Scala analysis: xen14-mclaren-nonoctave-31-5
31st root of 5 non-octave scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 89.881 cents 89.881088 2: 179.762 cents 179.762175 3: 269.643 cents 269.643263 4: 359.524 cents 359.524350 5: 449.405 cents 449.405438 6: 539.287 cents 539.286525 7: 629.168 cents 629.167613 8: 719.049 cents 719.048700 9: 808.930 cents 808.929788 10: 898.811 cents 898.810875 11: 988.692 cents 988.691963 12: 1078.573 cents 1078.573051 13: 1168.454 cents 1168.454138 14: 1258.335 cents 1258.335226 15: 1348.216 cents 1348.216313 16: 1438.097 cents 1438.097401 17: 1527.978 cents 1527.978488 18: 1617.860 cents 1617.859576 19: 1707.741 cents 1707.740663 20: 1797.622 cents 1797.621751 21: 1887.503 cents 1887.502838 22: 1977.384 cents 1977.383926 23: 2067.265 cents 2067.265014 24: 2157.146 cents 2157.146101 25: 2247.027 cents 2247.027189 26: 2336.908 cents 2336.908276 27: 2426.789 cents 2426.789364 28: 2516.670 cents 2516.670451 29: 2606.552 cents 2606.551539 30: 2696.433 cents 2696.432626 31: 5/1 2786.313714 major 17th
SHOW/INTERVAL
0: 89.8811 cents 89.8811 1: 89.8811 cents 89.8811 2: 89.8811 cents 89.8811 3: 89.8811 cents 89.8811 4: 89.8811 cents 89.8811 5: 89.8811 cents 89.8811 6: 89.8811 cents 89.8811 7: 89.8811 cents 89.8811 8: 89.8811 cents 89.8811 9: 89.8811 cents 89.8811 10: 89.8811 cents 89.8811 11: 89.8811 cents 89.8811 12: 89.8811 cents 89.8811 13: 89.8811 cents 89.8811 14: 89.8811 cents 89.8811 15: 89.8811 cents 89.8811 16: 89.8811 cents 89.8811 17: 89.8811 cents 89.8811 18: 89.8811 cents 89.8811 19: 89.8811 cents 89.8811 20: 89.8811 cents 89.8811 21: 89.8811 cents 89.8811 22: 89.8811 cents 89.8811 23: 89.8811 cents 89.8811 24: 89.8811 cents 89.8811 25: 89.8811 cents 89.8811 26: 89.8811 cents 89.8811 27: 89.8811 cents 89.8811 28: 89.8811 cents 89.8811 29: 89.8811 cents 89.8811 30: 89.8811 cents 89.8811 31: 89.8811 cents 89.8811
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 31 89.88109 cents 2: 31 179.76218 cents 3: 31 269.64326 cents 4: 31 359.52435 cents 5: 31 449.40544 cents 6: 31 539.28652 cents 7: 31 629.16761 cents 8: 31 719.04870 cents 9: 31 808.92979 cents 10: 31 898.81087 cents 11: 31 988.69196 cents 12: 31 1078.57305 cents 13: 31 1168.45414 cents 14: 31 1258.33523 cents 15: 31 1348.21631 cents 16: 31 1438.09740 cents 17: 31 1527.97849 cents 18: 31 1617.85958 cents 19: 31 1707.74066 cents 20: 31 1797.62175 cents 21: 31 1887.50284 cents 22: 31 1977.38393 cents 23: 31 2067.26501 cents 24: 31 2157.14610 cents 25: 31 2247.02719 cents 26: 31 2336.90828 cents 27: 31 2426.78936 cents 28: 31 2516.67045 cents 29: 31 2606.55154 cents 30: 31 2696.43263 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 31 0.0 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 89.9 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 179.8 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 269.6 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 359.5 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 449.4 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 539.3 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 629.2 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 719.0 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 808.9 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 898.8 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 988.7 : 