Scala analysis: 522_M30
Miscellaneous tetrachord 68/67 * 67/63 * 21/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/67 25.648381 2: 68/63 132.219501 supraminor second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 21/17 365.8255 submajor third 1: 68/67 25.6484 2: 67/63 106.5711 3: 21/17 365.8255 submajor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/67 25.648 cents 1: 1 67/63 106.571 cents 1: 1 21/17 365.825 cents submajor third 2: 1 68/63 132.220 cents supraminor second 2: 1 84/67 391.474 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 : 25.6 132.2 498.0 25.6 : 106.6 472.4 498.0 132.2: 365.8 391.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 25.6484 .. 365.8255 cents 1407/1156, 340.1771 cents 68/67, 25.6484 cents 2: 132.2195 .. 472.3966 cents 1407/1156, 340.1771 cents 1156/1323,-233.6060 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 : 21/17, 365.8255 cents Average / Smallest step : 6.472728 Largest / Average step : 2.203569 Largest / Smallest step : 14.263103 Median interval of one step : 67/63, 106.5711 cents, amount: 1 Least squares average step : 127.44446 cents, oct.: 382.33337 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1243-tone equal temperament with octave 4/3 degrees: 64 330 1243 Least number of segments generator : 622 of 249.223 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 688 of 275.668 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 : 0.519128 Lumma stability : 0.102996 Lumma impropriety factor : 0.469046 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 : 0.020948 Fundamental : 1/4221, -12.0434 octaves, 0.0620 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 2.870280E+05, 18.13083 octaves Euler's gradus suavitatis : 95 Sum of Mann's harmonic distance : 136.5, average 45.50000 Mersenne's string divisions : 123795 Sum of van Prooijen's expressibility: 4.10254, average 1.36751 Sum of Tenney's harmonic distance : 8.36961, average 2.78987 Vogel's harmonic complexity : 65.66667 Wille's k value : 703 Wilson's harmonic complexity : 97 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.01675, average 2.16946 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -2 .. 0 -1.00000 3 1 7: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 67: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 18 29 43| Scale is weakly epimorphic with val: <6 10 19 30 44| Scale is weakly epimorphic with val: <6 10 20 31 45| Scale is weakly epimorphic with val: <6 10 21 32 43| Scale is weakly epimorphic with val: <6 10 22 33 44| Scale is weakly epimorphic with val: <6 11 18 31 44| Scale is weakly epimorphic with val: <6 11 19 32 45| Scale is weakly epimorphic with val: <6 11 20 33 43| Scale is weakly epimorphic with val: <7 10 18 27 45| Scale is weakly epimorphic with val: <7 10 18 32 43| Scale is weakly epimorphic with val: <7 10 19 28 43| Scale is weakly epimorphic with val: <7 10 19 33 44| Scale is weakly epimorphic with val: <7 10 20 29 44| Scale is weakly epimorphic with val: <7 10 21 30 45| Scale is weakly epimorphic with val: <7 10 21 32 43| Scale is weakly epimorphic with val: <7 10 22 31 43| Scale is weakly epimorphic with val: <7 10 22 33 44| 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 weakly 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 weakly epimorphic with val: <7 11 19 32 45| Scale is weakly epimorphic with val: <7 11 20 27 43| Scale is weakly epimorphic with val: <7 11 20 29 44| Scale is JI-epimorphic with val: <7 11 20 30 43| Scale is weakly epimorphic with val: <7 11 20 32 44| Scale is weakly epimorphic with val: <7 11 20 33 43| Scale is weakly epimorphic with val: <7 11 21 27 45| Scale is weakly epimorphic with val: <7 11 21 28 44| Scale is weakly epimorphic with val: <7 11 21 30 45| Scale