Scala analysis: xen12-hanson-06-basic
Basic group of 19 of 53 tones, Figure 6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.925 cents 67.924528 2: 135.849 cents 135.849057 3: 203.774 cents 203.773585 4: 249.057 cents 249.056604 5: 316.981 cents 316.981132 6: 384.906 cents 384.905660 7: 452.830 cents 452.830189 8: 498.113 cents 498.113208 9: 566.038 cents 566.037736 10: 633.962 cents 633.962264 11: 701.887 cents 701.886792 12: 769.811 cents 769.811321 13: 815.094 cents 815.094340 14: 883.019 cents 883.018868 15: 950.943 cents 950.943396 16: 1018.868 cents 1018.867925 17: 1086.792 cents 1086.792453 18: 1132.075 cents 1132.075472 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 67.9245 cents 67.9245 1: 67.9245 cents 67.9245 2: 67.9245 cents 67.9245 3: 67.9245 cents 67.9245 4: 45.2830 cents 45.2830 5: 67.9245 cents 67.9245 6: 67.9245 cents 67.9245 7: 67.9245 cents 67.9245 8: 45.2830 cents 45.2830 9: 67.9245 cents 67.9245 10: 67.9245 cents 67.9245 11: 67.9245 cents 67.9245 12: 67.9245 cents 67.9245 13: 45.2830 cents 45.2830 14: 67.9245 cents 67.9245 15: 67.9245 cents 67.9245 16: 67.9245 cents 67.9245 17: 67.9245 cents 67.9245 18: 45.2830 cents 45.2830 19: 67.9245 cents 67.9245
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 45.28302 cents 1: 15 67.92453 cents 2: 8 113.20755 cents 2: 11 135.84906 cents 3: 12 181.13208 cents 3: 7 203.77359 cents 4: 16 249.05660 cents 4: 3 271.69811 cents 5: 1 294.33962 cents 5: 18 316.98113 cents 6: 5 362.26415 cents 6: 14 384.90566 cents 7: 9 430.18868 cents 7: 10 452.83019 cents 8: 13 498.11321 cents 8: 6 520.75472 cents 9: 17 566.03774 cents 9: 2 588.67924 cents 10: 2 611.32075 cents 10: 17 633.96226 cents 11: 6 679.24528 cents 11: 13 701.88679 cents 12: 10 747.16981 cents 12: 9 769.81132 cents 13: 14 815.09434 cents 13: 5 837.73585 cents 14: 18 883.01887 cents 14: 1 905.66038 cents 15: 3 928.30189 cents 15: 16 950.94340 cents 16: 7 996.22641 cents 16: 12 1018.86793 cents 17: 11 1064.15094 cents 17: 8 1086.79245 cents 18: 15 1132.07547 cents 18: 4 1154.71698 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 : 67.9 135.8 203.8 249.1 317.0 384.9 452.8 498.1 566.0 634.0 701.9 769.8 815.1 883.0 950.9 1018.9 1086.8 1132.1 1200.0 67.9 : 67.9 135.8 181.1 249.1 317.0 384.9 430.2 498.1 566.0 634.0 701.9 747.2 815.1 883.0 950.9 1018.9 1064.2 1132.1 1200.0 135.8 : 67.9 113.2 181.1 249.1 317.0 362.3 430.2 498.1 566.0 634.0 679.2 747.2 815.1 883.0 950.9 996.2 1064.2 1132.1 1200.0 203.8 : 45.3 113.2 181.1 249.1 294.3 362.3 430.2 498.1 566.0 611.3 679.2 747.2 815.1 883.0 928.3 996.2 1064.2 1132.1 1200.0 249.1 : 67.9 135.8 203.8 249.1 317.0 384.9 452.8 520.8 566.0 634.0 701.9 769.8 837.7 883.0 950.9 1018.9 1086.8 1154.7 1200.0 317.0 : 67.9 135.8 181.1 249.1 317.0 384.9 452.8 498.1 566.0 634.0 701.9 769.8 815.1 883.0 950.9 1018.9 1086.8 1132.1 1200.0 384.9 : 67.9 113.2 181.1 249.1 317.0 384.9 430.2 498.1 566.0 634.0 701.9 747.2 815.1 883.0 950.9 1018.9 1064.2 1132.1 1200.0 452.8 : 45.3 113.2 181.1 249.1 317.0 362.3 430.2 498.1 566.0 634.0 679.2 747.2 815.1 883.0 950.9 996.2 1064.2 1132.1 1200.0 498.1 : 67.9 135.8 203.8 271.7 317.0 384.9 452.8 520.8 588.7 634.0 701.9 769.8 837.7 905.7 950.9 1018.9 1086.8 1154.7 1200.0 566.0 : 67.9 135.8 203.8 249.1 317.0 384.9 