Scala analysis: 134_C1
Chromatic tetrachord 87/83 * 83/81 * 36/29
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 87/83 81.484877 2: 29/27 123.712192 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 36/29 374.3328 1: 87/83 81.4849 2: 83/81 42.2273 3: 36/29 374.3328
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83/81 42.227 cents 1: 1 87/83 81.485 cents 1: 1 36/29 374.333 cents 2: 1 29/27 123.712 cents 2: 1 332/261 416.560 cents 2: 1 108/83 455.818 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 : 81.5 123.7 498.0 81.5 : 42.2 416.6 498.0 123.7: 374.3 455.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 42.2273 .. 374.3328 cents 2916/2407, 332.1055 cents 83/81, 42.2273 cents 2: 123.7122 .. 455.8177 cents 2916/2407, 332.1055 cents 841/972,-250.6206 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 83/81, 42.2273 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 36/29, 374.3328 cents Average / Smallest step : 3.931460 Largest / Average step : 2.254813 Largest / Smallest step : 8.864708 Median interval of one step : 87/83, 81.4849 cents, amount: 1 Least squares average step : 130.21745 cents, oct.: 390.65234 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2017-tone equal temperament with octave 4/3 degrees: 330 501 2017 Least number of segments generator : 1009 of 249.146 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1308 of 322.976 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 : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 42.22731 cents Scale diversity : 0.565291 Lumma stability : 0.169572 Lumma impropriety factor : 0.503209 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 : 7047/6889, 39.2576 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 83 Odd number limit : 261 (O: 87 U: 261) Highest odd numerator or denominator: 87 Scale harmonicity : 0.014984 Fundamental : 1/2241, -11.1299 octaves, 0.1167 Hz. Guide tone : 348, 8.4429 octaves, 91045.697 Hz. Exponens Consonantiae : 7.798680E+05, 19.57287 octaves Euler's gradus suavitatis : 121 Sum of Mann's harmonic distance : 116.5, average 38.83333 Mersenne's string divisions : 4760 Sum of van Prooijen's expressibility: 3.87904, average 1.29301 Sum of Tenney's harmonic distance : 7.83154, average 2.61051 Vogel's harmonic complexity : 81.33333 Wille's k value : 1203 Wilson's harmonic complexity : 124 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 16.81256, average 2.80209 Lattice compactness (without 2's) : 14.04863, average 2.34144 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -3 .. 1 -1.00000 5 1 29: 0 .. 1 0.66667 2 1 83: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 33 45| Scale is weakly epimorphic with val: <6 11 36 45| Scale is weakly epimorphic with val: <6 11 38 46| Scale is weakly epimorphic with val: <7 10 33 47| Scale is weakly epimorphic with val: <7 10 38 45| Scale is weakly epimorphic with val: <7 11 32 45| Scale is weakly epimorphic with val: <7 11 34 46| Scale is JI-epimorphic with val: <7 11 35 45| Scale is weakly epimorphic with val: <7 11 37 46| Scale is weakly epimorphic with val: <7 11 38 45| Scale is weakly epimorphic with val: <7 12 37 46| Scale is weakly epimorphic with val: <8 11 36 46| Scale is weakly epimorphic with val: <8 11 37 45| Scale is weakly epimorphic with val: <8 12 38 47|
