Scala analysis: xen14-mclaren-nonoctave-25-5
Stockhausen's Studie II 25th root of 5 non-octave scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 111.453 cents 111.452549 2: 222.905 cents 222.905097 3: 334.358 cents 334.357646 4: 445.810 cents 445.810194 5: 557.263 cents 557.262743 6: 668.715 cents 668.715291 7: 780.168 cents 780.167840 8: 891.620 cents 891.620388 9: 1003.073 cents 1003.072937 10: 1114.525 cents 1114.525486 11: 1225.978 cents 1225.978034 12: 1337.431 cents 1337.430583 13: 1448.883 cents 1448.883131 14: 1560.336 cents 1560.335680 15: 1671.788 cents 1671.788228 16: 1783.241 cents 1783.240777 17: 1894.693 cents 1894.693325 18: 2006.146 cents 2006.145874 19: 2117.598 cents 2117.598423 20: 2229.051 cents 2229.050971 21: 2340.504 cents 2340.503520 22: 2451.956 cents 2451.956068 23: 2563.409 cents 2563.408617 24: 2674.861 cents 2674.861165 25: 5/1 2786.313714 major 17th
SHOW/INTERVAL
0: 111.4525 cents 111.4525 1: 111.4525 cents 111.4525 2: 111.4525 cents 111.4525 3: 111.4525 cents 111.4525 4: 111.4525 cents 111.4525 5: 111.4525 cents 111.4525 6: 111.4525 cents 111.4525 7: 111.4525 cents 111.4525 8: 111.4525 cents 111.4525 9: 111.4525 cents 111.4525 10: 111.4525 cents 111.4525 11: 111.4525 cents 111.4525 12: 111.4525 cents 111.4525 13: 111.4525 cents 111.4525 14: 111.4525 cents 111.4525 15: 111.4525 cents 111.4525 16: 111.4525 cents 111.4525 17: 111.4525 cents 111.4525 18: 111.4525 cents 111.4525 19: 111.4525 cents 111.4525 20: 111.4525 cents 111.4525 21: 111.4525 cents 111.4525 22: 111.4525 cents 111.4525 23: 111.4525 cents 111.4525 24: 111.4525 cents 111.4525 25: 111.4525 cents 111.4525
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 25 111.45255 cents 2: 25 222.90510 cents 3: 25 334.35765 cents 4: 25 445.81019 cents 5: 25 557.26274 cents 6: 25 668.71529 cents 7: 25 780.16784 cents 8: 25 891.62039 cents 9: 25 1003.07294 cents 10: 25 1114.52549 cents 11: 25 1225.97803 cents 12: 25 1337.43058 cents 13: 25 1448.88313 cents 14: 25 1560.33568 cents 15: 25 1671.78823 cents 16: 25 1783.24078 cents 17: 25 1894.69332 cents 18: 25 2006.14587 cents 19: 25 2117.59842 cents 20: 25 2229.05097 cents 21: 25 2340.50352 cents 22: 25 2451.95607 cents 23: 25 2563.40862 cents 24: 25 2674.86116 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 22 23 24 25 0.0 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 111.5 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 222.9 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 334.4 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 445.8 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 557.3 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 668.7 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 780.2 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 891.6 : 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1003.1: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1114.5: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1226.0: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1337.4: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1448.9: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1560.3: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1671.8: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1783.2: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 1894.7: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 2006.1: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 2117.6: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 2229.1: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 2340.5: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 2452.0: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 2563.4: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 2674.9: 111.5 222.9 334.4 445.8 557.3 668.7 780.2 891.6 1003.1 1114.5 1226.0 1337.4 1448.9 1560.3 1671.8 1783.2 1894.7 2006.1 2117.6 2229.1 2340.5 2452.0 2563.4 2674.9 2786.3 2786.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.4525 .. 111.4525 cents 1/1, 0.0000 cents 111.45255 cents 2: 222.9051 .. 222.9051 cents 1/1, 0.0000 cents 111.45255 cents 3: 334.3576 .. 334.3576 cents 1/1, 0.0000 cents 111.45255 cents 4: 445.8102 .. 