Scala analysis: 203_C12
Chromatic tetrachord 22/21 * 21/20 * 40/33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/33 333.0408 1: 22/21 80.5370 undecimal minor semitone 2: 21/20 84.4672 minor semitone 3: 40/33 333.0408
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 21/20 84.467 cents minor semitone 1: 1 40/33 333.041 cents 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 80/63 413.578 cents wide major third 2: 1 14/11 417.508 cents undecimal diminished fourth or major 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 : 80.5 165.0 498.0 80.5 : 84.5 417.5 498.0 165.0: 333.0 413.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 333.0408 cents 140/121, 252.5037 cents 22/21, 80.5370 cents 2: 165.0042 .. 417.5080 cents 140/121, 252.5037 cents 363/400,-168.0365 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 40/33, 333.0408 cents Average / Smallest step : 2.061350 Largest / Average step : 2.006088 Largest / Smallest step : 4.135250 Median interval of one step : 21/20, 84.4672 cents, amount: 1 Least squares average step : 136.04861 cents, oct.: 408.14582 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1144-tone equal temperament with octave 4/3 degrees: 185 379 1144 Least number of segments generator : 573 of 249.458 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 717 of 312.149 cents and inv. generated superset size: 47 = 44 more = 1566.667% 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 80.53704 cents Scale diversity : 0.901201 Lumma stability : 0.323413 Lumma impropriety factor : 0.337392 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 : 441/440, 3.9302 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 248.5736 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.024671 Average absolute harmonicity : 0.094831 Specific harmonicity : 0.111536 Fundamental : 1/210, -7.7142 octaves, 1.2458 Hz. Guide tone : 44, 5.4594 octaves, 11511.525 Hz. Exponens Consonantiae : 9.240000E+03, 13.17368 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 35.5, average 11.83333 Mersenne's string divisions : 903 Sum of van Prooijen's expressibility: 2.84073, average 0.94691 Sum of Tenney's harmonic distance : 5.78522, average 1.92841 Vogel's harmonic complexity : 18.00000 Wille's k value : 115 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.81002, average 2.30167 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 0.66667 4 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 11: 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 15 18 25| Scale is weakly epimorphic with val: <6 10 15 19 24| Scale is weakly epimorphic with val: <6 10 15 22 24| Scale is weakly epimorphic with val: <6 10 16 19 26| Scale is weakly epimorphic with val: <6 10 16 20 25| Scale is weakly epimorphic with val: <6 10 17 18 26| Scale is weakly epimorphic with val: <6 10 17 20 27| Scale is weakly epimorphic with val: <6 10 17 21 26| Scale is weakly epimorphic with val: <6 10 18 18 25| Scale is weakly epimorphic with val: <6 10 18 19 27| Scale is weakly epimorphic with val: <6 10 18 22 27| Scale is weakly epimorphic with val: <6 10 19 19 26| Scale is weakly epimorphic with val: <6 11 15 18 26| Scale is weakly epimorphic with