Scala analysis: xen14-mclaren-nonoctave-30-3
Erv Wilson's 30th 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: 63.398 cents 63.398500 2: 126.797 cents 126.797000 3: 190.195 cents 190.195500 4: 253.594 cents 253.594000 5: 316.993 cents 316.992500 6: 380.391 cents 380.391000 7: 443.789 cents 443.789500 8: 507.188 cents 507.188000 9: 570.587 cents 570.586500 10: 633.985 cents 633.985000 11: 697.384 cents 697.383500 12: 760.782 cents 760.782000 13: 824.181 cents 824.180500 14: 887.579 cents 887.579000 15: 950.977 cents 950.977500 16: 1014.376 cents 1014.376000 17: 1077.774 cents 1077.774500 18: 1141.173 cents 1141.173001 19: 1204.572 cents 1204.571501 20: 1267.970 cents 1267.970001 21: 1331.369 cents 1331.368501 22: 1394.767 cents 1394.767001 23: 1458.166 cents 1458.165501 24: 1521.564 cents 1521.564001 25: 1584.963 cents 1584.962501 26: 1648.361 cents 1648.361001 27: 1711.760 cents 1711.759501 28: 1775.158 cents 1775.158001 29: 1838.557 cents 1838.556501 30: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 63.3985 cents 63.3985 1: 63.3985 cents 63.3985 2: 63.3985 cents 63.3985 3: 63.3985 cents 63.3985 4: 63.3985 cents 63.3985 5: 63.3985 cents 63.3985 6: 63.3985 cents 63.3985 7: 63.3985 cents 63.3985 8: 63.3985 cents 63.3985 9: 63.3985 cents 63.3985 10: 63.3985 cents 63.3985 11: 63.3985 cents 63.3985 12: 63.3985 cents 63.3985 13: 63.3985 cents 63.3985 14: 63.3985 cents 63.3985 15: 63.3985 cents 63.3985 16: 63.3985 cents 63.3985 17: 63.3985 cents 63.3985 18: 63.3985 cents 63.3985 19: 63.3985 cents 63.3985 20: 63.3985 cents 63.3985 21: 63.3985 cents 63.3985 22: 63.3985 cents 63.3985 23: 63.3985 cents 63.3985 24: 63.3985 cents 63.3985 25: 63.3985 cents 63.3985 26: 63.3985 cents 63.3985 27: 63.3985 cents 63.3985 28: 63.3985 cents 63.3985 29: 63.3985 cents 63.3985 30: 63.3985 cents 63.3985
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 30 63.39850 cents 2: 30 126.79700 cents 3: 30 190.19550 cents 4: 30 253.59400 cents 5: 30 316.99250 cents 6: 30 380.39100 cents 7: 30 443.78950 cents 8: 30 507.18800 cents 9: 30 570.58650 cents 10: 30 633.98500 cents 11: 30 697.38350 cents 12: 30 760.78200 cents 13: 30 824.18050 cents 14: 30 887.57900 cents 15: 30 950.97750 cents 16: 30 1014.37600 cents 17: 30 1077.77450 cents 18: 30 1141.17300 cents 19: 30 1204.57150 cents 20: 30 1267.97000 cents 21: 30 1331.36850 cents 22: 30 1394.76700 cents 23: 30 1458.16550 cents 24: 30 1521.56400 cents 25: 30 1584.96250 cents 26: 30 1648.36100 cents 27: 30 1711.75950 cents 28: 30 1775.15800 cents 29: 30 1838.55650 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 25 26 27 28 29 30 0.0 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 63.4 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 126.8 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 190.2 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 253.6 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 317.0 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 380.4 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 443.8 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 507.2 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 570.6 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 634.0 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 697.4 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 760.8 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 