Scala analysis: 211_C13
Chromatic tetrachord 32/31 * 31/29 * 29/24, Schlesinger
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/31 54.964428 Greek enharmonic 1/4-tone 2: 32/29 170.422806 29th subharmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 29/24 327.6222 1: 32/31 54.9644 Greek enharmonic 1/4-tone 2: 31/29 115.4584 3: 29/24 327.6222
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 32/31 54.964 cents Greek enharmonic 1/4-tone 1: 1 31/29 115.458 cents 1: 1 29/24 327.622 cents 2: 1 32/29 170.423 cents 29th subharmonic 2: 1 116/93 382.587 cents 2: 1 31/24 443.081 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 : 55.0 170.4 498.0 55.0 : 115.5 443.1 498.0 170.4: 327.6 382.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.9644 .. 327.6222 cents 899/768, 272.6578 cents 32/31, 54.9644 cents 2: 170.4228 .. 443.0806 cents 899/768, 272.6578 cents 768/841,-157.1994 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 32/31, 54.9644 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 29/24, 327.6222 cents Average / Smallest step : 3.020408 Largest / Average step : 1.973449 Largest / Smallest step : 5.960622 Median interval of one step : 31/29, 115.4584 cents, amount: 1 Least squares average step : 134.99607 cents, oct.: 404.98822 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1169-tone equal temperament with octave 4/3 degrees: 129 400 1169 Least number of segments generator : 585 of 249.236 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1089 of 463.962 cents and inv. generated superset size: 19 = 16 more = 633.333% 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 54.96443 cents Scale diversity : 0.854954 Lumma stability : 0.220721 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 : 32/31, 54.9644 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 : 31 Odd number limit : 93 (O: 31 U: 93) Highest odd numerator or denominator: 31 Scale harmonicity : 0.016198 Fundamental : 1/2697, -11.3971 octaves, 0.0970 Hz. Guide tone : 32, 5.0000 octaves, 8372.018 Hz. Exponens Consonantiae : 8.630400E+04, 16.39714 octaves Euler's gradus suavitatis : 66 Sum of Mann's harmonic distance : 65.5, average 21.83333 Mersenne's string divisions : 3843 Sum of van Prooijen's expressibility: 3.43088, average 1.14363 Sum of Tenney's harmonic distance : 7.04324, average 2.34775 Vogel's harmonic complexity : 46.00000 Wille's k value : 449 Wilson's harmonic complexity : 63 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 19.81399, average 3.30233 Lattice compactness (without 2's) : 5.41421, average 0.90237 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 4.00000 12 3: -1 .. 0 -0.33333 1 1 29: -1 .. 0 -0.33333 1 1 31: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 3 / 3 = 1.00000 Scale is weakly epimorphic with val: <7 10 32 33| Scale is weakly epimorphic with val: <7 10 32 36| Scale is weakly epimorphic with val: <7 10 32 39| Scale is JI-epimorphic with val: <7 11 33 34| Scale is weakly epimorphic with val: <7 11 33 37| Scale is weakly epimorphic with val: <7 11 34 36| Scale is weakly epimorphic with val: <7 11 34 39| Scale is weakly epimorphic with val: <7 11 36 37| Scale is weakly epimorphic with val: <7 11 37 39| Scale is weakly epimorphic with val: <7 12 32 34| Scale is weakly epimorphic with val: <7 12 32 37| Scale is weakly epimorphic with val: <8 11 33 37| Scale is weakly epimorphic with val: <8 11 36 37| Scale is weakly epimorphic with val: <8 11 37 39| Scale is weakly epimorphic with val: <8 12 32 37| Scale is weakly epimorphic with val: <8 12 35 37| Scale is weakly epimorphic with val: <8 12 37 38|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.8356 c. M: 54.9644 c. 6: 1 1 4 N M DE S SD: 16.3895 c. M:-28.0431 c. 8: 1 2 5 N T3 SD: 10.3326 c. M:-16.3441 c. 9: 1 2 6 N T3 SD: 2.5540 c. M: 4.4078 c. 26: 3 6 17 N T3 SD: 1.8413 c. M:-2.5023 c. 35: 4 8 23 N T3 SD: 1.1452 c. M:-1.9550 c. 44: 5 10 29 N T3 SD: 1.0108 c. M:-1.6316 c. 53: 6 12 35 N T3 SD: 1.1011 c. M:-1.4180 c. 55: 6 13 36 N T3 SD: 1.0089 c. M:-1.6291 c. 64: 7 15 42 N T3 SD: 0.5321 c. M:-0.7802 c. 73: 8 17 48 N T3 SD: 0.2362 c. M: 0.3842 c. 82: 9 19 54 N T3 SD: 0.2703 c. M: 0.3587 c. 108: 12 25 71 N T3 SD: 0.2458 c. M:-0.3739 c. 117: 13 27 77 N T3 SD: 0.2328 c. M:-0.3739 c. 155: 17 36 102 N T3 SD: 0.2089 c. M: 0.3401 c. 181: 20 42 119 N T3 SD: 0.1102 c. M:-0.1782 c. 190: 21 44 125 N T3 SD: 0.0528 c. M:-0.0827 c. 263: 29 61 173 N T3 SD: 0.0278 c. M: 0.0469 c. 453: 50 105 298 N T3 SD: 0.0072 c. M: 0.0101 c. 716: 79 166 471 N T3 SD: 0.0074 c. M: 0.0125 c. 1169: 129 271 769 N T3 SD: 0.0042 c. M: 0.0054 c. 1622: 179 376 1067 N T3 SD: 0.0039 c. M: 0.0067 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 x 13:16 SD: 15.9251 cents 13 x 14:17 SD: 26.9472 cents 14 x 15:19 SD: 29.7401 cents 15:16:17:20 SD: 24.4104 cents 16:17:18:21 S SD: 22.0197 cents 17:18:19:23 SD: 18.4507 cents 18:19:20:24 S SD: 13.4845 cents 20:21:22:27 SD: 12.3031 cents 21:22:23:28 SD: 9.5518 cents 26:27:29:35 SD: 9.0001 cents 27:28:30:36 S SD: 4.8015 cents 30:31:33:40 SD: 1.9035 cents 57:59:63:76 SD: 1.8425 cents 66:68:73:88 SD: 1.7490 cents 87:90:96:116 SD: 1.2424 cents 96:99:106:128 SD: 0.6775 cents 126:130:139:168 SD: 0.3201 cents 279:288:308:372 SD: 0.2585 cents 309:319:341:412 SD: 0.0825 cents 435:449:480:580 SD: 0.0415 cents