Scala analysis: 190_C10
Chromatic tetrachord 23/22 * 22/21 * 28/23, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/22 76.956405 2: 23/21 157.493440 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 28/23 340.5516 1: 23/22 76.9564 2: 22/21 80.5370 undecimal minor semitone 3: 28/23 340.5516
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 23/22 76.956 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 28/23 340.552 cents 2: 1 23/21 157.493 cents 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 88/69 421.089 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 : 77.0 157.5 498.0 77.0 : 80.5 421.1 498.0 157.5: 340.6 417.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.9564 .. 340.5516 cents 616/529, 263.5952 cents 23/22, 76.9564 cents 2: 157.4934 .. 421.0886 cents 616/529, 263.5952 cents 529/588,-183.0581 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 23/22, 76.9564 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 28/23, 340.5516 cents Average / Smallest step : 2.157260 Largest / Average step : 2.051330 Largest / Smallest step : 4.425253 Median interval of one step : 22/21, 80.5370 cents, amount: 1 Least squares average step : 134.71988 cents, oct.: 404.15963 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1812-tone equal temperament with octave 4/3 degrees: 280 573 1812 Least number of segments generator : 907 of 249.297 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1429 of 392.774 cents and inv. generated superset size: 68 = 65 more = 2266.667% 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 76.95640 cents Scale diversity : 0.852181 Lumma stability : 0.309034 Lumma impropriety factor : 0.367553 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 : 484/483, 3.5806 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 : 2 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 Limited inverse transpositions with margin 260.0145 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 69 (O: 23 U: 69) Highest odd numerator or denominator: 23 Scale harmonicity : 0.013120 Average absolute harmonicity : 0.082925 Specific harmonicity : 0.058518 Fundamental : 1/462, -8.8517 octaves, 0.5663 Hz. Guide tone : 92, 6.5236 octaves, 24069.552 Hz. Exponens Consonantiae : 4.250400E+04, 15.37531 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 48.0, average 16.00000 Mersenne's string divisions : 13860 Sum of van Prooijen's expressibility: 3.20058, average 1.06686 Sum of Tenney's harmonic distance : 6.46728, average 2.15576 Vogel's harmonic complexity : 29.66667 Wille's k value : 241 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.61376, average 2.26896 Lattice compactness (without 2's) : 9.02458, average 1.50410 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.33333 3 3: -1 .. 0 -0.66667 2 1 7: -1 .. 0 -0.33333 1 11: -1 .. 0 -0.33333 1 23: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 18 23 32| Scale is weakly epimorphic with val: <6 10 18 24 31| Scale is weakly epimorphic with val: <6 10 18 26 35| Scale is weakly epimorphic with val: <6 10 18 27 31| Scale is weakly epimorphic with val: <6 10 19 24 33| Scale is weakly epimorphic with val: <6 10 19 25 32| Scale is weakly epimorphic with val: <6 10 19 27 36| Scale is weakly epimorphic with val: <6 10 20 23 33| Scale is weakly epimorphic with val: <6 10 20 25 34| Scale is weakly epimorphic with val: <6 10 20 26 33| Scale is weakly epimorphic with val: <6 10 21 23 32| Scale is weakly epimorphic with val: <6 10 21 24 34| Scale is weakly epimorphic with val: <6 10 21 26 35| Scale is weakly epimorphic with val: <6 10 21 27 34| Scale is weakly epimorphic with val: <6 10 22 24 33| Scale is weakly epimorphic with val: <6 10 22 25 35| Scale is weakly epimorphic with val: <6 10 22 27 36| Scale is weakly