Scala analysis: 133_C1
Chromatic tetrachord 87/85 * 85/81 * 36/29
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 87/85 40.263072 2: 29/27 123.712192 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 36/29 374.3328 1: 87/85 40.2631 2: 85/81 83.4491 3: 36/29 374.3328
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 87/85 40.263 cents 1: 1 85/81 83.449 cents 1: 1 36/29 374.333 cents 2: 1 29/27 123.712 cents 2: 1 108/85 414.596 cents 2: 1 340/261 457.782 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 : 40.3 123.7 498.0 40.3 : 83.4 457.8 498.0 123.7: 374.3 414.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.2631 .. 374.3328 cents 1020/841, 334.0697 cents 87/85, 40.2631 cents 2: 123.7122 .. 457.7819 cents 1020/841, 334.0697 cents 841/972,-250.6206 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 87/85, 40.2631 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 36/29, 374.3328 cents Average / Smallest step : 4.123257 Largest / Average step : 2.254813 Largest / Smallest step : 9.297175 Median interval of one step : 85/81, 83.4491 cents, amount: 1 Least squares average step : 127.27303 cents, oct.: 381.81910 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1707-tone equal temperament with octave 4/3 degrees: 138 424 1707 Least number of segments generator : 854 of 249.168 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 880 of 256.754 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 40.26307 cents Scale diversity : 0.557511 Lumma stability : 0.161684 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 : 87/85, 40.2631 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 29 Odd number limit : 261 (O: 87 U: 261) Highest odd numerator or denominator: 87 Scale harmonicity : 0.009685 Average absolute harmonicity : 0.080373 Specific harmonicity : 0.043656 Fundamental : 1/2295, -11.1643 octaves, 0.1140 Hz. Guide tone : 348, 8.4429 octaves, 91045.697 Hz. Exponens Consonantiae : 7.986600E+05, 19.60722 octaves Euler's gradus suavitatis : 59 Sum of Mann's harmonic distance : 117.5, average 39.16667 Mersenne's string divisions : 2408 Sum of van Prooijen's expressibility: 3.87904, average 1.29301 Sum of Tenney's harmonic distance : 7.84188, average 2.61396 Vogel's harmonic complexity : 40.66667 Wille's k value : 1232 Wilson's harmonic complexity : 63 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 17.95761, average 2.99294 Lattice compactness (without 2's) : 15.28674, average 2.54779 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.66667 2 3: -3 .. 1 -1.00000 5 1 5: -1 .. 0 -0.33333 1 17: -1 .. 0 -0.33333 1 29: 0 .. 1 0.66667 2 2 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 15 27 33| Scale is weakly epimorphic with val: <6 10 15 29 37| Scale is weakly epimorphic with val: <6 10 15 30 33| Scale is weakly epimorphic with val: <6 10 15 33 33| Scale is weakly epimorphic with val: <6 10 16 28 37| Scale is weakly epimorphic with val: <6 10 16 29 33| Scale is weakly epimorphic with val: <6 10 16 32 33| Scale is weakly epimorphic with val: <6 10 17 27 37| Scale is weakly epimorphic with val: <6 10 17 