824.2 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 887.6 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 951.0 : 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1014.4: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1077.8: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1141.2: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1204.6: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1268.0: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1331.4: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1394.8: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1458.2: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1521.6: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1585.0: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1648.4: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1711.8: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1775.2: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1838.6: 63.4 126.8 190.2 253.6 317.0 380.4 443.8 507.2 570.6 634.0 697.4 760.8 824.2 887.6 951.0 1014.4 1077.8 1141.2 1204.6 1268.0 1331.4 1394.8 1458.2 1521.6 1585.0 1648.4 1711.8 1775.2 1838.6 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.3985 .. 63.3985 cents 1/1, 0.0000 cents 63.39850 cents 2: 126.7970 .. 126.7970 cents 1/1, 0.0000 cents 63.39850 cents 3: 190.1955 .. 190.1955 cents 1/1, 0.0000 cents 63.39850 cents 4: 253.5940 .. 253.5940 cents 1/1, 0.0000 cents 63.39850 cents 5: 316.9925 .. 316.9925 cents 1/1, 0.0000 cents 63.39850 cents 6: 380.3910 .. 380.3910 cents 1/1, 0.0000 cents 63.39850 cents 7: 443.7895 .. 443.7895 cents 1/1, 0.0000 cents 63.39850 cents 8: 507.1880 .. 507.1880 cents 1/1, 0.0000 cents 63.39850 cents 9: 570.5865 .. 570.5865 cents 1/1, 0.0000 cents 63.39850 cents 10: 633.9850 .. 633.9850 cents 1/1, 0.0000 cents 63.39850 cents 11: 697.3835 .. 697.3835 cents 1/1, 0.0000 cents 63.39850 cents 12: 760.7820 .. 760.7820 cents 1/1, 0.0000 cents 63.39850 cents 13: 824.1805 .. 824.1805 cents 1/1, 0.0000 cents 63.39850 cents 14: 887.5790 .. 887.5790 cents 1/1, 0.0000 cents 63.39850 cents 15: 950.9775 .. 950.9775 cents 1/1, 0.0000 cents 63.39850 cents 16: 1014.3760 .. 1014.3760 cents 1/1, 0.0000 cents 63.39850 cents 17: 1077.7745 .. 1077.7745 cents 1/1, 0.0000 cents 63.39850 cents 18: 1141.1730 .. 1141.1730 cents 1/1, 0.0000 cents 63.39850 cents 19: 1204.5715 .. 1204.5715 cents 1/1, 0.0000 cents 63.39850 cents 20: 1267.9700 .. 1267.9700 cents 1/1, 0.0000 cents 63.39850 cents 21: 1331.3685 .. 1331.3685 cents 1/1, 0.0000 cents 63.39850 cents 22: 1394.7670 .. 1394.7670 cents 1/1, 0.0000 cents 63.39850 cents 23: 1458.1655 .. 1458.1655 cents 1/1, 0.0000 cents 63.39850 cents 24: 1521.5640 .. 1521.5640 cents 1/1, 0.0000 cents 63.39850 cents 25: 1584.9625 .. 1584.9625 cents 1/1, 0.0000 cents 63.39850 cents 26: 1648.3610 .. 1648.3610 cents 1/1, 0.0000 cents 63.39850 cents 27: 1711.7595 .. 1711.7595 cents 1/1, 0.0000 cents 63.39850 cents 28: 1775.1580 .. 1775.1580 cents 1/1, 0.0000 cents 63.39850 cents 29: 1838.5565 .. 1838.5565 cents 1/1, 0.0000 cents 63.39850 cents
SHOW DATA