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1078.6: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1168.5: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1258.3: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1348.2: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1438.1: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1528.0: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1617.9: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1707.7: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1797.6: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1887.5: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 1977.4: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2067.3: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2157.1: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2247.0: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2336.9: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2426.8: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2516.7: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2606.6: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2696.4: 89.9 179.8 269.6 359.5 449.4 539.3 629.2 719.0 808.9 898.8 988.7 1078.6 1168.5 1258.3 1348.2 1438.1 1528.0 1617.9 1707.7 1797.6 1887.5 1977.4 2067.3 2157.1 2247.0 2336.9 2426.8 2516.7 2606.6 2696.4 2786.3 2786.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.8811 .. 89.8811 cents 1/1, 0.0000 cents 89.88109 cents 2: 179.7622 .. 179.7622 cents 1/1, 0.0000 cents 89.88109 cents 3: 269.6433 .. 269.6433 cents 1/1, 0.0000 cents 89.88109 cents 4: 359.5244 .. 359.5244 cents 1/1, 0.0000 cents 89.88109 cents 5: 449.4054 .. 449.4054 cents 1/1, 0.0000 cents 89.88109 cents 6: 539.2865 .. 539.2865 cents 1/1, 0.0000 cents 89.88109 cents 7: 629.1676 .. 629.1676 cents 1/1, 0.0000 cents 89.88109 cents 8: 719.0487 .. 719.0487 cents 1/1, 0.0000 cents 89.88109 cents 9: 808.9298 .. 808.9298 cents 1/1, 0.0000 cents 89.88109 cents 10: 898.8109 .. 898.8109 cents 1/1, 0.0000 cents 89.88109 cents 11: 988.6920 .. 988.6920 cents 1/1, 0.0000 cents 89.88109 cents 12: 1078.5731 .. 1078.5731 cents 1/1, 0.0000 cents 89.88109 cents 13: 1168.4541 .. 1168.4541 cents 1/1, 0.0000 cents 89.88109 cents 14: 1258.3352 .. 1258.3352 cents 1/1, 0.0000 cents 89.88109 cents 15: 1348.2163 .. 1348.2163 cents 1/1, 0.0000 cents 89.88109 cents 16: 1438.0974 .. 1438.0974 cents 1/1, 0.0000 cents 89.88109 cents 17: 1527.9785 .. 1527.9785 cents 1/1, 0.0000 cents 89.88109 cents 18: 1617.8596 .. 1617.8596 cents 1/1, 0.0000 cents 89.88109 cents 19: 1707.7407 .. 1707.7407 cents 1/1, 0.0000 cents 89.88109 cents 20: 1797.6218 .. 1797.6218 cents 1/1, 0.0000 cents 89.88109 cents 21: 1887.5028 .. 1887.5028 cents 1/1, 0.0000 cents 89.88109 cents 22: 1977.3839 .. 1977.3839 cents 1/1, 0.0000 cents 89.88109 cents 23: 2067.2650 .. 2067.2650 cents 1/1, 0.0000 cents 89.88109 cents 24: 2157.1461 .. 2157.1461 cents 1/1, 0.0000 cents 89.88109 cents 25: 2247.0272 .. 2247.0272 cents 1/1, 0.0000 cents 89.88109 cents 26: 2336.9083 .. 2336.9083 cents 1/1, 0.0000 cents 89.88109 cents 27: 2426.7894 .. 2426.7894 cents 1/1, 0.0000 cents 89.88109 cents 28: 2516.6705 .. 2516.6705 cents 1/1, 0.0000 cents 89.88109 cents 29: 2606.5515 .. 2606.5515 cents 1/1, 0.0000 cents 89.88109 cents 30: 2696.4326 .. 2696.4326 cents 1/1, 0.0000 cents 89.88109 cents
SHOW DATA