28 33| Scale is weakly epimorphic with val: <6 10 17 31 33| Scale is weakly epimorphic with val: <6 10 18 27 33| Scale is weakly epimorphic with val: <6 10 18 30 33| Scale is weakly epimorphic with val: <6 10 18 33 33| Scale is weakly epimorphic with val: <6 10 19 29 33| Scale is weakly epimorphic with val: <6 10 19 32 33| Scale is weakly epimorphic with val: <6 11 15 27 36| Scale is weakly epimorphic with val: <6 11 15 28 35| Scale is weakly epimorphic with val: <6 11 15 30 36| Scale is weakly epimorphic with val: <6 11 15 31 38| Scale is weakly epimorphic with val: <6 11 15 33 36| Scale is weakly epimorphic with val: <6 11 16 27 35| Scale is weakly epimorphic with val: <6 11 16 29 36| Scale is weakly epimorphic with val: <6 11 16 30 38| Scale is weakly epimorphic with val: <6 11 16 32 36| Scale is weakly epimorphic with val: <6 11 17 28 36| Scale is weakly epimorphic with val: <6 11 17 29 38| Scale is weakly epimorphic with val: <6 11 17 31 36| Scale is weakly epimorphic with val: <6 11 18 27 36| Scale is weakly epimorphic with val: <6 11 18 28 38| Scale is weakly epimorphic with val: <6 11 18 30 36| Scale is weakly epimorphic with val: <6 11 18 33 36| Scale is weakly epimorphic with val: <6 11 19 27 38| Scale is weakly epimorphic with val: <6 11 19 29 36| Scale is weakly epimorphic with val: <6 11 19 32 36| Scale is weakly epimorphic with val: <7 10 15 27 35| Scale is weakly epimorphic with val: <7 10 15 29 33| Scale is weakly epimorphic with val: <7 10 15 30 38| Scale is weakly epimorphic with val: <7 10 15 32 33| Scale is weakly epimorphic with val: <7 10 16 28 33| Scale is weakly epimorphic with val: <7 10 16 29 38| Scale is weakly epimorphic with val: <7 10 16 31 33| Scale is weakly epimorphic with val: <7 10 17 27 33| Scale is weakly epimorphic with val: <7 10 17 28 38| Scale is weakly epimorphic with val: <7 10 17 30 33| Scale is weakly epimorphic with val: <7 10 17 33 33| Scale is weakly epimorphic with val: <7 10 18 27 38| Scale is weakly epimorphic with val: <7 10 18 29 33| Scale is weakly epimorphic with val: <7 10 18 32 33| Scale is weakly epimorphic with val: <7 10 19 28 33| Scale is weakly epimorphic with val: <7 10 19 31 33| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 27 35| Scale is weakly epimorphic with val: <7 11 15 27 38| Scale is weakly epimorphic with val: <7 11 15 28 34| Scale is weakly epimorphic with val: <7 11 15 28 37| Scale is weakly epimorphic with val: <7 11 15 30 32| Scale is JI-epimorphic with val: <7 11 15 30 35| Scale is weakly epimorphic with val: <7 11 15 30 38| Scale is weakly epimorphic with val: <7 11 15 31 34| Scale is weakly epimorphic with val: <7 11 15 31 37| Scale is weakly epimorphic with val: <7 11 15 33 35| Scale is weakly epimorphic with val: <7 11 15 33 38| Scale is weakly epimorphic with val: <7 11 16 27 34| Scale is weakly epimorphic with val: <7 11 16 27 37| Scale is weakly epimorphic with val: <7 11 16 29 32| Scale is JI-epimorphic with val: <7 11 16 29 35| Scale is weakly epimorphic with val: <7 11 16 29 38| Scale is weakly epimorphic with val: <7 11 16 30 34| Scale is weakly