Scala analysis: xen14-mclaren-nonoctave-16-3
16th 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: 118.872 cents 118.872188 2: 237.744 cents 237.744375 3: 356.617 cents 356.616563 4: 475.489 cents 475.488750 5: 594.361 cents 594.360938 6: 713.233 cents 713.233125 7: 832.105 cents 832.105313 8: 950.977 cents 950.977500 9: 1069.850 cents 1069.849688 10: 1188.722 cents 1188.721876 11: 1307.594 cents 1307.594063 12: 1426.466 cents 1426.466251 13: 1545.338 cents 1545.338438 14: 1664.211 cents 1664.210626 15: 1783.083 cents 1783.082813 16: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 118.8722 cents 118.8722 1: 118.8722 cents 118.8722 2: 118.8722 cents 118.8722 3: 118.8722 cents 118.8722 4: 118.8722 cents 118.8722 5: 118.8722 cents 118.8722 6: 118.8722 cents 118.8722 7: 118.8722 cents 118.8722 8: 118.8722 cents 118.8722 9: 118.8722 cents 118.8722 10: 118.8722 cents 118.8722 11: 118.8722 cents 118.8722 12: 118.8722 cents 118.8722 13: 118.8722 cents 118.8722 14: 118.8722 cents 118.8722 15: 118.8722 cents 118.8722 16: 118.8722 cents 118.8722
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 16 118.87219 cents 2: 16 237.74438 cents 3: 16 356.61656 cents 4: 16 475.48875 cents 5: 16 594.36094 cents 6: 16 713.23312 cents 7: 16 832.10531 cents 8: 16 950.97750 cents 9: 16 1069.84969 cents 10: 16 1188.72188 cents 11: 16 1307.59406 cents 12: 16 1426.46625 cents 13: 16 1545.33844 cents 14: 16 1664.21063 cents 15: 16 1783.08281 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 0.0 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 118.9 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 237.7 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 356.6 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 475.5 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 594.4 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 713.2 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 832.1 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 951.0 : 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 1069.8: 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 1188.7: 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 1307.6: 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 1426.5: 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 1545.3: 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 1664.2: 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 1783.1: 118.9 237.7 356.6 475.5 594.4 713.2 832.1 951.0 1069.8 1188.7 1307.6 1426.5 1545.3 1664.2 1783.1 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 118.8722 .. 118.8722 cents 1/1, 0.0000 cents 118.87219 cents 2: 237.7444 .. 237.7444 cents 1/1, 0.0000 cents 118.87219 cents 3: 356.6166 .. 356.6166 cents 1/1, 0.0000 cents 118.87219 cents 4: 475.4887 .. 475.4887 cents 1/1, 0.0000 cents 118.87219 cents 5: 594.3609 .. 594.3609 cents 1/1, 0.0000 cents 118.87219 cents 6: 713.2331 .. 713.2331 cents 1/1, 0.0000 cents 118.87219 cents 7: 832.1053 .. 832.1053 cents 1/1, 0.0000 cents 118.87219 cents 8: 950.9775 .. 950.9775 cents 1/1, 0.0000 cents 118.87219 cents 9: 1069.8497 .. 1069.8497 cents 1/1, 0.0000 cents 118.87219 cents 10: 1188.7219 .. 1188.7219 cents 1/1, 0.0000 cents 118.87219 cents 11: 1307.5941 .. 1307.5941 cents 1/1, 0.0000 cents 118.87219 cents 12: 1426.4663 .. 1426.4663 cents 1/1, 0.0000 cents 118.87219 cents 13: 1545.3384 .. 