452.8 520.8 566.0 634.0 701.9 769.8 837.7 883.0 950.9 1018.9 1086.8 1132.1 1200.0 634.0 : 67.9 135.8 181.1 249.1 317.0 384.9 452.8 498.1 566.0 634.0 701.9 769.8 815.1 883.0 950.9 1018.9 1064.2 1132.1 1200.0 701.9 : 67.9 113.2 181.1 249.1 317.0 384.9 430.2 498.1 566.0 634.0 701.9 747.2 815.1 883.0 950.9 996.2 1064.2 1132.1 1200.0 769.8 : 45.3 113.2 181.1 249.1 317.0 362.3 430.2 498.1 566.0 634.0 679.2 747.2 815.1 883.0 928.3 996.2 1064.2 1132.1 1200.0 815.1 : 67.9 135.8 203.8 271.7 317.0 384.9 452.8 520.8 588.7 634.0 701.9 769.8 837.7 883.0 950.9 1018.9 1086.8 1154.7 1200.0 883.0 : 67.9 135.8 203.8 249.1 317.0 384.9 452.8 520.8 566.0 634.0 701.9 769.8 815.1 883.0 950.9 1018.9 1086.8 1132.1 1200.0 950.9 : 67.9 135.8 181.1 249.1 317.0 384.9 452.8 498.1 566.0 634.0 701.9 747.2 815.1 883.0 950.9 1018.9 1064.2 1132.1 1200.0 1018.9: 67.9 113.2 181.1 249.1 317.0 384.9 430.2 498.1 566.0 634.0 679.2 747.2 815.1 883.0 950.9 996.2 1064.2 1132.1 1200.0 1086.8: 45.3 113.2 181.1 249.1 317.0 362.3 430.2 498.1 566.0 611.3 679.2 747.2 815.1 883.0 928.3 996.2 1064.2 1132.1 1200.0 1132.1: 67.9 135.8 203.8 271.7 317.0 384.9 452.8 520.8 566.0 634.0 701.9 769.8 837.7 883.0 950.9 1018.9 1086.8 1154.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 45.2830 .. 67.9245 cents 22.64151 cents 45.28302 cents 2: 113.2075 .. 135.8491 cents 22.64151 cents 45.28302 cents 3: 181.1321 .. 203.7736 cents 22.64151 cents 45.28302 cents 4: 249.0566 .. 271.6981 cents 22.64151 cents 45.28302 cents 5: 294.3396 .. 316.9811 cents 22.64151 cents 22.64151 cents 6: 362.2642 .. 384.9057 cents 22.64151 cents 45.28302 cents 7: 430.1887 .. 452.8302 cents 22.64151 cents 45.28302 cents 8: 498.1132 .. 520.7547 cents 22.64151 cents 45.28302 cents 9: 566.0377 .. 588.6792 cents 22.64151 cents 45.28302 cents 10: 611.3208 .. 633.9623 cents 22.64151 cents 22.64151 cents 11: 679.2453 .. 701.8868 cents 22.64151 cents 45.28302 cents 12: 747.1698 .. 769.8113 cents 22.64151 cents 45.28302 cents 13: 815.0943 .. 837.7358 cents 22.64151 cents 45.28302 cents 14: 883.0189 .. 905.6604 cents 22.64151 cents 45.28302 cents 15: 928.3019 .. 950.9434 cents 22.64151 cents 22.64151 cents 16: 996.2264 .. 1018.8679 cents 22.64151 cents 45.28302 cents 17: 1064.1509 .. 1086.7925 cents 22.64151 cents 45.28302 cents 18: 1132.0755 .. 1154.7170 cents 22.64151 cents 45.28302 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 45.28302 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 67.92453 cents Average / Smallest step : 1.394737 Largest / Average step : 1.075472 Largest / Smallest step : 1.500000 Median interval of one step : 67.92453 cents, amount: 15 Most common interval of one step : 67.92453 cents, amount: 15 Least squares average step : 63.38706 cents, oct.: 1204.35414 cents Scale is strictly proper Scale has Myhill's property chromas: 22.64151 cents and 22.64151 cents, ratio: 1.000000 generators: 5 of 316.98113 cents and 14 of 883.01887 cents Scale is maximally even in 53-tone equal temperament 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 53-tone equal temperament with octave 1200.000 cents degrees: 3 6 9 11 14 17 20 22 25 28 31 34 36 39 42 45 48 50 53 generators: 14 and 39 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 53-tone equal temperament Step