is JI-epimorphic with val: <7 11 21 31 44| Scale is weakly epimorphic with val: <7 11 21 33 45| Scale is weakly epimorphic with val: <7 11 22 28 43| Scale is weakly epimorphic with val: <7 11 22 29 45| Scale is weakly epimorphic with val: <7 11 22 31 43| Scale is JI-epimorphic with val: <7 11 22 32 45| Scale is weakly epimorphic with val: <7 12 18 31 44| Scale is weakly epimorphic with val: <7 12 18 32 43| Scale is weakly epimorphic with val: <7 12 19 32 45| Scale is weakly epimorphic with val: <7 12 19 33 44| Scale is weakly epimorphic with val: <7 12 20 33 43| Scale is weakly epimorphic with val: <7 12 21 32 43| Scale is weakly epimorphic with val: <7 12 22 33 44| Scale is weakly epimorphic with val: <8 11 18 27 45| Scale is weakly epimorphic with val: <8 11 18 31 44| Scale is weakly epimorphic with val: <8 11 19 28 43| Scale is weakly epimorphic with val: <8 11 19 32 45| Scale is weakly epimorphic with val: <8 11 20 29 44| Scale is weakly epimorphic with val: <8 11 20 30 43| Scale is weakly epimorphic with val: <8 11 21 30 45| Scale is weakly epimorphic with val: <8 11 21 31 44| Scale is weakly epimorphic with val: <8 11 22 31 43| Scale is weakly epimorphic with val: <8 11 22 32 45| Scale is weakly epimorphic with val: <8 12 18 29 43| Scale is weakly epimorphic with val: <8 12 18 31 44| Scale is weakly epimorphic with val: <8 12 19 30 44| Scale is weakly epimorphic with val: <8 12 19 32 45| Scale is weakly epimorphic with val: <8 12 20 30 43| Scale is weakly epimorphic with val: <8 12 20 31 45| Scale is weakly epimorphic with val: <8 12 21 31 44| Scale is weakly epimorphic with val: <8 12 21 32 43| Scale is weakly epimorphic with val: <8 12 22 32 45| Scale is weakly epimorphic with val: <8 12 22 33 44|
FIT/MODE
3: 0 1 2 N G T3 SD: 24.4947 c. M:-33.7955 c. 4: 0 1 3 N G T3 SD: 15.4624 c. M: 25.6484 c. 11: 1 2 8 N T3 SD: 11.5227 c. M:-19.6284 c. 12: 1 2 9 N T3 SD: 10.1786 c. M:-15.8554 c. 14: 1 3 10 N T3 SD: 8.1674 c. M:-10.0791 c. 15: 1 3 11 N T3 SD: 4.3751 c. M:-7.5546 c. 18: 1 4 13 N T3 SD: 3.7245 c. M:-6.1263 c. 19: 1 4 14 N T3 SD: 0.7422 c. M: 1.1550 c. 60: 3 13 44 N T3 SD: 0.5501 c. M: 0.7461 c. 75: 4 16 55 N T3 SD: 0.6289 c. M:-0.9140 c. 79: 4 17 58 N T3 SD: 0.2679 c. M: 0.4309 c. 98: 5 21 72 N T3 SD: 0.1459 c. M: 0.2379 c. 215: 11 46 158 N T3 SD: 0.1416 c. M: 0.1797 c. 252: 13 54 185 N T3 SD: 0.1167 c. M:-0.1972 c. 271: 14 58 199 N T3 SD: 0.0753 c. M:-0.1024 c. 290: 15 62 213 N T3 SD: 0.0660 c. M:-0.1126 c. 369: 19 79 271 N T3 SD: 0.0305 c. M:-0.0526 c. 388: 20 83 285 N T3 SD: 0.0144 c. M:-0.0240 c. 757: 39 162 556 N T3 SD: 0.0142 c. M:-0.0223 c. 855: 44 183 628 N T3 SD: 0.0119 c. M: 0.0180 c. 874: 45 187 642 N T3 SD: 0.0094 c. M: 0.0153 c. 1145: 59 245 841 N T3 SD: 0.0113 c. M:-0.0151 c. 1243: 64 266 913 N T3 SD: 0.0040 c. M: 0.0049 c. 1631: 84 349 1198 N T3 SD: 0.0017 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 67.3257 cents 7 x 8:9 S SD: 58.6432 cents 8 x 9:11 SD: 44.6585 cents 9 x 10:12 S SD: 25.0921 cents 10 x 11:13 SD: 27.3679 cents 11 x 12:15 S SD: 21.5225 cents 12 x 13:16 SD: 3.1766 cents 13 x 14:17 SD: 16.9226 cents 14 x 15:19 SD: 16.5996 cents 15 x 16:20 S SD: 10.2441 cents 16 x 17:21 SD: 19.2786 cents 17 x 18:23 SD: 20.8886 cents 18 x 19:24 SD: 19.3082 cents 19 x 21:25 SD: 23.5095 cents 20 x 22:27 SD: 19.6046 cents 21 x 23:28 SD: 12.6370 cents 30:31:32:40 S SD: 12.4192 cents 33:34:36:44 SD: 10.6300 cents 34:35:37:45 SD: 10.3603 cents 35:36:38:47 SD: 9.3664 cents 36:37:39:48 SD: 7.5644 cents 38:39:41:51 SD: 7.4732 cents 39:40:42:52 SD: 6.2002 cents 47:48:51:63 SD: 5.6307 cents 48:49:52:64 SD: 3.9628 cents 51:52:55:68 SD: 2.7028 cents 60:61:65:80 SD: 2.3374 cents 63:64:68:84 SD: 0.5386 cents 138:140:149:184 SD: 0.3075 cents 201:204:217:268 SD: 0.1266 cents