Scala analysis: 210_C13
Chromatic tetrachord 16/15 * 30/29 * 29/24, Schlesinger
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 32/29 170.422806 29th subharmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 29/24 327.6222 1: 16/15 111.7313 minor diatonic semitone 2: 30/29 58.6915 3: 29/24 327.6222
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 30/29 58.692 cents 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 29/24 327.622 cents 2: 1 32/29 170.423 cents 29th subharmonic 2: 1 5/4 386.314 cents major third 2: 1 58/45 439.353 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 : 111.7 170.4 498.0 111.7: 58.7 386.3 498.0 170.4: 327.6 439.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.6915 .. 327.6222 cents 841/720, 268.9307 cents 30/29, 58.6915 cents 2: 170.4228 .. 439.3535 cents 841/720, 268.9307 cents 768/841,-157.1994 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 30/29, 58.6915 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 29/24, 327.6222 cents Average / Smallest step : 2.828603 Largest / Average step : 1.973449 Largest / Smallest step : 5.582104 Median interval of one step : 16/15, 111.7313 cents, amount: 1 Least squares average step : 139.05085 cents, oct.: 417.15255 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2300-tone equal temperament with octave 4/3 degrees: 516 787 2300 Least number of segments generator : 1151 of 249.239 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1373 of 297.311 cents and inv. generated superset size: 28 = 25 more = 933.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 58.69152 cents Scale diversity : 0.875554 Lumma stability : 0.235688 Lumma impropriety factor : 0.315633 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 : 232/225, 53.0398 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 29 Odd number limit : 45 (O: 29 U: 45) Highest odd numerator or denominator: 29 Scale harmonicity : 0.014677 Average absolute harmonicity : 0.102581 Specific harmonicity : 0.076528 Fundamental : 1/435, -8.7649 octaves, 0.6014 Hz. Guide tone : 32, 5.0000 octaves, 8372.018 Hz. Exponens Consonantiae : 1.392000E+04, 13.76487 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 49.5, average 16.50000 Mersenne's string divisions : 13237 Sum of van Prooijen's expressibility: 3.11561, average 1.03854 Sum of Tenney's harmonic distance : 6.42694, average 2.14231 Vogel's harmonic complexity : 27.33333 Wille's k value : 72 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 19.13042, average 3.18840 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.66667 11 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 10 15 33| Scale is weakly epimorphic with val: <7 10 15 36| Scale is weakly epimorphic with val: <7 10 16 32| Scale is weakly epimorphic with val: <7 10 19 32| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 15 37| Scale is JI-epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 37| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 11 19 36| Scale is weakly epimorphic with val: <7 12 15 32| Scale is weakly epimorphic with val: <7 12 18 32| Scale is weakly epimorphic with val: <8 11 17 37| Scale is weakly epimorphic with val: <8 11 18 33| Scale is weakly epimorphic with val: <8 11 18 36| Scale is weakly epimorphic with val: <8 12 15 37| Scale is weakly epimorphic with val: <8 12 17 32| Scale is weakly epimorphic with val: <8 12 17 35| Scale is weakly epimorphic with val: <8 12 17 38| Scale is weakly epimorphic with val: <8 12 18 37|
FIT/MODE
3: 1 0 2 N G T3 SD: 31.4439 c. M:-54.2837 c. 4: 1 0 3 N G T3 SD: 27.5148 c. M: 45.9116 c. 5: 1 1 3 N M DE S SD: 18.0380 c. M:-28.7952 c. 6: 1 1 4 N M DE S SD: 16.7778 c. M: 28.7238 c. 8: 2 1 5 N T3 SD: 11.9785 c. M:-16.3441 c. 9: 2 1 6 N T3 SD: 2.6167 c. M: 4.4078 c. 23: 5 3 15 N T3 SD: 2.5738 c. M: 3.4606 c. 26: 6 3 17 N T3 SD: 2.1729 c. M:-3.2022 c. 32: 7 4 21 N T3 SD: 1.6692 c. M: 2.7839 c. 35: 8 4 23 N T3 SD: 1.2321 c. M:-2.1076 c. 44: 10 5 29 N T3 SD: 0.9195 c. M:-1.4608 c. 53: 12 6 35 N T3 SD: 0.9478 c. M: 1.2754 c. 58: 13 7 38 N T3 SD: 0.7625 c. M:-1.3168 c. 67: 15 8 44 N T3 SD: 0.3428 c. M:-0.5479 c. 76: 17 9 50 N T3 SD: 0.1898 c. M: 0.3265 c. 143: 32 17 94 N T3 SD: 0.2117 c. M: 0.2807 c. 178: 40 21 117 N T3 SD: 0.1835 c. M:-0.2555 c. 187: 42 22 123 N T3 SD: 0.0767 c. M:-0.1291 c. 263: 59 31 173 N T3 SD: 0.0064 c. M:-0.0108 c. 1774: 398 209 1167 N T3 SD: 0.0065 c. M: 0.0094 c. 1850: 415 218 1217 N T3 SD: 0.0076 c. M: 0.0107 c. 2037: 457 240 1340 N T3 SD: 0.0048 c. M: 0.0068 c. 2300: 516 271 1513 N T3 SD: 0.0036 c. M: 0.0048 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: 83.9987 cents 6 x 7:8 S SD: 48.2240 cents 7 x 8:9 S SD: 43.7458 cents 8 x 9:11 SD: 31.4619 cents 9 x 10:12 S SD: 5.9905 cents 10 x 11:13 SD: 22.0824 cents 11 x 12:15 S SD: 21.8239 cents 12:13 x 16 SD: 13.4207 cents 13:14 x 17 SD: 18.7389 cents 14:15 x 19 SD: 15.7988 cents 15:16:17:20 SD: 15.4213 cents 16:17:18:21 S SD: 14.5703 cents 17:18:19:23 SD: 11.9813 cents 18:19:20:24 S SD: 7.2432 cents 23 x 25:31 SD: 16.0462 cents 24:26 x 32 SD: 13.4207 cents 25:27:28:33 SD: 12.6036 cents 26:28:29:35 SD: 9.9771 cents 27:29:30:36 SD: 5.6479 cents 29:31:32:39 SD: 5.1069 cents 30:32:33:40 SD: 1.8062 cents 75:80:83:100 SD: 1.6807 cents 78:83:86:104 SD: 1.4639 cents 87:93:96:116 SD: 1.2424 cents 105:112:116:140 SD: 0.6866 cents 135:144:149:180 SD: 0.1336 cents 300:320:331:400 SD: 0.0601 cents 435:464:480:580 SD: 0.0000 cents