Scala analysis: 045_E1
Enharmonic tetrachord 36/35 * 70/69 * 23/18, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 24/23 73.680654 vicesimotertial minor semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/18 424.3643 vicesimotertial major third 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 70/69 24.9103 3: 23/18 424.3643 vicesimotertial major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 70/69 24.910 cents 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 23/18 424.364 cents vicesimotertial major third 2: 1 24/23 73.681 cents vicesimotertial minor semitone 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 46/35 473.135 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 : 48.8 73.7 498.0 48.8 : 24.9 449.3 498.0 73.7 : 424.4 473.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.9103 .. 424.3643 cents 529/420, 399.4541 cents 70/69, 24.9103 cents 2: 73.6807 .. 473.1347 cents 529/420, 399.4541 cents 432/529,-350.6837 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 70/69, 24.9103 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/18, 424.3643 cents Average / Smallest step : 6.664520 Largest / Average step : 2.556181 Largest / Smallest step : 17.035717 Median interval of one step : 36/35, 48.7704 cents, amount: 1 Least squares average step : 120.73333 cents, oct.: 362.20000 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1879-tone equal temperament with octave 4/3 degrees: 184 278 1879 Least number of segments generator : 940 of 249.155 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1100 of 291.564 cents and inv. generated superset size: 32 = 29 more = 1066.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 24.91027 cents Scale diversity : 0.209911 Lumma stability : 0.100032 Lumma impropriety factor : 0.704120 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 : 1242/1225, 23.8601 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 399.4541 cents: 2 -- Rational properties -- Prime limit : 23 Odd number limit : 69 (O: 35 U: 69) Highest odd numerator or denominator: 35 Scale harmonicity : 0.014332 Average absolute harmonicity : 0.092286 Specific harmonicity : 0.075477 Fundamental : 1/2415, -11.2378 octaves, 0.1083 Hz. Guide tone : 72, 6.1699 octaves, 18837.041 Hz. Exponens Consonantiae : 1.738800E+05, 17.40773 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 62.5, average 20.83333 Mersenne's string divisions : 23359 Sum of van Prooijen's expressibility: 3.38292, average 1.12764 Sum of Tenney's harmonic distance : 6.92149, average 2.30716 Vogel's harmonic complexity : 30.66667 Wille's k value : 402 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.71715, average 2.78619 Lattice compactness (without 2's) : 12.41640, average 2.06940 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -1 .. 2 0.66667 4 1 5: -1 .. 0 -0.33333 1 7: -1 .. 