1545.3384 cents 1/1, 0.0000 cents 118.87219 cents 14: 1664.2106 .. 1664.2106 cents 1/1, 0.0000 cents 118.87219 cents 15: 1783.0828 .. 1783.0828 cents 1/1, 0.0000 cents 118.87219 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 118.87219 cents, class 1 Average step (divided formal octave): 118.8722 cents Largest one step interval : 118.87219 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 118.87219 cents, amount: 16 Most common interval of one step : 118.87219 cents, amount: 16 Least squares average step : 118.87219 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 118.87219 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.062500 redundancy: 0.937500 Efficiency x scale size : 1.000000 Number of different interval sizes : 15 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 16, average 713.2331 cents Number of recognisable fourths : 0 Scale contains two identical disjunct pentachords 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
16: 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: 5.6391 cents 2 .. 6 match: 4 H SD: 10.9925 cents 3 .. 9 match: 6 H SD: 13.0636 cents 4 .. 12 match: 8 H SD: 8.5254 cents 5 .. 15 match: 10 H SD: 9.6407 cents 6 .. 18 match: 12 H SD: 8.5693 cents 7 .. 21 match: 13 S SD: 6.6175 cents 8 .. 24 match: 14 S SD: 6.4323 cents 9 .. 27 match: 15 SD: 8.7337 cents 10 .. 30 match: 15 SD: 6.5000 cents 11 .. 33 match: 15 SD: 8.0960 cents 12 .. 36 match: 16 SD: 5.4686 cents 13 .. 39 match: 16 SD: 4.5763 cents 14 .. 42 match: 16 SD: 4.2509 cents 18 .. 54 match: 16 SD: 3.9358 cents 19 .. 57 match: 16 SD: 3.8571 cents 21 .. 63 match: 16 SD: 3.8122 cents 22 .. 66 match: 16 SD: 3.1351 cents 25 .. 75 match: 16 SD: 2.8561 cents 26 .. 78 match: 16 SD: 2.2375 cents 29 .. 87 match: 16 SD: 2.0294 cents 39 .. 117 match: 16 SD: 1.6470 cents 41 .. 123 match: 16 SD: 1.4182 cents 47 .. 141 match: 16 SD: 1.3200 cents 53 .. 159 match: 16 SD: 1.2220 cents 56 .. 168 match: 16 SD: 1.1962 cents 57 .. 171 match: 16 SD: 1.0365 cents 61 .. 183 match: 16 SD: 0.9742 cents 69 .. 207 match: 16 SD: 0.9548 cents 70 .. 210 match: 16 SD: 0.7855 cents 82 .. 246 match: 16 SD: 0.7705 cents 83 .. 249 match: 16 SD: 0.6458 cents 96 .. 288 match: 16 SD: 0.6004 cents 110 .. 330 match: 16 SD: 0.5407 cents 123 .. 369 match: 16 SD: 0.5253 cents 127 .. 381 match: 16 SD: 0.4836 cents 130 .. 390 match: 16 SD: 0.4675 cents 139 .. 417 match: 16 SD: 0.4620 cents 143 .. 429 match: 16 SD: 0.4423 cents 149 .. 447 match: 16 SD: 0.3860 cents 157 .. 471 match: 16 SD: 0.3468 cents 171 .. 513 match: 16 SD: 0.3150 cents 210 .. 630 match: 16 SD: 0.2783 cents 224 .. 672 match: 16 SD: 0.2512 cents 237 .. 711 match: 16 SD: 0.2504 cents 240 .. 720 match: 16 SD: 0.2479 cents 253 .. 759 match: 16 SD: 0.2405 cents 266 .. 798 match: 16 SD: 0.2397 cents 271 .. 813 match: 16 SD: 0.2386 cents 279 .. 837 match: 16 SD: 0.2186 cents 297 .. 891 match: 16 SD: 0.2103 cents 298 .. 894 match: 16 SD: 0.1590 cents 366 .. 1098 match: 16 SD: 0.1546 cents 367 .. 1101 match: 16 SD: 0.1507 cents 380 .. 1140 match: 16 SD: 0.1490 cents 381 .. 1143 match: 16 SD: 0.1430 cents 408 .. 1224 match: 16 SD: 0.1166 cents 437 .. 1311 match: 16 SD: 0.1166 cents 481 .. 1443 match: 16 SD: 0.1098 cents 522 .. 1566 match: 16 SD: 0.1077 cents 537 .. 1611 match: 16 SD: 0.0919 cents 551 .. 1653 match: 16 SD: 0.0900 cents