val: <6 11 15 20 24| Scale is weakly epimorphic with val: <6 11 16 18 25| Scale is weakly epimorphic with val: <6 11 16 19 27| Scale is weakly epimorphic with val: <6 11 16 21 25| Scale is weakly epimorphic with val: <6 11 17 19 26| Scale is weakly epimorphic with val: <6 11 17 22 26| Scale is weakly epimorphic with val: <6 11 18 18 26| Scale is weakly epimorphic with val: <6 11 18 20 27| Scale is weakly epimorphic with val: <6 11 19 19 27| Scale is weakly epimorphic with val: <7 10 15 18 24| Scale is weakly epimorphic with val: <7 10 15 20 25| Scale is weakly epimorphic with val: <7 10 15 21 27| Scale is weakly epimorphic with val: <7 10 16 18 26| Scale is weakly epimorphic with val: <7 10 16 19 25| Scale is weakly epimorphic with val: <7 10 16 21 26| Scale is weakly epimorphic with val: <7 10 17 19 27| Scale is weakly epimorphic with val: <7 10 17 20 26| Scale is weakly epimorphic with val: <7 10 17 22 27| Scale is weakly epimorphic with val: <7 10 18 18 24| Scale is weakly epimorphic with val: <7 10 18 21 27| Scale is weakly epimorphic with val: <7 10 19 19 25| Scale is JI-epimorphic with val: <7 11 15 19 24| Scale is weakly epimorphic with val: <7 11 15 19 27| Scale is weakly epimorphic with val: <7 11 15 20 23| Scale is weakly epimorphic with val: <7 11 15 20 26| Scale is weakly epimorphic with val: <7 11 15 22 24| Scale is weakly epimorphic with val: <7 11 15 22 27| Scale is weakly epimorphic with val: <7 11 16 18 24| Scale is weakly epimorphic with val: <7 11 16 18 27| Scale is JI-epimorphic with val: <7 11 16 20 25| Scale is weakly epimorphic with val: <7 11 16 21 24| Scale is weakly epimorphic with val: <7 11 16 21 27| Scale is weakly epimorphic with val: <7 11 17 18 23| Scale is weakly epimorphic with val: <7 11 17 18 26| Scale is weakly epimorphic with val: <7 11 17 19 25| Scale is weakly epimorphic with val: <7 11 17 21 23| Scale is JI-epimorphic with val: <7 11 17 21 26| Scale is weakly epimorphic with val: <7 11 17 22 25| Scale is weakly epimorphic with val: <7 11 18 19 24| Scale is weakly epimorphic with val: <7 11 18 19 27| Scale is weakly epimorphic with val: <7 11 18 20 23| Scale is weakly epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 22 24| Scale is JI-epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 11 19 20 25| Scale is weakly epimorphic with val: <7 11 19 21 24| Scale is weakly epimorphic with val: <7 11 19 21 27| Scale is weakly epimorphic with val: <7 12 15 18 26| Scale is weakly epimorphic with val: <7 12 15 19 25| Scale is weakly epimorphic with val: <7 12 15 22 25| Scale is weakly epimorphic with val: <7 12 16 19 27| Scale is weakly epimorphic with val: <7 12 16 20 26| Scale is weakly epimorphic with val: <7 12 17 18 27| Scale is weakly epimorphic with val: <7 12 17 21 27| Scale is weakly epimorphic with val: <7 12 18 18 26| Scale is weakly epimorphic with val: <7 12 19 19 27| Scale is weakly epimorphic with val: <8 11 15 18 24| Scale is weakly epimorphic with val: <8 11 15 19 26| Scale is weakly epimorphic with val: <8 11 15 21 27| Scale is weakly epimorphic with val: <8 11 15 22 26| Scale is weakly epimorphic with val: <8 11 16 19 25| Scale is weakly epimorphic with val: <8 11 16 20 27| Scale is