Scala analysis: xen16-mclaren-nonoctave-20-3
20th root of 3, 12.6186 tones/octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 95.098 cents 95.097750 2: 190.195 cents 190.195500 3: 285.293 cents 285.293250 4: 380.391 cents 380.391000 5: 475.489 cents 475.488750 6: 570.587 cents 570.586500 7: 665.684 cents 665.684250 8: 760.782 cents 760.782000 9: 855.880 cents 855.879750 10: 950.977 cents 950.977500 11: 1046.075 cents 1046.075250 12: 1141.173 cents 1141.173001 13: 1236.271 cents 1236.270751 14: 1331.369 cents 1331.368501 15: 1426.466 cents 1426.466251 16: 1521.564 cents 1521.564001 17: 1616.662 cents 1616.661751 18: 1711.760 cents 1711.759501 19: 1806.857 cents 1806.857251 20: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 95.0977 cents 95.0977 1: 95.0977 cents 95.0977 2: 95.0978 cents 95.0978 3: 95.0978 cents 95.0978 4: 95.0977 cents 95.0977 5: 95.0978 cents 95.0978 6: 95.0977 cents 95.0977 7: 95.0978 cents 95.0978 8: 95.0977 cents 95.0977 9: 95.0977 cents 95.0977 10: 95.0977 cents 95.0977 11: 95.0978 cents 95.0978 12: 95.0978 cents 95.0978 13: 95.0977 cents 95.0977 14: 95.0978 cents 95.0978 15: 95.0977 cents 95.0977 16: 95.0977 cents 95.0977 17: 95.0978 cents 95.0978 18: 95.0978 cents 95.0978 19: 95.0977 cents 95.0977 20: 95.0977 cents 95.0977
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 20 95.09775 cents 2: 20 190.19550 cents 3: 20 285.29325 cents 4: 20 380.39100 cents 5: 20 475.48875 cents 6: 20 570.58650 cents 7: 20 665.68425 cents 8: 20 760.78200 cents 9: 20 855.87975 cents 10: 20 950.97750 cents 11: 20 1046.07525 cents 12: 20 1141.17300 cents 13: 20 1236.27075 cents 14: 20 1331.36850 cents 15: 20 1426.46625 cents 16: 20 1521.56400 cents 17: 20 1616.66175 cents 18: 20 1711.75950 cents 19: 20 1806.85725 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 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 95.1 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 190.2 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 285.3 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 380.4 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 475.5 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 570.6 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 665.7 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 760.8 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 855.9 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 951.0 : 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1046.1: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1141.2: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1236.3: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1331.4: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1426.5: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1521.6: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1616.7: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1711.8: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1806.9: 95.1 190.2 285.3 380.4 475.5 570.6 665.7 760.8 855.9 951.0 1046.1 1141.2 1236.3 1331.4 1426.5 1521.6 1616.7 1711.8 1806.9 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 95.0977 .. 95.0977 cents 1/1, 0.0000 cents 95.09775 cents 2: 190.1955 .. 190.1955 cents 1/1, 0.0000 cents 95.09775 cents 3: 285.2933 .. 285.2933 cents 1/1, 0.0000 cents 95.09775 cents 4: 380.3910 .. 380.3910 cents 1/1, 0.0000 cents 95.09775 cents 5: 475.4887 .. 475.4887 cents 1/1, 0.0000 cents 95.09775 cents 6: 570.5865 .. 570.5865 cents 1/1, 0.0000 cents 95.09775 cents 7: 665.6843 .. 665.6843 cents 1/1, 0.0000 cents 95.09775 cents 8: 760.7820 .. 760.7820 cents 1/1, 0.0000 cents 95.09775 cents 9: 855.8797 .. 855.8797 cents 1/1, 0.0000 cents 95.09775 cents 10: 950.9775 .. 