Scala analysis: 213_C14
Chromatic tetrachord 28/27 * 15/14 * 6/5, Ptolemy
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 10/9 182.403712 minor whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 15/14 119.4428 major diatonic semitone 3: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 6/5 315.641 cents minor third 2: 1 10/9 182.404 cents minor whole tone 2: 1 56/45 378.602 cents septimal narrow major third 2: 1 9/7 435.084 cents septimal major third, BP 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 : 63.0 182.4 498.0 63.0 : 119.4 435.1 498.0 182.4: 315.6 378.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 315.6413 cents 81/70, 252.6804 cents 28/27, 62.9609 cents 2: 182.4037 .. 435.0841 cents 81/70, 252.6804 cents 25/27,-133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 2.636795 Largest / Average step : 1.901282 Largest / Smallest step : 5.013290 Median interval of one step : 15/14, 119.4428 cents, amount: 1 Least squares average step : 137.27881 cents, oct.: 411.83643 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1155-tone equal temperament with octave 4/3 degrees: 146 423 1155 Least number of segments generator : 578 of 249.238 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 911 of 392.830 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 62.96090 cents Scale diversity : 0.941402 Lumma stability : 0.252832 Lumma impropriety factor : 0.267521 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 : 405/392, 56.4819 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 45 (O: 15 U: 45) Highest odd numerator or denominator: 27 Scale harmonicity : 0.037473 Average absolute harmonicity : 0.114038 Specific harmonicity : 0.191104 Fundamental : 1/27, -4.7549 octaves, 9.6898 Hz. Guide tone : 140, 7.1293 octaves, 36627.579 Hz. Exponens Consonantiae : 3.780000E+03, 11.88417 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 40.5, average 13.50000 Mersenne's string divisions : 7315 Sum of van Prooijen's expressibility: 2.86273, average 0.95424 Sum of Tenney's harmonic distance : 5.91195, average 1.97065 Vogel's harmonic complexity : 8.66667 Wille's k value : 7 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 14.39533, average 2.39922 Lattice compactness (without 2's) : 11.78068, average 1.96345 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -3 ..-1 -2.00000 6 1 5: 0 .. 1 0.33333 1 1 7: 0 .. 1 0.33333 1 1 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 15 21| Scale is weakly epimorphic with val: <6 10 17 19| Scale is weakly epimorphic with val: <6 10 17 22| Scale is weakly epimorphic with val: <6 10 18 21| Scale is weakly epimorphic with val: <6 11 19 20| Scale is weakly epimorphic with val: <7 10 15 19| Scale is weakly epimorphic with val: <7 10 16 18| Scale is weakly epimorphic with val: <7 10 16 21| Scale is weakly epimorphic with val: <7 10 18 19| Scale is weakly epimorphic with val: <7 11 16 18| Scale is weakly epimorphic with val: <7 11 16 21| Scale is JI-epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <8 11 15 20| Scale is weakly epimorphic with val: <8 11 17 18| Scale is weakly epimorphic with val: <8 11 17 21| Scale is weakly epimorphic with val: <8 11 18 20| Scale is weakly epimorphic with val: <8 12 19 19| Scale is weakly epimorphic with val: <8 12 19 22|
FIT/MODE
3: 0 1 2 N G T3 SD: 37.5618 c. M: 62.9609 c. 5: 1 1 3 N M DE S SD: 23.2795 c. M:-36.6481 c. 6: 1 1 4 N M DE S SD: 14.9494 c. M:-20.0466 c. 8: 1 2 5 N T3 SD: 2.5518 c. M:-4.3632 c. 25: 3 6 16 N T3 SD: 2.5734 c. M: 3.1955 c. 30: 4 7 19 N T3 SD: 1.9928 c. M:-3.4451 c. 33: 4 8 21 N T3 SD: 1.6731 c. M: 2.5918 c. 38: 5 9 24 N T3 SD: 1.6117 c. M:-2.5713 c. 41: 5 10 26 N T3 SD: 1.2886 c. M: 2.2237 c. 46: 6 11 29 N T3 SD: 1.5000 c. M:-2.0015 c. 47: 6 11 30 N T3 SD: 1.3528 c. M: 2.2598 c. 49: 6 12 31 N T3 SD: 1.1843 c. M: 1.9758 c. 55: 7 13 35 N T3 SD: 0.7880 c. M: 1.2964 c. 63: 8 15 40 N T3 SD: 0.3714 c. M: 0.5778 c. 71: 9 17 45 N T3 SD: 0.0998 c. M:-0.1716 c. 221: 28 53 140 N T3 SD: 0.1133 c. M:-0.1398 c. 292: 37 70 185 N T3 SD: 0.1026 c. M:-0.1475 c. 325: 41 78 206 N T3 SD: 0.0793 c. M: 0.1306 c. 388: 49 93 246 N T3 SD: 0.0833 c. M: 0.1295 c. 396: 50 95 251 N T3 SD: 0.0495 c. M: 0.0764 c. 467: 59 112 296 N T3 SD: 0.0306 c. M: 0.0387 c. 538: 68 129 341 N T3 SD: 0.0207 c. M: 0.0341 c. 546: 69 131 346 N T3 SD: 0.0214 c. M:-0.0304 c. 609: 77 146 386 N T3 SD: 0.0197 c. M: 0.0326 c. 617: 78 148 391 N T3 SD: 0.0141 c. M:-0.0244 c. 688: 87 165 436 N T3 SD: 0.0157 c. M:-0.0197 c. 1084: 137 260 687 N T3 SD: 0.0093 c. M: 0.0161 c. 1155: 146 277 732 N T3 SD: 0.0031 c. M: 0.0046 c. 2381: 301 571 1509 N T3 SD: 0.0020 c. M: 0.0034 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: 78.8780 cents 6 x 7:8 S SD: 42.2336 cents 7 x 8:9 S SD: 39.8203 cents 8 x 9:11 SD: 28.7251 cents 9 x 10:12 S SD: 0.0000 cents 10 x 11:13 SD: 23.5791 cents 11 x 12:15 S SD: 25.1136 cents 12 x 13:16 SD: 21.9155 cents 13 x 14:17 SD: 31.8493 cents 14:15:16:19 SD: 26.8901 cents 15:16:17:20 SD: 19.8715 cents 16:17:18:21 S SD: 18.1640 cents 17:18:19:23 SD: 15.0459 cents 18:19:20:24 S SD: 10.2140 cents 21:22:23:28 SD: 10.1623 cents 24:25:27:32 SD: 7.6157 cents 25:26:28:33 SD: 7.5824 cents 26:27:29:35 SD: 6.0026 cents 27:28:30:36 S SD: 0.0000 cents