Scala analysis: xen12-hanson-11-chain-34
Chain of minor thirds in 34EDO, Figure 11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 70.588 cents 70.588235 2: 141.176 cents 141.176471 3: 211.765 cents 211.764706 4: 247.059 cents 247.058824 5: 317.647 cents 317.647059 6: 388.235 cents 388.235294 7: 458.824 cents 458.823529 8: 494.118 cents 494.117647 9: 564.706 cents 564.705882 10: 635.294 cents 635.294118 11: 705.882 cents 705.882353 12: 776.471 cents 776.470588 13: 811.765 cents 811.764706 14: 882.353 cents 882.352941 15: 952.941 cents 952.941176 16: 1023.529 cents 1023.529412 17: 1094.118 cents 1094.117647 18: 1129.412 cents 1129.411765 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 70.5882 cents 70.5882 1: 70.5882 cents 70.5882 2: 70.5882 cents 70.5882 3: 70.5882 cents 70.5882 4: 35.2941 cents 35.2941 5: 70.5882 cents 70.5882 6: 70.5882 cents 70.5882 7: 70.5882 cents 70.5882 8: 35.2941 cents 35.2941 9: 70.5882 cents 70.5882 10: 70.5882 cents 70.5882 11: 70.5882 cents 70.5882 12: 70.5882 cents 70.5882 13: 35.2941 cents 35.2941 14: 70.5882 cents 70.5882 15: 70.5882 cents 70.5882 16: 70.5882 cents 70.5882 17: 70.5882 cents 70.5882 18: 35.2941 cents 35.2941 19: 70.5882 cents 70.5882
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 35.29412 cents 1: 15 70.58824 cents 2: 8 105.88235 cents 2: 11 141.17647 cents 3: 12 176.47059 cents 3: 7 211.76471 cents 4: 16 247.05882 cents 4: 3 282.35294 cents 5: 1 282.35294 cents 5: 18 317.64706 cents 6: 5 352.94118 cents 6: 14 388.23529 cents 7: 9 423.52941 cents 7: 10 458.82353 cents 8: 13 494.11765 cents 8: 6 529.41176 cents 9: 17 564.70588 cents 9: 2 600.00000 cents 10: 2 600.00000 cents 10: 17 635.29412 cents 11: 6 670.58824 cents 11: 13 705.88235 cents 12: 10 741.17647 cents 12: 9 776.47059 cents 13: 14 811.76471 cents 13: 5 847.05882 cents 14: 18 882.35294 cents 14: 1 917.64706 cents 15: 3 917.64706 cents 15: 16 952.94118 cents 16: 7 988.23529 cents 16: 12 1023.52941 cents 17: 11 1058.82353 cents 17: 8 1094.11765 cents 18: 15 1129.41176 cents 18: 4 1164.70588 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 : 70.6 141.2 211.8 247.1 317.6 388.2 458.8 494.1 564.7 635.3 705.9 776.5 811.8 882.4 952.9 1023.5 1094.1 1129.4 1200.0 70.6 : 70.6 141.2 176.5 247.1 317.6 388.2 423.5 494.1 564.7 635.3 705.9 741.2 811.8 882.4 952.9 1023.5 1058.8 1129.4 1200.0 141.2 : 70.6 105.9 176.5 247.1 317.6 352.9 423.5 494.1 564.7 635.3 670.6 741.2 811.8 882.4 952.9 988.2 1058.8 1129.4 1200.0 211.8 : 35.3 105.9 176.5 247.1 282.4 352.9 423.5 494.1 564.7 600.0 670.6 741.2 811.8 882.4 917.6 988.2 1058.8 1129.4 1200.0 247.1 : 70.6 141.2 211.8 247.1 317.6 388.2 458.8 529.4 564.7 635.3 705.9 776.5 847.1 882.4 952.9 1023.5 1094.1 1164.7 1200.0 317.6 : 70.6 141.2 176.5 247.1 317.6 388.2 458.8 494.1 564.7 635.3 705.9 776.5 811.8 882.4 952.9 1023.5 1094.1 1129.4 1200.0 388.2 : 70.6 105.9 176.5 247.1 317.6 388.2 423.5 494.1 564.7 635.3 705.9 741.2 811.8 882.4 952.9 1023.5 1058.8 1129.4 1200.0 458.8 : 35.3 105.9 176.5 247.1 317.6 352.9 423.5 494.1 564.7 635.3 670.6 741.2 811.8 882.4 952.9 988.2 1058.8 1129.4 1200.0 494.1 : 70.6 141.2 211.8 282.4 317.6 388.2 458.8 529.4 600.0 635.3 705.9 776.5 847.1 917.6 952.9 1023.5 1094.1 1164.7 1200.0 564.7 : 70.6 141.2 211.8 247.1 317.6 388.2 458.8 529.4 564.7 635.3 705.9 776.5 847.1 882.4 952.9 1023.5 1094.1 1129.4 1200.0 635.3 : 70.6 141.2 176.5 247.1 317.6 388.2 458.8 494.1 564.7 635.3 705.9 776.5 811.8 882.4 952.9 1023.5 1058.8 1129.4 1200.0 705.9 : 70.6 105.9 176.5 247.1 