Number of notes : 31 -- Interval properties -- Smallest interval : 89.88109 cents, class 1 Average step (divided formal octave): 89.8811 cents Largest one step interval : 89.88109 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 89.88109 cents, amount: 31 Most common interval of one step : 89.88109 cents, amount: 31 Least squares average step : 89.88109 cents, oct.: 2786.31371 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 89.88109 cents Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.032258 redundancy: 0.967742 Efficiency x scale size : 1.000000 Number of different interval sizes : 30 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 31, average 719.0487 cents Number of appreciable fifths : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct heptachords 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 : 5 (not all pitches rational)
FIT/MODE
31: 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 1 SP B ME I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 5 match: 4 H SD: 10.9592 cents 2 .. 10 match: 8 H SD: 7.2375 cents 3 .. 15 match: 12 H SD: 6.6691 cents 4 .. 20 match: 16 H SD: 6.2770 cents 5 .. 25 match: 19 SD: 6.5622 cents 6 .. 30 match: 22 S SD: 4.3742 cents 7 .. 35 match: 24 SD: 4.1184 cents 8 .. 40 match: 25 SD: 4.6971 cents 9 .. 45 match: 27 SD: 4.1741 cents 10 .. 50 match: 28 SD: 3.9372 cents 11 .. 55 match: 28 SD: 4.2857 cents 12 .. 60 match: 29 SD: 3.5956 cents 13 .. 65 match: 30 SD: 3.0721 cents 14 .. 70 match: 30 SD: 3.2499 cents 15 .. 75 match: 30 SD: 3.7226 cents 16 .. 80 match: 31 SD: 2.6413 cents 17 .. 85 match: 31 SD: 2.1708 cents 22 .. 110 match: 31 SD: 2.1121 cents 23 .. 115 match: 31 SD: 2.0744 cents 25 .. 125 match: 31 SD: 1.8373 cents 27 .. 135 match: 31 SD: 1.6158 cents 29 .. 145 match: 31 SD: 1.6010 cents 30 .. 150 match: 31 SD: 1.4042 cents 34 .. 170 match: 31 SD: 1.2912 cents 35 .. 175 match: 31 SD: 1.0479 cents 43 .. 215 match: 31 SD: 1.0204 cents 44 .. 220 match: 31 SD: 0.9007 cents 52 .. 260 match: 31 SD: 0.8334 cents 53 .. 265 match: 31 SD: 0.7812 cents 55 .. 275 match: 31 SD: 0.7724 cents 57 .. 285 match: 31 SD: 0.6121 cents 73 .. 365 match: 31 SD: 0.6109 cents 74 .. 370 match: 31 SD: 0.5261 cents 82 .. 410 match: 31 SD: 0.4311 cents 91 .. 455 match: 31 SD: 0.3527 cents 112 .. 560 match: 31 SD: 0.2953 cents 147 .. 735 match: 31 SD: 0.2944 cents 148 .. 740 match: 31 SD: 0.2192 cents 173 .. 865 match: 31 SD: 0.2025 cents 191 .. 955 match: 31 SD: 0.2006 cents 200 .. 1000 match: 31 SD: 0.1949 cents 208 .. 1040 match: 31 SD: 0.1854 cents 230 .. 1150 match: 31 SD: 0.1686 cents 244 .. 1220 match: 31 SD: 0.1603 cents 247 .. 1235 match: 31 SD: 0.1493 cents 274 .. 1370 match: 31 SD: 0.1439 cents 301 .. 1505 match: 31 SD: 0.1305 cents 304 .. 1520 match: 31 SD: 0.1247 cents 320 .. 1600 match: 31 SD: 0.1175 cents 338 .. 1690 match: 31 SD: 0.1113 cents 381 .. 1905 match: 31 SD: 0.1085 cents 391 .. 1955 match: 31 SD: 0.0929 cents 438 .. 2190 match: 31 SD: 0.0887 cents 449 .. 2245 match: 31 SD: 0.0884 cents 468 .. 2340 match: 31 SD: 0.0817 cents 482 .. 2410 match: 31 SD: 0.0809 cents 493 .. 2465 match: 31 SD: 0.0772 cents 509 .. 2545 match: 31 SD: 0.0767 cents 523 .. 2615 match: 31 SD: 0.0740 cents 529 .. 2645 match: 31 SD: 0.0723 cents 547 .. 2735 match: 31 SD: 0.0716 cents 559 .. 2795 match: 31 SD: 0.0689 cents 577 .. 2885 match: 31 SD: 0.0646 cents