Number of notes : 30 -- Interval properties -- Smallest interval : 63.39850 cents, class 1 Average step (divided formal octave): 63.3985 cents Largest one step interval : 63.39850 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 63.39850 cents, amount: 30 Most common interval of one step : 63.39850 cents, amount: 30 Least squares average step : 63.39850 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 63.39850 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.033333 redundancy: 0.966667 Efficiency x scale size : 1.000000 Number of different interval sizes : 29 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 30, average 697.3835 cents Number of recognisable fourths : 30, average 507.1880 cents Scale contains two identical disjunct "tetrachords" of 9 notes Best fifths 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
30: 1 1 1 1 1 1 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 .. 3 match: 2 H SD: 2.2858 cents 2 .. 6 match: 4 H SD: 1.6512 cents 3 .. 9 match: 6 H SD: 3.2435 cents 4 .. 12 match: 8 H SD: 4.0489 cents 5 .. 15 match: 10 H SD: 3.5982 cents 6 .. 18 match: 12 H SD: 3.9194 cents 7 .. 21 match: 14 H SD: 4.3377 cents 8 .. 24 match: 16 H SD: 3.8883 cents 9 .. 27 match: 18 H SD: 3.6698 cents 10 .. 30 match: 20 H SD: 3.3696 cents 11 .. 33 match: 21 SD: 4.7505 cents 12 .. 36 match: 23 SD: 3.0332 cents 13 .. 39 match: 24 S SD: 3.0058 cents 14 .. 42 match: 25 SD: 3.0658 cents 15 .. 45 match: 26 SD: 2.8572 cents 16 .. 48 match: 27 SD: 2.8027 cents 17 .. 51 match: 27 SD: 3.4757 cents 18 .. 54 match: 28 SD: 2.5251 cents 19 .. 57 match: 28 SD: 3.2537 cents 20 .. 60 match: 29 SD: 2.1542 cents 21 .. 63 match: 29 SD: 2.6724 cents 22 .. 66 match: 29 SD: 3.0015 cents 23 .. 69 match: 30 SD: 2.5388 cents 24 .. 72 match: 30 SD: 1.8908 cents 25 .. 75 match: 30 SD: 1.7610 cents 30 .. 90 match: 30 SD: 1.7516 cents 34 .. 102 match: 30 SD: 1.5217 cents 36 .. 108 match: 30 SD: 1.4381 cents 38 .. 114 match: 30 SD: 1.3696 cents 44 .. 132 match: 30 SD: 1.1034 cents 49 .. 147 match: 30 SD: 0.9635 cents 51 .. 153 match: 30 SD: 0.9464 cents 52 .. 156 match: 30 SD: 0.9106 cents 61 .. 183 match: 30 SD: 0.8504 cents 64 .. 192 match: 30 SD: 0.7752 cents 74 .. 222 match: 30 SD: 0.7138 cents 75 .. 225 match: 30 SD: 0.6949 cents 76 .. 228 match: 30 SD: 0.6418 cents 79 .. 237 match: 30 SD: 0.6217 cents 85 .. 255 match: 30 SD: 0.6179 cents 89 .. 267 match: 30 SD: 0.5398 cents 100 .. 300 match: 30 SD: 0.5318 cents 102 .. 306 match: 30 SD: 0.4912 cents 103 .. 309 match: 30 SD: 0.4296 cents 127 .. 381 match: 30 SD: 0.4125 cents 129 .. 387 match: 30 SD: 0.4091 cents 131 .. 393 match: 30 SD: 0.3735 cents 133 .. 399 match: 30 SD: 0.3525 cents 147 .. 441 match: 30 SD: 0.3448 cents 154 .. 462 match: 30 SD: 0.3058 cents 161 .. 483 match: 30 SD: 0.3015 cents 164 .. 492 match: 30 SD: 0.2962 cents 171 .. 513 match: 30 SD: 0.2910 cents 179 .. 537 match: 30 SD: 0.2623 cents 184 .. 552 match: 30 SD: 0.2621 cents 197 .. 591 match: 30 SD: 0.2526 cents 208 .. 624 match: 30 SD: 0.2054 cents 215 .. 645 match: 30 SD: 0.1932 cents 240 .. 720 match: 30 SD: 0.1765 cents 264 .. 792 match: 30 SD: 0.1688 cents 294 .. 882 match: 30 SD: 0.1591 cents 317 .. 951 match: 30 SD: 0.1448 cents 318 .. 954 match: 30 SD: 0.1416 cents 328 .. 984 match: 30 SD: 0.1398 cents 343 .. 1029 match: 30 SD: 0.1175 cents 373 .. 1119 match: 30 SD: 0.1173 cents 379 .. 1137 match: 30 SD: 0.1055 cents 423 .. 1269 match: 30 SD: 0.1040 cents 438 .. 1314 match: 30 SD: 0.1036 cents 448 .. 1344 match: 30 SD: 0.0906 cents 482 .. 1446 match: 30 SD: 0.0853 cents 500 .. 1500 match: 30 SD: 0.0831 cents 538 .. 1614 match: 30 SD: 0.0735 cents