317.6 388.2 423.5 494.1 564.7 635.3 705.9 741.2 811.8 882.4 952.9 988.2 1058.8 1129.4 1200.0 776.5 : 35.3 105.9 176.5 247.1 317.6 352.9 423.5 494.1 564.7 635.3 670.6 741.2 811.8 882.4 917.6 988.2 1058.8 1129.4 1200.0 811.8 : 70.6 141.2 211.8 282.4 317.6 388.2 458.8 529.4 600.0 635.3 705.9 776.5 847.1 882.4 952.9 1023.5 1094.1 1164.7 1200.0 882.4 : 70.6 141.2 211.8 247.1 317.6 388.2 458.8 529.4 564.7 635.3 705.9 776.5 811.8 882.4 952.9 1023.5 1094.1 1129.4 1200.0 952.9 : 70.6 141.2 176.5 247.1 317.6 388.2 458.8 494.1 564.7 635.3 705.9 741.2 811.8 882.4 952.9 1023.5 1058.8 1129.4 1200.0 1023.5: 70.6 105.9 176.5 247.1 317.6 388.2 423.5 494.1 564.7 635.3 670.6 741.2 811.8 882.4 952.9 988.2 1058.8 1129.4 1200.0 1094.1: 35.3 105.9 176.5 247.1 317.6 352.9 423.5 494.1 564.7 600.0 670.6 741.2 811.8 882.4 917.6 988.2 1058.8 1129.4 1200.0 1129.4: 70.6 141.2 211.8 282.4 317.6 388.2 458.8 529.4 564.7 635.3 705.9 776.5 847.1 882.4 952.9 1023.5 1094.1 1164.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.2941 .. 70.5882 cents 35.29412 cents 35.29412 cents 2: 105.8824 .. 141.1765 cents 35.29412 cents 35.29412 cents 3: 176.4706 .. 211.7647 cents 35.29412 cents 35.29412 cents 4: 247.0588 .. 282.3529 cents 35.29412 cents 35.29412 cents 5: 282.3529 .. 317.6471 cents 35.29412 cents 1/1, 0.0000 cents 6: 352.9412 .. 388.2353 cents 35.29412 cents 35.29412 cents 7: 423.5294 .. 458.8235 cents 35.29412 cents 35.29412 cents 8: 494.1176 .. 529.4118 cents 35.29412 cents 35.29412 cents 9: 564.7059 .. 600.0000 cents 35.29412 cents 35.29412 cents 10: 600.0000 .. 635.2941 cents 35.29412 cents 1/1, 0.0000 cents 11: 670.5882 .. 705.8824 cents 35.29412 cents 35.29412 cents 12: 741.1765 .. 776.4706 cents 35.29412 cents 35.29412 cents 13: 811.7647 .. 847.0588 cents 35.29412 cents 35.29412 cents 14: 882.3529 .. 917.6471 cents 35.29412 cents 35.29412 cents 15: 917.6471 .. 952.9412 cents 35.29412 cents 1/1, 0.0000 cents 16: 988.2353 .. 1023.5294 cents 35.29412 cents 35.29412 cents 17: 1058.8235 .. 1094.1176 cents 35.29412 cents 35.29412 cents 18: 1129.4118 .. 1164.7059 cents 35.29412 cents 35.29412 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 35.29412 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 70.58824 cents Average / Smallest step : 1.789474 Largest / Average step : 1.117647 Largest / Smallest step : 2.000000 Median interval of one step : 70.58824 cents, amount: 15 Most common interval of one step : 70.58824 cents, amount: 15 Least squares average step : 63.51512 cents, oct.: 1206.78733 cents Scale is proper Scale has Myhill's property chromas: 35.29412 cents and 0.00000 cents, ratio: 35294132.658931 generators: 5 of 317.64706 cents and 14 of 882.35294 cents Scale is maximally even in 34-tone equal temperament ET pair of linear temperament : 15&34 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 34-tone equal temperament with octave 1200.000 cents degrees: 2 4 6 7 9 11 13 14 16 18 20 22 23 25 27 29 31 32 34 generators: 9 and 25 Number of contiguous 1-step segments: 4 Scale is fully connected major-minor triadic in 34-tone equal temperament Step pattern alph. order: AAABAAABAAAABAAAABA Step pattern size order : LLLSLLLSLLLLSLLLLSL Interval vector is [ 4 15 8 11 12 7 16 4 18 5 14 9 10 13 6 17 2 ] Scale is not a Constant Structure Scale diversity : 1.197634 Rothenberg stability : 0.964912 = 55/57 Lumma stability : 0.470588 Number of different interval sizes : 33 = 1.83333 / 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 : 35.29412 cents Most