Scala analysis: xen12-hanson-11-chain-87
Chain of minor thirds in 87EDO, Figure 11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68.966 cents 68.965517 2: 137.931 cents 137.931034 3: 206.897 cents 206.896552 4: 248.276 cents 248.275862 5: 317.241 cents 317.241379 6: 386.207 cents 386.206897 7: 455.172 cents 455.172414 8: 496.552 cents 496.551724 9: 565.517 cents 565.517241 10: 634.483 cents 634.482759 11: 703.448 cents 703.448276 12: 772.414 cents 772.413793 13: 813.793 cents 813.793103 14: 882.759 cents 882.758621 15: 951.724 cents 951.724138 16: 1020.690 cents 1020.689655 17: 1089.655 cents 1089.655172 18: 1131.034 cents 1131.034483 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 68.9655 cents 68.9655 1: 68.9655 cents 68.9655 2: 68.9655 cents 68.9655 3: 68.9655 cents 68.9655 4: 41.3793 cents 41.3793 5: 68.9655 cents 68.9655 6: 68.9655 cents 68.9655 7: 68.9655 cents 68.9655 8: 41.3793 cents 41.3793 9: 68.9655 cents 68.9655 10: 68.9655 cents 68.9655 11: 68.9655 cents 68.9655 12: 68.9655 cents 68.9655 13: 41.3793 cents 41.3793 14: 68.9655 cents 68.9655 15: 68.9655 cents 68.9655 16: 68.9655 cents 68.9655 17: 68.9655 cents 68.9655 18: 41.3793 cents 41.3793 19: 68.9655 cents 68.9655
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 41.37931 cents 1: 15 68.96552 cents 2: 8 110.34483 cents 2: 11 137.93103 cents 3: 12 179.31034 cents 3: 7 206.89655 cents 4: 16 248.27586 cents 4: 3 275.86207 cents 5: 1 289.65517 cents 5: 18 317.24138 cents 6: 5 358.62069 cents 6: 14 386.20690 cents 7: 9 427.58621 cents 7: 10 455.17241 cents 8: 13 496.55172 cents 8: 6 524.13793 cents 9: 17 565.51724 cents 9: 2 593.10345 cents 10: 2 606.89655 cents 10: 17 634.48276 cents 11: 6 675.86207 cents 11: 13 703.44828 cents 12: 10 744.82759 cents 12: 9 772.41379 cents 13: 14 813.79310 cents 13: 5 841.37931 cents 14: 18 882.75862 cents 14: 1 910.34483 cents 15: 3 924.13793 cents 15: 16 951.72414 cents 16: 7 993.10345 cents 16: 12 1020.68966 cents 17: 11 1062.06897 cents 17: 8 1089.65517 cents 18: 15 1131.03448 cents 18: 4 1158.62069 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 : 69.0 137.9 206.9 248.3 317.2 386.2 455.2 496.6 565.5 634.5 703.4 772.4 813.8 882.8 951.7 1020.7 1089.7 1131.0 1200.0 69.0 : 69.0 137.9 179.3 248.3 317.2 386.2 427.6 496.6 565.5 634.5 703.4 744.8 813.8 882.8 951.7 1020.7 1062.1 1131.0 1200.0 137.9 : 69.0 110.3 179.3 248.3 317.2 358.6 427.6 496.6 565.5 634.5 675.9 744.8 813.8 882.8 951.7 993.1 1062.1 1131.0 1200.0 206.9 : 41.4 110.3 179.3 248.3 289.7 358.6 427.6 496.6 565.5 606.9 675.9 744.8 813.8 882.8 924.1 993.1 1062.1 1131.0 1200.0 248.3 : 69.0 137.9 206.9 248.3 317.2 386.2 455.2 524.1 565.5 634.5 703.4 772.4 841.4 882.8 951.7 1020.7 1089.7 1158.6 1200.0 317.2 : 69.0 137.9 179.3 248.3 317.2 386.2 455.2 496.6 565.5 634.5 703.4 772.4 813.8 882.8 951.7 1020.7 1089.7 1131.0 1200.0 386.2 : 69.0 110.3 179.3 248.3 317.2 386.2 427.6 496.6 565.5 634.5 703.4 744.8 813.8 882.8 951.7 1020.7 1062.1 1131.0 1200.0 455.2 : 41.4 110.3 179.3 248.3 317.2 358.6 427.6 496.6 565.5 634.5 675.9 744.8 813.8 882.8 951.7 993.1 1062.1 1131.0 1200.0 496.6 : 69.0 137.9 206.9 275.9 317.2 386.2 455.2 524.1 593.1 634.5 703.4 772.4 841.4 910.3 951.7 1020.7 1089.7 1158.6 1200.0 565.5 : 69.0 137.9 206.9 248.3 317.2 386.2 455.2 524.1 565.5 634.5 703.4 772.4 841.4 882.8 951.7 1020.7 1089.7 1131.0 1200.0 634.5 : 69.0 137.9 179.3 248.3 317.2 386.2 455.2 496.6 565.5 634.5 703.4 772.4 813.8 882.8 951.7 1020.7 1062.1 1131.0 1200.0 703.4 : 69.0 110.3 179.3 248.3 317.2 386.2 427.6 496.6 565.5 634.5 