Scala analysis: 097_E11
Enharmonic tetrachord 60/59 * 118/113 * 113/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60/59 29.097055 2: 120/113 104.053960 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 113/90 393.9910 1: 60/59 29.0971 2: 118/113 74.9569 3: 113/90 393.9910
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 60/59 29.097 cents 1: 1 118/113 74.957 cents 1: 1 113/90 393.991 cents 2: 1 120/113 104.054 cents 2: 1 226/177 423.088 cents 2: 1 59/45 468.948 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 : 29.1 104.1 498.0 29.1 : 75.0 468.9 498.0 104.1: 394.0 423.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.0971 .. 393.9910 cents 6667/5400, 364.8940 cents 60/59, 29.0971 cents 2: 104.0540 .. 468.9479 cents 6667/5400, 364.8940 cents 10800/12769,-289.9371 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 60/59, 29.0971 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 113/90, 393.9910 cents Average / Smallest step : 5.705560 Largest / Average step : 2.373226 Largest / Smallest step : 13.540581 Median interval of one step : 118/113, 74.9569 cents, amount: 1 Least squares average step : 123.66714 cents, oct.: 371.00142 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1455-tone equal temperament with octave 4/3 degrees: 85 304 1455 Least number of segments generator : 728 of 249.194 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 766 of 262.201 cents and inv. generated superset size: 52 = 49 more = 1733.333% 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 29.09706 cents Scale diversity : 0.401490 Lumma stability : 0.116845 Lumma impropriety factor : 0.582150 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 : 60/59, 29.0971 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 : 113 Odd number limit : 177 (O: 113 U: 177) Highest odd numerator or denominator: 113 Scale harmonicity : 0.067873 Fundamental : 1/20001, -14.2878 octaves, 0.0131 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 2.400120E+06, 21.19468 octaves Euler's gradus suavitatis : 182 Sum of Mann's harmonic distance : 179.5, average 59.83333 Mersenne's string divisions : 27727 Sum of van Prooijen's expressibility: 4.30105, average 1.43368 Sum of Tenney's harmonic distance : 8.76044, average 2.92015 Vogel's harmonic complexity : 124.33333 Wille's k value : 3333 Wilson's harmonic complexity : 183 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.68774, average 2.28129 Lattice compactness (without 2's) : 8.30056, average 1.38343 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 59: -1 .. 0 -0.33333 1 1 113: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 15 42 48| Scale is weakly epimorphic with val: <7 11 15 44 49| Scale is weakly epimorphic with val: <7 11 16 42 50| Scale is weakly epimorphic with val: <7 11 16 43 49| Scale is weakly epimorphic with val: <7 11 17 43 48| Scale is weakly epimorphic with val: <7 11 17 44 50| Scale is JI-epimorphic with val: <7 11 18 42 48| Scale is weakly epimorphic with val: <7 11 18 44 49| Scale is weakly epimorphic with val: <7 11 19 42 50| Scale