Scala analysis: 567_M75
Miscellaneous tetrachord 16/15 * 280/243 * 243/224
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: 896/729 357.095901 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 243/224 140.9491 Archytas' 2/3-tone 1: 16/15 111.7313 minor diatonic semitone 2: 280/243 245.3646 3: 243/224 140.9491 Archytas' 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 243/224 140.949 cents Archytas' 2/3-tone 1: 1 280/243 245.365 cents 2: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 1 896/729 357.096 cents 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 : 111.7 357.1 498.0 111.7: 245.4 386.3 498.0 357.1: 140.9 252.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 245.3646 cents 175/162, 133.6333 cents 16/15, 111.7313 cents 2: 252.6804 .. 386.3137 cents 175/162, 133.6333 cents 19683/19600, 7.3158 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 : 280/243, 245.3646 cents Average / Smallest step : 1.485842 Largest / Average step : 1.477967 Largest / Smallest step : 2.196024 Median interval of one step : 243/224, 140.9491 cents, amount: 1 Least squares average step : 165.71843 cents, oct.: 497.15530 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1159-tone equal temperament with octave 4/3 degrees: 260 831 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: 10 = 7 more = 333.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.173838 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.463368 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 : 19683/19600, 7.3158 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 classes 1 and 2 combined -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 243 U: 729) Highest odd numerator or denominator: 729 Scale harmonicity : 0.025198 Average absolute harmonicity : 0.106953 Specific harmonicity : 0.132169 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 896, 9.8074 octaves, 234416.507 Hz. Exponens Consonantiae : 3.265920E+06, 21.63906 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 831.5, average 277.16667 Mersenne's string divisions : 352625 Sum of van Prooijen's expressibility: 4.51594, average 1.50531 Sum of Tenney's harmonic distance : 9.27443, average 3.09148 Vogel's harmonic complexity : 20.00000 Wille's k value : 607 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 8 Triangular lattice diameter : 5 Lattice compactness : 31.12982, average 5.18830 Lattice compactness (without 2's) : 19.79215, average 3.29869 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 7 4.33333 13 3: -6 ..-1 -2.66667 8 1 5: -1 .. 0 -0.33333 1 1 7: 0 .. 1 0.33333 1 1 Average exponent except 2's :-8 / 3 =-2.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 16 21| Scale is weakly epimorphic with val: <6 10 19 21| Scale is weakly epimorphic with val: <7 10 15 19| Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <8 11 18 20| Scale is weakly epimorphic with val: <8 12 15 19| Scale is weakly epimorphic with val: <8 12 17 18| Scale is weakly epimorphic with val: <8 12 17 21| Scale is weakly epimorphic with val: <8 12 18 19|
FIT/MODE
3: 1 1 1 SP B ME I SD: 34.5206 c. M:-54.2837 c. 4: 1 2 1 P M ME I SD: 12.0212 c. M:-16.4378 c. 10: 2 5 3 P T3 SD: 8.5361 c. M: 12.1223 c. 13: 3 6 4 SP T3 SD: 7.3356 c. M: 12.2955 c. 14: 3 7 4 P T3 SD: 2.9941 c. M: 5.0074 c. 18: 4 9 5 P T3 SD: 1.6216 c. M:-2.6033 c. 35: 8 17 10 SP T3 SD: 1.4449 c. M:-2.1076 c. 49: 11 24 14 SP T3 SD: 0.7803 c. M: 1.3495 c. 53: 12 26 15 SP T3 SD: 0.5968 c. M:-1.0336 c. 67: 15 33 19 SP T3 SD: 0.2121 c. M: 0.2875 c. 120: 27 59 34 SP T3 SD: 0.2121 c. M:-0.3288 c. 138: 31 68 39 SP T3 SD: 0.1425 c. M:-0.1973 c. 187: 42 92 53 SP T3 SD: 0.1414 c. M: 0.2080 c. 205: 46 101 58 SP T3 SD: 0.0267 c. M:-0.0388 c. 477: 107 235 135 SP T3 SD: 0.0073 c. M: 0.0105 c. 682: 153 336 193 SP T3 SD: 0.0039 c. M:-0.0067 c. 1159: 260 571 328 SP T3 SD: 0.0025 c. M: 0.0042 c. 1841: 413 907 521 SP T3 SD: 0.0024 c. M:-0.0032 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: 29.2178 cents 5 x 6:7 S SD: 47.0457 cents 6 x 7:8 S SD: 45.1125 cents 7:8 x 9 S SD: 67.5105 cents 8:9:10:11 H SD: 36.8007 cents 9:10:11:12 H SD: 23.7778 cents 12:13:15:16 SD: 13.2251 cents 13:14:16:17 S SD: 12.5177 cents 17:18:21:23 SD: 9.8783 cents 18:19:22:24 SD: 6.8515 cents 27:29:33:36 SD: 5.1359 cents 30:32:37:40 SD: 1.9931 cents 57:61:70:76 SD: 1.9537 cents 75:80:92:100 SD: 1.1347 cents 105:112:129:140 SD: 0.2393 cents 240:256:295:320 SD: 0.0403 cents 585:624:719:780 SD: 0.0099 cents