Scala analysis: xen16-mclaren-nonoctave-29-3
29th root of 3, 18.297 tones/octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65.585 cents 65.584655 2: 131.169 cents 131.169310 3: 196.754 cents 196.753966 4: 262.339 cents 262.338621 5: 327.923 cents 327.923276 6: 393.508 cents 393.507931 7: 459.093 cents 459.092586 8: 524.677 cents 524.677242 9: 590.262 cents 590.261897 10: 655.847 cents 655.846552 11: 721.431 cents 721.431207 12: 787.016 cents 787.015862 13: 852.601 cents 852.600518 14: 918.185 cents 918.185173 15: 983.770 cents 983.769828 16: 1049.354 cents 1049.354483 17: 1114.939 cents 1114.939138 18: 1180.524 cents 1180.523794 19: 1246.108 cents 1246.108449 20: 1311.693 cents 1311.693104 21: 1377.278 cents 1377.277759 22: 1442.862 cents 1442.862414 23: 1508.447 cents 1508.447070 24: 1574.032 cents 1574.031725 25: 1639.616 cents 1639.616380 26: 1705.201 cents 1705.201035 27: 1770.786 cents 1770.785690 28: 1836.370 cents 1836.370346 29: 3/1 1901.955001 perfect 12th
SHOW/INTERVAL
0: 65.5847 cents 65.5847 1: 65.5847 cents 65.5847 2: 65.5847 cents 65.5847 3: 65.5847 cents 65.5847 4: 65.5847 cents 65.5847 5: 65.5847 cents 65.5847 6: 65.5847 cents 65.5847 7: 65.5847 cents 65.5847 8: 65.5847 cents 65.5847 9: 65.5847 cents 65.5847 10: 65.5847 cents 65.5847 11: 65.5847 cents 65.5847 12: 65.5847 cents 65.5847 13: 65.5847 cents 65.5847 14: 65.5847 cents 65.5847 15: 65.5847 cents 65.5847 16: 65.5847 cents 65.5847 17: 65.5847 cents 65.5847 18: 65.5847 cents 65.5847 19: 65.5847 cents 65.5847 20: 65.5847 cents 65.5847 21: 65.5847 cents 65.5847 22: 65.5847 cents 65.5847 23: 65.5847 cents 65.5847 24: 65.5847 cents 65.5847 25: 65.5847 cents 65.5847 26: 65.5847 cents 65.5847 27: 65.5847 cents 65.5847 28: 65.5847 cents 65.5847 29: 65.5847 cents 65.5847
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 29 65.58465 cents 2: 29 131.16931 cents 3: 29 196.75397 cents 4: 29 262.33862 cents 5: 29 327.92328 cents 6: 29 393.50793 cents 7: 29 459.09259 cents 8: 29 524.67724 cents 9: 29 590.26190 cents 10: 29 655.84655 cents 11: 29 721.43121 cents 12: 29 787.01586 cents 13: 29 852.60052 cents 14: 29 918.18517 cents 15: 29 983.76983 cents 16: 29 1049.35448 cents 17: 29 1114.93914 cents 18: 29 1180.52379 cents 19: 29 1246.10845 cents 20: 29 1311.69310 cents 21: 29 1377.27776 cents 22: 29 1442.86241 cents 23: 29 1508.44707 cents 24: 29 1574.03172 cents 25: 29 1639.61638 cents 26: 29 1705.20104 cents 27: 29 1770.78569 cents 28: 29 1836.37035 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 0.0 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 65.6 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 131.2 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 196.8 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 262.3 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 327.9 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 393.5 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 459.1 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 524.7 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 590.3 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 655.8 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 721.4 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 787.0 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 