Scala analysis: xen16-mclaren-nonoctave-24-7
24th root of 7, 8.549 tones/octave
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 140.368 cents 140.367746 2: 280.735 cents 280.735492 3: 421.103 cents 421.103238 4: 561.471 cents 561.470984 5: 701.839 cents 701.838731 6: 842.206 cents 842.206477 7: 982.574 cents 982.574223 8: 1122.942 cents 1122.941969 9: 1263.310 cents 1263.309715 10: 1403.677 cents 1403.677461 11: 1544.045 cents 1544.045207 12: 1684.413 cents 1684.412953 13: 1824.781 cents 1824.780699 14: 1965.148 cents 1965.148445 15: 2105.516 cents 2105.516192 16: 2245.884 cents 2245.883938 17: 2386.252 cents 2386.251684 18: 2526.619 cents 2526.619430 19: 2666.987 cents 2666.987176 20: 2807.355 cents 2807.354922 21: 2947.723 cents 2947.722668 22: 3088.090 cents 3088.090414 23: 3228.458 cents 3228.458160 24: 7/1 3368.825906 harmonic 21st
SHOW/INTERVAL
0: 140.3677 cents 140.3677 1: 140.3677 cents 140.3677 2: 140.3677 cents 140.3677 3: 140.3677 cents 140.3677 4: 140.3677 cents 140.3677 5: 140.3677 cents 140.3677 6: 140.3677 cents 140.3677 7: 140.3677 cents 140.3677 8: 140.3677 cents 140.3677 9: 140.3677 cents 140.3677 10: 140.3677 cents 140.3677 11: 140.3677 cents 140.3677 12: 140.3677 cents 140.3677 13: 140.3677 cents 140.3677 14: 140.3677 cents 140.3677 15: 140.3677 cents 140.3677 16: 140.3677 cents 140.3677 17: 140.3677 cents 140.3677 18: 140.3677 cents 140.3677 19: 140.3677 cents 140.3677 20: 140.3677 cents 140.3677 21: 140.3677 cents 140.3677 22: 140.3677 cents 140.3677 23: 140.3677 cents 140.3677 24: 140.3677 cents 140.3677
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 24 140.36775 cents 2: 24 280.73549 cents 3: 24 421.10324 cents 4: 24 561.47098 cents 5: 24 701.83873 cents 6: 24 842.20648 cents 7: 24 982.57422 cents 8: 24 1122.94197 cents 9: 24 1263.30971 cents 10: 24 1403.67746 cents 11: 24 1544.04521 cents 12: 24 1684.41295 cents 13: 24 1824.78070 cents 14: 24 1965.14845 cents 15: 24 2105.51619 cents 16: 24 2245.88394 cents 17: 24 2386.25168 cents 18: 24 2526.61943 cents 19: 24 2666.98718 cents 20: 24 2807.35492 cents 21: 24 2947.72267 cents 22: 24 3088.09041 cents 23: 24 3228.45816 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 : 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 140.4 : 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 280.7 : 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 421.1 : 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 561.5 : 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 701.8 : 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 842.2 : 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 982.6 : 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 1122.9: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 1263.3: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 1403.7: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 1544.0: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 1684.4: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 1824.8: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 1965.1: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 2105.5: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 2245.9: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 2386.3: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 2526.6: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 2667.0: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 2807.4: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 2947.7: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 3088.1: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 3228.5: 140.4 280.7 421.1 561.5 701.8 842.2 982.6 1122.9 1263.3 1403.7 1544.0 1684.4 1824.8 1965.1 2105.5 2245.9 2386.3 2526.6 2667.0 2807.4 2947.7 3088.1 3228.5 3368.8 3368.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.3677 .. 140.3677 cents 1/1, 0.0000 cents 140.36775 cents 2: 280.7355 .. 280.7355 cents 1/1, 0.0000 cents 140.36775 cents 3: 421.1032 .. 421.1032 cents 1/1, 0.0000 cents 140.36775 cents 4: 561.4710 .. 