 54495 Sum of van Prooijen's expressibility: 3.74733, average 1.24911 Sum of Tenney's harmonic distance : 7.65560, average 2.55187 Vogel's harmonic complexity : 31.66667 Wille's k value : 931 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 20.27609, average 3.37935 Lattice compactness (without 2's) : 15.55475, average 2.59246 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -4 .. 0 -1.66667 5 1 11: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 23 32| Scale is weakly epimorphic with val: <6 10 24 31| Scale is weakly epimorphic with val: <6 10 26 35| Scale is weakly epimorphic with val: <6 10 27 31| Scale is weakly epimorphic with val: <6 11 24 35| Scale is weakly epimorphic with val: <6 11 25 34| Scale is weakly epimorphic with val: <6 11 27 35| Scale is weakly epimorphic with val: <7 10 24 34| Scale is JI-epimorphic with val: <7 11 24 32| Scale is weakly epimorphic with val: <7 11 24 35| Scale is weakly epimorphic with val: <7 11 25 31| Scale is weakly epimorphic with val: <7 11 25 34| Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 27 35| Scale is weakly epimorphic with val: <7 12 25 35| Scale is weakly epimorphic with val: <8 11 24 35| Scale is weakly epimorphic with val: <8 11 25 31| Scale is weakly epimorphic with val: <8 12 23 34| Scale is weakly epimorphic with val: <8 12 25 35|
FIT/MODE
3: 0 1 2 N G T3 SD: 54.4240 c. M: 76.9564 c. 4: 1 1 2 P M ME S SD: 32.0292 c. M:-47.5548 c. 5: 1 1 3 N M DE S SD: 17.9269 c. M:-22.6526 c. 6: 1 2 3 P T3 SD: 16.8598 c. M:-28.5682 c. 7: 1 2 4 N T3 SD: 5.2540 c. M: 7.0065 c. 18: 3 5 10 N T3 SD: 3.5319 c. M:-6.0511 c. 20: 3 6 11 N T3 SD: 2.4833 c. M:-3.6659 c. 25: 4 7 14 N T3 SD: 1.7498 c. M:-2.7308 c. 32: 5 9 18 N T3 SD: 1.5596 c. M: 2.5597 c. 38: 6 11 21 N T3 SD: 1.6711 c. M:-2.3553 c. 45: 7 13 25 N T3 SD: 0.5988 c. M:-0.8990 c. 52: 8 15 29 N T3 SD: 0.2152 c. M: 0.3341 c. 97: 15 28 54 N T3 SD: 0.1929 c. M:-0.3285 c. 149: 23 43 83 N T3 SD: 0.1005 c. M:-0.1562 c. 201: 31 58 112 N T3 SD: 0.0930 c. M: 0.1435 c. 278: 43 80 155 N T3 SD: 0.0720 c. M: 0.0963 c. 323: 50 93 180 N T3 SD: 0.0846 c. M:-0.1403 c. 330: 51 95 184 N T3 SD: 0.0624 c. M: 0.1072 c. 375: 58 108 209 N T3 SD: 0.0438 c. M:-0.0746 c. 427: 66 123 238 N T3 SD: 0.0151 c. M:-0.0248 c. 479: 74 138 267 N T3 SD: 0.0167 c. M: 0.0252 c. 906: 140 261 505 N T3 SD: 0.0102 c. M: 0.0172 c. 1003: 155 289 559 N T3 SD: 0.0109 c. M:-0.0162 c. 1055: 163 304 588 N T3 SD: 0.0059 c. M:-0.0073 c. 1482: 229 427 826 N T3 SD: 0.0020 c. M:-0.0028 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 x 11:13 SD: 35.3408 cents 11 x 13:15 SD: 39.4999 cents 12:13:14:16 S SD: 25.7144 cents 13:14:15:17 SD: 22.3872 cents 14:15:16:19 SD: 17.8230 cents 15:16:17:20 SD: 11.6595 cents 20:21:23:27 SD: 10.4427 cents 21:22:24:28 S SD: 3.7673 cents 44:46:50:59 SD: 3.2820 cents 45:47:51:60 SD: 1.3742 cents 66:69:75:88 SD: 0.2850 cents 177:185:201:236 SD: 0.1772 cents 243:254:276:324 SD: 0.1033 cents 309:323:351:412 SD: 0.1015 cents 552:577:627:736 SD: 0.0971 cents