Scala analysis: xen07-chalmers-19-equal
19-Equal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.200 cents 63.200000 2: 126.300 cents 126.300000 3: 189.500 cents 189.500000 4: 252.600 cents 252.600000 5: 315.800 cents 315.800000 6: 378.900 cents 378.900000 7: 442.100 cents 442.100000 8: 505.300 cents 505.300000 9: 568.400 cents 568.400000 10: 631.600 cents 631.600000 11: 694.700 cents 694.700000 12: 757.900 cents 757.900000 13: 821.100 cents 821.100000 14: 884.200 cents 884.200000 15: 947.400 cents 947.400000 16: 1010.500 cents 1010.500000 17: 1073.700 cents 1073.700000 18: 1136.800 cents 1136.800000 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 63.2000 cents 63.2000 1: 63.2000 cents 63.2000 2: 63.1000 cents 63.1000 3: 63.2000 cents 63.2000 4: 63.1000 cents 63.1000 5: 63.2000 cents 63.2000 6: 63.1000 cents 63.1000 7: 63.2000 cents 63.2000 8: 63.2000 cents 63.2000 9: 63.1000 cents 63.1000 10: 63.2000 cents 63.2000 11: 63.1000 cents 63.1000 12: 63.2000 cents 63.2000 13: 63.2000 cents 63.2000 14: 63.1000 cents 63.1000 15: 63.2000 cents 63.2000 16: 63.1000 cents 63.1000 17: 63.2000 cents 63.2000 18: 63.1000 cents 63.1000 19: 63.2000 cents 63.2000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 63.10000 cents 1: 11 63.20000 cents 2: 16 126.30000 cents 2: 3 126.40000 cents 3: 5 189.40000 cents 3: 14 189.50000 cents 4: 13 252.60000 cents 4: 6 252.70000 cents 5: 2 315.70000 cents 5: 17 315.80000 cents 6: 10 378.90000 cents 6: 9 379.00000 cents 7: 18 442.10000 cents 7: 1 442.20000 cents 8: 7 505.20000 cents 8: 12 505.30000 cents 9: 15 568.40000 cents 9: 4 568.50000 cents 10: 4 631.50000 cents 10: 15 631.60000 cents 11: 12 694.70000 cents 11: 7 694.80000 cents 12: 1 757.80000 cents 12: 18 757.90000 cents 13: 9 821.00000 cents 13: 10 821.10000 cents 14: 17 884.20000 cents 14: 2 884.30000 cents 15: 6 947.30000 cents 15: 13 947.40000 cents 16: 14 1010.50000 cents 16: 5 1010.60000 cents 17: 3 1073.60000 cents 17: 16 1073.70000 cents 18: 11 1136.80000 cents 18: 8 1136.90000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 63.2 126.3 189.5 252.6 315.8 378.9 442.1 505.3 568.4 631.6 694.7 757.9 821.1 884.2 947.4 1010.5 1073.7 1136.8 1200.0 63.2 : 63.1 126.3 189.4 252.6 315.7 378.9 442.1 505.2 568.4 631.5 694.7 757.9 821.0 884.2 947.3 1010.5 1073.6 1136.8 1200.0 126.3 : 63.2 126.3 189.5 252.6 315.8 379.0 442.1 505.3 568.4 631.6 694.8 757.9 821.1 884.2 947.4 1010.5 1073.7 1136.9 1200.0 189.5 : 63.1 126.3 189.4 252.6 315.8 378.9 442.1 505.2 568.4 631.6 694.7 757.9 821.0 884.2 947.3 1010.5 1073.7 1136.8 1200.0 252.6 : 63.2 126.3 189.5 252.7 315.8 379.0 442.1 505.3 568.5 631.6 694.8 757.9 821.1 884.2 947.4 1010.6 1073.7 1136.9 1200.0 315.8 : 63.1 126.3 189.5 252.6 315.8 378.9 442.1 505.3 568.4 631.6 694.7 757.9 821.0 884.2 947.4 1010.5 1073.7 1136.8 1200.0 378.9 : 63.2 126.4 189.5 252.7 315.8 379.0 442.2 505.3 568.5 631.6 694.8 757.9 821.1 884.3 947.4 1010.6 1073.7 1136.9 1200.0 442.1 : 63.2 126.3 189.5 252.6 315.8 379.0 442.1 505.3 568.4 631.6 694.7 757.9 821.1 884.2 947.4 1010.5 1073.7 1136.8 1200.0 505.3 : 63.1 126.3 189.4 252.6 315.8 378.9 442.1 505.2 568.4 631.5 694.7 757.9 821.0 884.2 947.3 1010.5 1073.6 1136.8 1200.0 568.4 : 63.2 126.3 189.5 252.7 315.8 379.0 442.1 505.3 568.4 631.6 694.8 757.9 821.1 884.2 947.4 1010.5 1073.7 1136.9 1200.0 631.6 : 63.1 126.3 189.5 252.6 315.8 378.9 442.1 