epimorphic with val: <7 11 16 30 37| Scale is weakly epimorphic with val: <7 11 16 32 32| Scale is weakly epimorphic with val: <7 11 16 32 35| Scale is weakly epimorphic with val: <7 11 16 32 38| Scale is weakly epimorphic with val: <7 11 16 33 34| Scale is weakly epimorphic with val: <7 11 16 33 37| Scale is weakly epimorphic with val: <7 11 17 28 32| Scale is JI-epimorphic with val: <7 11 17 28 35| Scale is weakly epimorphic with val: <7 11 17 28 38| Scale is weakly epimorphic with val: <7 11 17 29 34| Scale is weakly epimorphic with val: <7 11 17 29 37| Scale is weakly epimorphic with val: <7 11 17 31 32| Scale is weakly epimorphic with val: <7 11 17 31 35| Scale is weakly epimorphic with val: <7 11 17 31 38| Scale is weakly epimorphic with val: <7 11 17 32 34| Scale is weakly epimorphic with val: <7 11 17 32 37| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is JI-epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 27 38| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 18 28 37| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is weakly epimorphic with val: <7 11 18 30 35| Scale is weakly epimorphic with val: <7 11 18 30 38| Scale is weakly epimorphic with val: <7 11 18 31 34| Scale is weakly epimorphic with val: <7 11 18 31 37| Scale is weakly epimorphic with val: <7 11 18 33 35| Scale is weakly epimorphic with val: <7 11 18 33 38| Scale is weakly epimorphic with val: <7 11 19 27 34| Scale is weakly epimorphic with val: <7 11 19 27 37| Scale is weakly epimorphic with val: <7 11 19 29 32| Scale is weakly epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 19 29 38| Scale is weakly epimorphic with val: <7 11 19 30 34| Scale is weakly epimorphic with val: <7 11 19 30 37| Scale is weakly epimorphic with val: <7 11 19 32 32| Scale is weakly epimorphic with val: <7 11 19 32 35| Scale is weakly epimorphic with val: <7 11 19 32 38| Scale is weakly epimorphic with val: <7 11 19 33 34| Scale is weakly epimorphic with val: <7 11 19 33 37| Scale is weakly epimorphic with val: <7 12 15 28 34| Scale is weakly epimorphic with val: <7 12 15 31 37| Scale is weakly epimorphic with val: <7 12 16 27 34| Scale is weakly epimorphic with val: <7 12 16 30 37| Scale is weakly epimorphic with val: <7 12 17 29 37| Scale is weakly epimorphic with val: <7 12 18 28 37| Scale is weakly epimorphic with val: <7 12 19 27 37| Scale is weakly epimorphic with val: <8 11 15 27 34| Scale is weakly epimorphic with val: <8 11 15 28 36| Scale is weakly epimorphic with val: <8 11 15 30 37| Scale is weakly epimorphic with val: <8 11 15 31 36| Scale is weakly epimorphic with val: <8 11 16 27 36| Scale is weakly epimorphic with val: <8 11 16 29 37| Scale is weakly epimorphic with val: <8 11 16 30 36| Scale is weakly epimorphic with val: <8 11 16 33 36| Scale is weakly epimorphic with val: <8 11 17 28 37| Scale is weakly epimorphic with val: <8 11 17 29 36| Scale is weakly epimorphic with val: <8 11 17 32 36| Scale is weakly epimorphic with val: <8 11 18 27 37| Scale is weakly epimorphic with val: <8 11 18 28 36| Scale is weakly epimorphic with val: <8 11 18 31 36| Scale