703.4 744.8 813.8 882.8 951.7 993.1 1062.1 1131.0 1200.0 772.4 : 41.4 110.3 179.3 248.3 317.2 358.6 427.6 496.6 565.5 634.5 675.9 744.8 813.8 882.8 924.1 993.1 1062.1 1131.0 1200.0 813.8 : 69.0 137.9 206.9 275.9 317.2 386.2 455.2 524.1 593.1 634.5 703.4 772.4 841.4 882.8 951.7 1020.7 1089.7 1158.6 1200.0 882.8 : 69.0 137.9 206.9 248.3 317.2 386.2 455.2 524.1 565.5 634.5 703.4 772.4 813.8 882.8 951.7 1020.7 1089.7 1131.0 1200.0 951.7 : 69.0 137.9 179.3 248.3 317.2 386.2 455.2 496.6 565.5 634.5 703.4 744.8 813.8 882.8 951.7 1020.7 1062.1 1131.0 1200.0 1020.7: 69.0 110.3 179.3 248.3 317.2 386.2 427.6 496.6 565.5 634.5 675.9 744.8 813.8 882.8 951.7 993.1 1062.1 1131.0 1200.0 1089.7: 41.4 110.3 179.3 248.3 317.2 358.6 427.6 496.6 565.5 606.9 675.9 744.8 813.8 882.8 924.1 993.1 1062.1 1131.0 1200.0 1131.0: 69.0 137.9 206.9 275.9 317.2 386.2 455.2 524.1 565.5 634.5 703.4 772.4 841.4 882.8 951.7 1020.7 1089.7 1158.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.3793 .. 68.9655 cents 27.58621 cents 41.37931 cents 2: 110.3448 .. 137.9310 cents 27.58621 cents 41.37931 cents 3: 179.3103 .. 206.8966 cents 27.58621 cents 41.37931 cents 4: 248.2759 .. 275.8621 cents 27.58621 cents 41.37931 cents 5: 289.6552 .. 317.2414 cents 27.58621 cents 13.79310 cents 6: 358.6207 .. 386.2069 cents 27.58621 cents 41.37931 cents 7: 427.5862 .. 455.1724 cents 27.58621 cents 41.37931 cents 8: 496.5517 .. 524.1379 cents 27.58621 cents 41.37931 cents 9: 565.5172 .. 593.1034 cents 27.58621 cents 41.37931 cents 10: 606.8966 .. 634.4828 cents 27.58621 cents 13.79310 cents 11: 675.8621 .. 703.4483 cents 27.58621 cents 41.37931 cents 12: 744.8276 .. 772.4138 cents 27.58621 cents 41.37931 cents 13: 813.7931 .. 841.3793 cents 27.58621 cents 41.37931 cents 14: 882.7586 .. 910.3448 cents 27.58621 cents 41.37931 cents 15: 924.1379 .. 951.7241 cents 27.58621 cents 13.79310 cents 16: 993.1034 .. 1020.6897 cents 27.58621 cents 41.37931 cents 17: 1062.0690 .. 1089.6552 cents 27.58621 cents 41.37931 cents 18: 1131.0345 .. 1158.6207 cents 27.58621 cents 41.37931 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 41.37931 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 68.96552 cents Average / Smallest step : 1.526316 Largest / Average step : 1.091954 Largest / Smallest step : 1.666667 Median interval of one step : 68.96552 cents, amount: 15 Most common interval of one step : 68.96552 cents, amount: 15 Least squares average step : 63.43711 cents, oct.: 1205.30504 cents Scale is strictly proper Scale has Myhill's property chromas: 27.58621 cents and 13.79310 cents, ratio: 2.000000 generators: 5 of 317.24138 cents and 14 of 882.75862 cents ET pair of linear temperament : 15&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 87-tone equal temperament with octave 1200.000 cents degrees: 5 10 15 18 23 28 33 36 41 46 51 56 59 64 69 74 79 82 87 generators: 23 and 64 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 87-tone equal temperament Step pattern alph. order: AAABAAABAAAABAAAABA Step pattern size order : LLLSLLLSLLLLSLLLLSL Interval vector is [ 0 0 4 0 15 0 0 8 0 11 0 0 12 0 7 0 0 16 0 3 1 0 18 0 0 5 0 14 0 0 9 0 10 0 0 13 0 6 0 0 17 0 2 ] Scale is a Constant Structure, by a margin of 13.79310 cents Scale diversity : 1.203198 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.586207 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 : 13.79310 cents Most common intervals : 317.24138 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 427.586 882.759 cents Most common triad is 0.0 317.241 882.759 