Scala analysis: 108_E13
Enharmonic tetrachord 40/39 * 26/25 * 5/4, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 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: 40/39 43.8311 tridecimal minor diesis 2: 26/25 67.9002 tridecimal 1/3-tone 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 50/39 430.145 cents 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 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 : 43.8 111.7 498.0 43.8 : 67.9 454.2 498.0 111.7: 386.3 430.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 386.3137 cents 39/32, 342.4827 cents 40/39, 43.8311 cents 2: 111.7313 .. 454.2139 cents 39/32, 342.4827 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.787612 Largest / Average step : 2.326981 Largest / Smallest step : 8.813699 Median interval of one step : 26/25, 67.9002 cents, amount: 1 Least squares average step : 125.81633 cents, oct.: 377.44899 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1159-tone equal temperament with octave 4/3 degrees: 102 260 1159 Least number of segments generator : 580 of 249.237 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 865 of 371.707 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 : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 43.83105 cents Scale diversity : 0.497676 Lumma stability : 0.176012 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 : 507/500, 24.0692 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 All steps are superparticular (epimoric) 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% Scale is differentially coherent in interval class 1 Limited inverse transpositions with margin 318.4135 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 25 U: 39) Highest odd numerator or denominator: 39 Scale harmonicity : 0.024027 Average absolute harmonicity : 0.106679 Specific harmonicity : 0.127123 Fundamental : 1/195, -7.6073 octaves, 1.3417 Hz. Guide tone : 80, 6.3219 octaves, 20930.045 Hz. Exponens Consonantiae : 1.560000E+04, 13.92926 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 58.5, average 19.50000 Mersenne's string divisions : 17143 Sum of van Prooijen's expressibility: 3.24428, average 1.08143 Sum of Tenney's harmonic distance : 6.65252, average 2.21751 Vogel's harmonic complexity : 16.66667 Wille's k value : 32 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.36042, average 2.72674 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 ..-1 -1.00000 3 1 5: -1 .. 1 0.00000 2 1 13: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 15 27| Scale is weakly epimorphic with val: <7 10 15 30| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <8 11 17 27| Scale is weakly epimorphic with val: <8 11 18 27| Scale is weakly epimorphic with val: <8 11 18 30| Scale is weakly epimorphic with val: <8 12 17 27| Scale is weakly epimorphic with val: <8 12 17 30| Scale is weakly epimorphic with val: <8 12 18 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 40.2819 c. M:-54.2837 c. 4: 0 1 3 N G T3 SD: 26.3596 c. M: 43.8311 c. 5: 0 1 4 N G T3 SD: 26.2559 c. M: 43.8311 c. 6: 0 1 5 N G T3 SD: 30.2557 c. M: 43.8311 c. 8: 1 1 6 N M DE S SD: 12.9459 c. M:-18.4246 c. 9: 1 1 7 N M DE S SD: 6.6716 c. M:-11.5073 c. 13: 1 2 10 N T3 SD: 3.6843 c. M: 5.5199 c. 22: 2 3 17 N T3 SD: 1.1866 c. M:-1.4608 c. 45: 4 6 35 N T3 SD: 0.6597 c. M: 1.0546 c. 58: 5 8 45 N T3 SD: 0.5206 c. M: 0.8961 c. 67: 6 9 52 N T3 SD: 0.4637 c. M:-0.7700 c. 80: 7 11 62 N T3 SD: 0.2392 c. M:-0.3288 c. 125: 11 17 97 N T3 SD: 0.0977 c. M: 0.1692 c. 205: 18 28 159 N T3 SD: 0.0597 c. M: 0.1003 c. 330: 29 45 256 N T3 SD: 0.0461 c. M: 0.0635 c. 352: 31 48 273 N T3 SD: 0.0319 c. M:-0.0459 c. 477: 42 65 370 N T3 SD: 0.0141 c. M:-0.0220 c. 682: 60 93 529 N T3 SD: 0.0085 c. M: 0.0148 c. 1159: 102 158 899 N T3 SD: 0.0024 c. M: 0.0042 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 x 20:25 S SD: 16.2144 cents 20 x 21:27 SD: 17.3627 cents 21 x 22:28 SD: 15.5971 cents 22:23 x 29 SD: 19.2923 cents 23:24:25:31 SD: 16.0051 cents 24:25:26:32 SD: 12.6531 cents 25:26:27:33 SD: 12.2229 cents 26:27:28:35 S SD: 10.6011 cents 27:28:29:36 SD: 7.5240 cents 29:30:31:39 SD: 7.1146 cents 30:31:32:40 S SD: 4.3119 cents 33:34:35:44 SD: 4.2026 cents 42:43:45:56 SD: 2.7697 cents 45:46:48:60 S SD: 1.9268 cents 72:74:77:96 SD: 1.9222 cents 75:77:80:100 SD: 0.5768 cents 120:123:128:160 SD: 0.3608 cents 195:200:208:260 S SD: 0.0000 cents