Scala analysis: xen16-mclaren-nonoctave-20-5
20th root of 5, 8.6135 tones/octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 139.316 cents 139.315686 2: 278.631 cents 278.631371 3: 417.947 cents 417.947057 4: 557.263 cents 557.262743 5: 696.578 cents 696.578428 6: 835.894 cents 835.894114 7: 975.210 cents 975.209800 8: 1114.525 cents 1114.525486 9: 1253.841 cents 1253.841171 10: 1393.157 cents 1393.156857 11: 1532.473 cents 1532.472543 12: 1671.788 cents 1671.788228 13: 1811.104 cents 1811.103914 14: 1950.420 cents 1950.419600 15: 2089.735 cents 2089.735285 16: 2229.051 cents 2229.050971 17: 2368.367 cents 2368.366657 18: 2507.682 cents 2507.682342 19: 2646.998 cents 2646.998028 20: 5/1 2786.313714 major 17th
SHOW/INTERVAL
0: 139.3157 cents 139.3157 1: 139.3157 cents 139.3157 2: 139.3157 cents 139.3157 3: 139.3157 cents 139.3157 4: 139.3157 cents 139.3157 5: 139.3157 cents 139.3157 6: 139.3157 cents 139.3157 7: 139.3157 cents 139.3157 8: 139.3157 cents 139.3157 9: 139.3157 cents 139.3157 10: 139.3157 cents 139.3157 11: 139.3157 cents 139.3157 12: 139.3157 cents 139.3157 13: 139.3157 cents 139.3157 14: 139.3157 cents 139.3157 15: 139.3157 cents 139.3157 16: 139.3157 cents 139.3157 17: 139.3157 cents 139.3157 18: 139.3157 cents 139.3157 19: 139.3157 cents 139.3157 20: 139.3157 cents 139.3157
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 20 139.31569 cents 2: 20 278.63137 cents 3: 20 417.94706 cents 4: 20 557.26274 cents 5: 20 696.57843 cents 6: 20 835.89411 cents 7: 20 975.20980 cents 8: 20 1114.52549 cents 9: 20 1253.84117 cents 10: 20 1393.15686 cents 11: 20 1532.47254 cents 12: 20 1671.78823 cents 13: 20 1811.10391 cents 14: 20 1950.41960 cents 15: 20 2089.73528 cents 16: 20 2229.05097 cents 17: 20 2368.36666 cents 18: 20 2507.68234 cents 19: 20 2646.99803 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 0.0 : 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 139.3 : 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 278.6 : 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 417.9 : 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 557.3 : 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 696.6 : 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 835.9 : 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 975.2 : 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 1114.5: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 1253.8: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 1393.2: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 1532.5: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 1671.8: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 1811.1: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 1950.4: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 2089.7: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 2229.1: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 2368.4: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 2507.7: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 2647.0: 139.3 278.6 417.9 557.3 696.6 835.9 975.2 1114.5 1253.8 1393.2 1532.5 1671.8 1811.1 1950.4 2089.7 2229.1 2368.4 2507.7 2647.0 2786.3 2786.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 139.3157 .. 139.3157 cents 1/1, 0.0000 cents 139.31569 cents 2: 278.6314 .. 278.6314 cents 1/1, 0.0000 cents 139.31568 cents 3: 417.9471 .. 417.9471 cents 1/1, 0.0000 cents 139.31569 cents 4: 557.2627 .. 557.2627 cents 1/1, 0.0000 cents 139.31569 cents 5: 696.5784 .. 696.5784 cents 1/1, 0.0000 cents 139.31568 cents 6: 835.8941 .. 835.8941 cents 1/1, 0.0000 cents 139.31569 cents 7: 975.2098 .. 975.2098 cents 1/1, 0.0000 cents 139.31569 cents 8: 1114.5255 .. 