Scala analysis: 486_R10
Reduplicated tetrachord 22/21 * 147/121 * 22/21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 22/21 80.5370 undecimal minor semitone 2: 147/121 336.9709 3: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 147/121 336.971 cents 2: 1 484/441 161.074 cents two (undecimal minor semitone) 2: 2 14/11 417.508 cents undecimal diminished fourth or 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 : 80.5 417.5 498.0 80.5 : 337.0 417.5 498.0 417.5: 80.5 161.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 336.9709 cents 3087/2662, 256.4339 cents 22/21, 80.5370 cents 2: 161.0741 .. 417.5080 cents 3087/2662, 256.4339 cents 58564/64827,-175.8969 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 147/121, 336.9709 cents Average / Smallest step : 2.061350 Largest / Average step : 2.029762 Largest / Smallest step : 4.184049 Median interval of one step : 22/21, 80.5370 cents, amount: 2 Most common interval of one step : 22/21, 80.5370 cents, amount: 2 Least squares average step : 172.12057 cents, oct.: 516.36171 cents Scale is not proper Scale has Myhill's property chromas: 3087/2662, 256.4339 cents and 64827/58564, 175.8969 cents, ratio: 1.457865 generators: 1 of 80.53704 cents and 2 of 417.50796 cents ET pair of linear temperament : 62&136 Scale is distributional even Scale is a mode of a 235-tone equal temperament with octave 4/3 degrees: 38 197 235 generators: 38 and 197 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Scale is a Constant Structure, by a margin of 80.53704 cents Scale diversity : 0.875181 Lumma stability : 0.323413 Lumma impropriety factor : 0.353175 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 : 22/21, 80.5370 cents Most common intervals : 22/21, 80.5370 cents & inv., amount: 2 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 : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 11 Odd number limit : 441 (O: 147 U: 441) Highest odd numerator or denominator: 21 Scale harmonicity : 0.016233 Average absolute harmonicity : 0.093113 Specific harmonicity : 0.085346 Fundamental : 1/231, -7.8517 octaves, 1.1326 Hz. Guide tone : 308, 8.2668 octaves, 80580.674 Hz. Exponens Consonantiae : 7.114800E+04, 16.11854 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 37.5, average 12.50000 Mersenne's string divisions : 7525 Sum of van Prooijen's expressibility: 2.84073, average 0.94691 Sum of Tenney's harmonic distance : 5.93134, average 1.97711 Vogel's harmonic complexity : 20.33333 Wille's k value : 73 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.70017, average 2.11669 Lattice compactness (without 2's) : 10.29253, average 1.71542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 7: -1 .. 1 0.00000 2 11: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 18 27| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 20 23| Scale is JI-epimorphic with val: <7 11 20 25| = patent Scale is weakly epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 11 21 23| Scale is weakly epimorphic with val: <7 11 21 24| Scale is JI-epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 22 24| Scale is weakly epimorphic with val: <7 11 22 25| Scale is JI-epimorphic with val: <7 11 22 27|
FIT/MODE
3: 0 2 1 N G T3 SD: 67.8053 c. M: 85.4780 c. 4: 1 2 1 P M ME I SD: 35.9048 c. M: 43.9742 c. 5: 1 3 1 N M DE I SD: 15.5722 c. M: 19.0720 c. 6: 1 4 1 N M DE I SD: 2.0171 c. M: 2.4705 c. 19: 3 13 3 N M DE I SD: 1.5500 c. M: 1.8984 c. 25: 4 17 4 N M DE I SD: 0.6939 c. M: 0.8498 c. 31: 5 21 5 N M DE I SD: 0.1692 c. M: 0.2072 c. 68: 11 46 11 N M DE I SD: 0.0237 c. M: 0.0291 c. 167: 27 113 27 N M DE I SD: 0.0121 c. M: 0.0148 c. 235: 38 159 38 N M DE I SD: 0.0017 c. M: 0.0021 c. 538: 87 364 87 N M DE I SD: 0.0015 c. M: 0.0018 c. 773: 125 523 125 N M DE I SD: 0.0005 c. M: 0.0006 c. 1008: 163 682 163 N M DE I SD: 0.0000 c. M: 0.0000 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: 31.1943 cents 5 x 6:7 S SD: 66.1656 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 75.8295 cents 8:9:10:11 H SD: 45.9855 cents 9:10:11:12 H SD: 41.2187 cents 10:11:13 x SD: 46.0490 cents 11:12:14:15 S SD: 26.7243 cents 12:13:15:16 SD: 21.9626 cents 13:14 x 17 SD: 29.2030 cents 14:15:18:19 S SD: 17.5167 cents 15:16:19:20 SD: 10.7568 cents 18:19:23:24 SD: 4.9186 cents 39:41:50:52 SD: 4.6691 cents 40:42:51:53 SD: 3.9833 cents 44:46:56:59 SD: 3.4806 cents 45:47:57:60 SD: 3.2642 cents 59:62:75:79 SD: 3.0977 cents 60:63:76:80 SD: 3.0502 cents 62:65:79:83 SD: 2.4522 cents 63:66:80:84 SD: 1.3101 cents 66:69:84:88 SD: 1.1935 cents 81:85:103:108 SD: 1.0961 cents 84:88:107:112 SD: 0.4905 cents 147:154:187:196 SD: 0.2805 cents 231:242:294:308 SD: 0.0000 cents