FIT/MODE
3: 1 0 2 N G T3 SD: 54.5737 c. M:-84.5301 c. 4: 1 0 3 N G T3 SD: 24.8456 c. M:-43.0264 c. 5: 1 0 4 N G T3 SD: 17.4112 c. M: 24.1032 c. 7: 1 1 5 N M DE S SD: 12.2784 c. M:-18.5864 c. 8: 1 1 6 N M DE S SD: 11.1116 c. M: 19.2293 c. 11: 2 1 8 N T3 SD: 8.7387 c. M:-12.1183 c. 12: 2 1 9 N T3 SD: 0.9928 c. M:-1.5226 c. 56: 9 5 42 N T3 SD: 0.9518 c. M: 1.4419 c. 61: 10 5 46 N T3 SD: 0.7232 c. M: 1.2421 c. 68: 11 6 51 N T3 SD: 0.7030 c. M: 0.9188 c. 73: 12 6 55 N T3 SD: 0.5688 c. M: 0.9066 c. 80: 13 7 60 N T3 SD: 0.5609 c. M:-0.7991 c. 85: 14 7 64 N T3 SD: 0.4971 c. M: 0.6658 c. 92: 15 8 69 N T3 SD: 0.4892 c. M:-0.7991 c. 97: 16 8 73 N T3 SD: 0.4759 c. M:-0.6669 c. 104: 17 9 78 N T3 SD: 0.4633 c. M:-0.7991 c. 105: 17 9 79 N T3 SD: 0.5386 c. M: 0.8490 c. 109: 18 9 82 N T3 SD: 0.4820 c. M:-0.7611 c. 116: 19 10 87 N T3 SD: 0.4643 c. M:-0.7991 c. 117: 19 10 88 N T3 SD: 0.3818 c. M: 0.6058 c. 129: 21 11 97 N T3 SD: 0.2542 c. M: 0.4078 c. 141: 23 12 106 N T3 SD: 0.1487 c. M: 0.2435 c. 153: 25 13 115 N T3 SD: 0.0612 c. M: 0.1050 c. 165: 27 14 124 N T3 SD: 0.0268 c. M:-0.0444 c. 318: 52 27 239 N T3 SD: 0.0268 c. M: 0.0436 c. 483: 79 41 363 N T3 SD: 0.0203 c. M:-0.0257 c. 648: 106 55 487 N T3 SD: 0.0195 c. M:-0.0305 c. 813: 133 69 611 N T3 SD: 0.0199 c. M:-0.0333 c. 978: 160 83 735 N T3 SD: 0.0205 c. M:-0.0352 c. 1131: 185 96 850 N T3 SD: 0.0196 c. M:-0.0284 c. 1143: 187 97 859 N T3 SD: 0.0211 c. M:-0.0365 c. 1192: 195 101 896 N T3 SD: 0.0218 c. M: 0.0366 c. 1204: 197 102 905 N T3 SD: 0.0167 c. M: 0.0283 c. 1216: 199 103 914 N T3 SD: 0.0167 c. M:-0.0208 c. 1357: 222 115 1020 N T3 SD: 0.0159 c. M: 0.0267 c. 1369: 224 116 1029 N T3 SD: 0.0119 c. M: 0.0195 c. 1522: 249 129 1144 N T3 SD: 0.0113 c. M: 0.0190 c. 1534: 251 130 1153 N T3 SD: 0.0085 c. M: 0.0126 c. 1687: 276 143 1268 N T3 SD: 0.0076 c. M: 0.0128 c. 1699: 278 144 1277 N T3 SD: 0.0062 c. M:-0.0081 c. 1852: 303 157 1392 N T3 SD: 0.0045 c. M: 0.0077 c. 2017: 330 171 1516 N T3 SD: 0.0020 c. M: 0.0034 c. 2182: 357 185 1640 N T3 SD: 0.0006 c. M:-0.0009 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 71.5794 cents 7 x 8:9 S SD: 62.2739 cents 8 x 9:11 SD: 48.1396 cents 9 x 10:12 S SD: 29.3458 cents 10 x 11:13 SD: 30.1089 cents 11 x 12:15 S SD: 23.6570 cents 12 x 13:16 SD: 7.4302 cents 13 x 14:17 SD: 16.9643 cents 14 x 15:19 SD: 15.4691 cents 15 x 16:20 S SD: 5.9905 cents 16 x 17:21 SD: 16.5465 cents 17:18 x 23 SD: 15.3620 cents 18:19 x 24 SD: 6.0591 cents 19:20 x 25 S SD: 12.0347 cents 20:21 x 27 SD: 10.8560 cents 23:24:25:31 SD: 9.6451 cents 24:25:26:32 SD: 6.1259 cents 32 x 34:43 SD: 11.5470 cents 33:35 x 44 SD: 10.1909 cents 35:37:38:47 SD: 8.9240 cents 36:38:39:48 SD: 6.3917 cents 37:39:40:49 SD: 6.3042 cents 38:40:41:51 SD: 5.2049 cents 39:41:42:52 SD: 2.2850 cents 42:44:45:56 SD: 1.4578 cents 81:85:87:108 SD: 0.6547 cents 123:129:132:164 SD: 0.5834 cents 147:154:158:196 SD: 0.5144 cents 189:198:203:252 SD: 0.3159 cents 228:239:245:304 SD: 0.2634 cents 270:283:290:360 SD: 0.0246 cents