Scala analysis: xen16-mclaren-nonoctave-24-5
24th root of 5, 10.3362 tones/octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.096 cents 116.096405 2: 232.193 cents 232.192809 3: 348.289 cents 348.289214 4: 464.386 cents 464.385619 5: 580.482 cents 580.482024 6: 696.578 cents 696.578428 7: 812.675 cents 812.674833 8: 928.771 cents 928.771238 9: 1044.868 cents 1044.867643 10: 1160.964 cents 1160.964047 11: 1277.060 cents 1277.060452 12: 1393.157 cents 1393.156857 13: 1509.253 cents 1509.253262 14: 1625.350 cents 1625.349666 15: 1741.446 cents 1741.446071 16: 1857.542 cents 1857.542476 17: 1973.639 cents 1973.638881 18: 2089.735 cents 2089.735285 19: 2205.832 cents 2205.831690 20: 2321.928 cents 2321.928095 21: 2438.024 cents 2438.024500 22: 2554.121 cents 2554.120904 23: 2670.217 cents 2670.217309 24: 5/1 2786.313714 major 17th
SHOW/INTERVAL
0: 116.0964 cents 116.0964 1: 116.0964 cents 116.0964 2: 116.0964 cents 116.0964 3: 116.0964 cents 116.0964 4: 116.0964 cents 116.0964 5: 116.0964 cents 116.0964 6: 116.0964 cents 116.0964 7: 116.0964 cents 116.0964 8: 116.0964 cents 116.0964 9: 116.0964 cents 116.0964 10: 116.0964 cents 116.0964 11: 116.0964 cents 116.0964 12: 116.0964 cents 116.0964 13: 116.0964 cents 116.0964 14: 116.0964 cents 116.0964 15: 116.0964 cents 116.0964 16: 116.0964 cents 116.0964 17: 116.0964 cents 116.0964 18: 116.0964 cents 116.0964 19: 116.0964 cents 116.0964 20: 116.0964 cents 116.0964 21: 116.0964 cents 116.0964 22: 116.0964 cents 116.0964 23: 116.0964 cents 116.0964 24: 116.0964 cents 116.0964
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 24 116.09640 cents 2: 24 232.19281 cents 3: 24 348.28921 cents 4: 24 464.38562 cents 5: 24 580.48202 cents 6: 24 696.57843 cents 7: 24 812.67483 cents 8: 24 928.77124 cents 9: 24 1044.86764 cents 10: 24 1160.96405 cents 11: 24 1277.06045 cents 12: 24 1393.15686 cents 13: 24 1509.25326 cents 14: 24 1625.34967 cents 15: 24 1741.44607 cents 16: 24 1857.54248 cents 17: 24 1973.63888 cents 18: 24 2089.73528 cents 19: 24 2205.83169 cents 20: 24 2321.92810 cents 21: 24 2438.02450 cents 22: 24 2554.12090 cents 23: 24 2670.21731 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 0.0 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 116.1 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 232.2 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 348.3 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 464.4 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 580.5 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 696.6 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 812.7 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 928.8 : 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1044.9: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1161.0: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1277.1: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1393.2: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1509.3: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1625.3: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1741.4: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1857.5: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 1973.6: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 2089.7: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 2205.8: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 2321.9: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 2438.0: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 2554.1: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 2670.2: 116.1 232.2 348.3 464.4 580.5 696.6 812.7 928.8 1044.9 1161.0 1277.1 1393.2 1509.3 1625.3 1741.4 1857.5 1973.6 2089.7 2205.8 2321.9 2438.0 2554.1 2670.2 2786.3 2786.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.0964 .. 116.0964 cents 1/1, 0.0000 cents 116.09640 cents 2: 232.1928 .. 232.1928 cents 1/1, 0.0000 cents 116.09640 cents 3: 348.2892 .. 348.2892 cents 1/1, 0.0000 cents 116.09640 cents 4: 464.3856 .. 464.3856 cents 1/1, 0.0000 cents 116.09640 cents 5: 580.4820 .. 580.4820 cents 1/1, 0.0000 cents 116.09641 cents 6: 696.5784 .. 