Scala analysis: xen14-mclaren-nonoctave-21-17
21st root of 17 non-octave scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 233.569 cents 233.569305 2: 467.139 cents 467.138610 3: 700.708 cents 700.707916 4: 934.277 cents 934.277221 5: 1167.847 cents 1167.846526 6: 1401.416 cents 1401.415831 7: 1634.985 cents 1634.985137 8: 1868.554 cents 1868.554442 9: 2102.124 cents 2102.123747 10: 2335.693 cents 2335.693052 11: 2569.262 cents 2569.262357 12: 2802.832 cents 2802.831663 13: 3036.401 cents 3036.400968 14: 3269.970 cents 3269.970273 15: 3503.540 cents 3503.539578 16: 3737.109 cents 3737.108883 17: 3970.678 cents 3970.678189 18: 4204.247 cents 4204.247494 19: 4437.817 cents 4437.816799 20: 4671.386 cents 4671.386104 21: 17/1 4904.955410 17th harmonic +4 octaves
SHOW/INTERVAL
0: 233.5693 cents 233.5693 1: 233.5693 cents 233.5693 2: 233.5693 cents 233.5693 3: 233.5693 cents 233.5693 4: 233.5693 cents 233.5693 5: 233.5693 cents 233.5693 6: 233.5693 cents 233.5693 7: 233.5693 cents 233.5693 8: 233.5693 cents 233.5693 9: 233.5693 cents 233.5693 10: 233.5693 cents 233.5693 11: 233.5693 cents 233.5693 12: 233.5693 cents 233.5693 13: 233.5693 cents 233.5693 14: 233.5693 cents 233.5693 15: 233.5693 cents 233.5693 16: 233.5693 cents 233.5693 17: 233.5693 cents 233.5693 18: 233.5693 cents 233.5693 19: 233.5693 cents 233.5693 20: 233.5693 cents 233.5693 21: 233.5693 cents 233.5693
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 21 233.56931 cents 2: 21 467.13861 cents 3: 21 700.70792 cents 4: 21 934.27722 cents 5: 21 1167.84653 cents 6: 21 1401.41583 cents 7: 21 1634.98514 cents 8: 21 1868.55444 cents 9: 21 2102.12375 cents 10: 21 2335.69305 cents 11: 21 2569.26236 cents 12: 21 2802.83166 cents 13: 21 3036.40097 cents 14: 21 3269.97027 cents 15: 21 3503.53958 cents 16: 21 3737.10888 cents 17: 21 3970.67819 cents 18: 21 4204.24749 cents 19: 21 4437.81680 cents 20: 21 4671.38610 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 18 19 20 21 0.0 : 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 233.6 : 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 467.1 : 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 700.7 : 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 934.3 : 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 1167.8: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 1401.4: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 1635.0: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 1868.6: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 2102.1: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 2335.7: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 2569.3: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 2802.8: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 3036.4: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 3270.0: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 3503.5: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 3737.1: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 3970.7: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 4204.2: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 4437.8: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 4671.4: 233.6 467.1 700.7 934.3 1167.8 1401.4 1635.0 1868.6 2102.1 2335.7 2569.3 2802.8 3036.4 3270.0 3503.5 3737.1 3970.7 4204.2 4437.8 4671.4 4905.0 4905.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 233.5693 .. 233.5693 cents 1/1, 0.0000 cents 233.56931 cents 2: 467.1386 .. 467.1386 cents 1/1, 0.0000 cents 233.56930 cents 3: 700.7079 .. 700.7079 cents 1/1, 0.0000 cents 233.56931 cents 4: 934.2772 .. 934.2772 cents 1/1, 0.0000 cents 233.56931 cents 5: 1167.8465 .. 