common intervals : 317.64706 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 423.529 882.353 cents Most common triad is 0.0 317.647 882.353 cents, amount: 17 Number of recognisable fifths : 13, average 705.8824 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: 11.6006 c. M: 22.2910 c. 27: 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 2 2 0 2 N D3 SD: 13.1849 c. M: 20.9150 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: 11.4066 c. M: 18.2556 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: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.9637 cents 3 .. 6 match: 3 H SD: 1.4700 cents 4 .. 8 match: 4 H SD: 4.1189 cents 5 .. 10 match: 5 H SD: 3.7946 cents 6 .. 12 match: 6 H SD: 5.5145 cents 7 .. 14 match: 7 H SD: 6.4905 cents 8 .. 16 match: 8 H SD: 4.6333 cents 9 .. 18 match: 9 H SD: 5.7771 cents 10 .. 20 match: 10 H SD: 4.9322 cents 11 .. 22 match: 11 H SD: 6.0218 cents 12 .. 24 match: 12 H SD: 4.3081 cents 13 .. 26 match: 13 H SD: 5.8969 cents 14 .. 28 match: 14 H SD: 5.0813 cents 15 .. 30 match: 15 H SD: 4.2019 cents 16 .. 32 match: 16 H SD: 3.9533 cents 17 .. 34 match: 16 SD: 5.8385 cents 18 .. 36 match: 17 SD: 4.3893 cents 19 .. 38 match: 15 SD: 4.7216 cents 20 .. 40 match: 17 SD: 3.2182 cents 21 .. 42 match: 17 S SD: 3.6368 cents 22 .. 44 match: 17 SD: 3.9653 cents 23 .. 46 match: 19 SD: 3.1590 cents 24 .. 48 match: 18 SD: 2.5459 cents 25 .. 50 match: 18 SD: 2.5288 cents 27 .. 54 match: 18 SD: 2.6279 cents 28 .. 56 match: 17 SD: 3.0464 cents 29 .. 58 match: 18 SD: 3.0706 cents 30 .. 60 match: 19 SD: 2.6340 cents 32 .. 64 match: 19 SD: 2.4978 cents 33 .. 66 match: 19 SD: 2.3480 cents 35 .. 70 match: 18 SD: 2.6464 cents 36 .. 72 match: 19 SD: 2.2314 cents 39 .. 78 match: 19 SD: 1.7772 cents 45 .. 90 match: 19 SD: 1.4693 cents 52 .. 104 match: 19 SD: 1.3727 cents 59 .. 118 match: 19 SD: 1.3404 cents 60 .. 120 match: 19 SD: 1.1000 cents 69 .. 138 match: 19 SD: 1.0706 cents 70 .. 140 match: 19 SD: 0.9830 cents 72 .. 144 match: 19 SD: 0.9075 cents 83 .. 166 match: 19 SD: 0.8585 cents 90 .. 180 match: 19 SD: 0.8297 cents 92 .. 184 match: 19 SD: 0.7891 cents 93 .. 186 match: 19 SD: 0.7215 cents 99 .. 198 match: 19 SD: 0.5767 cents 115 .. 230 match: 19 SD: 0.5617 cents 119 .. 238 match: 19 SD: 0.5565 cents 124 .. 248 match: 19 SD: 0.5377 cents 139 .. 278 match: 19 SD: 0.4700 cents 145 .. 290 match: 19 SD: 0.4696 cents 155 .. 310 match: 19 SD: 0.4374 cents 163 .. 326 match: 19 SD: 0.4310 cents 164 .. 328 match: 19 SD: 0.4022 cents 169 .. 338 match: 19 SD: 0.3950 cents 184 .. 368 match: 19 SD: 0.3873 cents 187 .. 374 match: 19 SD: 0.3399 cents 191 .. 382 match: 19 SD: 0.3374 cents 214 .. 428 match: 19 SD: 0.2913 cents 215 .. 430 match: 19 SD: 0.2875 cents 239 .. 478 match: 19 SD: 0.2837 cents 247 .. 494 match: 19 SD: 0.2816 cents 248 .. 496 match: 19 SD: 0.2672 cents 260 .. 520 match: 19 SD: 0.2517 cents 286 .. 572 match: 19 SD: 0.2367 cents 293 .. 586 match: 19 SD: 0.2011 cents 314 .. 628 match: 19 SD: 0.1981 cents 338 .. 676 match: 19 SD: 0.1960 cents 339 .. 678 match: 19 SD: 0.1682 cents 378 .. 756 match: 19 SD: 0.1643 cents 413 .. 826 match: 19 SD: 0.1643 cents 433 .. 866 match: 19 SD: 0.1498 cents 438 .. 876 match: 19 SD: 0.1380 cents 481 .. 962 match: 19 SD: 0.1360 cents 505 .. 1010 match: 19 SD: 0.1324 cents 508 .. 1016 match: 19 SD: 0.1320 cents 521 .. 1042 match: 19 SD: 0.1156 cents 530 .. 1060 match: 19 SD: 0.1051 cents 576 .. 1152 match: 19 SD: 0.1032 cents 600 .. 1200 match: 19 SD: 0.0869 cents