Scala analysis: 478_R2
Reduplicated tetrachord 12/11 * 12/11 * 121/108, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 144/121 301.274117 two (undecimal neutral second, 3/4-tone) 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 121/108 196.7709 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 121/108 196.7709
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 121/108 196.771 cents 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 2 11/9 347.408 cents undecimal neutral 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 : 150.6 301.3 498.0 150.6: 150.6 347.4 498.0 301.3: 196.8 347.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 196.7709 cents 1331/1296, 46.1338 cents 12/11, 150.6371 cents 2: 301.2741 .. 347.4079 cents 1331/1296, 46.1338 cents 15552/14641, 104.5032 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 121/108, 196.7709 cents Average / Smallest step : 1.102086 Largest / Average step : 1.185260 Largest / Smallest step : 1.306258 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Most common interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 160.52288 cents, oct.: 481.56863 cents Scale is strictly proper Scale has Myhill's property chromas: 1331/1296, 46.1338 cents and 15552/14641, 104.5032 cents, ratio: 2.265219 generators: 1 of 150.63706 cents and 347.40794 cents ET pair of linear temperament : 20&66 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 367-tone equal temperament with octave 4/3 degrees: 111 222 367 generators: 111 and 256 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAB Step pattern size order : SSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 104.50323 cents Scale diversity : 1.328004 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.814740 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 : 1331/1296, 46.1338 cents Most common intervals : 12/11, 150.6371 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 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 n-1 differentially coherent in interval class 1 Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 11 Odd number limit : 121 (O: 121 U: 121) Highest odd numerator or denominator: 121 Scale harmonicity : 0.020677 Average absolute harmonicity : 0.093311 Specific harmonicity : 0.096420 Fundamental : 1/363, -8.5038 octaves, 0.7207 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 5.227200E+04, 15.67375 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 147.5, average 49.16667 Mersenne's string divisions : 42665 Sum of van Prooijen's expressibility: 3.60130, average 1.20043 Sum of Tenney's harmonic distance : 7.44090, average 2.48030 Vogel's harmonic complexity : 18.66667 Wille's k value : 60 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 18.39320, average 3.06553 Lattice compactness (without 2's) : 12.49847, average 2.08308 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -1 .. 2 0.66667 4 1 11: -2 .. 0 -1.00000 3 2 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 23| Scale is JI-epimorphic with val: <7 11 24| Scale is weakly epimorphic with val: <7 11 26| Scale is weakly epimorphic with val: <7 11 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 19.8528 c. M:-30.7559 c. 7: 2 2 3 SP M ME S SD: 10.7649 c. M: 16.6770 c. 10: 3 3 4 SP M ME S SD: 1.5796 c. M: 2.4471 c. 23: 7 7 9 SP M DE S SD: 1.2159 c. M:-1.8837 c. 33: 10 10 13 SP M DE S SD: 0.3688 c. M:-0.5713 c. 43: 13 13 17 SP M DE S SD: 0.0843 c. M: 0.1306 c. 119: 36 36 47 SP M DE S SD: 0.0413 c. M:-0.0640 c. 162: 49 49 64 SP M DE S SD: 0.0080 c. M:-0.0124 c. 367: 111 111 145 SP M DE S SD: 0.0028 c. M: 0.0044 c. 529: 160 160 209 SP M DE S SD: 0.0005 c. M:-0.0007 c. 1425: 431 431 563 SP M DE S SD: 0.0004 c. M: 0.0006 c. 1954: 591 591 772 SP M DE S SD: 0.0001 c. M: 0.0002 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: 85.0396 cents 5 x 6:7 S SD: 42.8402 cents 6 x 7:8 S SD: 17.2016 cents 7 x 8:9 S SD: 47.1118 cents 8:9:10:11 H SD: 37.8708 cents 9:10:11:12 H SD: 18.6710 cents 10:11:12:13 H SD: 16.1038 cents 11:12:13:15 SD: 13.5778 cents 12:13:14:16 S SD: 12.1524 cents 20:22:24:27 S SD: 9.8621 cents 21:23:25:28 SD: 2.2934 cents 57:62:68:76 SD: 2.1973 cents 75:82:89:100 SD: 2.0958 cents 78:85:93:104 SD: 1.2420 cents 90:98:107:120 SD: 1.2164 cents 99:108:118:132 SD: 0.8899 cents 111:121:132:148 SD: 0.6129 cents 132:144:157:176 SD: 0.3341 cents 210:229:250:280 SD: 0.2981 cents 231:252:275:308 SD: 0.1908 cents 342:373:407:456 SD: 0.1411 cents 363:396:432:484 SD: 0.0000 cents