0 -0.33333 1 1 23: -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 19 31| Scale is weakly epimorphic with val: <7 11 15 19 34| Scale is JI-epimorphic with val: <7 11 15 20 30| Scale is weakly epimorphic with val: <7 11 15 20 33| Scale is weakly epimorphic with val: <7 11 15 20 36| Scale is weakly epimorphic with val: <7 11 15 22 31| Scale is weakly epimorphic with val: <7 11 15 22 34| Scale is weakly epimorphic with val: <7 11 16 18 31| Scale is weakly epimorphic with val: <7 11 16 18 34| Scale is JI-epimorphic with val: <7 11 16 19 30| Scale is weakly epimorphic with val: <7 11 16 19 33| Scale is weakly epimorphic with val: <7 11 16 19 36| Scale is weakly epimorphic with val: <7 11 16 21 31| Scale is weakly epimorphic with val: <7 11 16 21 34| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 16 22 33| Scale is weakly epimorphic with val: <7 11 16 22 36| Scale is JI-epimorphic with val: <7 11 17 18 30| Scale is weakly epimorphic with val: <7 11 17 18 33| Scale is weakly epimorphic with val: <7 11 17 18 36| Scale is weakly epimorphic with val: <7 11 17 20 31| Scale is weakly epimorphic with val: <7 11 17 20 34| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 21 33| Scale is weakly epimorphic with val: <7 11 17 21 36| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 19 34| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 11 18 20 33| Scale is weakly epimorphic with val: <7 11 18 20 36| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is weakly epimorphic with val: <7 11 18 22 34| Scale is weakly epimorphic with val: <7 11 19 19 30| Scale is weakly epimorphic with val: <7 11 19 19 33| Scale is weakly epimorphic with val: <7 11 19 19 36| Scale is weakly epimorphic with val: <7 11 19 21 31| Scale is weakly epimorphic with val: <7 11 19 21 34| Scale is weakly epimorphic with val: <7 11 19 22 30| Scale is weakly epimorphic with val: <7 11 19 22 33| Scale is weakly epimorphic with val: <7 11 19 22 36| Scale is weakly epimorphic with val: <7 12 15 19 30| Scale is weakly epimorphic with val: <7 12 15 20 32| Scale is weakly epimorphic with val: <7 12 15 20 35| Scale is weakly epimorphic with val: <7 12 15 22 30| Scale is weakly epimorphic with val: <7 12 16 18 30| Scale is weakly epimorphic with val: <7 12 16 19 32| Scale is weakly epimorphic with val: <7 12 16 19 35| Scale is weakly epimorphic with val: <7 12 16 21 30| Scale is weakly epimorphic with val: <7 12 17 18 32| Scale is weakly epimorphic with val: <7 12 17 18 35| Scale is weakly epimorphic with val: <7 12 17 20 30| Scale is weakly epimorphic with val: <7 12 18 19 30| Scale is weakly epimorphic with val: <7 12 18 22 30| Scale is weakly epimorphic with val: <7 12 19 21 30| Scale is weakly epimorphic with val: <8 11 15 19 32| Scale is weakly epimorphic with val: <8 11 15 20 31| Scale is weakly epimorphic with val: <8 11 15 20 34| Scale is weakly epimorphic with val: <8 11 15 22 32| Scale is weakly epimorphic with val: <8 11 16 18 32| Scale is weakly epimorphic with val: <8 11 16 19 31| Scale is weakly epimorphic with val: <8 11 16 19 34| Scale is weakly epimorphic with val: <8 11 16 21 32| Scale is weakly epimorphic with val: <8 11 17 18 31| Scale is weakly epimorphic with val: <8 11 17 18 34| Scale is weakly epimorphic with val: <8 11 17 20 32| Scale is weakly epimorphic with val: <8 11 18 19 32| Scale is weakly epimorphic with val: <8 11 18 22 32| Scale is weakly epimorphic with val: <8 11 19 21 32| Scale is weakly epimorphic with val: <8 12 15 20 33| Scale is weakly epimorphic with val: <8 12 15 22 31| Scale is weakly epimorphic with val: <8 12 15 22 34| Scale is weakly epimorphic with val: <8 12 16 19 33| Scale is weakly epimorphic with val: <8 12 16 21 31| Scale is weakly epimorphic with val: <8 12 16 21 34| Scale is weakly epimorphic with val: <8 12 16 22 33| Scale is weakly epimorphic with val: <8 12 17 18 33| Scale is weakly epimorphic with val: <8 12 17 20 31| Scale is weakly epimorphic with val: <8 12 17 20 34| Scale is weakly epimorphic with val: <8 12 17 21 33| Scale is weakly epimorphic with val: <8 12 18 19 31| Scale is weakly epimorphic with val: <8 12 18 19 34| Scale is weakly epimorphic with val: <8 12 18 20 33| Scale is weakly epimorphic with val: <8 12 19 19 33| Scale is weakly epimorphic with val: <8 12 19 22 33|
