Scala analysis: xen12-hanson-11-chain-19
Chain of minor thirds in 19EDO, Figure 11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63.158 cents 63.157895 2: 126.316 cents 126.315789 3: 189.474 cents 189.473684 4: 252.632 cents 252.631579 5: 315.789 cents 315.789474 6: 378.947 cents 378.947368 7: 442.105 cents 442.105263 8: 505.263 cents 505.263158 9: 568.421 cents 568.421053 10: 631.579 cents 631.578947 11: 694.737 cents 694.736842 12: 757.895 cents 757.894737 13: 821.053 cents 821.052632 14: 884.211 cents 884.210526 15: 947.368 cents 947.368421 16: 1010.526 cents 1010.526316 17: 1073.684 cents 1073.684211 18: 1136.842 cents 1136.842105 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 63.1579 cents 63.1579 1: 63.1579 cents 63.1579 2: 63.1579 cents 63.1579 3: 63.1579 cents 63.1579 4: 63.1579 cents 63.1579 5: 63.1579 cents 63.1579 6: 63.1579 cents 63.1579 7: 63.1579 cents 63.1579 8: 63.1579 cents 63.1579 9: 63.1579 cents 63.1579 10: 63.1579 cents 63.1579 11: 63.1579 cents 63.1579 12: 63.1579 cents 63.1579 13: 63.1579 cents 63.1579 14: 63.1579 cents 63.1579 15: 63.1579 cents 63.1579 16: 63.1579 cents 63.1579 17: 63.1579 cents 63.1579 18: 63.1579 cents 63.1579 19: 63.1579 cents 63.1579
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 19 63.15790 cents 2: 19 126.31579 cents 3: 19 189.47368 cents 4: 19 252.63158 cents 5: 19 315.78947 cents 6: 19 378.94737 cents 7: 19 442.10526 cents 8: 19 505.26316 cents 9: 19 568.42105 cents 10: 19 631.57895 cents 11: 19 694.73684 cents 12: 19 757.89474 cents 13: 19 821.05263 cents 14: 19 884.21053 cents 15: 19 947.36842 cents 16: 19 1010.52632 cents 17: 19 1073.68421 cents 18: 19 1136.84210 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 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 : 63.2 126.3 189.5 252.6 315.8 378.9 442.1 505.3 568.4 631.6 694.7 757.9 821.1 884.2 947.4 1010.5 1073.7 1136.8 1200.0 126.3 : 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 1200.0 189.5 : 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 1200.0 252.6 : 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 1200.0 315.8 : 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 1200.0 378.9 : 63.2 126.3 189.5 252.6 315.8 378.9 442.1 505.3 568.4 631.6 694.7 757.9 821.1 884.2 947.4 1010.5 1073.7 1136.8 1200.0 442.1 : 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 1200.0 505.3 : 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 1200.0 568.4 : 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 1200.0 631.6 : 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 1200.0 694.7 : 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 1200.0 757.9 : 63.2 126.3 189.5 252.6 315.8 378.9 442.1 505.3 568.4 631.6 694.7 757.9 821.1 884.2 947.4 1010.5 1073.7 1136.8 1200.0 821.1 : 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 1200.0 884.2 : 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 1200.0 947.4 : 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 1010.5: 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 1073.7: 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 1136.8: 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 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.1579 .. 63.1579 cents 1/1, 0.0000 cents 63.15790 cents 2: 126.3158 .. 126.3158 cents 1/1, 0.0000 cents 63.15789 cents 3: 189.4737 .. 189.4737 cents 1/1, 0.0000 cents 63.15789 cents 4: 252.6316 .. 252.6316 cents 1/1, 0.0000 cents 63.15790 cents 5: 315.7895 .. 315.7895 cents 1/1, 0.0000 cents 63.15789 cents 6: 378.9474 .. 378.9474 cents 1/1, 0.0000 cents 63.15789 cents 7: 442.1053 .. 442.1053 cents 1/1, 0.0000 cents 63.15790 cents 8: 505.2632 .. 505.2632 cents 1/1, 0.0000 cents 63.15789 cents 9: 568.4211 .. 568.4211 cents 1/1, 0.0000 cents 63.15790 cents 10: 631.5789 .. 631.5789 cents 1/1, 0.0000 cents 63.15789 cents 11: 694.7368 .. 694.7368 cents 1/1, 0.0000 cents 63.15790 cents 12: 757.8947 .. 757.8947 cents 1/1, 0.0000 cents 63.15789 cents 13: 821.0526 .. 821.0526 cents 1/1, 0.0000 cents 63.15790 cents 14: 884.2105 .. 