Scala analysis: 296_C21
Chromatic tetrachord 68/67 * 67/60 * 20/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/67 25.648381 2: 17/15 216.686695 septendecimal whole tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 68/67 25.6484 2: 67/60 191.0383 3: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/67 25.648 cents 1: 1 67/60 191.038 cents 1: 1 20/17 281.358 cents septendecimal augmented second 2: 1 17/15 216.687 cents septendecimal whole tone 2: 1 80/67 307.007 cents 2: 1 67/51 472.397 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 : 25.6 216.7 498.0 25.6 : 191.0 472.4 498.0 216.7: 281.4 307.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.6484 .. 281.3583 cents 335/289, 255.7099 cents 68/67, 25.6484 cents 2: 216.6867 .. 472.3966 cents 335/289, 255.7099 cents 289/300,-64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/67, 25.6484 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 6.472728 Largest / Average step : 1.694776 Largest / Smallest step : 10.969827 Median interval of one step : 67/60, 191.0383 cents, amount: 1 Least squares average step : 139.51120 cents, oct.: 418.53359 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1340-tone equal temperament with octave 4/3 degrees: 69 583 1340 Least number of segments generator : 671 of 249.394 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 859 of 319.269 cents and inv. generated superset size: 55 = 52 more = 1833.333% 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 25.64838 cents Scale diversity : 0.577971 Lumma stability : 0.102996 Lumma impropriety factor : 0.129851 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 : 68/67, 25.6484 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 : 67 Odd number limit : 67 (O: 67 U: 67) Highest odd numerator or denominator: 67 Scale harmonicity : 0.024281 Fundamental : 1/1005, -9.9730 octaves, 0.2603 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 6.834000E+04, 16.06044 octaves Euler's gradus suavitatis : 91 Sum of Mann's harmonic distance : 87.0, average 29.00000 Mersenne's string divisions : 30240 Sum of van Prooijen's expressibility: 3.53364, average 1.17788 Sum of Tenney's harmonic distance : 7.14431, average 2.38144 Vogel's harmonic complexity : 61.66667 Wille's k value : 569 Wilson's harmonic complexity : 92 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 12.51738, average 2.08623 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 67: -1 .. 0 -0.33333 1 1 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 28 45| Scale is weakly epimorphic with val: <6 10 16 29 43| Scale is weakly epimorphic with val: <6 10 17 30 44| Scale is weakly epimorphic with val: <6 10 18 31 45| Scale is weakly epimorphic with val: <6 10 19 32 43| Scale is weakly epimorphic with val: <6 11 15 29 45| Scale is weakly epimorphic with val: <6 11 16 30 43| Scale is weakly epimorphic with val: <6 11 17 31 44| Scale is weakly epimorphic with val: <6 11 18 32 45| Scale is weakly epimorphic with val: <6 11 19 33 43| Scale is weakly epimorphic with val: <7 10 15 28 43| Scale is weakly epimorphic with val: <7 10 15 33 44| Scale is weakly epimorphic with val: <7 10 16 29 44| Scale is weakly epimorphic with val: <7 10 17 30 45| Scale is weakly epimorphic with val: <7 10 17 32 43| Scale is weakly epimorphic with val: <7 10 18 31 43| Scale is weakly epimorphic with val: <7 10 18 33 44| Scale is weakly epimorphic with val: <7 10 19 32 44| Scale is weakly epimorphic with val: <7 11 15 27 45| Scale is weakly epimorphic with val: <7 11 15 28 44| Scale is weakly epimorphic with val: <7 11 15 30 45| Scale is weakly epimorphic with val: <7 11 15 31 44| Scale is weakly epimorphic with val: <7 11 15 33 45| Scale is weakly epimorphic with val: <7 11 16 28 43| Scale is weakly epimorphic with val: <7 11 16 29 45| Scale is weakly epimorphic with val: <7 11 16 31 43| Scale is weakly epimorphic with val: <7 11 16 32 45| Scale is weakly epimorphic with val: <7 11 17 27 43| Scale is weakly epimorphic with val: <7 11 17 29 44| Scale is JI-epimorphic with val: <7 11 17 30 43| Scale is weakly epimorphic with val: <7 11 17 32 44| Scale is