Scala analysis: 256_C17
Chromatic tetrachord 49/48 * 54/49 * 32/27, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 54/49 168.2132 Zalzal's mujannab 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 54/49 168.213 cents Zalzal's mujannab 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 98/81 329.832 cents 2: 1 64/49 462.348 cents 2 septatones or septatonic 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 : 35.7 203.9 498.0 35.7 : 168.2 462.3 498.0 203.9: 294.1 329.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 294.1350 cents 512/441, 258.4382 cents 49/48, 35.6968 cents 2: 203.9100 .. 462.3482 cents 512/441, 258.4382 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 4.650695 Largest / Average step : 1.771737 Largest / Smallest step : 8.239811 Median interval of one step : 54/49, 168.2132 cents, amount: 1 Least squares average step : 138.40370 cents, oct.: 415.21110 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1507-tone equal temperament with octave 4/3 degrees: 108 617 1507 Least number of segments generator : 754 of 249.188 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1271 of 420.050 cents and inv. generated superset size: 27 = 24 more = 900.000% 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 35.69681 cents Scale diversity : 0.720213 Lumma stability : 0.143348 Lumma impropriety factor : 0.181158 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 : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 : 7 Odd number limit : 81 (O: 49 U: 81) Highest odd numerator or denominator: 49 Scale harmonicity : 0.028926 Average absolute harmonicity : 0.123666 Specific harmonicity : 0.146277 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 1764, 10.7846 octaves, 461507.497 Hz. Exponens Consonantiae : 8.467200E+04, 16.36960 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 60.5, average 20.16667 Mersenne's string divisions : 11543 Sum of van Prooijen's expressibility: 3.12156, average 1.04052 Sum of Tenney's harmonic distance : 6.30795, average 2.10265 Vogel's harmonic complexity : 10.00000 Wille's k value : 24 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 26.32136, average 4.38689 Lattice compactness (without 2's) : 13.84162, average 2.30694 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.66667 9 3: -1 .. 2 0.00000 4 2 7: 0 .. 2 0.66667 2 1 Average exponent except 2's : 2 / 3 = 0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 19| Scale is weakly epimorphic with val: <7 11 22| Scale is weakly epimorphic with val: <7 12 19| Scale is weakly epimorphic with val: <7 12 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 30.0571 c. M: 37.8950 c. 5: 0 2 3 N G T3 SD: 20.7868 c. M: 35.6968 c. 7: 1 2 4 N T3 SD: 21.1963 c. M:-35.4525 c. 8: 0 3 5 N G T3 SD: 22.8630 c. M: 35.6968 c. 9: 1 3 5 N T3 SD: 15.1664 c. M:-19.6415 c. 10: 1 3 6 N T3 SD: 8.5837 c. M:-14.1077 c. 12: 1 4 7 N T3 SD: 3.9473 c. M:-5.8069 c. 15: 1 5 9 N T3 SD: 3.0678 c. M: 4.6920 c. 27: 2 9 16 N T3 SD: 0.9008 c. M:-1.1954 c. 44: 3 15 26 N T3 SD: 1.0086 c. M: 1.7392 c. 56: 4 19 33 N T3 SD: 0.3786 c. M:-0.6442 c. 71: 5 24 42 N T3 SD: 0.4553 c. M: 0.6232 c. 83: 6 28 49 N T3 SD: 0.1877 c. M:-0.3064 c. 154: 11 52 91 N T3 SD: 0.1182 c. M: 0.1643 c. 210: 15 71 124 N T3 SD: 0.0765 c. M: 0.1222 c. 237: 17 80 140 N T3 SD: 0.0429 c. M: 0.0688 c. 293: 21 99 173 N T3 SD: 0.0390 c. M:-0.0675 c. 447: 32 151 264 N T3 SD: 0.0256 c. M: 0.0426 c. 530: 38 179 313 N T3 SD: 0.0079 c. M:-0.0121 c. 977: 70 330 577 N T3 SD: 0.0076 c. M: 0.0129 c. 1507: 108 509 890 N T3 SD: 0.0024 c. M: 0.0041 c. 2037: 146 688 1203 N T3 SD: 0.0014 c. M:-0.0024 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: 70.0332 cents 6 x 7:8 S SD: 31.4805 cents 7 x 8:9 S SD: 34.3053 cents 8 x 9:11 SD: 26.6365 cents 9 x 10:12 S SD: 10.7531 cents 10 x 11:13 SD: 29.3037 cents 11 x 12:15 S SD: 32.9836 cents 12 x 14:16 S SD: 31.4805 cents 13 x 15:17 SD: 27.6192 cents 15:16:17:20 SD: 25.7002 cents 16:17:18:21 S SD: 24.8106 cents 17:18:19:23 SD: 23.0198 cents 18:19:20:24 S SD: 20.5903 cents 21:22:24:28 S SD: 17.4928 cents 22:23:25:29 SD: 16.3183 cents 23:24:26:31 SD: 14.3863 cents 24:25:27:32 SD: 11.6585 cents 27:28:30:36 S SD: 11.5751 cents 29:30:33:39 SD: 11.2599 cents 30:31:34:40 SD: 8.2137 cents 31:32:35:41 SD: 8.2065 cents 32:33:36:43 SD: 7.3819 cents 33:34:37:44 SD: 5.6729 cents 39:40:44:52 SD: 3.1697 cents 48:49:54:64 SD: 0.0000 cents