Scala analysis: 571_M79
Miscellaneous tetrachord 16/15 * 12/11 * 55/48
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 64/55 262.368344 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 55/48 235.6767 undecimal semi-augmented whole tone 1: 16/15 111.7313 minor diatonic semitone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 55/48 235.6767 undecimal semi-augmented whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 55/48 235.677 cents undecimal semi-augmented whole tone 2: 1 64/55 262.368 cents 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 5/4 386.314 cents major 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 : 111.7 262.4 498.0 111.7: 150.6 386.3 498.0 262.4: 235.7 347.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 235.6767 cents 275/256, 123.9454 cents 16/15, 111.7313 cents 2: 262.3683 .. 386.3137 cents 275/256, 123.9454 cents 3072/3025, 26.6917 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 55/48, 235.6767 cents Average / Smallest step : 1.485842 Largest / Average step : 1.419611 Largest / Smallest step : 2.109317 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 152.18593 cents, oct.: 456.55778 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 896-tone equal temperament with octave 4/3 degrees: 201 472 896 Least number of segments generator : 449 of 249.578 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 507 of 281.818 cents and inv. generated superset size: 12 = 9 more = 400.000% 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 26.69169 cents Scale diversity : 1.248261 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.502272 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 : 3072/3025, 26.6917 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle 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 n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 55 Scale harmonicity : 0.030077 Average absolute harmonicity : 0.107838 Specific harmonicity : 0.144388 Fundamental : 1/165, -7.3663 octaves, 1.5856 Hz. Guide tone : 64, 6.0000 octaves, 16744.036 Hz. Exponens Consonantiae : 1.056000E+04, 13.36632 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 78.5, average 26.16667 Mersenne's string divisions : 3689 Sum of van Prooijen's expressibility: 3.39358, average 1.13119 Sum of Tenney's harmonic distance : 7.00594, average 2.33531 Vogel's harmonic complexity : 14.00000 Wille's k value : 27 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 21.68758, average 3.61460 Lattice compactness (without 2's) : 7.97469, average 1.32912 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 6 4.00000 12 3: -1 .. 0 -0.66667 2 1 5: -1 .. 0 -0.66667 2 1 11: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 15 25| Scale is weakly epimorphic with val: <7 10 16 23| Scale is weakly epimorphic with val: <7 11 15 23| Scale is weakly epimorphic with val: <7 11 15 26| Scale is JI-epimorphic with val: <7 11 16 24| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 12 15 24| Scale is weakly epimorphic with val: <8 11 18 23| Scale is weakly epimorphic with val: <8 11 18 26| Scale is weakly epimorphic with val: <8 12 17 23| Scale is weakly epimorphic with val: <8 12 17 26| Scale is weakly epimorphic with val: <8 12 18 27|
FIT/MODE
3: 0 1 2 N G T3 SD: 85.1819 c. M: 111.7313 c. 4: 1 1 2 P M ME S SD: 10.6683 c. M: 13.3458 c. 9: 2 3 4 SP T3 SD: 8.2920 c. M:-14.3233 c. 13: 3 4 6 SP T3 SD: 3.8300 c. M:-5.8097 c. 17: 4 5 8 SP T3 SD: 3.2384 c. M:-5.4558 c. 23: 5 7 11 SP T3 SD: 2.4712 c. M: 3.4606 c. 27: 6 8 13 SP T3 SD: 2.4569 c. M: 4.1228 c. 32: 7 10 15 SP T3 SD: 2.0551 c. M: 2.7839 c. 36: 8 11 17 SP T3 SD: 0.6711 c. M: 1.0546 c. 40: 9 12 19 SP T3 SD: 0.5504 c. M: 0.8947 c. 76: 17 23 36 SP T3 SD: 0.2337 c. M: 0.3265 c. 129: 29 39 61 SP T3 SD: 0.1652 c. M:-0.2323 c. 165: 37 50 78 SP T3 SD: 0.1398 c. M:-0.2372 c. 205: 46 62 97 SP T3 SD: 0.0173 c. M:-0.0252 c. 691: 155 209 327 SP T3 SD: 0.0104 c. M: 0.0135 c. 896: 201 271 424 SP T3 SD: 0.0041 c. M: 0.0054 c. 1101: 247 333 521 SP T3 SD: 0.0009 c. M: 0.0013 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 6:7 S SD: 49.9317 cents 6 x 7:8 S SD: 2.2513 cents 7 x 8:9 S SD: 35.1325 cents 8 x 9:11 SD: 39.5455 cents 9:10 x 12 S SD: 35.3362 cents 10:11:12:13 H SD: 29.0539 cents 11:12:13:15 SD: 20.4064 cents 12:13:14:16 S SD: 9.0721 cents 18:19:21:24 SD: 6.2264 cents 30:32:35:40 SD: 1.5009 cents 104:111:121:139 SD: 1.4309 cents 105:112:122:140 SD: 0.8594 cents 135:144:157:180 SD: 0.3341 cents 165:176:192:220 SD: 0.0000 cents