weakly epimorphic with val: <8 11 17 20 26| Scale is weakly epimorphic with val: <8 11 18 18 24| Scale is weakly epimorphic with val: <8 11 18 21 27| Scale is weakly epimorphic with val: <8 11 19 19 25| Scale is weakly epimorphic with val: <8 12 15 18 25| Scale is weakly epimorphic with val: <8 12 15 20 26| Scale is weakly epimorphic with val: <8 12 16 18 27| Scale is weakly epimorphic with val: <8 12 16 19 26| Scale is weakly epimorphic with val: <8 12 16 21 27| Scale is weakly epimorphic with val: <8 12 17 20 27| Scale is weakly epimorphic with val: <8 12 18 18 25| Scale is weakly epimorphic with val: <8 12 19 19 26|
FIT/MODE
3: 0 1 2 N G T3 SD: 46.5017 c. M: 80.5370 c. 4: 0 1 3 N G T3 SD: 52.0445 c. M: 80.5370 c. 5: 1 1 3 N M DE S SD: 22.6151 c. M:-34.2138 c. 6: 1 1 4 N M DE S SD: 1.5411 c. M:-2.4705 c. 49: 8 8 33 N M DE S SD: 1.4439 c. M: 2.3773 c. 55: 9 9 37 N M DE S SD: 1.2851 c. M: 2.0077 c. 57: 9 10 38 N T3 SD: 1.2417 c. M: 1.8984 c. 61: 10 10 41 N M DE S SD: 1.1773 c. M: 1.7108 c. 63: 10 11 42 N T3 SD: 1.0358 c. M: 1.4823 c. 67: 11 11 45 N M DE S SD: 1.1059 c. M: 1.4671 c. 69: 11 12 46 N T3 SD: 0.8790 c. M: 1.1386 c. 75: 12 13 50 N T3 SD: 0.7624 c. M:-1.0108 c. 81: 13 14 54 N T3 SD: 0.6798 c. M:-1.0108 c. 87: 14 15 58 N T3 SD: 0.6259 c. M:-1.0108 c. 93: 15 16 62 N T3 SD: 0.5957 c. M:-1.0108 c. 99: 16 17 66 N T3 SD: 0.5841 c. M:-1.0108 c. 100: 16 17 67 N T3 SD: 0.6175 c. M: 0.8498 c. 105: 17 18 70 N T3 SD: 0.5864 c. M:-1.0108 c. 106: 17 18 71 N T3 SD: 0.4989 c. M: 0.6619 c. 112: 18 19 75 N T3 SD: 0.3943 c. M: 0.4941 c. 118: 19 20 79 N T3 SD: 0.3027 c. M: 0.3961 c. 124: 20 21 83 N T3 SD: 0.2240 c. M: 0.3281 c. 130: 21 22 87 N T3 SD: 0.1611 c. M: 0.2663 c. 136: 22 23 91 N T3 SD: 0.1224 c. M: 0.2099 c. 142: 23 24 95 N T3 SD: 0.1191 c. M: 0.1583 c. 266: 43 45 178 N T3 SD: 0.1379 c. M: 0.2375 c. 278: 45 47 186 N T3 SD: 0.1160 c. M: 0.1836 c. 347: 56 59 232 N T3 SD: 0.0980 c. M: 0.1609 c. 353: 57 60 236 N T3 SD: 0.0784 c. M: 0.1162 c. 359: 58 61 240 N T3 SD: 0.0651 c. M:-0.0859 c. 365: 59 62 244 N T3 SD: 0.0611 c. M:-0.1011 c. 371: 60 63 248 N T3 SD: 0.0671 c. M:-0.1158 c. 483: 78 82 323 N T3 SD: 0.0631 c. M: 0.1074 c. 489: 79 83 327 N T3 SD: 0.0440 c. M: 0.0758 c. 495: 80 84 331 N T3 SD: 0.0261 c. M: 0.0449 c. 501: 81 85 335 N T3 SD: 0.0129 c. M:-0.0167 c. 1008: 163 171 674 N T3 SD: 0.0130 c. M:-0.0226 c. 1138: 184 193 761 N T3 SD: 0.0082 c. M: 0.0104 c. 1144: 185 194 765 N T3 SD: 0.0035 c. M: 0.0051 c. 1645: 266 279 1100 N T3 SD: 0.0015 c. M: 0.0021 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: 86.3514 cents 6 x 7:8 S SD: 50.9333 cents 7 x 8:9 S SD: 45.6687 cents 8 x 9:11 SD: 32.9836 cents 9 x 10:12 S SD: 8.6997 cents 10 x 11:13 SD: 21.9155 cents 11 x 12:15 S SD: 20.7369 cents 12 x 13:16 SD: 13.2158 cents 13 x 14:17 SD: 24.8870 cents 14:15 x 19 SD: 24.7619 cents 15:16:17:20 SD: 20.1223 cents 16:17:18:21 S SD: 17.8053 cents 17:18:19:23 SD: 13.8931 cents 18:19:20:24 S SD: 7.2531 cents 21:22:23:28 SD: 2.5036 cents 39:41:43:52 SD: 2.4212 cents 60:63:66:80 SD: 1.3101 cents 81:85:89:108 SD: 1.1671 cents 129:135:142:172 SD: 0.7333 cents 150:157:165:200 SD: 0.5249 cents 189:198:208:252 SD: 0.2775 cents 210:220:231:280 SD: 0.0000 cents