Scala analysis: 116_E13
Enharmonic tetrachord 68/65 * 5/4 * 52/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/65 78.114034 Valentine semitone 2: 17/13 464.427748 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/51 33.6173 1: 68/65 78.1140 Valentine semitone 2: 5/4 386.3137 major third 3: 52/51 33.6173
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 68/65 78.114 cents Valentine semitone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 65/51 419.931 cents 2: 1 17/13 464.428 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 : 78.1 464.4 498.0 78.1 : 386.3 419.9 498.0 464.4: 33.6 111.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 386.3137 cents 255/208, 352.6965 cents 52/51, 33.6173 cents 2: 111.7313 .. 464.4277 cents 255/208, 352.6965 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 4.938387 Largest / Average step : 2.326981 Largest / Smallest step : 11.491532 Median interval of one step : 68/65, 78.1140 cents, amount: 1 Least squares average step : 178.65032 cents, oct.: 535.95097 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 165 981 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 683 of 323.351 cents and inv. generated superset size: 33 = 30 more = 1100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 33.61725 cents Scale diversity : 0.462919 Lumma stability : 0.134997 Lumma impropriety factor : 0.551321 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 : 52/51, 33.6173 cents Number of recognisable fifths : 0 Number of recognisable fourths : 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 -- Rational properties -- Prime limit : 17 Odd number limit : 65 (O: 65 U: 65) Highest odd numerator or denominator: 65 Scale harmonicity : 0.015788 Average absolute harmonicity : 0.083299 Specific harmonicity : 0.065497 Fundamental : 1/195, -7.6073 octaves, 1.3417 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 1.326000E+04, 13.69479 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 85.0, average 28.33333 Mersenne's string divisions : 3990 Sum of van Prooijen's expressibility: 3.52048, average 1.17349 Sum of Tenney's harmonic distance : 7.06900, average 2.35633 Vogel's harmonic complexity : 22.33333 Wille's k value : 127 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 13.17785, average 2.19631 Lattice compactness (without 2's) : 8.87832, average 1.47972 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.66667 2 17: 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 16 25 32| Scale is weakly epimorphic with val: <6 10 16 26 33| Scale is weakly epimorphic with val: <6 10 17 25 28| Scale is weakly epimorphic with val: <6 10 17 26 29| Scale is weakly epimorphic with val: <6 10 17 27 30| Scale is weakly epimorphic with val: <6 10 17 28 31| Scale is weakly epimorphic with val: <6 10 17 29 32| Scale is weakly epimorphic with val: <6 10 17 30 33| Scale is weakly epimorphic with val: <6 11 16 25 28| Scale is weakly epimorphic with val: <6 11 16 26 29| Scale is weakly epimorphic with val: <6 11 16 27 30| Scale is weakly epimorphic with val: <6 11 16 28 31| Scale is weakly epimorphic with val: <6 11 16 29 32| Scale is weakly epimorphic with val: <6 11 16 30 33| Scale is weakly epimorphic with val: <6 11 17 25 33| Scale is weakly epimorphic with val: <6 11 19 25 28| Scale is weakly epimorphic with val: <6 11 19 26 29| Scale is weakly epimorphic with val: <6 11 19 27 30| Scale is weakly epimorphic with val: <6 11 19 28 31| Scale is weakly epimorphic with val: <6 11 19 29 32| Scale is weakly epimorphic with val: <6 11 19 30 33| Scale is weakly epimorphic