FIT/MODE
3: 0 0 3 N M DE S SD: 51.0143 c. M: 73.6807 c. 5: 1 0 4 N G T3 SD: 32.9487 c. M:-50.8386 c. 6: 1 0 5 N G T3 SD: 20.4872 c. M:-34.2371 c. 7: 1 0 6 N G T3 SD: 13.0029 c. M:-22.3789 c. 8: 1 0 7 N G T3 SD: 10.2043 c. M:-13.4852 c. 11: 1 1 9 N M DE S SD: 9.9482 c. M:-16.8730 c. 12: 1 1 10 N M DE S SD: 6.8263 c. M:-9.3268 c. 13: 1 1 11 N M DE S SD: 6.2729 c. M: 10.4592 c. 18: 2 1 15 N T3 SD: 6.5860 c. M:-9.3268 c. 19: 2 1 16 N T3 SD: 3.5564 c. M:-4.9580 c. 20: 2 1 17 N T3 SD: 0.8411 c. M:-1.0341 c. 41: 4 2 35 N T3 SD: 0.4713 c. M: 0.7960 c. 61: 6 3 52 N T3 SD: 0.1701 c. M:-0.2177 c. 142: 14 7 121 N T3 SD: 0.1926 c. M:-0.3326 c. 203: 20 10 173 N T3 SD: 0.1779 c. M:-0.2981 c. 236: 23 12 201 N T3 SD: 0.1703 c. M: 0.2321 c. 256: 25 13 218 N T3 SD: 0.1625 c. M:-0.2479 c. 257: 25 13 219 N T3 SD: 0.1876 c. M: 0.3224 c. 264: 26 13 225 N T3 SD: 0.1726 c. M:-0.2795 c. 277: 27 14 236 N T3 SD: 0.1314 c. M: 0.2245 c. 297: 29 15 253 N T3 SD: 0.1005 c. M: 0.1397 c. 317: 31 16 270 N T3 SD: 0.1009 c. M:-0.1620 c. 338: 33 17 288 N T3 SD: 0.0836 c. M: 0.1447 c. 358: 35 18 305 N T3 SD: 0.0546 c. M: 0.0788 c. 399: 39 20 340 N T3 SD: 0.0554 c. M: 0.0893 c. 419: 41 21 357 N T3 SD: 0.0225 c. M: 0.0357 c. 480: 47 24 409 N T3 SD: 0.0069 c. M: 0.0115 c. 1399: 137 70 1192 N T3 SD: 0.0067 c. M:-0.0115 c. 1460: 143 73 1244 N T3 SD: 0.0064 c. M:-0.0107 c. 1859: 182 93 1584 N T3 SD: 0.0069 c. M: 0.0107 c. 1879: 184 94 1601 N T3 SD: 0.0033 c. M:-0.0056 c. 2359: 231 118 2010 N T3 SD: 0.0013 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: 96.5951 cents 7 x 8:9 S SD: 84.8060 cents 8 x 9:11 SD: 70.3521 cents 9 x 10:12 S SD: 54.3615 cents 10 x 11:13 SD: 50.6487 cents 11 x 12:15 S SD: 43.1160 cents 12 x 13:16 SD: 32.4460 cents 13 x 14:17 SD: 32.0671 cents 14 x 15:19 SD: 27.5369 cents 15 x 16:20 S SD: 19.0253 cents 16 x 17:21 SD: 20.7451 cents 17 x 18:23 SD: 17.8714 cents 18 x 19:24 SD: 9.9612 cents 19 x 20:25 S SD: 13.7334 cents 20 x 21:27 SD: 12.0299 cents 21 x 22:28 SD: 3.4282 cents 22 x 23:29 SD: 10.0275 cents 23 x 24:31 SD: 9.3581 cents 24 x 25:32 SD: 1.5041 cents 25 x 26:33 SD: 9.1673 cents 26 x 27:35 SD: 9.2746 cents 27 x 28:36 SD: 5.3599 cents 28:29 x 37 SD: 9.8059 cents 29:30 x 39 SD: 8.9340 cents 30:31 x 40 SD: 3.9982 cents 31:32 x 41 SD: 7.6628 cents 32:33 x 43 SD: 7.1026 cents 33:34 x 44 SD: 1.4560 cents 34:35 x 45 SD: 6.4273 cents 39:40:41:52 SD: 4.6041 cents 42:43:44:56 SD: 3.5205 cents 53 x 55:71 SD: 6.2778 cents 54 x 56:72 SD: 5.3599 cents 55 x 57:73 SD: 7.1150 cents 56:58 x 75 SD: 7.1241 cents 57:59 x 76 SD: 5.4666 cents 60:62:63:80 SD: 4.4758 cents 62:64:65:83 SD: 4.1220 cents 63:65:66:84 SD: 2.8958 cents 66:68:69:88 SD: 1.4610 cents 69:71:72:92 SD: 0.2323 cents 348:358:363:464 SD: 0.2269 cents 390:401:407:520 SD: 0.2146 cents 417:429:435:556 SD: 0.2079 cents 459:472:479:612 SD: 0.1492 cents 528:543:551:704 SD: 0.1018 cents 597:614:623:796 SD: 0.0671 cents