696.5784 cents 1/1, 0.0000 cents 116.09640 cents 7: 812.6748 .. 812.6748 cents 1/1, 0.0000 cents 116.09640 cents 8: 928.7712 .. 928.7712 cents 1/1, 0.0000 cents 116.09640 cents 9: 1044.8676 .. 1044.8676 cents 1/1, 0.0000 cents 116.09640 cents 10: 1160.9640 .. 1160.9640 cents 1/1, 0.0000 cents 116.09640 cents 11: 1277.0605 .. 1277.0605 cents 1/1, 0.0000 cents 116.09640 cents 12: 1393.1569 .. 1393.1569 cents 1/1, 0.0000 cents 116.09640 cents 13: 1509.2533 .. 1509.2533 cents 1/1, 0.0000 cents 116.09640 cents 14: 1625.3497 .. 1625.3497 cents 1/1, 0.0000 cents 116.09640 cents 15: 1741.4461 .. 1741.4461 cents 1/1, 0.0000 cents 116.09640 cents 16: 1857.5425 .. 1857.5425 cents 1/1, 0.0000 cents 116.09640 cents 17: 1973.6389 .. 1973.6389 cents 1/1, 0.0000 cents 116.09640 cents 18: 2089.7353 .. 2089.7353 cents 1/1, 0.0000 cents 116.09640 cents 19: 2205.8317 .. 2205.8317 cents 1/1, 0.0000 cents 116.09640 cents 20: 2321.9281 .. 2321.9281 cents 1/1, 0.0000 cents 116.09641 cents 21: 2438.0245 .. 2438.0245 cents 1/1, 0.0000 cents 116.09640 cents 22: 2554.1209 .. 2554.1209 cents 1/1, 0.0000 cents 116.09640 cents 23: 2670.2173 .. 2670.2173 cents 1/1, 0.0000 cents 116.09640 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 116.09640 cents, class 1 Average step (divided formal octave): 116.0964 cents Largest one step interval : 116.09640 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 116.09640 cents, amount: 24 Most common interval of one step : 116.09640 cents, amount: 24 Least squares average step : 116.09640 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 116.09640 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.041667 redundancy: 0.958333 Efficiency x scale size : 1.000000 Number of different interval sizes : 23 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 24, average 696.5784 cents Number of recognisable fourths : 0 Scale contains two identical disjunct pentachords Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties -- Prime limit : 5 (not all pitches rational)
FIT/MODE
24: 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: 17.5751 cents 2 .. 10 match: 8 H SD: 12.7127 cents 3 .. 15 match: 12 H SD: 9.8264 cents 4 .. 20 match: 15 SD: 8.9055 cents 5 .. 25 match: 18 SD: 6.5073 cents 6 .. 30 match: 19 SD: 7.3030 cents 7 .. 35 match: 21 SD: 5.5663 cents 8 .. 40 match: 22 SD: 5.4491 cents 9 .. 45 match: 22 SD: 6.2532 cents 10 .. 50 match: 23 SD: 4.2569 cents 11 .. 55 match: 23 SD: 5.6114 cents 12 .. 60 match: 24 SD: 4.0965 cents 13 .. 65 match: 24 SD: 3.2336 cents 17 .. 85 match: 24 SD: 3.1829 cents 18 .. 90 match: 24 SD: 2.7654 cents 20 .. 100 match: 24 SD: 2.6274 cents 22 .. 110 match: 24 SD: 2.2102 cents 23 .. 115 match: 24 SD: 2.0936 cents 26 .. 130 match: 24 SD: 1.9961 cents 27 .. 135 match: 24 SD: 1.7359 cents 28 .. 140 match: 24 SD: 1.6052 cents 30 .. 150 match: 24 SD: 1.4003 cents 40 .. 200 match: 24 SD: 1.1223 cents 41 .. 205 match: 24 SD: 1.1096 cents 42 .. 210 match: 24 SD: 0.9726 cents 55 .. 275 match: 24 SD: 0.7680 cents 58 .. 290 match: 24 SD: 0.7558 cents 63 .. 315 match: 24 SD: 0.7326 cents 68 .. 340 match: 24 SD: 0.6262 cents 72 .. 360 match: 24 SD: 0.6224 cents 75 .. 375 match: 24 SD: 0.5472 cents 85 .. 425 match: 24 SD: 0.4738 cents 90 .. 450 match: 24 SD: 0.4645 cents 103 .. 515 match: 24 SD: 0.4312 cents 111 .. 555 match: 24 SD: 0.4108 cents 113 .. 565 match: 24 SD: 0.3482 cents 117 .. 585 match: 24 SD: 0.3157 cents 140 .. 700 match: 24 SD: 0.3088 cents 153 .. 765 match: 24 SD: 0.2901 cents 158 .. 790 match: 24 SD: 0.2758 cents 174 .. 870 match: 24 SD: 0.2650 cents 175 .. 875 match: 24 SD: 0.2375 cents 188 .. 940 match: 24 SD: 0.2241 cents 215 .. 1075 match: 24 SD: 0.2179 cents 228 .. 1140 match: 24 SD: 0.1766 cents 244 .. 1220 match: 24 SD: 0.1637 cents 273 .. 1365 match: 24 SD: 0.1554 cents 286 .. 1430 match: 24 SD: 0.1431 cents 287 .. 1435 match: 24 SD: 0.1377 cents 314 .. 1570 match: 24 SD: 0.1352 cents 319 .. 1595 match: 24 SD: 0.1282 cents 361 .. 1805 match: 24 SD: 0.1155 cents 377 .. 1885 match: 24 SD: 0.1075 cents 404 .. 2020 match: 24 SD: 0.0785 cents 507 .. 2535 match: 24 SD: 0.0772 cents 517 .. 2585 match: 24 SD: 0.0706 cents