561.4710 cents 1/1, 0.0000 cents 140.36775 cents 5: 701.8387 .. 701.8387 cents 1/1, 0.0000 cents 140.36775 cents 6: 842.2065 .. 842.2065 cents 1/1, 0.0000 cents 140.36775 cents 7: 982.5742 .. 982.5742 cents 1/1, 0.0000 cents 140.36775 cents 8: 1122.9420 .. 1122.9420 cents 1/1, 0.0000 cents 140.36775 cents 9: 1263.3097 .. 1263.3097 cents 1/1, 0.0000 cents 140.36775 cents 10: 1403.6775 .. 1403.6775 cents 1/1, 0.0000 cents 140.36775 cents 11: 1544.0452 .. 1544.0452 cents 1/1, 0.0000 cents 140.36775 cents 12: 1684.4130 .. 1684.4130 cents 1/1, 0.0000 cents 140.36775 cents 13: 1824.7807 .. 1824.7807 cents 1/1, 0.0000 cents 140.36775 cents 14: 1965.1484 .. 1965.1484 cents 1/1, 0.0000 cents 140.36775 cents 15: 2105.5162 .. 2105.5162 cents 1/1, 0.0000 cents 140.36775 cents 16: 2245.8839 .. 2245.8839 cents 1/1, 0.0000 cents 140.36775 cents 17: 2386.2517 .. 2386.2517 cents 1/1, 0.0000 cents 140.36775 cents 18: 2526.6194 .. 2526.6194 cents 1/1, 0.0000 cents 140.36775 cents 19: 2666.9872 .. 2666.9872 cents 1/1, 0.0000 cents 140.36775 cents 20: 2807.3549 .. 2807.3549 cents 1/1, 0.0000 cents 140.36775 cents 21: 2947.7227 .. 2947.7227 cents 1/1, 0.0000 cents 140.36775 cents 22: 3088.0904 .. 3088.0904 cents 1/1, 0.0000 cents 140.36775 cents 23: 3228.4582 .. 3228.4582 cents 1/1, 0.0000 cents 140.36775 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 140.36775 cents, class 1 Average step (divided formal octave): 140.3677 cents Largest one step interval : 140.36775 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 140.36775 cents, amount: 24 Most common interval of one step : 140.36775 cents, amount: 24 Least squares average step : 140.36775 cents, oct.: 3368.82591 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 140.36775 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 701.8387 cents Number of recognisable fourths : 0 Scale contains two identical disjunct pentachords Best fifths form a closed circle Limited transpositions : all Inversional symmetry on degrees : all Inversional symmetry on intervals : all -- Rational properties -- Prime limit : 7 (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 .. 7 match: 6 H SD: 15.6574 cents 2 .. 14 match: 12 H SD: 11.4132 cents 3 .. 21 match: 16 SD: 9.4698 cents 4 .. 28 match: 18 SD: 8.5801 cents 5 .. 35 match: 20 SD: 7.0665 cents 6 .. 42 match: 21 SD: 7.2860 cents 7 .. 49 match: 22 SD: 7.0023 cents 8 .. 56 match: 23 SD: 4.8577 cents 9 .. 63 match: 23 SD: 6.1236 cents 10 .. 70 match: 24 SD: 4.3625 cents 11 .. 77 match: 24 SD: 3.5517 cents 14 .. 98 match: 24 SD: 3.4547 cents 16 .. 112 match: 24 SD: 2.7542 cents 18 .. 126 match: 24 SD: 2.7369 cents 21 .. 147 match: 24 SD: 2.1927 cents 22 .. 154 match: 24 SD: 1.8869 cents 24 .. 168 match: 24 SD: 1.6574 cents 32 .. 224 match: 24 SD: 1.4370 cents 34 .. 238 match: 24 SD: 1.1691 cents 40 .. 280 match: 24 SD: 1.1463 cents 44 .. 308 match: 24 SD: 1.0155 cents 46 .. 322 match: 24 SD: 0.9023 cents 50 .. 350 match: 24 SD: 0.8676 cents 56 .. 392 match: 24 SD: 0.8135 cents 58 .. 406 match: 24 SD: 0.7566 cents 62 .. 434 match: 24 SD: 0.6319 cents 68 .. 476 match: 24 SD: 0.5053 cents 80 .. 560 match: 24 SD: 0.4179 cents 96 .. 672 match: 24 SD: 0.4138 cents 102 .. 714 match: 24 SD: 0.3728 cents 118 .. 826 match: 24 SD: 0.3635 cents 120 .. 840 match: 24 SD: 0.2891 cents 152 .. 1064 match: 24 SD: 0.2139 cents 164 .. 1148 match: 24 SD: 0.2026 cents 188 .. 1316 match: 24 SD: 0.1917 cents 200 .. 1400 match: 24 SD: 0.1880 cents 204 .. 1428 match: 24 SD: 0.1691 cents 228 .. 1596 match: 24 SD: 0.1606 cents 250 .. 1750 match: 24 SD: 0.1454 cents 272 .. 1904 match: 24 SD: 0.1431 cents 284 .. 1988 match: 24 SD: 0.0987 cents 392 .. 2744 match: 24 SD: 0.0946 cents 402 .. 2814 match: 24 SD: 0.0865 cents 404 .. 2828 match: 24 SD: 0.0854 cents 428 .. 2996 match: 24 SD: 0.0813 cents 436 .. 3052 match: 24 SD: 0.0811 cents 472 .. 3304 match: 24 SD: 0.0728 cents 512 .. 3584 match: 24 SD: 0.0685 cents 556 .. 3892 match: 24 SD: 0.0674 cents 592 .. 4144 match: 24 SD: 0.0596 cents