505.2 568.4 631.6 694.7 757.9 821.0 884.2 947.3 1010.5 1073.7 1136.8 1200.0 694.7 : 63.2 126.4 189.5 252.7 315.8 379.0 442.1 505.3 568.5 631.6 694.8 757.9 821.1 884.2 947.4 1010.6 1073.7 1136.9 1200.0 757.9 : 63.2 126.3 189.5 252.6 315.8 378.9 442.1 505.3 568.4 631.6 694.7 757.9 821.0 884.2 947.4 1010.5 1073.7 1136.8 1200.0 821.1 : 63.1 126.3 189.4 252.6 315.7 378.9 442.1 505.2 568.4 631.5 694.7 757.8 821.0 884.2 947.3 1010.5 1073.6 1136.8 1200.0 884.2 : 63.2 126.3 189.5 252.6 315.8 379.0 442.1 505.3 568.4 631.6 694.7 757.9 821.1 884.2 947.4 1010.5 1073.7 1136.9 1200.0 947.4 : 63.1 126.3 189.4 252.6 315.8 378.9 442.1 505.2 568.4 631.5 694.7 757.9 821.0 884.2 947.3 1010.5 1073.7 1136.8 1200.0 1010.5: 63.2 126.3 189.5 252.7 315.8 379.0 442.1 505.3 568.4 631.6 694.8 757.9 821.1 884.2 947.4 1010.6 1073.7 1136.9 1200.0 1073.7: 63.1 126.3 189.5 252.6 315.8 378.9 442.1 505.2 568.4 631.6 694.7 757.9 821.0 884.2 947.4 1010.5 1073.7 1136.8 1200.0 1136.8: 63.2 126.4 189.5 252.7 315.8 379.0 442.1 505.3 568.5 631.6 694.8 757.9 821.1 884.3 947.4 1010.6 1073.7 1136.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.1000 .. 63.2000 cents 0.10000 cents 63.10000 cents 2: 126.3000 .. 126.4000 cents 0.10000 cents 63.10000 cents 3: 189.4000 .. 189.5000 cents 0.10000 cents 63.00000 cents 4: 252.6000 .. 252.7000 cents 0.10000 cents 63.10000 cents 5: 315.7000 .. 315.8000 cents 0.10000 cents 63.00000 cents 6: 378.9000 .. 379.0000 cents 0.10000 cents 63.10000 cents 7: 442.1000 .. 442.2000 cents 0.10000 cents 63.10000 cents 8: 505.2000 .. 505.3000 cents 0.10000 cents 63.00000 cents 9: 568.4000 .. 568.5000 cents 0.10000 cents 63.10000 cents 10: 631.5000 .. 631.6000 cents 0.10000 cents 63.00000 cents 11: 694.7000 .. 694.8000 cents 0.10000 cents 63.10000 cents 12: 757.8000 .. 757.9000 cents 0.10000 cents 63.00000 cents 13: 821.0000 .. 821.1000 cents 0.10000 cents 63.10000 cents 14: 884.2000 .. 884.3000 cents 0.10000 cents 63.10000 cents 15: 947.3000 .. 947.4000 cents 0.10000 cents 63.00000 cents 16: 1010.5000 .. 1010.6000 cents 0.10000 cents 63.10000 cents 17: 1073.6000 .. 1073.7000 cents 0.10000 cents 63.00000 cents 18: 1136.8000 .. 1136.9000 cents 0.10000 cents 63.10000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 63.10000 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 63.20000 cents Average / Smallest step : 1.000918 Largest / Average step : 1.000667 Largest / Smallest step : 1.001585 Median interval of one step : 63.20000 cents, amount: 11 Most common interval of one step : 63.20000 cents, amount: 11 Least squares average step : 63.15777 cents, oct.: 1199.99769 cents Scale is strictly proper Scale has Myhill's property chromas: 0.10000 cents and 63.00000 cents, ratio: 630.000000 generators: 7 of 442.10000 cents and 12 of 757.90000 cents ET pair of linear temperament : 11&19 Scale is maximally even for L / S <= 2 Scale is distributional even Step pattern alph. order: ABABABAABABAABABABA Step pattern size order : LSLSLSLLSLSLLSLSLSL Scale is a Constant Structure, by a margin of 63.00000 cents Scale diversity : 1.001019 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.998500 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 0.10000 cents Most common intervals : 442.10000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 442.100 884.200 cents Most common triad is 0.0 442.100 757.900 cents, amount: 17 Number of recognisable fifths : 19, average 694.7368 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 19 = 100.0000% Limited transpositions : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Limited inverse transpositions : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Inversional symmetry on degrees : 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11 11-12 12-13 13-14 14-15 15-16 16-17 17-18 18-19 -- Rational properties --