445.8102 cents 1/1, 0.0000 cents 111.45255 cents 5: 557.2627 .. 557.2627 cents 1/1, 0.0000 cents 111.45255 cents 6: 668.7153 .. 668.7153 cents 1/1, 0.0000 cents 111.45255 cents 7: 780.1678 .. 780.1678 cents 1/1, 0.0000 cents 111.45255 cents 8: 891.6204 .. 891.6204 cents 1/1, 0.0000 cents 111.45255 cents 9: 1003.0729 .. 1003.0729 cents 1/1, 0.0000 cents 111.45255 cents 10: 1114.5255 .. 1114.5255 cents 1/1, 0.0000 cents 111.45255 cents 11: 1225.9780 .. 1225.9780 cents 1/1, 0.0000 cents 111.45255 cents 12: 1337.4306 .. 1337.4306 cents 1/1, 0.0000 cents 111.45255 cents 13: 1448.8831 .. 1448.8831 cents 1/1, 0.0000 cents 111.45255 cents 14: 1560.3357 .. 1560.3357 cents 1/1, 0.0000 cents 111.45255 cents 15: 1671.7882 .. 1671.7882 cents 1/1, 0.0000 cents 111.45255 cents 16: 1783.2408 .. 1783.2408 cents 1/1, 0.0000 cents 111.45255 cents 17: 1894.6933 .. 1894.6933 cents 1/1, 0.0000 cents 111.45255 cents 18: 2006.1459 .. 2006.1459 cents 1/1, 0.0000 cents 111.45255 cents 19: 2117.5984 .. 2117.5984 cents 1/1, 0.0000 cents 111.45255 cents 20: 2229.0510 .. 2229.0510 cents 1/1, 0.0000 cents 111.45255 cents 21: 2340.5035 .. 2340.5035 cents 1/1, 0.0000 cents 111.45255 cents 22: 2451.9561 .. 2451.9561 cents 1/1, 0.0000 cents 111.45255 cents 23: 2563.4086 .. 2563.4086 cents 1/1, 0.0000 cents 111.45255 cents 24: 2674.8612 .. 2674.8612 cents 1/1, 0.0000 cents 111.45255 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 111.45255 cents, class 1 Average step (divided formal octave): 111.4525 cents Largest one step interval : 111.45255 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 111.45255 cents, amount: 25 Most common interval of one step : 111.45255 cents, amount: 25 Least squares average step : 111.45255 cents, oct.: 2786.31371 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 111.45255 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.040000 redundancy: 0.960000 Efficiency x scale size : 1.000000 Number of different interval sizes : 24 = 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 : 5 (not all pitches rational)
FIT/MODE
25: 1 1 1 1 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 .. 5 match: 4 H SD: 14.6352 cents 2 .. 10 match: 8 H SD: 12.1651 cents 3 .. 15 match: 12 H SD: 8.0878 cents 4 .. 20 match: 15 S SD: 9.6169 cents 5 .. 25 match: 18 SD: 5.3596 cents 6 .. 30 match: 20 SD: 5.8375 cents 7 .. 35 match: 21 SD: 5.3503 cents 8 .. 40 match: 22 SD: 5.7564 cents 9 .. 45 match: 23 SD: 4.7692 cents 10 .. 50 match: 24 SD: 4.2014 cents 11 .. 55 match: 24 SD: 4.4844 cents 13 .. 65 match: 25 SD: 3.1120 cents 18 .. 90 match: 25 SD: 3.0892 cents 19 .. 95 match: 25 SD: 2.5418 cents 23 .. 115 match: 25 SD: 2.2178 cents 24 .. 120 match: 25 SD: 2.0439 cents 27 .. 135 match: 25 SD: 1.8497 cents 28 .. 140 match: 25 SD: 1.4703 cents 30 .. 150 match: 25 SD: 1.4459 cents 34 .. 170 match: 25 SD: 1.4199 cents 37 .. 185 match: 25 SD: 1.3143 cents 42 .. 210 match: 25 SD: 0.9557 cents 51 .. 255 match: 25 SD: 0.9124 cents 58 .. 290 match: 25 SD: 0.7551 cents 61 .. 305 match: 25 SD: 0.5925 cents 74 .. 370 match: 25 SD: 0.4554 cents 95 .. 475 match: 25 SD: 0.4377 cents 102 .. 510 match: 25 SD: 0.3687 cents 116 .. 580 match: 25 SD: 0.3580 cents 123 .. 615 match: 25 SD: 0.3157 cents 132 .. 660 match: 25 SD: 0.2951 cents 153 .. 765 match: 25 SD: 0.2677 cents 163 .. 815 match: 25 SD: 0.2675 cents 168 .. 840 match: 25 SD: 0.2456 cents 195 .. 975 match: 25 SD: 0.2255 cents 197 .. 985 match: 25 SD: 0.1856 cents 227 .. 1135 match: 25 SD: 0.1854 cents 239 .. 1195 match: 25 SD: 0.1754 cents 242 .. 1210 match: 25 SD: 0.1680 cents 255 .. 1275 match: 25 SD: 0.1556 cents 269 .. 1345 match: 25 SD: 0.1487 cents 297 .. 1485 match: 25 SD: 0.1336 cents 327 .. 1635 match: 25 SD: 0.1260 cents 334 .. 1670 match: 25 SD: 0.1194 cents 343 .. 1715 match: 25 SD: 0.1166 cents 371 .. 1855 match: 25 SD: 0.1042 cents 395 .. 1975 match: 25 SD: 0.0997 cents 408 .. 2040 match: 25 SD: 0.0983 cents 422 .. 2110 match: 25 SD: 0.0932 cents 437 .. 2185 match: 25 SD: 0.0803 cents 466 .. 2330 match: 25 SD: 0.0745 cents 511 .. 2555 match: 25 SD: 0.0742 cents 539 .. 2695 match: 25 SD: 0.0738 cents 558 .. 2790 match: 25 SD: 0.0653 cents