pattern alph. order: AAABAAABAAAABAAAABA Step pattern size order : LLLSLLLSLLLLSLLLLSL Interval vector is [ 0 4 15 0 8 11 0 12 7 0 16 3 1 18 0 5 14 0 9 10 0 13 6 0 17 2 ] Scale is a Constant Structure, by a margin of 22.64151 cents Scale diversity : 1.187979 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.660377 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 : 22.64151 cents Most common intervals : 316.98113 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 430.189 883.019 cents Most common triad is 0.0 316.981 883.019 cents, amount: 17 Number of recognisable fifths : 13, average 701.8868 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: 7.4419 c. M: 14.2999 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: 4.1587 c. M:-7.9911 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: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0341 cents 3 .. 6 match: 3 H SD: 0.4472 cents 4 .. 8 match: 4 H SD: 4.4845 cents 5 .. 10 match: 5 H SD: 3.3275 cents 6 .. 12 match: 6 H SD: 5.8904 cents 7 .. 14 match: 7 H SD: 5.7357 cents 8 .. 16 match: 8 H SD: 4.3075 cents 9 .. 18 match: 9 H SD: 5.1367 cents 10 .. 20 match: 10 H SD: 5.1068 cents 11 .. 22 match: 11 H SD: 6.2620 cents 12 .. 24 match: 12 H SD: 4.5275 cents 13 .. 26 match: 13 H SD: 5.1987 cents 14 .. 28 match: 14 H SD: 4.5118 cents 15 .. 30 match: 15 H SD: 3.9326 cents 16 .. 32 match: 16 H SD: 3.7956 cents 17 .. 34 match: 16 SD: 5.7437 cents 18 .. 36 match: 17 S SD: 3.9489 cents 19 .. 38 match: 16 SD: 4.9933 cents 20 .. 40 match: 18 SD: 3.3384 cents 21 .. 42 match: 18 S SD: 3.6001 cents 22 .. 44 match: 17 SD: 4.1089 cents 23 .. 46 match: 19 SD: 3.2060 cents 24 .. 48 match: 19 SD: 2.5628 cents 28 .. 56 match: 18 SD: 3.0835 cents 29 .. 58 match: 18 SD: 2.9483 cents 30 .. 60 match: 19 SD: 2.4927 cents 33 .. 66 match: 19 SD: 2.4546 cents 34 .. 68 match: 19 SD: 2.2963 cents 36 .. 72 match: 19 SD: 2.2303 cents 39 .. 78 match: 19 SD: 1.9313 cents 40 .. 80 match: 19 SD: 1.7819 cents 45 .. 90 match: 19 SD: 1.6907 cents 46 .. 92 match: 19 SD: 1.6820 cents 47 .. 94 match: 19 SD: 1.6641 cents 48 .. 96 match: 19 SD: 1.4063 cents 50 .. 100 match: 19 SD: 1.2687 cents 63 .. 126 match: 19 SD: 1.2613 cents 64 .. 128 match: 19 SD: 1.0993 cents 70 .. 140 match: 19 SD: 0.9414 cents 72 .. 144 match: 19 SD: 0.9389 cents 80 .. 160 match: 19 SD: 0.8788 cents 90 .. 180 match: 19 SD: 0.7747 cents 96 .. 192 match: 19 SD: 0.6155 cents 120 .. 240 match: 19 SD: 0.4828 cents 144 .. 288 match: 19 SD: 0.4620 cents 150 .. 300 match: 19 SD: 0.3881 cents 168 .. 336 match: 19 SD: 0.3249 cents 220 .. 440 match: 19 SD: 0.3096 cents 224 .. 448 match: 19 SD: 0.3060 cents 245 .. 490 match: 19 SD: 0.2936 cents 246 .. 492 match: 19 SD: 0.2592 cents 258 .. 516 match: 19 SD: 0.2352 cents 298 .. 596 match: 19 SD: 0.1933 cents 318 .. 636 match: 19 SD: 0.1912 cents 328 .. 656 match: 19 SD: 0.1856 cents 354 .. 708 match: 19 SD: 0.1674 cents 394 .. 788 match: 19 SD: 0.1663 cents 402 .. 804 match: 19 SD: 0.1527 cents 418 .. 836 match: 19 SD: 0.1393 cents 466 .. 932 match: 19 SD: 0.1377 cents 478 .. 956 match: 19 SD: 0.1274 cents 502 .. 1004 match: 19 SD: 0.1231 cents 504 .. 1008 match: 19 SD: 0.1166 cents 522 .. 1044 match: 19 SD: 0.1059 cents 600 .. 1200 match: 19 SD: 0.1043 cents