1114.5255 cents 1/1, 0.0000 cents 139.31569 cents 9: 1253.8412 .. 1253.8412 cents 1/1, 0.0000 cents 139.31568 cents 10: 1393.1569 .. 1393.1569 cents 1/1, 0.0000 cents 139.31569 cents 11: 1532.4725 .. 1532.4725 cents 1/1, 0.0000 cents 139.31569 cents 12: 1671.7882 .. 1671.7882 cents 1/1, 0.0000 cents 139.31568 cents 13: 1811.1039 .. 1811.1039 cents 1/1, 0.0000 cents 139.31569 cents 14: 1950.4196 .. 1950.4196 cents 1/1, 0.0000 cents 139.31569 cents 15: 2089.7353 .. 2089.7353 cents 1/1, 0.0000 cents 139.31568 cents 16: 2229.0510 .. 2229.0510 cents 1/1, 0.0000 cents 139.31569 cents 17: 2368.3667 .. 2368.3667 cents 1/1, 0.0000 cents 139.31569 cents 18: 2507.6823 .. 2507.6823 cents 1/1, 0.0000 cents 139.31568 cents 19: 2646.9980 .. 2646.9980 cents 1/1, 0.0000 cents 139.31569 cents
SHOW DATA
Number of notes : 20 -- Interval properties -- Smallest interval : 139.31568 cents, class 1 Average step (divided formal octave): 139.3157 cents Largest one step interval : 139.31569 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 139.31569 cents, amount: 20 Most common interval of one step : 139.31569 cents, amount: 20 Least squares average step : 139.31569 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 139.31569 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.050000 redundancy: 0.950000 Efficiency x scale size : 1.000000 Number of different interval sizes : 19 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 20, average 696.5784 cents Number of recognisable fourths : 0 Scale contains two identical disjunct pentachords Best major 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
20: 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: 19.7616 cents 2 .. 10 match: 8 H SD: 15.1347 cents 3 .. 15 match: 12 H SD: 11.4527 cents 4 .. 20 match: 14 SD: 10.5220 cents 5 .. 25 match: 16 SD: 7.4684 cents 6 .. 30 match: 17 SD: 9.2317 cents 7 .. 35 match: 18 SD: 8.3015 cents 8 .. 40 match: 19 SD: 5.6587 cents 9 .. 45 match: 19 SD: 7.7090 cents 10 .. 50 match: 20 SD: 5.1605 cents 11 .. 55 match: 20 SD: 4.0573 cents 16 .. 80 match: 20 SD: 3.2919 cents 18 .. 90 match: 20 SD: 3.1117 cents 21 .. 105 match: 20 SD: 2.3339 cents 22 .. 110 match: 20 SD: 2.2888 cents 24 .. 120 match: 20 SD: 2.0031 cents 29 .. 145 match: 20 SD: 1.7180 cents 32 .. 160 match: 20 SD: 1.6967 cents 34 .. 170 match: 20 SD: 1.1973 cents 45 .. 225 match: 20 SD: 1.0043 cents 47 .. 235 match: 20 SD: 1.0031 cents 50 .. 250 match: 20 SD: 0.9125 cents 58 .. 290 match: 20 SD: 0.7326 cents 63 .. 315 match: 20 SD: 0.7229 cents 69 .. 345 match: 20 SD: 0.6332 cents 73 .. 365 match: 20 SD: 0.6056 cents 81 .. 405 match: 20 SD: 0.5271 cents 85 .. 425 match: 20 SD: 0.4799 cents 95 .. 475 match: 20 SD: 0.4773 cents 111 .. 555 match: 20 SD: 0.4720 cents 119 .. 595 match: 20 SD: 0.4713 cents 121 .. 605 match: 20 SD: 0.3891 cents 131 .. 655 match: 20 SD: 0.3359 cents 132 .. 660 match: 20 SD: 0.2989 cents 143 .. 715 match: 20 SD: 0.2740 cents 155 .. 775 match: 20 SD: 0.2711 cents 176 .. 880 match: 20 SD: 0.2639 cents 177 .. 885 match: 20 SD: 0.2396 cents 190 .. 950 match: 20 SD: 0.2000 cents 224 .. 1120 match: 20 SD: 0.1977 cents 242 .. 1210 match: 20 SD: 0.1967 cents 250 .. 1250 match: 20 SD: 0.1650 cents 271 .. 1355 match: 20 SD: 0.1642 cents 274 .. 1370 match: 20 SD: 0.1499 cents 300 .. 1500 match: 20 SD: 0.1464 cents 311 .. 1555 match: 20 SD: 0.1373 cents 319 .. 1595 match: 20 SD: 0.1334 cents 321 .. 1605 match: 20 SD: 0.1214 cents 345 .. 1725 match: 20 SD: 0.1150 cents 385 .. 1925 match: 20 SD: 0.1103 cents 395 .. 1975 match: 20 SD: 0.1053 cents 406 .. 2030 match: 20 SD: 0.0883 cents 487 .. 2435 match: 20 SD: 0.0835 cents 527 .. 2635 match: 20 SD: 0.0686 cents