with val: <7 10 15 25 28| Scale is weakly epimorphic with val: <7 10 15 26 29| Scale is weakly epimorphic with val: <7 10 15 27 30| Scale is weakly epimorphic with val: <7 10 15 28 31| Scale is weakly epimorphic with val: <7 10 15 29 32| Scale is weakly epimorphic with val: <7 10 15 30 33| Scale is weakly epimorphic with val: <7 10 16 25 30| Scale is weakly epimorphic with val: <7 10 16 26 31| Scale is weakly epimorphic with val: <7 10 16 27 32| Scale is weakly epimorphic with val: <7 10 16 28 33| Scale is weakly epimorphic with val: <7 10 18 25 28| Scale is weakly epimorphic with val: <7 10 18 26 29| Scale is weakly epimorphic with val: <7 10 18 27 30| Scale is weakly epimorphic with val: <7 10 18 28 31| Scale is weakly epimorphic with val: <7 10 18 29 32| Scale is weakly epimorphic with val: <7 10 18 30 33| Scale is weakly epimorphic with val: <7 10 19 25 33| Scale is JI-epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 25 33| Scale is JI-epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is JI-epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is JI-epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is JI-epimorphic with val: <7 11 15 29 31| Scale is JI-epimorphic with val: <7 11 15 30 32| Scale is weakly epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 25 32| Scale is weakly epimorphic with val: <7 11 16 26 27| Scale is weakly epimorphic with val: <7 11 16 26 30| Scale is weakly epimorphic with val: <7 11 16 26 33| Scale is weakly epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 16 27 31| Scale is weakly epimorphic with val: <7 11 16 28 29| Scale is weakly epimorphic with val: <7 11 16 28 32| Scale is weakly epimorphic with val: <7 11 16 29 30| Scale is weakly epimorphic with val: <7 11 16 29 33| Scale is weakly epimorphic with val: <7 11 16 30 31| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is weakly epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is weakly epimorphic with val: <7 11 19 25 32| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is weakly epimorphic with val: <7 11 19 26 30| Scale is weakly epimorphic with val: <7 11 19 26 33| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 29 30| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 19 30 31| Scale is weakly epimorphic with val: <7 12 15 25 29| Scale is weakly epimorphic with val: <7 12 15 26 30| Scale is weakly epimorphic with val: <7 12 15 27 31| Scale is weakly epimorphic with val: <7 12 15 28 32| Scale is weakly epimorphic with val: <7 12 15 29 33| Scale is weakly epimorphic with val: <7 12 16 25 28| Scale is weakly epimorphic with val: <7 12 16 26 29| Scale is weakly epimorphic with val: <7 12 16 27 30| Scale is weakly epimorphic with val: <7 12 16 28 31| Scale is weakly epimorphic with val: <7 12 16 29 32| Scale is weakly epimorphic with val: <7 12 16 30 33| Scale is weakly epimorphic with val: <7 12 18 25 32| Scale is weakly epimorphic with val: <7 12 18 26 33| Scale is weakly epimorphic with val: <7 12 19 25 28| Scale is weakly epimorphic with val: <7 12 19 26 29| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 28 31| Scale is weakly epimorphic with val: <7 12 19 29 32| Scale is weakly epimorphic with val: <7 12 19 30 33| Scale is weakly epimorphic with val: <8 11 15 25 28| Scale is weakly epimorphic with val: <8 11 15 26 29| Scale is weakly epimorphic with val: <8 11 15 27 30| Scale is weakly epimorphic with val: <8 11 15 28 31| Scale is weakly epimorphic with val: <8 11 15 29 32| Scale is weakly epimorphic with val: <8 11 15 30 33| Scale is weakly epimorphic with val: <8 