Scala analysis: leapday17
Leapday[17] in 46-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 78.261 cents 78.260870 2: 130.435 cents 130.434783 3: 208.696 cents 208.695652 4: 286.957 cents 286.956522 5: 339.130 cents 339.130435 6: 417.391 cents 417.391304 7: 495.652 cents 495.652174 8: 573.913 cents 573.913043 9: 626.087 cents 626.086957 10: 704.348 cents 704.347826 11: 782.609 cents 782.608696 12: 834.783 cents 834.782609 13: 913.043 cents 913.043478 14: 991.304 cents 991.304348 15: 1043.478 cents 1043.478261 16: 1121.739 cents 1121.739130 17: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 78.2609 cents 78.2609 1: 78.2609 cents 78.2609 2: 52.1739 cents 52.1739 3: 78.2609 cents 78.2609 4: 78.2609 cents 78.2609 5: 52.1739 cents 52.1739 6: 78.2609 cents 78.2609 7: 78.2609 cents 78.2609 8: 78.2609 cents 78.2609 9: 52.1739 cents 52.1739 10: 78.2609 cents 78.2609 11: 78.2609 cents 78.2609 12: 52.1739 cents 52.1739 13: 78.2609 cents 78.2609 14: 78.2609 cents 78.2609 15: 52.1739 cents 52.1739 16: 78.2609 cents 78.2609 17: 78.2609 cents 78.2609
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 52.17391 cents 1: 12 78.26087 cents 2: 10 130.43478 cents 2: 7 156.52174 cents 3: 15 208.69565 cents 3: 2 234.78261 cents 4: 3 260.86956 cents 4: 14 286.95652 cents 5: 8 339.13043 cents 5: 9 365.21739 cents 6: 13 417.39130 cents 6: 4 443.47826 cents 7: 1 469.56522 cents 7: 16 495.65217 cents 8: 6 547.82609 cents 8: 11 573.91304 cents 9: 11 626.08696 cents 9: 6 652.17391 cents 10: 16 704.34783 cents 10: 1 730.43478 cents 11: 4 756.52174 cents 11: 13 782.60870 cents 12: 9 834.78261 cents 12: 8 860.86957 cents 13: 14 913.04348 cents 13: 3 939.13044 cents 14: 2 965.21739 cents 14: 15 991.30435 cents 15: 7 1043.47826 cents 15: 10 1069.56522 cents 16: 12 1121.73913 cents 16: 5 1147.82609 cents 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 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 78.3 130.4 208.7 287.0 339.1 417.4 495.7 573.9 626.1 704.3 782.6 834.8 913.0 991.3 1043.5 1121.7 1200.0 78.3 : 52.2 130.4 208.7 260.9 339.1 417.4 495.7 547.8 626.1 704.3 756.5 834.8 913.0 965.2 1043.5 1121.7 1200.0 130.4 : 78.3 156.5 208.7 287.0 365.2 443.5 495.7 573.9 652.2 704.3 782.6 860.9 913.0 991.3 1069.6 1147.8 1200.0 208.7 : 78.3 130.4 208.7 287.0 365.2 417.4 495.7 573.9 626.1 704.3 782.6 834.8 913.0 991.3 1069.6 1121.7 1200.0 287.0 : 52.2 130.4 208.7 287.0 339.1 417.4 495.7 547.8 626.1 704.3 756.5 834.8 913.0 991.3 1043.5 1121.7 1200.0 339.1 : 78.3 156.5 234.8 287.0 365.2 443.5 495.7 573.9 652.2 704.3 782.6 860.9 939.1 991.3 1069.6 1147.8 1200.0 417.4 : 78.3 156.5 208.7 287.0 365.2 417.4 495.7 573.9 626.1 704.3 782.6 860.9 913.0 991.3 1069.6 1121.7 1200.0 495.7 : 78.3 130.4 208.7 287.0 339.1 417.4 495.7 547.8 626.1 704.3 782.6 834.8 913.0 991.3 1043.5 1121.7 1200.0 573.9 : 52.2 130.4 208.7 260.9 339.1 417.4 469.6 547.8 626.1 704.3 756.5 834.8 913.0 965.2 1043.5 1121.7 1200.0 626.1 : 78.3 156.5 208.7 287.0 365.2 417.4 495.7 573.9 652.2 704.3 782.6 860.9 913.0 991.3 1069.6 1147.8 1200.0 704.3 : 78.3 130.4 208.7 287.0 339.1 417.4 495.7 573.9 626.1 704.3 