1167.8465 cents 1/1, 0.0000 cents 233.56930 cents 6: 1401.4158 .. 1401.4158 cents 1/1, 0.0000 cents 233.56930 cents 7: 1634.9851 .. 1634.9851 cents 1/1, 0.0000 cents 233.56931 cents 8: 1868.5544 .. 1868.5544 cents 1/1, 0.0000 cents 233.56931 cents 9: 2102.1237 .. 2102.1237 cents 1/1, 0.0000 cents 233.56931 cents 10: 2335.6931 .. 2335.6931 cents 1/1, 0.0000 cents 233.56930 cents 11: 2569.2624 .. 2569.2624 cents 1/1, 0.0000 cents 233.56930 cents 12: 2802.8317 .. 2802.8317 cents 1/1, 0.0000 cents 233.56931 cents 13: 3036.4010 .. 3036.4010 cents 1/1, 0.0000 cents 233.56930 cents 14: 3269.9703 .. 3269.9703 cents 1/1, 0.0000 cents 233.56930 cents 15: 3503.5396 .. 3503.5396 cents 1/1, 0.0000 cents 233.56931 cents 16: 3737.1089 .. 3737.1089 cents 1/1, 0.0000 cents 233.56931 cents 17: 3970.6782 .. 3970.6782 cents 1/1, 0.0000 cents 233.56931 cents 18: 4204.2475 .. 4204.2475 cents 1/1, 0.0000 cents 233.56930 cents 19: 4437.8168 .. 4437.8168 cents 1/1, 0.0000 cents 233.56931 cents 20: 4671.3861 .. 4671.3861 cents 1/1, 0.0000 cents 233.56931 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 233.56930 cents, class 1 Average step (divided formal octave): 233.5693 cents Largest one step interval : 233.56931 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 233.56931 cents, amount: 21 Most common interval of one step : 233.56931 cents, amount: 21 Least squares average step : 233.56931 cents, oct.: 4904.95541 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 233.56931 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.047619 redundancy: 0.952381 Efficiency x scale size : 1.000000 Number of different interval sizes : 20 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 21, average 700.7079 cents Number of recognisable fourths : 0 Scale contains two identical disjunct "tetrachords" of 3 notes 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 : 17 (not all pitches rational)
FIT/MODE
21: 1 1 1 1 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 .. 17 match: 13 SD: 14.9423 cents 2 .. 34 match: 17 SD: 8.7493 cents 3 .. 51 match: 19 SD: 7.7897 cents 4 .. 68 match: 20 SD: 7.3922 cents 6 .. 102 match: 21 SD: 5.9407 cents 7 .. 119 match: 21 SD: 5.3871 cents 10 .. 170 match: 21 SD: 4.6962 cents 12 .. 204 match: 21 SD: 3.4701 cents 13 .. 221 match: 21 SD: 3.3370 cents 14 .. 238 match: 21 SD: 2.5836 cents 16 .. 272 match: 21 SD: 2.4625 cents 19 .. 323 match: 21 SD: 2.3046 cents 20 .. 340 match: 21 SD: 1.5381 cents 22 .. 374 match: 21 SD: 1.5380 cents 26 .. 442 match: 21 SD: 1.4181 cents 28 .. 476 match: 21 SD: 1.0192 cents 35 .. 595 match: 21 SD: 1.0020 cents 36 .. 612 match: 21 SD: 0.8679 cents 42 .. 714 match: 21 SD: 0.7244 cents 48 .. 816 match: 21 SD: 0.6327 cents 49 .. 833 match: 21 SD: 0.6327 cents 54 .. 918 match: 21 SD: 0.6201 cents 56 .. 952 match: 21 SD: 0.5145 cents 68 .. 1156 match: 21 SD: 0.4900 cents 70 .. 1190 match: 21 SD: 0.4733 cents 74 .. 1258 match: 21 SD: 0.4582 cents 77 .. 1309 match: 21 SD: 0.4294 cents 84 .. 1428 match: 21 SD: 0.2648 cents 110 .. 1870 match: 21 SD: 0.2451 cents 126 .. 2142 match: 21 SD: 0.2224 cents 138 .. 2346 match: 21 SD: 0.1969 cents 158 .. 2686 match: 21 SD: 0.1462 cents 187 .. 3179 match: 21 SD: 0.1393 cents 194 .. 3298 match: 21 SD: 0.1245 cents 242 .. 4114 match: 21 SD: 0.1048 cents 291 .. 4947 match: 21 SD: 0.0963 cents 319 .. 5423 match: 21 SD: 0.0961 cents 333 .. 5661 match: 21 SD: 0.0869 cents 345 .. 5865 match: 21 SD: 0.0803 cents 381 .. 6477 match: 21 SD: 0.0740 cents 401 .. 6817 match: 21 SD: 0.0655 cents 429 .. 7293 match: 21 SD: 0.0571 cents 471 .. 8007 match: 21 SD: 0.0508 cents 555 .. 9435 match: 21 SD: 0.0471 cents