11 17 25 29| Scale is weakly epimorphic with val: <8 11 17 26 30| Scale is weakly epimorphic with val: <8 11 17 27 31| Scale is weakly epimorphic with val: <8 11 17 28 32| Scale is weakly epimorphic with val: <8 11 17 29 33| Scale is weakly epimorphic with val: <8 11 18 25 28| Scale is weakly epimorphic with val: <8 11 18 26 29| Scale is weakly epimorphic with val: <8 11 18 27 30| Scale is weakly epimorphic with val: <8 11 18 28 31| Scale is weakly epimorphic with val: <8 11 18 29 32| Scale is weakly epimorphic with val: <8 11 18 30 33| Scale is weakly epimorphic with val: <8 12 15 25 27| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 15 27 29| Scale is weakly epimorphic with val: <8 12 15 28 30| Scale is weakly epimorphic with val: <8 12 15 29 31| Scale is weakly epimorphic with val: <8 12 15 30 32| Scale is weakly epimorphic with val: <8 12 17 25 28| Scale is weakly epimorphic with val: <8 12 17 26 29| Scale is weakly epimorphic with val: <8 12 17 27 30| Scale is weakly epimorphic with val: <8 12 17 28 31| Scale is weakly epimorphic with val: <8 12 17 29 32| Scale is weakly epimorphic with val: <8 12 17 30 33| Scale is weakly epimorphic with val: <8 12 18 25 30| Scale is weakly epimorphic with val: <8 12 18 26 31| Scale is weakly epimorphic with val: <8 12 18 27 32| Scale is weakly epimorphic with val: <8 12 18 28 33|
FIT/MODE
3: 0 3 0 N M DE I SD: 49.0983 c. M: 78.1140 c. 4: 1 3 0 N G T3 SD: 33.0798 c. M:-46.3972 c. 5: 1 4 0 N G T3 SD: 23.0373 c. M:-33.6173 c. 6: 1 5 0 N G T3 SD: 19.6135 c. M:-33.6173 c. 8: 1 6 1 N M DE I SD: 18.9001 c. M: 28.6384 c. 9: 1 7 1 N M DE I SD: 18.1708 c. M: 22.7757 c. 11: 2 8 1 N T3 SD: 9.8436 c. M:-12.4396 c. 12: 2 9 1 N T3 SD: 5.3586 c. M: 7.8865 c. 13: 2 10 1 N T3 SD: 2.8436 c. M: 4.6939 c. 27: 4 21 2 N T3 SD: 3.1343 c. M: 4.3296 c. 30: 5 23 2 N T3 SD: 2.8353 c. M:-4.8935 c. 31: 5 24 2 N T3 SD: 1.5401 c. M:-2.2158 c. 32: 5 25 2 N T3 SD: 1.4473 c. M:-2.4894 c. 44: 7 34 3 N T3 SD: 0.6761 c. M:-1.1204 c. 45: 7 35 3 N T3 SD: 0.4403 c. M: 0.6404 c. 89: 14 69 6 N T3 SD: 0.1350 c. M:-0.2301 c. 134: 21 104 9 N T3 SD: 0.1026 c. M:-0.1665 c. 223: 35 173 15 N T3 SD: 0.0742 c. M:-0.1165 c. 312: 49 242 21 N T3 SD: 0.0816 c. M:-0.1046 c. 325: 51 252 22 N T3 SD: 0.0605 c. M: 0.0966 c. 370: 58 287 25 N T3 SD: 0.0314 c. M: 0.0421 c. 459: 72 356 31 N T3 SD: 0.0130 c. M: 0.0198 c. 593: 93 460 40 N T3 SD: 0.0133 c. M:-0.0223 c. 963: 151 747 65 N T3 SD: 0.0114 c. M: 0.0198 c. 1052: 165 816 71 N T3 SD: 0.0024 c. M:-0.0039 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 5 x S SD: 78.1140 cents 5 x x 7 SD: 84.4672 cents 6:7 x 8 S SD: 94.3784 cents 7:8:9 x S SD: 77.9237 cents 8:9:10:11 H SD: 52.4557 cents 9:10 x 12 S SD: 52.1448 cents 10:11:13 x SD: 43.7442 cents 11:12:14:15 S SD: 31.5783 cents 12:13 x 16 SD: 30.2293 cents 13:14:17 x SD: 25.0921 cents 14:15:18:19 S SD: 19.7429 cents 15:16 x 20 S SD: 16.8086 cents 16:17:21 x SD: 13.7915 cents 17:18:22:23 SD: 12.4698 cents 18:19 x 24 SD: 7.7445 cents 19:20:25 x S SD: 7.5566 cents 22:23:29 x SD: 6.9399 cents 23:24:30:31 S SD: 6.5795 cents 25:26:33 x SD: 9.5830 cents 26:27:34:35 SD: 6.9738 cents 28:29 x 37 SD: 11.6463 cents 29:30:38:39 SD: 8.2353 cents 30:31:39:40 SD: 7.8883 cents 31:32 x 41 SD: 13.5316 cents 32:33:42:43 SD: 9.6549 cents 33:35:43:44 SD: 8.1814 cents 35:37:46:47 SD: 7.8521 cents 36:38:47:48 SD: 5.2485 cents 39:41:51:52 SD: 2.8219 cents 42:44:55:56 S SD: 1.1422 cents 108:113:141:144 SD: 0.9470 cents 111:116:145:148 SD: 0.8654 cents 150:157:196:200 SD: 0.5339 cents 153:160:200:204 SD: 0.3138 cents 195:204:255:260 SD: 0.0000 cents