Scala analysis: 251_C17
Chromatic tetrachord 33/32 * 12/11 * 32/27, Barbour?
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-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: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 32/27 294.135 cents Pythagorean minor third 2: 1 9/8 203.910 cents major whole tone 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 128/99 444.772 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 : 53.3 203.9 498.0 53.3 : 150.6 444.8 498.0 203.9: 294.1 347.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 294.1350 cents 1024/891, 240.8621 cents 33/32, 53.2729 cents 2: 203.9100 .. 444.7721 cents 1024/891, 240.8621 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 3.116310 Largest / Average step : 1.771737 Largest / Smallest step : 5.521283 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 139.65914 cents, oct.: 418.97742 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1739-tone equal temperament with octave 4/3 degrees: 186 712 1739 Least number of segments generator : 870 of 249.166 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 984 of 281.815 cents and inv. generated superset size: 33 = 30 more = 1100.000% 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 53.27294 cents Scale diversity : 0.899955 Lumma stability : 0.213928 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 : 33/32, 53.2729 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 33 U: 99) Highest odd numerator or denominator: 33 Scale harmonicity : 0.030137 Average absolute harmonicity : 0.124324 Specific harmonicity : 0.152073 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 3.801600E+04, 15.21432 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 44.5, average 14.83333 Mersenne's string divisions : 7735 Sum of van Prooijen's expressibility: 2.94988, average 0.98329 Sum of Tenney's harmonic distance : 5.96018, average 1.98673 Vogel's harmonic complexity : 11.66667 Wille's k value : 49 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 26.66668, average 4.44445 Lattice compactness (without 2's) : 11.06450, average 1.84408 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -2.00000 10 3: -1 .. 2 0.66667 4 2 11: 0 .. 1 0.33333 1 1 Average exponent except 2's : 3 / 3 = 1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 11 23| Scale is weakly epimorphic with val: <7 11 26| Scale is weakly epimorphic with val: <7 12 24| Scale is weakly epimorphic with val: <7 12 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 37.7449 c. M: 53.2729 c. 5: 0 2 3 N G T3 SD: 30.8762 c. M: 53.2729 c. 7: 1 2 4 N T3 SD: 11.6981 c. M:-17.8763 c. 8: 1 2 5 N T3 SD: 11.1740 c. M: 17.1431 c. 9: 1 3 5 N T3 SD: 10.1413 c. M:-17.4433 c. 10: 1 3 6 N T3 SD: 3.3687 c. M: 4.6920 c. 17: 2 5 10 N T3 SD: 3.1449 c. M:-5.3206 c. 27: 3 8 16 N T3 SD: 1.3256 c. M:-2.0654 c. 37: 4 11 22 N T3 SD: 1.2006 c. M: 1.9999 c. 46: 5 14 27 N T3 SD: 1.1546 c. M:-1.8042 c. 56: 6 17 33 N T3 SD: 0.3755 c. M:-0.6442 c. 66: 7 20 39 N T3 SD: 0.2766 c. M: 0.4500 c. 93: 10 28 55 N T3 SD: 0.2857 c. M: 0.4077 c. 122: 13 37 72 N T3 SD: 0.1671 c. M:-0.2068 c. 149: 16 45 88 N T3 SD: 0.1205 c. M:-0.2084 c. 205: 22 62 121 N T3 SD: 0.1400 c. M:-0.1758 c. 215: 23 65 127 N T3 SD: 0.0343 c. M: 0.0590 c. 486: 52 147 287 N T3 SD: 0.0156 c. M:-0.0220 c. 701: 75 212 414 N T3 SD: 0.0076 c. M:-0.0129 c. 1253: 134 379 740 N T3 SD: 0.0061 c. M: 0.0103 c. 1468: 157 444 867 N T3 SD: 0.0074 c. M: 0.0101 c. 1739: 186 526 1027 N T3 SD: 0.0033 c. M:-0.0049 c. 1954: 209 591 1154 N T3 SD: 0.0017 c. M: 0.0021 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 13:14:15:17 SD: 31.0556 cents 14:15:16:19 SD: 25.9502 cents 15:16:17:20 SD: 19.9461 cents 16:17:18:21 S SD: 19.4776 cents 17:18:19:23 SD: 17.8091 cents 18:19:20:24 S SD: 15.2353 cents 21:22:24:28 S SD: 12.8524 cents 22:23:25:29 SD: 11.8092 cents 23:24:26:31 SD: 9.6401 cents 24:25:27:32 SD: 5.7998 cents 30:31:34:40 SD: 4.4153 cents 33:34:37:44 SD: 2.0172 cents 63:65:71:84 SD: 1.0541 cents 96:99:108:128 SD: 0.0000 cents