is JI-epimorphic with val: <7 11 19 43 49| Scale is weakly epimorphic with val: <7 12 18 43 48| Scale is weakly epimorphic with val: <7 12 19 42 48| Scale is weakly epimorphic with val: <7 12 19 44 49| Scale is weakly epimorphic with val: <8 11 16 42 48| Scale is weakly epimorphic with val: <8 11 17 43 49| Scale is weakly epimorphic with val: <8 11 18 42 49| Scale is weakly epimorphic with val: <8 11 18 44 50| Scale is weakly epimorphic with val: <8 11 19 43 50| Scale is weakly epimorphic with val: <8 12 15 44 48| Scale is weakly epimorphic with val: <8 12 16 42 49| Scale is weakly epimorphic with val: <8 12 17 42 48| Scale is weakly epimorphic with val: <8 12 17 43 50| Scale is weakly epimorphic with val: <8 12 18 43 49| Scale is weakly epimorphic with val: <8 12 19 44 50|
FIT/MODE
3: 0 1 2 N G T3 SD: 39.5213 c. M:-61.9610 c. 4: 0 1 3 N G T3 SD: 20.5357 c. M: 29.0971 c. 5: 0 1 4 N G T3 SD: 16.9941 c. M: 29.0971 c. 9: 1 1 7 N M DE S SD: 15.6255 c. M:-26.2413 c. 10: 1 1 8 N M DE S SD: 12.2278 c. M:-20.7074 c. 13: 1 2 10 N T3 SD: 8.2313 c. M:-10.8795 c. 14: 1 2 11 N T3 SD: 4.0451 c. M:-6.4776 c. 15: 1 2 12 N T3 SD: 3.4936 c. M: 4.4450 c. 19: 1 3 15 N T3 SD: 1.7277 c. M: 2.8842 c. 33: 2 5 26 N T3 SD: 1.1131 c. M:-1.5919 c. 34: 2 5 27 N T3 SD: 0.8824 c. M: 1.5153 c. 52: 3 8 41 N T3 SD: 0.7803 c. M:-1.3017 c. 53: 3 8 42 N T3 SD: 0.6561 c. M: 0.9058 c. 67: 4 10 53 N T3 SD: 0.3679 c. M:-0.6370 c. 86: 5 13 68 N T3 SD: 0.1357 c. M:-0.1880 c. 153: 9 23 121 N T3 SD: 0.1323 c. M:-0.1997 c. 206: 12 31 163 N T3 SD: 0.0727 c. M: 0.0931 c. 273: 16 41 216 N T3 SD: 0.0657 c. M:-0.0924 c. 292: 17 44 231 N T3 SD: 0.0588 c. M: 0.1013 c. 359: 21 54 284 N T3 SD: 0.0213 c. M:-0.0365 c. 445: 26 67 352 N T3 SD: 0.0184 c. M:-0.0318 c. 651: 38 98 515 N T3 SD: 0.0153 c. M: 0.0253 c. 804: 47 121 636 N T3 SD: 0.0134 c. M:-0.0175 c. 1010: 59 152 799 N T3 SD: 0.0044 c. M: 0.0069 c. 1455: 85 219 1151 N T3 SD: 0.0030 c. M:-0.0049 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: 81.4085 cents 7 x 8:9 S SD: 70.9288 cents 8 x 9:11 SD: 56.5889 cents 9 x 10:12 S SD: 39.1749 cents 10 x 11:13 SD: 37.5370 cents 11 x 12:15 S SD: 30.3465 cents 12 x 13:16 SD: 17.2594 cents 13 x 14:17 SD: 20.7238 cents 14 x 15:19 SD: 17.1446 cents 15 x 16:20 S SD: 3.8387 cents 16 x 17:21 SD: 13.6395 cents 17 x 18:23 SD: 12.8916 cents 18 x 19:24 SD: 5.2255 cents 19 x 20:25 S SD: 13.7702 cents 20 x 21:27 SD: 14.5444 cents 21 x 22:28 SD: 11.7585 cents 22 x 23:29 SD: 16.7761 cents 23 x 24:31 SD: 17.8384 cents 24 x 25:32 SD: 16.6908 cents 25 x 27:33 SD: 16.9884 cents 26:27:28:35 S SD: 15.5478 cents 27:28:29:36 SD: 13.0521 cents 28:29:30:37 SD: 12.8231 cents 29:30:31:39 SD: 11.6749 cents 30:31:32:40 S SD: 9.5717 cents 32:33:34:43 SD: 9.2304 cents 33:34:35:44 SD: 7.5637 cents 36:37:38:48 SD: 7.0354 cents 42:43:45:56 SD: 6.4317 cents 44:45:47:59 SD: 5.7265 cents 45:46:48:60 S SD: 3.9315 cents 48:49:51:64 SD: 2.2203 cents 63:64:67:84 SD: 1.0379 cents 111:113:118:148 SD: 0.8573 cents 114:116:121:152 SD: 0.4484 cents 177:180:188:236 SD: 0.1087 cents 468:476:497:624 SD: 0.0828 cents