epimorphic with val: <6 11 18 24 32| Scale is weakly epimorphic with val: <6 11 18 25 34| Scale is weakly epimorphic with val: <6 11 18 27 32| Scale is weakly epimorphic with val: <6 11 19 23 32| Scale is weakly epimorphic with val: <6 11 19 25 33| Scale is weakly epimorphic with val: <6 11 19 26 35| Scale is weakly epimorphic with val: <6 11 20 23 34| Scale is weakly epimorphic with val: <6 11 20 24 33| Scale is weakly epimorphic with val: <6 11 20 26 34| Scale is weakly epimorphic with val: <6 11 20 27 36| Scale is weakly epimorphic with val: <6 11 21 24 35| Scale is weakly epimorphic with val: <6 11 21 25 34| Scale is weakly epimorphic with val: <6 11 21 27 35| Scale is weakly epimorphic with val: <6 11 22 23 32| Scale is weakly epimorphic with val: <6 11 22 25 36| Scale is weakly epimorphic with val: <6 11 22 26 35| Scale is weakly epimorphic with val: <7 10 18 23 33| Scale is weakly epimorphic with val: <7 10 18 25 31| Scale is weakly epimorphic with val: <7 10 18 26 36| Scale is weakly epimorphic with val: <7 10 19 23 32| Scale is weakly epimorphic with val: <7 10 19 24 34| Scale is weakly epimorphic with val: <7 10 19 26 32| Scale is weakly epimorphic with val: <7 10 20 24 33| Scale is weakly epimorphic with val: <7 10 20 25 35| Scale is weakly epimorphic with val: <7 10 20 27 33| Scale is weakly epimorphic with val: <7 10 21 23 33| Scale is weakly epimorphic with val: <7 10 21 25 34| Scale is weakly epimorphic with val: <7 10 21 26 36| Scale is weakly epimorphic with val: <7 10 22 23 35| Scale is weakly epimorphic with val: <7 10 22 24 34| Scale is weakly epimorphic with val: <7 10 22 26 35| Scale is JI-epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 23 34| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 24 36| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 26 34| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 18 27 36| Scale is JI-epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 24 35| Scale is weakly epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 27 35| Scale is weakly epimorphic with val: <7 11 20 23 32| Scale is weakly epimorphic with val: <7 11 20 23 35| Scale is weakly epimorphic with val: <7 11 20 25 30| Scale is JI-epimorphic with val: <7 11 20 25 33| = patent Scale is weakly epimorphic with val: <7 11 20 25 36| Scale is weakly epimorphic with val: <7 11 20 26 32| Scale is weakly epimorphic with val: <7 11 20 26 35| Scale is weakly epimorphic with val: <7 11 21 23 31| Scale is weakly epimorphic with val: <7 11 21 23 34| Scale is weakly epimorphic with val: <7 11 21 24 30| Scale is weakly epimorphic with val: <7 11 21 24 33| Scale is weakly epimorphic with val: <7 11 21 24 36| Scale is weakly epimorphic with val: <7 11 21 26 31| Scale is JI-epimorphic with val: <7 11 21 26 34| Scale is weakly epimorphic with val: <7 11 21 27 30| Scale is weakly epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 21 27 36| Scale is weakly epimorphic with val: <7 11 22 24 32| Scale is weakly epimorphic with val: <7 11 22 24 35| Scale is weakly epimorphic with val: <7 11 22 25 31| Scale is weakly epimorphic with val: <7 11 22 25 34| Scale is weakly epimorphic with val: <7 11 22 27 32| Scale is JI-epimorphic with val: <7 11 22 27 35| Scale is weakly epimorphic with val: <7 12 18 24 34| Scale is weakly epimorphic with val: <7 12 18 25 33| Scale is weakly epimorphic with val: <7 12 19 23 34| Scale is weakly epimorphic with val: <7 12 19 25 35| Scale is weakly epimorphic with val: <7 12 19 26 34| Scale is weakly epimorphic with val: <7 12 20 23 33| Scale is weakly epimorphic with val: <7 12 20 24 35| Scale is weakly epimorphic with val: <7 12 20 26 36| Scale is weakly epimorphic with val: <7 12 20 27 35| Scale is weakly epimorphic with val: <7 12 21 24 34| Scale