852.6 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 918.2 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 983.8 : 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1049.4: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1114.9: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1180.5: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1246.1: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1311.7: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1377.3: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1442.9: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1508.4: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1574.0: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1639.6: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1705.2: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1770.8: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1836.4: 65.6 131.2 196.8 262.3 327.9 393.5 459.1 524.7 590.3 655.8 721.4 787.0 852.6 918.2 983.8 1049.4 1114.9 1180.5 1246.1 1311.7 1377.3 1442.9 1508.4 1574.0 1639.6 1705.2 1770.8 1836.4 1902.0 1902.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 65.5847 .. 65.5847 cents 1/1, 0.0000 cents 65.58465 cents 2: 131.1693 .. 131.1693 cents 1/1, 0.0000 cents 65.58466 cents 3: 196.7540 .. 196.7540 cents 1/1, 0.0000 cents 65.58466 cents 4: 262.3386 .. 262.3386 cents 1/1, 0.0000 cents 65.58466 cents 5: 327.9233 .. 327.9233 cents 1/1, 0.0000 cents 65.58465 cents 6: 393.5079 .. 393.5079 cents 1/1, 0.0000 cents 65.58465 cents 7: 459.0926 .. 459.0926 cents 1/1, 0.0000 cents 65.58466 cents 8: 524.6772 .. 524.6772 cents 1/1, 0.0000 cents 65.58466 cents 9: 590.2619 .. 590.2619 cents 1/1, 0.0000 cents 65.58465 cents 10: 655.8466 .. 655.8466 cents 1/1, 0.0000 cents 65.58465 cents 11: 721.4312 .. 721.4312 cents 1/1, 0.0000 cents 65.58466 cents 12: 787.0159 .. 787.0159 cents 1/1, 0.0000 cents 65.58465 cents 13: 852.6005 .. 852.6005 cents 1/1, 0.0000 cents 65.58466 cents 14: 918.1852 .. 918.1852 cents 1/1, 0.0000 cents 65.58465 cents 15: 983.7698 .. 983.7698 cents 1/1, 0.0000 cents 65.58465 cents 16: 1049.3545 .. 1049.3545 cents 1/1, 0.0000 cents 65.58466 cents 17: 1114.9391 .. 1114.9391 cents 1/1, 0.0000 cents 65.58465 cents 18: 1180.5238 .. 1180.5238 cents 1/1, 0.0000 cents 65.58466 cents 19: 1246.1084 .. 1246.1084 cents 1/1, 0.0000 cents 65.58465 cents 20: 1311.6931 .. 1311.6931 cents 1/1, 0.0000 cents 65.58465 cents 21: 1377.2778 .. 1377.2778 cents 1/1, 0.0000 cents 65.58466 cents 22: 1442.8624 .. 1442.8624 cents 1/1, 0.0000 cents 65.58465 cents 23: 1508.4471 .. 1508.4471 cents 1/1, 0.0000 cents 65.58466 cents 24: 1574.0317 .. 1574.0317 cents 1/1, 0.0000 cents 65.58465 cents 25: 1639.6164 .. 1639.6164 cents 1/1, 0.0000 cents 65.58465 cents 26: 1705.2010 .. 1705.2010 cents 1/1, 0.0000 cents 65.58466 cents 27: 1770.7857 .. 1770.7857 cents 1/1, 0.0000 cents 65.58465 cents 28: 1836.3703 .. 1836.3703 cents 1/1, 0.0000 cents 65.58466 cents
SHOW DATA