950.9775 cents 1/1, 0.0000 cents 95.09775 cents 11: 1046.0752 .. 1046.0752 cents 1/1, 0.0000 cents 95.09775 cents 12: 1141.1730 .. 1141.1730 cents 1/1, 0.0000 cents 95.09775 cents 13: 1236.2708 .. 1236.2708 cents 1/1, 0.0000 cents 95.09775 cents 14: 1331.3685 .. 1331.3685 cents 1/1, 0.0000 cents 95.09775 cents 15: 1426.4663 .. 1426.4663 cents 1/1, 0.0000 cents 95.09775 cents 16: 1521.5640 .. 1521.5640 cents 1/1, 0.0000 cents 95.09775 cents 17: 1616.6618 .. 1616.6618 cents 1/1, 0.0000 cents 95.09775 cents 18: 1711.7595 .. 1711.7595 cents 1/1, 0.0000 cents 95.09775 cents 19: 1806.8573 .. 1806.8573 cents 1/1, 0.0000 cents 95.09775 cents
SHOW DATA
Number of notes : 20 -- Interval properties -- Smallest interval : 95.09775 cents, class 1 Average step (divided formal octave): 95.0978 cents Largest one step interval : 95.09775 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 95.09775 cents, amount: 20 Most common interval of one step : 95.09775 cents, amount: 20 Least squares average step : 95.09775 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 95.09775 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 : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct hexachords Best fifths 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
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 .. 3 match: 2 H SD: 18.1354 cents 2 .. 6 match: 4 H SD: 14.9000 cents 3 .. 9 match: 6 H SD: 11.1256 cents 4 .. 12 match: 8 H SD: 9.6659 cents 5 .. 15 match: 10 H SD: 9.0219 cents 6 .. 18 match: 12 H SD: 7.0265 cents 7 .. 21 match: 14 H SD: 6.9213 cents 8 .. 24 match: 15 S SD: 6.7625 cents 9 .. 27 match: 16 SD: 7.1674 cents 10 .. 30 match: 17 SD: 6.5233 cents 11 .. 33 match: 18 SD: 5.1596 cents 12 .. 36 match: 19 SD: 5.3653 cents 13 .. 39 match: 19 SD: 4.5240 cents 14 .. 42 match: 19 SD: 5.7957 cents 15 .. 45 match: 20 SD: 4.1514 cents 16 .. 48 match: 20 SD: 3.6713 cents 17 .. 51 match: 20 SD: 3.2248 cents 22 .. 66 match: 20 SD: 3.1223 cents 23 .. 69 match: 20 SD: 2.9204 cents 25 .. 75 match: 20 SD: 2.5619 cents 28 .. 84 match: 20 SD: 2.3203 cents 29 .. 87 match: 20 SD: 2.2836 cents 32 .. 96 match: 20 SD: 2.1108 cents 33 .. 99 match: 20 SD: 1.8127 cents 34 .. 102 match: 20 SD: 1.7396 cents 36 .. 108 match: 20 SD: 1.7195 cents 41 .. 123 match: 20 SD: 1.4976 cents 44 .. 132 match: 20 SD: 1.3882 cents 49 .. 147 match: 20 SD: 1.2206 cents 51 .. 153 match: 20 SD: 1.0772 cents 61 .. 183 match: 20 SD: 1.0447 cents 66 .. 198 match: 20 SD: 0.9849 cents 67 .. 201 match: 20 SD: 0.9794 cents 69 .. 207 match: 20 SD: 0.8146 cents 72 .. 216 match: 20 SD: 0.8055 cents 77 .. 231 match: 20 SD: 0.8018 cents 85 .. 255 match: 20 SD: 0.6821 cents 89 .. 267 match: 20 SD: 0.5181 cents 105 .. 315 match: 20 SD: 0.4382 cents 123 .. 369 match: 20 SD: 0.4069 cents 139 .. 417 match: 20 SD: 0.3423 cents 164 .. 492 match: 20 SD: 0.3313 cents 179 .. 537 match: 20 SD: 0.3137 cents 183 .. 549 match: 20 SD: 0.3059 cents 190 .. 570 match: 20 SD: 0.2937 cents 208 .. 624 match: 20 SD: 0.2734 cents 212 .. 636 match: 20 SD: 0.2688 cents 224 .. 672 match: 20 SD: 0.2687 cents 228 .. 684 match: 20 SD: 0.2253 cents 241 .. 723 match: 20 SD: 0.2173 cents 266 .. 798 match: 20 SD: 0.2077 cents 269 .. 807 match: 20 SD: 0.1856 cents 284 .. 852 match: 20 SD: 0.1753 cents 317 .. 951 match: 20 SD: 0.1672 cents 335 .. 1005 match: 20 SD: 0.1421 cents 386 .. 1158 match: 20 SD: 0.1339 cents 407 .. 1221 match: 20 SD: 0.1268 cents 424 .. 1272 match: 20 SD: 0.1253 cents 430 .. 1290 match: 20 SD: 0.1232 cents 464 .. 1392 match: 20 SD: 0.1229 cents 475 .. 1425 match: 20 SD: 0.1152 cents 480 .. 1440 match: 20 SD: 0.1063 cents 497 .. 1491 match: 20 SD: 0.0935 cents 569 .. 1707 match: 20 SD: 0.0767 cents 586 .. 1758 match: 20 SD: 0.0766 cents