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.0288 c. M: 0.0474 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 3.6275 cents 3 .. 6 match: 3 H SD: 2.4189 cents 4 .. 8 match: 4 H SD: 5.9512 cents 5 .. 10 match: 5 H SD: 3.4900 cents 6 .. 12 match: 6 H SD: 5.0035 cents 7 .. 14 match: 7 H SD: 5.5694 cents 8 .. 16 match: 8 H SD: 5.0864 cents 9 .. 18 match: 9 H SD: 5.1215 cents 10 .. 20 match: 10 H SD: 5.0856 cents 11 .. 22 match: 11 H SD: 6.4903 cents 12 .. 24 match: 12 H SD: 4.6742 cents 13 .. 26 match: 13 H SD: 4.3522 cents 14 .. 28 match: 14 H SD: 4.0641 cents 15 .. 30 match: 15 H SD: 4.0164 cents 16 .. 32 match: 16 H SD: 4.1446 cents 17 .. 34 match: 16 S SD: 5.1585 cents 18 .. 36 match: 17 SD: 3.5939 cents 19 .. 38 match: 17 SD: 4.8390 cents 20 .. 40 match: 18 SD: 3.1773 cents 21 .. 42 match: 18 SD: 3.7357 cents 22 .. 44 match: 18 SD: 4.5275 cents 23 .. 46 match: 19 SD: 3.5516 cents 24 .. 48 match: 19 SD: 2.8152 cents 25 .. 50 match: 19 SD: 2.5529 cents 30 .. 60 match: 19 SD: 2.5488 cents 33 .. 66 match: 19 SD: 2.4530 cents 34 .. 68 match: 19 SD: 2.3990 cents 36 .. 72 match: 19 SD: 2.1034 cents 38 .. 76 match: 19 SD: 2.0128 cents 41 .. 82 match: 19 SD: 1.8920 cents 44 .. 88 match: 19 SD: 1.5109 cents 51 .. 102 match: 19 SD: 1.2777 cents 59 .. 118 match: 19 SD: 1.2518 cents 62 .. 124 match: 19 SD: 1.2086 cents 69 .. 138 match: 19 SD: 0.9667 cents 77 .. 154 match: 19 SD: 0.8160 cents 89 .. 178 match: 19 SD: 0.8099 cents 95 .. 190 match: 19 SD: 0.7344 cents 102 .. 204 match: 19 SD: 0.7251 cents 103 .. 206 match: 19 SD: 0.7188 cents 106 .. 212 match: 19 SD: 0.6032 cents 114 .. 228 match: 19 SD: 0.5952 cents 120 .. 240 match: 19 SD: 0.5952 cents 129 .. 258 match: 19 SD: 0.5576 cents 130 .. 260 match: 19 SD: 0.5375 cents 135 .. 270 match: 19 SD: 0.5265 cents 140 .. 280 match: 19 SD: 0.5178 cents 144 .. 288 match: 19 SD: 0.4958 cents 154 .. 308 match: 19 SD: 0.4721 cents 155 .. 310 match: 19 SD: 0.4413 cents 159 .. 318 match: 19 SD: 0.4347 cents 165 .. 330 match: 19 SD: 0.4294 cents 180 .. 360 match: 19 SD: 0.3633 cents 198 .. 396 match: 19 SD: 0.3493 cents 209 .. 418 match: 19 SD: 0.2766 cents 241 .. 482 match: 19 SD: 0.2573 cents 250 .. 500 match: 19 SD: 0.2557 cents 265 .. 530 match: 19 SD: 0.2430 cents 275 .. 550 match: 19 SD: 0.2006 cents 320 .. 640 match: 19 SD: 0.1953 cents 330 .. 660 match: 19 SD: 0.1945 cents 355 .. 710 match: 19 SD: 0.1944 cents 357 .. 714 match: 19 SD: 0.1908 cents 371 .. 742 match: 19 SD: 0.1640 cents 381 .. 762 match: 19 SD: 0.1499 cents 425 .. 850 match: 19 SD: 0.1471 cents 433 .. 866 match: 19 SD: 0.1451 cents 434 .. 868 match: 19 SD: 0.1376 cents 450 .. 900 match: 19 SD: 0.1310 cents 486 .. 972 match: 19 SD: 0.1244 cents 540 .. 1080 match: 19 SD: 0.1210 cents 543 .. 1086 match: 19 SD: 0.1207 cents 555 .. 1110 match: 19 SD: 0.1199 cents 561 .. 1122 match: 19 SD: 0.1174 cents 597 .. 1194 match: 19 SD: 0.1065 cents