884.2105 cents 1/1, 0.0000 cents 63.15789 cents 15: 947.3684 .. 947.3684 cents 1/1, 0.0000 cents 63.15790 cents 16: 1010.5263 .. 1010.5263 cents 1/1, 0.0000 cents 63.15789 cents 17: 1073.6842 .. 1073.6842 cents 1/1, 0.0000 cents 63.15790 cents 18: 1136.8421 .. 1136.8421 cents 1/1, 0.0000 cents 63.15789 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 63.15789 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 63.15790 cents Average / Smallest step : 1.000000 Largest / Average step : 1.000000 Largest / Smallest step : 1.000000 Median interval of one step : 63.15790 cents, amount: 19 Most common interval of one step : 63.15790 cents, amount: 19 Least squares average step : 63.15789 cents, oct.: 1200.00000 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 63.15789 cents Ratio Whole / Half tone : 1.500000 ( 3/2 ) Scale diversity : 1.000000 Rothenberg stability : 1.000000 = 1 Lumma stability : 1.000000 Rothenberg efficiency : 0.052632 redundancy: 0.947368 Efficiency x scale size : 1.000000 Number of different interval sizes : 18 = 1.00000 / class Number of one step interval sizes : 1 Mean interval variety : 1.00000 = 1 Lowest interval variety : 1 Number of recognisable fifths : 19, average 694.7368 cents 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 --
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: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 3.6091 cents 3 .. 6 match: 3 H SD: 2.4066 cents 4 .. 8 match: 4 H SD: 5.9518 cents 5 .. 10 match: 5 H SD: 3.4804 cents 6 .. 12 match: 6 H SD: 4.9959 cents 7 .. 14 match: 7 H SD: 5.5696 cents 8 .. 16 match: 8 H SD: 5.0924 cents 9 .. 18 match: 9 H SD: 5.1263 cents 10 .. 20 match: 10 H SD: 5.0824 cents 11 .. 22 match: 11 H SD: 6.4928 cents 12 .. 24 match: 12 H SD: 4.6703 cents 13 .. 26 match: 13 H SD: 4.3553 cents 14 .. 28 match: 14 H SD: 4.0659 cents 15 .. 30 match: 15 H SD: 4.0153 cents 16 .. 32 match: 16 H SD: 4.1454 cents 17 .. 34 match: 16 S SD: 5.1587 cents 18 .. 36 match: 17 SD: 3.5951 cents 19 .. 38 match: 17 SD: 4.8388 cents 20 .. 40 match: 18 SD: 3.1770 cents 21 .. 42 match: 18 SD: 3.7377 cents 22 .. 44 match: 18 SD: 4.5282 cents 23 .. 46 match: 19 SD: 3.5528 cents 24 .. 48 match: 19 SD: 2.8162 cents 25 .. 50 match: 19 SD: 2.5519 cents 30 .. 60 match: 19 SD: 2.5466 cents 33 .. 66 match: 19 SD: 2.4526 cents 34 .. 68 match: 19 SD: 2.4003 cents 36 .. 72 match: 19 SD: 2.1006 cents 38 .. 76 match: 19 SD: 2.0129 cents 41 .. 82 match: 19 SD: 1.8951 cents 44 .. 88 match: 19 SD: 1.5113 cents 51 .. 102 match: 19 SD: 1.2793 cents 59 .. 118 match: 19 SD: 1.2540 cents 62 .. 124 match: 19 SD: 1.2062 cents 69 .. 138 match: 19 SD: 0.9661 cents 77 .. 154 match: 19 SD: 0.8171 cents 89 .. 178 match: 19 SD: 0.8059 cents 95 .. 190 match: 19 SD: 0.7372 cents 102 .. 204 match: 19 SD: 0.7259 cents 103 .. 206 match: 19 SD: 0.7201 cents 106 .. 212 match: 19 SD: 0.6026 cents 114 .. 228 match: 19 SD: 0.5946 cents 129 .. 258 match: 19 SD: 0.5572 cents 130 .. 260 match: 19 SD: 0.5376 cents 135 .. 270 match: 19 SD: 0.5279 cents 140 .. 280 match: 19 SD: 0.5172 cents 144 .. 288 match: 19 SD: 0.4945 cents 154 .. 308 match: 19 SD: 0.4709 cents 155 .. 310 match: 19 SD: 0.4421 cents 159 .. 318 match: 19 SD: 0.4322 cents 165 .. 330 match: 19 SD: 0.4314 cents 180 .. 360 match: 19 SD: 0.3637 cents 198 .. 396 match: 19 SD: 0.3481 cents 209 .. 418 match: 19 SD: 0.2782 cents 241 .. 482 match: 19 SD: 0.2568 cents 265 .. 530 match: 19 SD: 0.2440 cents 275 .. 550 match: 19 SD: 0.2004 cents 320 .. 640 match: 19 SD: 0.1963 cents 330 .. 660 match: 19 SD: 0.1916 cents 355 .. 710 match: 19 SD: 0.1915 cents 371 .. 742 match: 19 SD: 0.1658 cents 381 .. 762 match: 19 SD: 0.1488 cents 425 .. 850 match: 19 SD: 0.1464 cents 433 .. 866 match: 19 SD: 0.1454 cents 434 .. 868 match: 19 SD: 0.1365 cents 450 .. 900 match: 19 SD: 0.1321 cents 486 .. 972 match: 19 SD: 0.1254 cents 516 .. 1032 match: 19 SD: 0.1242 cents 540 .. 1080 match: 19 SD: 0.1200 cents 561 .. 1122 match: 19 SD: 0.1179 cents 597 .. 1194 match: 19 SD: 0.1046 cents