Scala analysis: 109_E13
Enharmonic tetrachord 25/24 * 128/125 * 5/4, Salinas
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 128/125 41.0589 minor diesis, diesis 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/125 41.059 cents minor diesis, diesis 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 125/96 456.986 cents classic augmented third 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 : 70.7 111.7 498.0 70.7 : 41.1 427.4 498.0 111.7: 386.3 457.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 386.3137 cents 625/512, 345.2549 cents 128/125, 41.0589 cents 2: 111.7313 .. 456.9861 cents 625/512, 345.2549 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 4.043342 Largest / Average step : 2.326981 Largest / Smallest step : 9.408779 Median interval of one step : 25/24, 70.6724 cents, amount: 1 Least squares average step : 127.73357 cents, oct.: 383.20071 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1783-tone equal temperament with octave 4/3 degrees: 253 400 1783 Least number of segments generator : 892 of 249.162 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1477 of 412.570 cents and inv. generated superset size: 23 = 20 more = 766.667% 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 41.05886 cents Scale diversity : 0.489665 Lumma stability : 0.164880 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 : 3125/3072, 29.6136 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 -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 125) Highest odd numerator or denominator: 25 Scale harmonicity : 0.034642 Average absolute harmonicity : 0.114989 Specific harmonicity : 0.180586 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 400, 8.6439 octaves, 104650.226 Hz. Exponens Consonantiae : 4.800000E+04, 15.55075 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 43.5, average 14.50000 Mersenne's string divisions : 1519 Sum of van Prooijen's expressibility: 3.05115, average 1.01705 Sum of Tenney's harmonic distance : 6.23754, average 2.07918 Vogel's harmonic complexity : 10.66667 Wille's k value : 62 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 25.45737, average 4.24290 Lattice compactness (without 2's) : 10.65028, average 1.77505 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 1.00000 9 3: -1 ..-1 -1.00000 3 1 5: -1 .. 2 0.33333 3 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: <7 10 15| Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 11 18| Scale is weakly epimorphic with val: <7 12 18| Scale is weakly epimorphic with val: <8 11 18|
FIT/MODE
3: 0 1 2 N G T3 SD: 51.4500 c. M: 70.6724 c. 4: 1 0 3 N G T3 SD: 31.9476 c. M:-53.8388 c. 5: 1 0 4 N G T3 SD: 18.1133 c. M:-28.9366 c. 6: 1 0 5 N G T3 SD: 18.0482 c. M: 28.7238 c. 7: 1 1 5 N M DE S SD: 17.6502 c. M:-30.5673 c. 8: 1 1 6 N M DE S SD: 8.8350 c. M:-12.7800 c. 9: 1 1 7 N M DE S SD: 8.8741 c. M: 15.3341 c. 12: 2 1 9 N T3 SD: 10.2548 c. M:-12.7800 c. 13: 2 1 10 N T3 SD: 3.9011 c. M:-5.9499 c. 14: 2 1 11 N T3 SD: 2.9041 c. M: 5.0074 c. 22: 3 2 17 N T3 SD: 1.8015 c. M: 2.7572 c. 35: 5 3 27 N T3 SD: 1.2476 c. M:-2.1076 c. 36: 5 3 28 N T3 SD: 1.0584 c. M: 1.4995 c. 49: 7 4 38 N T3 SD: 0.2787 c. M:-0.4769 c. 85: 12 7 66 N T3 SD: 0.3123 c. M: 0.4036 c. 120: 17 10 93 N T3 SD: 0.2013 c. M:-0.3288 c. 134: 19 11 104 N T3 SD: 0.1357 c. M: 0.2287 c. 183: 26 15 142 N T3 SD: 0.0991 c. M: 0.1474 c. 254: 36 21 197 N T3 SD: 0.0521 c. M: 0.0834 c. 303: 43 25 235 N T3 SD: 0.0241 c. M:-0.0412 c. 437: 62 36 339 N T3 SD: 0.0249 c. M: 0.0416 c. 486: 69 40 377 N T3 SD: 0.0277 c. M:-0.0377 c. 691: 98 57 536 N T3 SD: 0.0233 c. M: 0.0380 c. 740: 105 61 574 N T3 SD: 0.0050 c. M: 0.0077 c. 1043: 148 86 809 N T3 SD: 0.0038 c. M:-0.0065 c. 1783: 253 147 1383 N T3 SD: 0.0012 c. M: 0.0020 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: 77.5698 cents 7 x 8:9 S SD: 67.5105 cents 8 x 9:11 SD: 53.2328 cents 9 x 10:12 S SD: 35.3362 cents 10 x 11:13 SD: 34.4934 cents 11 x 12:15 S SD: 27.5105 cents 12 x 13:16 SD: 13.4207 cents 13 x 14:17 SD: 18.7389 cents 14 x 15:19 SD: 15.7988 cents 15 x 16:20 S SD: 0.0000 cents 16 x 17:21 SD: 14.0467 cents 17 x 18:23 SD: 14.1599 cents 18 x 19:24 SD: 9.0641 cents 19:20 x 25 S SD: 14.6155 cents 20:21 x 27 SD: 12.7751 cents 21:22 x 28 SD: 4.9323 cents 22:23 x 29 SD: 10.3798 cents 24:25:26:32 SD: 8.9471 cents 26:27:28:35 S SD: 8.0097 cents 27:28:29:36 SD: 4.7494 cents 30:31:32:40 S SD: 4.6352 cents 36 x 38:48 SD: 9.0641 cents 37:39 x 49 SD: 11.7965 cents 38:40:41:51 SD: 9.7198 cents 39:41:42:52 SD: 7.6558 cents 40:42:43:53 SD: 7.3758 cents 41:43:44:55 SD: 6.3277 cents 42:44:45:56 SD: 4.1737 cents 44:46:47:59 SD: 3.9685 cents 45:47:48:60 SD: 1.5368 cents 72:75:77:96 SD: 1.5009 cents 75:78:80:100 S SD: 0.9241 cents 120:125:128:160 SD: 0.0000 cents