is weakly epimorphic with val: <7 12 21 25 36| Scale is weakly epimorphic with val: <7 12 22 25 35| Scale is weakly epimorphic with val: <8 11 18 23 32| Scale is weakly epimorphic with val: <8 11 18 25 36| Scale is weakly epimorphic with val: <8 11 18 26 32| Scale is weakly epimorphic with val: <8 11 19 23 34| Scale is weakly epimorphic with val: <8 11 19 24 33| Scale is weakly epimorphic with val: <8 11 19 27 33| Scale is weakly epimorphic with val: <8 11 20 24 35| Scale is weakly epimorphic with val: <8 11 20 25 34| Scale is weakly epimorphic with val: <8 11 21 23 35| Scale is weakly epimorphic with val: <8 11 21 25 36| Scale is weakly epimorphic with val: <8 11 21 26 35| Scale is weakly epimorphic with val: <8 11 22 23 34| Scale is weakly epimorphic with val: <8 11 22 24 36| Scale is weakly epimorphic with val: <8 11 22 27 36| Scale is weakly epimorphic with val: <8 12 18 23 33| Scale is weakly epimorphic with val: <8 12 18 24 35| Scale is weakly epimorphic with val: <8 12 18 26 33| Scale is weakly epimorphic with val: <8 12 19 24 34| Scale is weakly epimorphic with val: <8 12 19 25 36| Scale is weakly epimorphic with val: <8 12 19 27 34| Scale is weakly epimorphic with val: <8 12 20 23 34| Scale is weakly epimorphic with val: <8 12 20 25 35| Scale is weakly epimorphic with val: <8 12 21 23 36| Scale is weakly epimorphic with val: <8 12 21 24 35| Scale is weakly epimorphic with val: <8 12 21 26 36| Scale is weakly epimorphic with val: <8 12 22 25 36|
FIT/MODE
3: 0 1 2 N G T3 SD: 44.7024 c. M: 76.9564 c. 4: 0 1 3 N G T3 SD: 48.3395 c. M: 76.9564 c. 5: 1 1 3 N M DE S SD: 27.4109 c. M:-41.7246 c. 6: 1 1 4 N M DE S SD: 6.0341 c. M:-8.5216 c. 13: 2 2 9 N M DE S SD: 2.4606 c. M: 4.2488 c. 19: 3 3 13 N M DE S SD: 0.9792 c. M:-1.6823 c. 51: 8 8 35 N M DE S SD: 0.9853 c. M: 1.2440 c. 70: 11 11 48 N M DE S SD: 0.9384 c. M:-1.3078 c. 79: 12 13 54 N T3 SD: 0.7558 c. M: 1.3040 c. 85: 13 14 58 N T3 SD: 0.6107 c. M: 0.7848 c. 98: 15 16 67 N T3 SD: 0.4196 c. M: 0.7250 c. 104: 16 17 71 N T3 SD: 0.3666 c. M:-0.5401 c. 117: 18 19 80 N T3 SD: 0.1929 c. M: 0.3341 c. 136: 21 22 93 N T3 SD: 0.0331 c. M: 0.0524 c. 427: 66 69 292 N T3 SD: 0.0233 c. M: 0.0319 c. 563: 87 91 385 N T3 SD: 0.0176 c. M: 0.0298 c. 699: 108 113 478 N T3 SD: 0.0168 c. M: 0.0286 c. 835: 129 135 571 N T3 SD: 0.0177 c. M: 0.0277 c. 971: 150 157 664 N T3 SD: 0.0189 c. M: 0.0271 c. 977: 151 158 668 N T3 SD: 0.0183 c. M:-0.0254 c. 1094: 169 177 748 N T3 SD: 0.0174 c. M:-0.0235 c. 1113: 172 180 761 N T3 SD: 0.0127 c. M:-0.0194 c. 1249: 193 202 854 N T3 SD: 0.0087 c. M:-0.0148 c. 1385: 214 224 947 N T3 SD: 0.0065 c. M:-0.0110 c. 1521: 235 246 1040 N T3 SD: 0.0060 c. M:-0.0080 c. 1676: 259 271 1146 N T3 SD: 0.0053 c. M:-0.0088 c. 1812: 280 293 1239 N T3 SD: 0.0025 c. M:-0.0042 c. 1948: 301 315 1332 N T3 SD: 0.0005 c. M: 0.0008 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: 89.6458 cents 6 x 7:8 S SD: 54.6887 cents 7 x 8:9 S SD: 48.4585 cents 8 x 9:11 SD: 35.3288 cents 9 x 10:12 S SD: 12.4551 cents 10 x 11:13 SD: 22.2350 cents 11 x 12:15 S SD: 19.7527 cents 12 x 13:16 SD: 9.4604 cents 13 x 14:17 SD: 22.2625 cents 14 x 15:19 SD: 24.4274 cents 15:16 x 20 S SD: 17.3874 cents 17:18:19:23 SD: 16.1665 cents 18:19:20:24 S SD: 9.9868 cents 20:21:22:27 SD: 7.9954 cents 21:22:23:28 SD: 1.1935 cents 114:119:125:152 SD: 1.1008 cents 135:141:148:180 SD: 0.7885 cents 156:163:171:208 SD: 0.5798 cents 177:185:194:236 SD: 0.4481 cents 198:207:217:264 SD: 0.3800 cents 219:229:240:292 SD: 0.3622 cents 243:254:266:324 SD: 0.3266 cents 264:276:289:352 SD: 0.2852 cents 285:298:312:380 SD: 0.2785 cents 378:395:414:504 SD: 0.2656 cents 399:417:437:532 SD: 0.1887 cents 420:439:460:560 SD: 0.1195 cents 441:461:483:588 SD: 0.0569 cents 462:483:506:616 SD: 0.0000 cents