Scala analysis: xen14-mclaren-nonoctave-17-3
17th root of 3 non-octave scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 111.880 cents 111.879706 2: 223.759 cents 223.759412 3: 335.639 cents 335.639118 4: 447.519 cents 447.518824 5: 559.399 cents 559.398530 6: 671.278 cents 671.278236 7: 783.158 cents 783.157942 8: 895.038 cents 895.037647 9: 1006.917 cents 1006.917353 10: 1118.797 cents 1118.797059 11: 1230.677 cents 1230.676765 12: 1342.556 cents 1342.556471 13: 1454.436 cents 1454.436177 14: 1566.316 cents 1566.315883 15: 1678.196 cents 1678.195589 16: 1790.075 cents 1790.075295 17: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 111.8797 cents 111.8797 1: 111.8797 cents 111.8797 2: 111.8797 cents 111.8797 3: 111.8797 cents 111.8797 4: 111.8797 cents 111.8797 5: 111.8797 cents 111.8797 6: 111.8797 cents 111.8797 7: 111.8797 cents 111.8797 8: 111.8797 cents 111.8797 9: 111.8797 cents 111.8797 10: 111.8797 cents 111.8797 11: 111.8797 cents 111.8797 12: 111.8797 cents 111.8797 13: 111.8797 cents 111.8797 14: 111.8797 cents 111.8797 15: 111.8797 cents 111.8797 16: 111.8797 cents 111.8797 17: 111.8797 cents 111.8797
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 17 111.87971 cents 2: 17 223.75941 cents 3: 17 335.63912 cents 4: 17 447.51882 cents 5: 17 559.39853 cents 6: 17 671.27824 cents 7: 17 783.15794 cents 8: 17 895.03765 cents 9: 17 1006.91735 cents 10: 17 1118.79706 cents 11: 17 1230.67676 cents 12: 17 1342.55647 cents 13: 17 1454.43618 cents 14: 17 1566.31588 cents 15: 17 1678.19559 cents 16: 17 1790.07529 cents Only one interval per interval class, scale is equal tempered Average number of different intervals per interval class: 1.00000 = 1
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 111.9 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 223.8 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 335.6 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 447.5 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 559.4 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 671.3 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 783.2 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 895.0 : 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1006.9: 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1118.8: 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1230.7: 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1342.6: 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1454.4: 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1566.3: 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1678.2: 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1790.1: 111.9 223.8 335.6 447.5 559.4 671.3 783.2 895.0 1006.9 1118.8 1230.7 1342.6 1454.4 1566.3 1678.2 1790.1 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.8797 .. 111.8797 cents 1/1, 0.0000 cents 111.87971 cents 2: 223.7594 .. 223.7594 cents 1/1, 0.0000 cents 111.87971 cents 3: 335.6391 .. 335.6391 cents 1/1, 0.0000 cents 111.87971 cents 4: 447.5188 .. 447.5188 cents 1/1, 0.0000 cents 111.87971 cents 5: 559.3985 .. 559.3985 cents 1/1, 0.0000 cents 111.87971 cents 6: 671.2782 .. 671.2782 cents 1/1, 0.0000 cents 111.87971 cents 7: 783.1579 .. 783.1579 cents 1/1, 0.0000 cents 111.87971 cents 8: 895.0376 .. 895.0376 cents 1/1, 0.0000 cents 111.87970 cents 9: 1006.9174 .. 1006.9174 cents 1/1, 0.0000 cents 111.87971 cents 10: 1118.7971 .. 1118.7971 cents 1/1, 0.0000 cents 111.87971 cents 11: 1230.6768 .. 1230.6768 cents 1/1, 0.0000 cents 111.87971 cents 12: 1342.5565 .. 1342.5565 cents 1/1, 0.0000 cents 111.87971 cents 13: 1454.4362 .. 1454.4362 cents 1/1, 0.0000 cents 111.87971 cents 14: 1566.3159 .. 1566.3159 cents 1/1, 0.0000 cents 111.87971 cents 15: 1678.1956 .. 1678.1956 cents 1/1, 0.0000 cents 111.87971 cents 16: 1790.0753 .. 1790.0753 cents 1/1, 0.0000 cents 111.87971 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 111.87970 cents, class 1 Average step (divided formal octave): 111.8797 cents Largest one step interval : 111.87971 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 111.87971 cents, amount: 17 Most common interval of one step : 111.87971 cents, amount: 17 Least squares average step : 111.87971 cents, oct.: 1901.95500 cents Scale is strictly proper Scale is equal tempered Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a Constant Structure, by a margin of 111.87971 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.058824 redundancy: 0.941176 Efficiency x scale size : 1.000000 Number of different interval sizes : 16 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct pentachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties -- Prime limit : 3 (not all pitches rational)
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: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 3 match: 2 H SD: 15.3384 cents 2 .. 6 match: 4 H SD: 11.9427 cents 3 .. 9 match: 6 H SD: 10.7453 cents 4 .. 12 match: 8 H SD: 12.7205 cents 5 .. 15 match: 10 H SD: 8.1396 cents 6 .. 18 match: 12 H SD: 8.0540 cents 7 .. 21 match: 13 S SD: 8.5347 cents 8 .. 24 match: 14 SD: 8.8776 cents 9 .. 27 match: 15 SD: 6.7900 cents 10 .. 30 match: 16 SD: 5.9411 cents 11 .. 33 match: 16 SD: 6.6410 cents 13 .. 39 match: 17 SD: 4.5427 cents 18 .. 54 match: 17 SD: 4.5097 cents 19 .. 57 match: 17 SD: 3.3755 cents 23 .. 69 match: 17 SD: 2.8594 cents 27 .. 81 match: 17 SD: 2.6018 cents 28 .. 84 match: 17 SD: 1.7862 cents 42 .. 126 match: 17 SD: 1.4286 cents 44 .. 132 match: 17 SD: 1.3114 cents 47 .. 141 match: 17 SD: 1.2432 cents 57 .. 171 match: 17 SD: 0.9796 cents 65 .. 195 match: 17 SD: 0.8821 cents 74 .. 222 match: 17 SD: 0.7497 cents 87 .. 261 match: 17 SD: 0.7216 cents 89 .. 267 match: 17 SD: 0.5416 cents 108 .. 324 match: 17 SD: 0.4389 cents 145 .. 435 match: 17 SD: 0.4135 cents 152 .. 456 match: 17 SD: 0.3739 cents 165 .. 495 match: 17 SD: 0.3553 cents 194 .. 582 match: 17 SD: 0.3463 cents 196 .. 588 match: 17 SD: 0.2459 cents 238 .. 714 match: 17 SD: 0.2308 cents 275 .. 825 match: 17 SD: 0.2026 cents 281 .. 843 match: 17 SD: 0.1918 cents 285 .. 855 match: 17 SD: 0.1699 cents 304 .. 912 match: 17 SD: 0.1635 cents 346 .. 1038 match: 17 SD: 0.1390 cents 393 .. 1179 match: 17 SD: 0.1220 cents 420 .. 1260 match: 17 SD: 0.1164 cents 448 .. 1344 match: 17 SD: 0.1070 cents 477 .. 1431 match: 17 SD: 0.1049 cents 556 .. 1668 match: 17 SD: 0.1016 cents 566 .. 1698 match: 17 SD: 0.0837 cents