782.6 834.8 913.0 991.3 1069.6 1121.7 1200.0 782.6 : 52.2 130.4 208.7 260.9 339.1 417.4 495.7 547.8 626.1 704.3 756.5 834.8 913.0 991.3 1043.5 1121.7 1200.0 834.8 : 78.3 156.5 208.7 287.0 365.2 443.5 495.7 573.9 652.2 704.3 782.6 860.9 939.1 991.3 1069.6 1147.8 1200.0 913.0 : 78.3 130.4 208.7 287.0 365.2 417.4 495.7 573.9 626.1 704.3 782.6 860.9 913.0 991.3 1069.6 1121.7 1200.0 991.3 : 52.2 130.4 208.7 287.0 339.1 417.4 495.7 547.8 626.1 704.3 782.6 834.8 913.0 991.3 1043.5 1121.7 1200.0 1043.5: 78.3 156.5 234.8 287.0 365.2 443.5 495.7 573.9 652.2 730.4 782.6 860.9 939.1 991.3 1069.6 1147.8 1200.0 1121.7: 78.3 156.5 208.7 287.0 365.2 417.4 495.7 573.9 652.2 704.3 782.6 860.9 913.0 991.3 1069.6 1121.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 52.1739 .. 78.2609 cents 26.08696 cents 52.17391 cents 2: 130.4348 .. 156.5217 cents 26.08696 cents 52.17391 cents 3: 208.6957 .. 234.7826 cents 26.08696 cents 52.17391 cents 4: 260.8696 .. 286.9565 cents 26.08696 cents 26.08696 cents 5: 339.1304 .. 365.2174 cents 26.08696 cents 52.17391 cents 6: 417.3913 .. 443.4783 cents 26.08696 cents 52.17391 cents 7: 469.5652 .. 495.6522 cents 26.08696 cents 26.08696 cents 8: 547.8261 .. 573.9130 cents 26.08696 cents 52.17391 cents 9: 626.0870 .. 652.1739 cents 26.08696 cents 52.17391 cents 10: 704.3478 .. 730.4348 cents 26.08696 cents 52.17391 cents 11: 756.5217 .. 782.6087 cents 26.08696 cents 26.08696 cents 12: 834.7826 .. 860.8696 cents 26.08696 cents 52.17391 cents 13: 913.0435 .. 939.1304 cents 26.08696 cents 52.17391 cents 14: 965.2174 .. 991.3043 cents 26.08696 cents 26.08696 cents 15: 1043.4783 .. 1069.5652 cents 26.08696 cents 52.17391 cents 16: 1121.7391 .. 1147.8261 cents 26.08696 cents 52.17391 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 52.17391 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 78.26087 cents Average / Smallest step : 1.352941 Largest / Average step : 1.108696 Largest / Smallest step : 1.500000 Median interval of one step : 78.26087 cents, amount: 12 Most common interval of one step : 78.26087 cents, amount: 12 Least squares average step : 70.26672 cents, oct.: 1194.53416 cents Scale is strictly proper Scale has Myhill's property chromas: 26.08696 cents and 26.08696 cents, ratio: 1.000000 generators: 7 of 495.65217 cents and 10 of 704.34783 cents Scale is maximally even in 46-tone equal temperament ET pair of linear temperament : 12&17 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 46-tone equal temperament with octave 1200.000 cents degrees: 3 5 8 11 13 16 19 22 24 27 30 32 35 38 40 43 46 generators: 19 and 27 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABAABAABAA Step pattern size order : LSLLSLLLSLLSLLSLL Interval vector is [ 0 5 12 0 10 7 0 15 2 3 14 0 8 9 0 13 4 1 16 0 6 11 0 ] Scale is a Constant Structure, by a margin of 26.08696 cents Ratio Whole / Half tone : 2.666667 Scale diversity : 1.193209 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.652174 Rothenberg efficiency : 0.705882 redundancy: 0.294118 Efficiency x scale size : 12.000000 Number of different interval sizes : 32 = 