Scala analysis: xen16-mclaren-nonoctave-24-3
24th root of 3, 15.1423 tones/octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 79.248 cents 79.248125 2: 158.496 cents 158.496250 3: 237.744 cents 237.744375 4: 316.993 cents 316.992500 5: 396.241 cents 396.240625 6: 475.489 cents 475.488750 7: 554.737 cents 554.736875 8: 633.985 cents 633.985000 9: 713.233 cents 713.233125 10: 792.481 cents 792.481250 11: 871.729 cents 871.729375 12: 950.977 cents 950.977500 13: 1030.226 cents 1030.225625 14: 1109.474 cents 1109.473751 15: 1188.722 cents 1188.721876 16: 1267.970 cents 1267.970001 17: 1347.218 cents 1347.218126 18: 1426.466 cents 1426.466251 19: 1505.714 cents 1505.714376 20: 1584.963 cents 1584.962501 21: 1664.211 cents 1664.210626 22: 1743.459 cents 1743.458751 23: 1822.707 cents 1822.706876 24: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 79.2481 cents 79.2481 1: 79.2481 cents 79.2481 2: 79.2481 cents 79.2481 3: 79.2481 cents 79.2481 4: 79.2481 cents 79.2481 5: 79.2481 cents 79.2481 6: 79.2481 cents 79.2481 7: 79.2481 cents 79.2481 8: 79.2481 cents 79.2481 9: 79.2481 cents 79.2481 10: 79.2481 cents 79.2481 11: 79.2481 cents 79.2481 12: 79.2481 cents 79.2481 13: 79.2481 cents 79.2481 14: 79.2481 cents 79.2481 15: 79.2481 cents 79.2481 16: 79.2481 cents 79.2481 17: 79.2481 cents 79.2481 18: 79.2481 cents 79.2481 19: 79.2481 cents 79.2481 20: 79.2481 cents 79.2481 21: 79.2481 cents 79.2481 22: 79.2481 cents 79.2481 23: 79.2481 cents 79.2481 24: 79.2481 cents 79.2481
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 24 79.24813 cents 2: 24 158.49625 cents 3: 24 237.74438 cents 4: 24 316.99250 cents 5: 24 396.24062 cents 6: 24 475.48875 cents 7: 24 554.73688 cents 8: 24 633.98500 cents 9: 24 713.23312 cents 10: 24 792.48125 cents 11: 24 871.72937 cents 12: 24 950.97750 cents 13: 24 1030.22563 cents 14: 24 1109.47375 cents 15: 24 1188.72188 cents 16: 24 1267.97000 cents 17: 24 1347.21813 cents 18: 24 1426.46625 cents 19: 24 1505.71438 cents 20: 24 1584.96250 cents 21: 24 1664.21063 cents 22: 24 1743.45875 cents 23: 24 1822.70688 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 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 79.2 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 158.5 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 237.7 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 317.0 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 396.2 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 475.5 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 554.7 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 634.0 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 713.2 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 792.5 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 871.7 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 951.0 : 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1030.2: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1109.5: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1188.7: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1268.0: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1347.2: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1426.5: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1505.7: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1585.0: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1664.2: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1743.5: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1822.7: 79.2 158.5 237.7 317.0 396.2 475.5 554.7 634.0 713.2 792.5 871.7 951.0 1030.2 1109.5 1188.7 1268.0 1347.2 1426.5 1505.7 1585.0 1664.2 1743.5 1822.7 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.2481 .. 79.2481 cents 1/1, 0.0000 cents 79.24813 cents 2: 158.4962 .. 158.4962 cents 1/1, 0.0000 cents 79.24812 cents 3: 237.7444 .. 237.7444 cents 1/1, 0.0000 cents 79.24813 cents 4: 316.9925 .. 316.9925 cents 1/1, 0.0000 cents 79.24813 cents 5: 396.2406 .. 396.2406 cents 1/1, 0.0000 cents 79.24812 cents 6: 475.4887 .. 475.4887 cents 1/1, 0.0000 cents 79.24813 cents 7: 554.7369 .. 554.7369 cents 1/1, 0.0000 cents 79.24813 cents 8: 633.9850 .. 633.9850 cents 1/1, 0.0000 cents 79.24812 cents 9: 713.2331 .. 713.2331 cents 1/1, 0.0000 cents 79.24812 cents 10: 792.4812 .. 792.4812 cents 1/1, 0.0000 cents 79.24813 cents 11: 871.7294 .. 871.7294 cents 1/1, 0.0000 cents 79.24813 cents 12: 950.9775 .. 