weakly epimorphic with val: <7 11 17 33 43| Scale is weakly epimorphic with val: <7 11 18 27 45| Scale is weakly epimorphic with val: <7 11 18 28 44| Scale is weakly epimorphic with val: <7 11 18 30 45| Scale is JI-epimorphic with val: <7 11 18 31 44| Scale is weakly epimorphic with val: <7 11 18 33 45| Scale is weakly epimorphic with val: <7 11 19 28 43| Scale is weakly epimorphic with val: <7 11 19 29 45| Scale is weakly epimorphic with val: <7 11 19 31 43| Scale is JI-epimorphic with val: <7 11 19 32 45| Scale is weakly epimorphic with val: <7 12 15 30 43| Scale is weakly epimorphic with val: <7 12 16 31 44| Scale is weakly epimorphic with val: <7 12 16 32 43| Scale is weakly epimorphic with val: <7 12 17 32 45| Scale is weakly epimorphic with val: <7 12 17 33 44| Scale is weakly epimorphic with val: <7 12 18 33 43| Scale is weakly epimorphic with val: <7 12 19 32 43| Scale is weakly epimorphic with val: <8 11 15 29 44| Scale is weakly epimorphic with val: <8 11 15 30 43| Scale is weakly epimorphic with val: <8 11 16 30 45| Scale is weakly epimorphic with val: <8 11 16 31 44| Scale is weakly epimorphic with val: <8 11 17 31 43| Scale is weakly epimorphic with val: <8 11 17 32 45| Scale is weakly epimorphic with val: <8 11 18 30 43| Scale is weakly epimorphic with val: <8 11 18 32 44| Scale is weakly epimorphic with val: <8 11 19 31 44| Scale is weakly epimorphic with val: <8 11 19 33 45| Scale is weakly epimorphic with val: <8 12 15 30 44| Scale is weakly epimorphic with val: <8 12 15 32 45| Scale is weakly epimorphic with val: <8 12 16 30 43| Scale is weakly epimorphic with val: <8 12 16 31 45| Scale is weakly epimorphic with val: <8 12 17 31 44| Scale is weakly epimorphic with val: <8 12 17 32 43| Scale is weakly epimorphic with val: <8 12 18 32 45| Scale is weakly epimorphic with val: <8 12 18 33 44| Scale is weakly epimorphic with val: <8 12 19 30 43|
FIT/MODE
3: 0 1 2 N G T3 SD: 32.7895 c. M: 50.6717 c. 4: 0 2 2 P M DE S SD: 23.8289 c. M:-32.3358 c. 5: 0 2 3 N G T3 SD: 17.9164 c. M: 25.6484 c. 7: 0 3 4 N G T3 SD: 14.9257 c. M: 25.6484 c. 11: 1 4 6 N T3 SD: 12.6401 c. M:-19.6284 c. 12: 1 4 7 N T3 SD: 10.5742 c. M:-15.8554 c. 13: 1 5 7 N T3 SD: 10.5525 c. M:-13.1802 c. 14: 1 5 8 N T3 SD: 6.0283 c. M:-9.9263 c. 16: 1 6 9 N T3 SD: 3.2395 c. M:-5.4794 c. 18: 1 7 10 N T3 SD: 2.9360 c. M:-4.6666 c. 21: 1 8 12 N T3 SD: 2.1773 c. M: 3.2388 c. 37: 2 14 21 N T3 SD: 1.0570 c. M: 1.3159 c. 39: 2 15 22 N T3 SD: 0.2446 c. M:-0.4098 c. 115: 6 44 65 N T3 SD: 0.2117 c. M:-0.3366 c. 138: 7 53 78 N T3 SD: 0.2377 c. M: 0.3852 c. 154: 8 59 87 N T3 SD: 0.1294 c. M:-0.2241 c. 193: 10 74 109 N T3 SD: 0.1015 c. M:-0.1571 c. 232: 12 89 131 N T3 SD: 0.1013 c. M:-0.1346 c. 253: 13 97 143 N T3 SD: 0.0902 c. M: 0.1454 c. 292: 15 112 165 N T3 SD: 0.0552 c. M: 0.0712 c. 331: 17 127 187 N T3 SD: 0.0407 c. M: 0.0690 c. 446: 23 171 252 N T3 SD: 0.0346 c. M: 0.0483 c. 485: 25 186 274 N T3 SD: 0.0154 c. M:-0.0240 c. 524: 27 201 296 N T3 SD: 0.0141 c. M:-0.0199 c. 816: 42 313 461 N T3 SD: 0.0108 c. M: 0.0137 c. 1301: 67 499 735 N T3 SD: 0.0071 c. M: 0.0122 c. 1340: 69 514 757 N T3 SD: 0.0016 c. M: 0.0028 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: 65.0514 cents 6 x 7:8 S SD: 25.0921 cents 7 x 8:9 S SD: 32.3031 cents 8 x 9:11 SD: 27.3918 cents 9 x 10:12 S SD: 17.1415 cents 10 x 11:13 SD: 33.8830 cents 11 x 12:15 S SD: 38.3282 cents 12 x 14:16 S SD: 25.0921 cents 13 x 15:17 SD: 22.8828 cents 20:21:23:27 SD: 22.5116 cents 21:22:24:28 S SD: 18.9228 cents 22:23:25:29 SD: 18.3949 cents 23:24:26:31 SD: 17.2467 cents 24:25:27:32 SD: 15.6006 cents 27:28:31:36 SD: 14.5211 cents 28:29:32:37 SD: 13.6755 cents 29:30:33:39 SD: 12.3009 cents 30:31:34:40 SD: 10.3728 cents 35:36:40:47 SD: 9.9797 cents 36:37:41:48 SD: 7.7909 cents 38:39:43:51 SD: 7.5232 cents 39:40:44:52 SD: 6.6018 cents 43:44:49:57 SD: 6.5949 cents 44:45:50:59 SD: 5.7091 cents 45:46:51:60 SD: 4.1341 cents 51:52:58:68 SD: 3.3211 cents 54:55:61:72 SD: 2.7798 cents 60:61:68:80 SD: 0.9892 cents 75:76:85:100 SD: 0.9059 cents 129:131:146:172 SD: 0.8557 cents 135:137:153:180 SD: 0.0629 cents 600:609:680:800 SD: 0.0424 cents