is weakly epimorphic with val: <8 11 19 27 36| Scale is weakly epimorphic with val: <8 11 19 30 36| Scale is weakly epimorphic with val: <8 11 19 33 36| Scale is weakly epimorphic with val: <8 12 15 29 35| Scale is weakly epimorphic with val: <8 12 15 32 38| Scale is weakly epimorphic with val: <8 12 16 28 35| Scale is weakly epimorphic with val: <8 12 16 31 38| Scale is weakly epimorphic with val: <8 12 17 27 35| Scale is weakly epimorphic with val: <8 12 17 30 38| Scale is weakly epimorphic with val: <8 12 18 29 38| Scale is weakly epimorphic with val: <8 12 19 28 38|
FIT/MODE
3: 0 1 2 N G T3 SD: 33.7177 c. M:-42.3028 c. 4: 0 1 3 N G T3 SD: 23.2505 c. M: 40.2631 c. 5: 0 1 4 N G T3 SD: 27.0929 c. M: 40.2631 c. 7: 1 1 5 N M DE S SD: 20.8119 c. M:-30.8862 c. 8: 1 1 6 N M DE S SD: 12.7058 c. M:-21.9926 c. 9: 1 1 7 N M DE S SD: 11.5064 c. M:-15.0753 c. 11: 1 2 8 N T3 SD: 7.5717 c. M:-12.1183 c. 12: 1 2 9 N T3 SD: 0.8520 c. M:-1.2407 c. 61: 5 10 46 N T3 SD: 0.7867 c. M: 1.2421 c. 73: 6 12 55 N T3 SD: 0.6516 c. M: 0.9066 c. 85: 7 14 64 N T3 SD: 0.5800 c. M:-0.7524 c. 97: 8 16 73 N T3 SD: 0.5463 c. M:-0.8128 c. 100: 8 17 75 N T3 SD: 0.5210 c. M:-0.7991 c. 101: 8 17 76 N T3 SD: 0.5325 c. M: 0.8140 c. 112: 9 19 84 N T3 SD: 0.4820 c. M:-0.7991 c. 113: 9 19 85 N T3 SD: 0.3858 c. M: 0.5958 c. 125: 10 21 94 N T3 SD: 0.2676 c. M: 0.4195 c. 137: 11 23 103 N T3 SD: 0.1705 c. M: 0.2741 c. 149: 12 25 112 N T3 SD: 0.0903 c. M: 0.1521 c. 161: 13 27 121 N T3 SD: 0.0316 c. M: 0.0483 c. 334: 27 56 251 N T3 SD: 0.0309 c. M:-0.0535 c. 495: 40 83 372 N T3 SD: 0.0275 c. M:-0.0444 c. 656: 53 110 493 N T3 SD: 0.0271 c. M:-0.0398 c. 817: 66 137 614 N T3 SD: 0.0273 c. M:-0.0371 c. 829: 67 139 623 N T3 SD: 0.0285 c. M:-0.0481 c. 890: 72 149 669 N T3 SD: 0.0284 c. M: 0.0403 c. 978: 79 164 735 N T3 SD: 0.0276 c. M:-0.0352 c. 1027: 83 172 772 N T3 SD: 0.0295 c. M: 0.0496 c. 1039: 84 174 781 N T3 SD: 0.0230 c. M: 0.0398 c. 1051: 85 176 790 N T3 SD: 0.0199 c. M: 0.0302 c. 1200: 97 201 902 N T3 SD: 0.0181 c. M: 0.0310 c. 1212: 98 203 911 N T3 SD: 0.0139 c. M: 0.0228 c. 1224: 99 205 920 N T3 SD: 0.0143 c. M:-0.0200 c. 1361: 110 228 1023 N T3 SD: 0.0151 c. M: 0.0243 c. 1373: 111 230 1032 N T3 SD: 0.0099 c. M: 0.0171 c. 1385: 112 232 1041 N T3 SD: 0.0091 c. M:-0.0120 c. 1534: 124 257 1153 N T3 SD: 0.0076 c. M: 0.0126 c. 1546: 125 259 1162 N T3 SD: 0.0049 c. M: 0.0063 c. 1707: 138 286 1283 N T3 SD: 0.0019 c. M: 0.0033 c. 1868: 151 313 1404 N T3 SD: 0.0021 c. M: 0.0035 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 x 18:23 SD: 17.6898 cents 18 x 19:24 SD: 15.0546 cents 19 x 20:25 S SD: 20.8843 cents 20 x 21:27 SD: 22.3757 cents 21:22:23:28 SD: 17.5219 cents 22:23:24:29 SD: 16.5423 cents 23:24:25:31 SD: 14.5032 cents 24:25:26:32 SD: 11.2821 cents 26:27:28:35 S SD: 10.1336 cents 27:28:29:36 SD: 7.5659 cents 30:31:32:40 S SD: 6.7980 cents 36:37:39:48 SD: 5.5001 cents 38:39:41:51 SD: 4.8586 cents 39:40:42:52 SD: 1.9368 cents 42:43:45:56 SD: 1.4319 cents 81:83:87:108 SD: 0.6547 cents 174:178:187:232 SD: 0.4590 cents 216:221:232:288 SD: 0.2150 cents 297:304:319:396 SD: 0.0223 cents