Number of notes : 29 -- Interval properties -- Smallest interval : 65.58465 cents, class 1 Average step (divided formal octave): 65.5847 cents Largest one step interval : 65.58465 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 65.58465 cents, amount: 29 Most common interval of one step : 65.58465 cents, amount: 29 Least squares average step : 65.58466 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 65.58466 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.034483 redundancy: 0.965517 Efficiency x scale size : 1.000000 Number of different interval sizes : 28 = 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 "tetrachords" of 9 notes Best fifths form a closed circle Best major thirds 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
29: 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: 9.7381 cents 2 .. 6 match: 4 H SD: 7.5394 cents 3 .. 9 match: 6 H SD: 8.6999 cents 4 .. 12 match: 8 H SD: 5.9593 cents 5 .. 15 match: 10 H SD: 5.3508 cents 6 .. 18 match: 12 H SD: 5.9136 cents 7 .. 21 match: 14 H SD: 5.2016 cents 8 .. 24 match: 16 H SD: 4.4601 cents 9 .. 27 match: 18 H SD: 4.2356 cents 10 .. 30 match: 20 H SD: 3.6861 cents 11 .. 33 match: 21 SD: 4.5362 cents 12 .. 36 match: 23 SD: 3.6498 cents 13 .. 39 match: 24 S SD: 3.2731 cents 14 .. 42 match: 25 SD: 3.3436 cents 15 .. 45 match: 25 SD: 3.7282 cents 16 .. 48 match: 26 SD: 3.3162 cents 17 .. 51 match: 27 SD: 2.6710 cents 18 .. 54 match: 27 SD: 3.2791 cents 19 .. 57 match: 28 SD: 2.4757 cents 20 .. 60 match: 28 SD: 2.6636 cents 21 .. 63 match: 28 SD: 3.1811 cents 22 .. 66 match: 29 SD: 2.7266 cents 23 .. 69 match: 29 SD: 2.0145 cents 24 .. 72 match: 29 SD: 1.9924 cents 29 .. 87 match: 29 SD: 1.9779 cents 30 .. 90 match: 29 SD: 1.8582 cents 31 .. 93 match: 29 SD: 1.8014 cents 33 .. 99 match: 29 SD: 1.6429 cents 35 .. 105 match: 29 SD: 1.5978 cents 37 .. 111 match: 29 SD: 1.4985 cents 39 .. 117 match: 29 SD: 1.4350 cents 42 .. 126 match: 29 SD: 1.2095 cents 43 .. 129 match: 29 SD: 1.1154 cents 47 .. 141 match: 29 SD: 1.0915 cents 50 .. 150 match: 29 SD: 0.8877 cents 59 .. 177 match: 29 SD: 0.8754 cents 66 .. 198 match: 29 SD: 0.8066 cents 72 .. 216 match: 29 SD: 0.7831 cents 73 .. 219 match: 29 SD: 0.6724 cents 74 .. 222 match: 29 SD: 0.6488 cents 76 .. 228 match: 29 SD: 0.6390 cents 85 .. 255 match: 29 SD: 0.6091 cents 91 .. 273 match: 29 SD: 0.5555 cents 99 .. 297 match: 29 SD: 0.4947 cents 102 .. 306 match: 29 SD: 0.4519 cents 116 .. 348 match: 29 SD: 0.4419 cents 124 .. 372 match: 29 SD: 0.4030 cents 126 .. 378 match: 29 SD: 0.3781 cents 133 .. 399 match: 29 SD: 0.3710 cents 149 .. 447 match: 29 SD: 0.3230 cents 165 .. 495 match: 29 SD: 0.3134 cents 167 .. 501 match: 29 SD: 0.3099 cents 176 .. 528 match: 29 SD: 0.2996 cents 178 .. 534 match: 29 SD: 0.2912 cents 182 .. 546 match: 29 SD: 0.2740 cents 187 .. 561 match: 29 SD: 0.2733 cents 189 .. 567 match: 29 SD: 0.2721 cents 200 .. 600 match: 29 SD: 0.2508 cents 207 .. 621 match: 29 SD: 0.2244 cents 226 .. 678 match: 29 SD: 0.1868 cents 259 .. 777 match: 29 SD: 0.1832 cents 263 .. 789 match: 29 SD: 0.1634 cents 282 .. 846 match: 29 SD: 0.1606 cents 283 .. 849 match: 29 SD: 0.1593 cents 306 .. 918 match: 29 SD: 0.1303 cents 356 .. 1068 match: 29 SD: 0.1237 cents 365 .. 1095 match: 29 SD: 0.1176 cents 408 .. 1224 match: 29 SD: 0.1079 cents 490 .. 1470 match: 29 SD: 0.1015 cents 495 .. 1485 match: 29 SD: 0.0967 cents 497 .. 1491 match: 29 SD: 0.0858 cents 571 .. 1713 match: 29 SD: 0.0845 cents 575 .. 1725 match: 29 SD: 0.0841 cents 593 .. 1779 match: 29 SD: 0.0822 cents 599 .. 1797 match: 29 SD: 0.0691 cents