cents, amount: 17 Number of recognisable fifths : 13, average 703.4483 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 : 13 = 68.4211% Limited inverse transpositions : 11 Inversional symmetry on degrees : 15 Inversional symmetry on intervals : 5-6 -- 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: 9.0671 c. M: 17.4229 c. 29: 2 1 2 1 2 1 2 1 2 1 2 2 1 1 2 2 1 1 2 P D3 S SD: 10.9616 c. M:-13.7931 c. 31: 2 2 1 1 2 2 2 1 2 1 2 2 1 2 2 1 2 1 2 P D3 S SD: 10.5371 c. M:-16.9077 c. 34: 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 2 2 1 2 P M ME S SD: 2.5335 c. M:-4.8682 c. 53: 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3 3 3 2 3 SP M ME S SD: 1.6252 c. M: 3.1230 c. 87: 5 5 5 3 5 5 5 3 5 5 5 5 3 5 5 5 5 3 5 SP M DE S 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: 0.7466 cents 3 .. 6 match: 3 H SD: 0.7295 cents 4 .. 8 match: 4 H SD: 4.2918 cents 5 .. 10 match: 5 H SD: 3.4697 cents 6 .. 12 match: 6 H SD: 5.7129 cents 7 .. 14 match: 7 H SD: 5.9838 cents 8 .. 16 match: 8 H SD: 4.3695 cents 9 .. 18 match: 9 H SD: 5.3407 cents 10 .. 20 match: 10 H SD: 5.0249 cents 11 .. 22 match: 11 H SD: 6.1499 cents 12 .. 24 match: 12 H SD: 4.4204 cents 13 .. 26 match: 13 H SD: 5.4682 cents 14 .. 28 match: 14 H SD: 4.7125 cents 15 .. 30 match: 15 H SD: 4.0407 cents 16 .. 32 match: 16 H SD: 3.8475 cents 17 .. 34 match: 16 SD: 5.7604 cents 18 .. 36 match: 17 S SD: 4.1117 cents 19 .. 38 match: 16 SD: 4.9186 cents 20 .. 40 match: 17 SD: 3.2467 cents 21 .. 42 match: 18 S SD: 3.5941 cents 22 .. 44 match: 17 SD: 4.0726 cents 23 .. 46 match: 19 SD: 3.1804 cents 24 .. 48 match: 19 SD: 2.6176 cents 25 .. 50 match: 18 SD: 2.3886 cents 28 .. 56 match: 18 SD: 3.1471 cents 29 .. 58 match: 18 SD: 2.9817 cents 30 .. 60 match: 19 SD: 2.6076 cents 32 .. 64 match: 19 SD: 2.5068 cents 33 .. 66 match: 19 SD: 2.4156 cents 34 .. 68 match: 19 SD: 2.3281 cents 36 .. 72 match: 19 SD: 2.2115 cents 39 .. 78 match: 19 SD: 1.8139 cents 45 .. 90 match: 19 SD: 1.6436 cents 46 .. 92 match: 19 SD: 1.6063 cents 48 .. 96 match: 19 SD: 1.4378 cents 50 .. 100 match: 19 SD: 1.3864 cents 57 .. 114 match: 19 SD: 1.2891 cents 60 .. 120 match: 19 SD: 1.1549 cents 64 .. 128 match: 19 SD: 1.1224 cents 70 .. 140 match: 19 SD: 0.9773 cents 72 .. 144 match: 19 SD: 0.8788 cents 80 .. 160 match: 19 SD: 0.8682 cents 93 .. 186 match: 19 SD: 0.7564 cents 96 .. 192 match: 19 SD: 0.6457 cents 117 .. 234 match: 19 SD: 0.6019 cents 120 .. 240 match: 19 SD: 0.5655 cents 124 .. 248 match: 19 SD: 0.5288 cents 142 .. 284 match: 19 SD: 0.5203 cents 143 .. 286 match: 19 SD: 0.4768 cents 144 .. 288 match: 19 SD: 0.4610 cents 156 .. 312 match: 19 SD: 0.4214 cents 168 .. 336 match: 19 SD: 0.4041 cents 169 .. 338 match: 19 SD: 0.3867 cents 180 .. 360 match: 19 SD: 0.3667 cents 194 .. 388 match: 19 SD: 0.3634 cents 195 .. 390 match: 19 SD: 0.3444 cents 203 .. 406 match: 19 SD: 0.3306 cents 213 .. 426 match: 19 SD: 0.3194 cents 219 .. 438 match: 19 SD: 0.2953 cents 220 .. 440 match: 19 SD: 0.2497 cents 253 .. 506 match: 19 SD: 0.2129 cents 292 .. 584 match: 19 SD: 0.1920 cents 323 .. 646 match: 19 SD: 0.1795 cents 363 .. 726 match: 19 SD: 0.1768 cents 373 .. 746 match: 19 SD: 0.1720 cents 388 .. 776 match: 19 SD: 0.1640 cents 397 .. 794 match: 19 SD: 0.1597 cents 409 .. 818 match: 19 SD: 0.1540 cents 443 .. 886 match: 19 SD: 0.1413 cents 448 .. 896 match: 19 SD: 0.1216 cents 472 .. 944 match: 19 SD: 0.1195 cents 543 .. 1086 match: 19 SD: 0.1192 cents 565 .. 1130 match: 19 SD: 0.1052 cents 592 .. 1184 match: 19 SD: 0.0964 cents