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 : 26.08696 cents Most common intervals : 495.65217 cents & inv., amount: 16 Scale is a chain of 8 triads 0.0 495.652 991.304 cents Most common triad is 0.0 495.652 704.348 cents, amount: 15 Number of recognisable fifths : 16, average 704.3478 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best fifths form a closed circle Formal octave complements present : 13 = 76.4706% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 11-12 -- Rational properties --
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.1200 c. M:-15.3453 c. 29: 2 1 2 2 1 2 2 2 1 2 2 1 2 2 1 2 2 P M ME S SD: 4.7600 c. M: 8.9955 c. 46: 3 2 3 3 2 3 3 3 2 3 3 2 3 3 2 3 3 SP M ME S SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.1964 cents 3 .. 6 match: 3 H SD: 9.5948 cents 4 .. 8 match: 4 H SD: 9.6074 cents 5 .. 10 match: 5 H SD: 8.3441 cents 6 .. 12 match: 6 H SD: 5.9450 cents 7 .. 14 match: 7 H SD: 6.5345 cents 8 .. 16 match: 8 H SD: 7.0307 cents 9 .. 18 match: 9 H SD: 5.5147 cents 10 .. 20 match: 10 H SD: 6.6631 cents 11 .. 22 match: 11 H SD: 6.1809 cents 12 .. 24 match: 12 H SD: 4.9521 cents 13 .. 26 match: 13 H SD: 5.8619 cents 14 .. 28 match: 14 H SD: 4.6936 cents 15 .. 30 match: 13 SD: 5.9930 cents 16 .. 32 match: 15 SD: 4.3789 cents 17 .. 34 match: 15 SD: 5.4333 cents 18 .. 36 match: 16 SD: 3.5724 cents 19 .. 38 match: 16 SD: 4.9206 cents 20 .. 40 match: 16 SD: 5.2034 cents 21 .. 42 match: 17 S SD: 3.9371 cents 22 .. 44 match: 17 SD: 3.2414 cents 23 .. 46 match: 17 SD: 2.5056 cents 25 .. 50 match: 16 SD: 3.3453 cents 26 .. 52 match: 17 SD: 2.9489 cents 28 .. 56 match: 17 SD: 2.8694 cents 33 .. 66 match: 17 SD: 2.6790 cents 34 .. 68 match: 17 SD: 2.6730 cents 36 .. 72 match: 17 SD: 2.3320 cents 37 .. 74 match: 17 SD: 2.1556 cents 39 .. 78 match: 17 SD: 1.8772 cents 40 .. 80 match: 17 SD: 1.6898 cents 48 .. 96 match: 17 SD: 1.5208 cents 56 .. 112 match: 17 SD: 1.4648 cents 60 .. 120 match: 17 SD: 1.3299 cents 61 .. 122 match: 17 SD: 1.2574 cents 63 .. 126 match: 17 SD: 1.1637 cents 66 .. 132 match: 17 SD: 0.9773 cents 78 .. 156 match: 17 SD: 0.9339 cents 84 .. 168 match: 17 SD: 0.8750 cents 87 .. 174 match: 17 SD: 0.7536 cents 88 .. 176 match: 17 SD: 0.7462 cents 102 .. 204 match: 17 SD: 0.6764 cents 110 .. 220 match: 17 SD: 0.6287 cents 115 .. 230 match: 17 SD: 0.5797 cents 124 .. 248 match: 17 SD: 0.5460 cents 133 .. 266 match: 17 SD: 0.5136 cents 150 .. 300 match: 17 SD: 0.4607 cents 157 .. 314 match: 17 SD: 0.4475 cents 166 .. 332 match: 17 SD: 0.4181 cents 179 .. 358 match: 17 SD: 0.3854 cents 190 .. 380 match: 17 SD: 0.3770 cents 193 .. 386 match: 17 SD: 0.3347 cents 216 .. 432 match: 17 SD: 0.3226 cents 217 .. 434 match: 17 SD: 0.3059 cents 239 .. 478 match: 17 SD: 0.2813 cents 257 .. 514 match: 17 SD: 0.2704 cents 259 .. 518 match: 17 SD: 0.2530 cents 278 .. 556 match: 17 SD: 0.2502 cents 282 .. 564 match: 17 SD: 0.2109 cents 305 .. 610 match: 17 SD: 0.1376 cents 476 .. 952 match: 17 SD: 0.1181 cents 498 .. 996 match: 17 SD: 0.1149 cents 560 .. 1120 match: 17 SD: 0.1094 cents 586 .. 1172 match: 17 SD: 0.1087 cents