Scala analysis: 475_D17
Diatonic tetrachord 10/9 * 10/9 * 27/25, Al-Farabi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 100/81 364.807424 grave major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 1: 10/9 182.4037 minor whole tone 2: 10/9 182.4037 minor whole tone 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 2 10/9 182.404 cents minor whole tone 2: 2 6/5 315.641 cents minor third 2: 1 100/81 364.807 cents grave major third Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 182.4 364.8 498.0 182.4: 182.4 315.6 498.0 364.8: 133.2 315.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 182.4037 cents 250/243, 49.1661 cents 27/25, 133.2376 cents 2: 315.6413 .. 364.8074 cents 250/243, 49.1661 cents 27/25, 133.2376 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.246007 Largest / Average step : 1.098718 Largest / Smallest step : 1.369011 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Most common interval of one step : 10/9, 182.4037 cents, amount: 2 Least squares average step : 171.86811 cents, oct.: 515.60433 cents Scale is strictly proper Scale has Myhill's property chromas: 250/243, 49.1661 cents and 6561/6250, 84.0714 cents, ratio: 1.709946 generators: 1 of 182.40371 cents and 315.64129 cents ET pair of linear temperament : 22&60 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 314-tone equal temperament with octave 4/3 degrees: 115 230 314 generators: 115 and 199 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : LLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 133.23757 cents Scale diversity : 1.214351 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.802563 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 250/243, 49.1661 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Steps are decreasing 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 Scale is n-1 differentially coherent in interval class 2 Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 27 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.039267 Average absolute harmonicity : 0.110695 Specific harmonicity : 0.185042 Fundamental : 1/81, -6.3399 octaves, 3.2299 Hz. Guide tone : 100, 6.6439 octaves, 26162.557 Hz. Exponens Consonantiae : 8.100000E+03, 12.98371 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 103.5, average 34.50000 Mersenne's string divisions : 24073 Sum of van Prooijen's expressibility: 3.33985, average 1.11328 Sum of Tenney's harmonic distance : 6.94191, average 2.31397 Vogel's harmonic complexity : 11.66667 Wille's k value : 22 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.37163, average 2.89527 Lattice compactness (without 2's) : 14.96404, average 2.49401 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -4 ..-1 -2.33333 7 1 5: 0 .. 2 1.00000 3 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is JI-epimorphic with val: <7 11 16| Scale is weakly epimorphic with val: <7 11 17| = patent Scale is weakly epimorphic with val: <7 11 19|
FIT/MODE
3: 1 1 1 SP B ME I SD: 21.1577 c. M: 32.7774 c. 8: 3 3 2 SP M ME S SD: 5.6328 c. M:-8.7263 c. 11: 4 4 3 SP M ME S SD: 1.6737 c. M: 2.5929 c. 19: 7 7 5 SP M DE S SD: 1.4027 c. M:-2.1731 c. 30: 11 11 8 SP M DE S SD: 0.2747 c. M:-0.4256 c. 41: 15 15 11 SP M DE S SD: 0.2480 c. M: 0.3843 c. 71: 26 26 19 SP M DE S SD: 0.0272 c. M: 0.0421 c. 172: 63 63 46 SP M DE S SD: 0.0255 c. M:-0.0395 c. 243: 89 89 65 SP M DE S SD: 0.0101 c. M:-0.0157 c. 314: 115 115 84 SP M DE S SD: 0.0017 c. M:-0.0026 c. 699: 256 256 187 SP M DE S SD: 0.0012 c. M: 0.0019 c. 1013: 371 371 271 SP M DE S SD: 0.0003 c. M: 0.0005 c. 1327: 486 486 355 SP M DE S SD: 0.0001 c. M:-0.0002 c. 2340: 857 857 626 SP M DE S SD: 0.0001 c. M: 0.0001 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: 21.5063 cents 5 x 6:7 S SD: 48.8672 cents 6:7 x 8 S SD: 42.2336 cents 7:8 x 9 S SD: 39.8203 cents 8:9:10:11 H SD: 20.4479 cents 9:10:11:12 H SD: 5.7998 cents 34:38:42:45 SD: 5.4506 cents 35:39:43:47 SD: 5.2417 cents 38:42:47:51 SD: 4.9721 cents 39:43:48:52 SD: 4.7980 cents 42:47:52:56 SD: 4.4250 cents 43:48:53:57 SD: 4.4020 cents 46:51:57:61 SD: 3.9999 cents 47:52:58:63 SD: 3.9356 cents 51:57:63:68 SD: 3.4016 cents 54:60:67:72 SD: 2.8782 cents 63:70:78:84 SD: 1.6464 cents 72:80:89:96 SD: 0.7209 cents 81:90:100:108 SD: 0.0000 cents