Scala analysis: xen16-mclaren-nonoctave-16-5
16th root of 5, 6.8908 tones/octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 174.145 cents 174.144607 2: 348.289 cents 348.289214 3: 522.434 cents 522.433821 4: 696.578 cents 696.578428 5: 870.723 cents 870.723036 6: 1044.868 cents 1044.867643 7: 1219.012 cents 1219.012250 8: 1393.157 cents 1393.156857 9: 1567.301 cents 1567.301464 10: 1741.446 cents 1741.446071 11: 1915.591 cents 1915.590678 12: 2089.735 cents 2089.735285 13: 2263.880 cents 2263.879893 14: 2438.024 cents 2438.024500 15: 2612.169 cents 2612.169107 16: 5/1 2786.313714 major 17th
SHOW/INTERVAL
0: 174.1446 cents 174.1446 1: 174.1446 cents 174.1446 2: 174.1446 cents 174.1446 3: 174.1446 cents 174.1446 4: 174.1446 cents 174.1446 5: 174.1446 cents 174.1446 6: 174.1446 cents 174.1446 7: 174.1446 cents 174.1446 8: 174.1446 cents 174.1446 9: 174.1446 cents 174.1446 10: 174.1446 cents 174.1446 11: 174.1446 cents 174.1446 12: 174.1446 cents 174.1446 13: 174.1446 cents 174.1446 14: 174.1446 cents 174.1446 15: 174.1446 cents 174.1446 16: 174.1446 cents 174.1446
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 16 174.14461 cents 2: 16 348.28921 cents 3: 16 522.43382 cents 4: 16 696.57843 cents 5: 16 870.72304 cents 6: 16 1044.86764 cents 7: 16 1219.01225 cents 8: 16 1393.15686 cents 9: 16 1567.30146 cents 10: 16 1741.44607 cents 11: 16 1915.59068 cents 12: 16 2089.73528 cents 13: 16 2263.87989 cents 14: 16 2438.02450 cents 15: 16 2612.16911 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 : 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 174.1 : 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 348.3 : 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 522.4 : 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 696.6 : 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 870.7 : 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 1044.9: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 1219.0: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 1393.2: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 1567.3: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 1741.4: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 1915.6: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 2089.7: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 2263.9: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 2438.0: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 2612.2: 174.1 348.3 522.4 696.6 870.7 1044.9 1219.0 1393.2 1567.3 1741.4 1915.6 2089.7 2263.9 2438.0 2612.2 2786.3 2786.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 174.1446 .. 174.1446 cents 1/1, 0.0000 cents 174.14461 cents 2: 348.2892 .. 348.2892 cents 1/1, 0.0000 cents 174.14461 cents 3: 522.4338 .. 522.4338 cents 1/1, 0.0000 cents 174.14461 cents 4: 696.5784 .. 696.5784 cents 1/1, 0.0000 cents 174.14461 cents 5: 870.7230 .. 870.7230 cents 1/1, 0.0000 cents 174.14461 cents 6: 1044.8676 .. 1044.8676 cents 1/1, 0.0000 cents 174.14461 cents 7: 1219.0122 .. 1219.0122 cents 1/1, 0.0000 cents 174.14461 cents 8: 1393.1569 .. 1393.1569 cents 1/1, 0.0000 cents 174.14461 cents 9: 1567.3015 .. 1567.3015 cents 1/1, 0.0000 cents 174.14461 cents 10: 1741.4461 .. 1741.4461 cents 1/1, 0.0000 cents 174.14461 cents 11: 1915.5907 .. 1915.5907 cents 1/1, 0.0000 cents 174.14461 cents 12: 2089.7353 .. 2089.7353 cents 1/1, 0.0000 cents 174.14461 cents 13: 2263.8799 .. 2263.8799 cents 1/1, 0.0000 cents 174.14461 cents 14: 2438.0245 .. 2438.0245 cents 1/1, 0.0000 cents 174.14461 cents 15: 2612.1691 .. 2612.1691 cents 1/1, 0.0000 cents 174.14461 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 174.14461 cents, class 1 Average step (divided formal octave): 174.1446 cents Largest one step interval : 174.14461 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 174.14461 cents, amount: 16 Most common interval of one step : 174.14461 cents, amount: 16 Least squares average step : 174.14461 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 174.14461 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 696.5784 cents Number of recognisable fourths : 0 Scale contains two identical disjunct tetrachords Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties -- Prime limit : 5 (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 .. 5 match: 4 H SD: 11.1615 cents 2 .. 10 match: 8 H SD: 11.6640 cents 3 .. 15 match: 11 S SD: 10.4933 cents 4 .. 20 match: 13 SD: 8.7399 cents 5 .. 25 match: 14 SD: 10.0200 cents 6 .. 30 match: 15 SD: 8.0566 cents 7 .. 35 match: 15 SD: 10.8810 cents 8 .. 40 match: 16 SD: 5.6831 cents 12 .. 60 match: 16 SD: 4.4089 cents 17 .. 85 match: 16 SD: 3.2030 cents 18 .. 90 match: 16 SD: 2.9980 cents 22 .. 110 match: 16 SD: 2.9525 cents 23 .. 115 match: 16 SD: 2.8528 cents 26 .. 130 match: 16 SD: 2.1064 cents 28 .. 140 match: 16 SD: 1.9929 cents 31 .. 155 match: 16 SD: 1.8813 cents 34 .. 170 match: 16 SD: 1.8179 cents 35 .. 175 match: 16 SD: 1.7098 cents 36 .. 180 match: 16 SD: 1.6277 cents 37 .. 185 match: 16 SD: 1.3985 cents 40 .. 200 match: 16 SD: 1.1007 cents 46 .. 230 match: 16 SD: 0.8527 cents 75 .. 375 match: 16 SD: 0.7577 cents 76 .. 380 match: 16 SD: 0.5959 cents 85 .. 425 match: 16 SD: 0.5660 cents 93 .. 465 match: 16 SD: 0.4627 cents 113 .. 565 match: 16 SD: 0.4479 cents 121 .. 605 match: 16 SD: 0.4386 cents 122 .. 610 match: 16 SD: 0.4190 cents 125 .. 625 match: 16 SD: 0.4079 cents 131 .. 655 match: 16 SD: 0.3755 cents 133 .. 665 match: 16 SD: 0.3608 cents 139 .. 695 match: 16 SD: 0.3049 cents 162 .. 810 match: 16 SD: 0.2922 cents 170 .. 850 match: 16 SD: 0.2250 cents 216 .. 1080 match: 16 SD: 0.1590 cents 301 .. 1505 match: 16 SD: 0.1484 cents 309 .. 1545 match: 16 SD: 0.1386 cents 349 .. 1745 match: 16 SD: 0.1185 cents 369 .. 1845 match: 16 SD: 0.1171 cents 426 .. 2130 match: 16 SD: 0.1147 cents 444 .. 2220 match: 16 SD: 0.1071 cents 454 .. 2270 match: 16 SD: 0.0897 cents 462 .. 2310 match: 16 SD: 0.0829 cents 539 .. 2695 match: 16 SD: 0.0737 cents 588 .. 2940 match: 16 SD: 0.0723 cents