950.9775 cents 1/1, 0.0000 cents 79.24813 cents 13: 1030.2256 .. 1030.2256 cents 1/1, 0.0000 cents 79.24813 cents 14: 1109.4738 .. 1109.4738 cents 1/1, 0.0000 cents 79.24813 cents 15: 1188.7219 .. 1188.7219 cents 1/1, 0.0000 cents 79.24813 cents 16: 1267.9700 .. 1267.9700 cents 1/1, 0.0000 cents 79.24812 cents 17: 1347.2181 .. 1347.2181 cents 1/1, 0.0000 cents 79.24813 cents 18: 1426.4663 .. 1426.4663 cents 1/1, 0.0000 cents 79.24812 cents 19: 1505.7144 .. 1505.7144 cents 1/1, 0.0000 cents 79.24813 cents 20: 1584.9625 .. 1584.9625 cents 1/1, 0.0000 cents 79.24813 cents 21: 1664.2106 .. 1664.2106 cents 1/1, 0.0000 cents 79.24813 cents 22: 1743.4588 .. 1743.4588 cents 1/1, 0.0000 cents 79.24813 cents 23: 1822.7069 .. 1822.7069 cents 1/1, 0.0000 cents 79.24813 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 79.24812 cents, class 1 Average step (divided formal octave): 79.2481 cents Largest one step interval : 79.24813 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 79.24813 cents, amount: 24 Most common interval of one step : 79.24813 cents, amount: 24 Least squares average step : 79.24813 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 79.24813 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 713.2331 cents Number of recognisable fourths : 0 Scale contains two identical disjunct heptachords Best major 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
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 .. 3 match: 2 H SD: 5.6391 cents 2 .. 6 match: 4 H SD: 4.0017 cents 3 .. 9 match: 6 H SD: 9.7881 cents 4 .. 12 match: 8 H SD: 4.4086 cents 5 .. 15 match: 10 H SD: 5.9579 cents 6 .. 18 match: 12 H SD: 6.0414 cents 7 .. 21 match: 14 H SD: 5.8068 cents 8 .. 24 match: 16 H SD: 4.5642 cents 9 .. 27 match: 17 S SD: 6.1935 cents 10 .. 30 match: 19 SD: 3.7966 cents 11 .. 33 match: 20 SD: 3.9360 cents 12 .. 36 match: 21 SD: 3.7416 cents 13 .. 39 match: 22 SD: 4.9946 cents 14 .. 42 match: 22 SD: 4.2045 cents 15 .. 45 match: 23 SD: 3.7571 cents 16 .. 48 match: 23 SD: 3.2921 cents 17 .. 51 match: 23 SD: 4.4183 cents 18 .. 54 match: 24 SD: 3.3747 cents 19 .. 57 match: 24 SD: 2.9041 cents 20 .. 60 match: 24 SD: 2.5980 cents 21 .. 63 match: 24 SD: 2.4891 cents 23 .. 69 match: 24 SD: 2.4750 cents 26 .. 78 match: 24 SD: 2.3452 cents 28 .. 84 match: 24 SD: 2.2699 cents 29 .. 87 match: 24 SD: 1.9808 cents 34 .. 102 match: 24 SD: 1.7261 cents 38 .. 114 match: 24 SD: 1.6019 cents 39 .. 117 match: 24 SD: 1.4635 cents 40 .. 120 match: 24 SD: 1.4053 cents 41 .. 123 match: 24 SD: 1.3613 cents 45 .. 135 match: 24 SD: 1.3597 cents 47 .. 141 match: 24 SD: 1.3086 cents 50 .. 150 match: 24 SD: 1.1074 cents 55 .. 165 match: 24 SD: 1.0837 cents 59 .. 177 match: 24 SD: 1.0007 cents 60 .. 180 match: 24 SD: 0.9279 cents 61 .. 183 match: 24 SD: 0.8208 cents 70 .. 210 match: 24 SD: 0.8078 cents 74 .. 222 match: 24 SD: 0.7870 cents 75 .. 225 match: 24 SD: 0.7649 cents 79 .. 237 match: 24 SD: 0.7453 cents 81 .. 243 match: 24 SD: 0.6912 cents 82 .. 246 match: 24 SD: 0.6797 cents 85 .. 255 match: 24 SD: 0.6579 cents 86 .. 258 match: 24 SD: 0.5894 cents 90 .. 270 match: 24 SD: 0.5602 cents 101 .. 303 match: 24 SD: 0.5516 cents 104 .. 312 match: 24 SD: 0.4801 cents 124 .. 372 match: 24 SD: 0.3551 cents 145 .. 435 match: 24 SD: 0.3274 cents 165 .. 495 match: 24 SD: 0.3168 cents 175 .. 525 match: 24 SD: 0.3141 cents 186 .. 558 match: 24 SD: 0.2954 cents 190 .. 570 match: 24 SD: 0.2650 cents 209 .. 627 match: 24 SD: 0.2456 cents 210 .. 630 match: 24 SD: 0.2382 cents 231 .. 693 match: 24 SD: 0.2331 cents 238 .. 714 match: 24 SD: 0.2115 cents 253 .. 759 match: 24 SD: 0.1961 cents 272 .. 816 match: 24 SD: 0.1877 cents 284 .. 852 match: 24 SD: 0.1869 cents 294 .. 882 match: 24 SD: 0.1807 cents 300 .. 900 match: 24 SD: 0.1744 cents 304 .. 912 match: 24 SD: 0.1731 cents 314 .. 942 match: 24 SD: 0.1702 cents 333 .. 999 match: 24 SD: 0.1610 cents 339 .. 1017 match: 24 SD: 0.1574 cents 355 .. 1065 match: 24 SD: 0.1538 cents 362 .. 1086 match: 24 SD: 0.1515 cents 365 .. 1095 match: 24 SD: 0.1340 cents 389 .. 1167 match: 24 SD: 0.1242 cents 408 .. 1224 match: 24 SD: 0.1070 cents 448 .. 1344 match: 24 SD: 0.1069 cents 489 .. 1467 match: 24 SD: 0.1069 cents 512 .. 1536 match: 24 SD: 0.1025 cents 522 .. 1566 match: 24 SD: 0.0959 cents 529 .. 1587 match: 24 SD: 0.0919 cents 551 .. 1653 match: 24 SD: 0.0853 cents 572 .. 1716 match: 24 SD: 0.0824 cents 598 .. 1794 match: 24 SD: 0.0781 cents