Scala analysis: xen12-hanson-11-chain-72
Chain of minor thirds in 72EDO, Figure 11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.667 cents 66.666667 2: 133.333 cents 133.333333 3: 200.000 cents 200.000000 4: 250.000 cents 250.000000 5: 316.667 cents 316.666667 6: 383.333 cents 383.333333 7: 450.000 cents 450.000000 8: 500.000 cents 500.000000 9: 566.667 cents 566.666667 10: 633.333 cents 633.333333 11: 700.000 cents 700.000000 12: 766.667 cents 766.666667 13: 816.667 cents 816.666667 14: 883.333 cents 883.333333 15: 950.000 cents 950.000000 16: 1016.667 cents 1016.666667 17: 1083.333 cents 1083.333333 18: 1133.333 cents 1133.333333 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 66.6667 cents 66.6667 1: 66.6667 cents 66.6667 2: 66.6667 cents 66.6667 3: 66.6667 cents 66.6667 4: 50.0000 cents 50.0000 5: 66.6667 cents 66.6667 6: 66.6667 cents 66.6667 7: 66.6667 cents 66.6667 8: 50.0000 cents 50.0000 9: 66.6667 cents 66.6667 10: 66.6667 cents 66.6667 11: 66.6667 cents 66.6667 12: 66.6667 cents 66.6667 13: 50.0000 cents 50.0000 14: 66.6667 cents 66.6667 15: 66.6667 cents 66.6667 16: 66.6667 cents 66.6667 17: 66.6667 cents 66.6667 18: 50.0000 cents 50.0000 19: 66.6667 cents 66.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 50.00000 cents 1: 15 66.66667 cents 2: 8 116.66667 cents 2: 11 133.33333 cents 3: 12 183.33333 cents 3: 7 200.00000 cents 4: 16 250.00000 cents 4: 3 266.66667 cents 5: 1 300.00000 cents 5: 18 316.66667 cents 6: 5 366.66667 cents 6: 14 383.33333 cents 7: 9 433.33333 cents 7: 10 450.00000 cents 8: 13 500.00000 cents 8: 6 516.66667 cents 9: 17 566.66667 cents 9: 2 583.33333 cents 10: 2 616.66667 cents 10: 17 633.33333 cents 11: 6 683.33333 cents 11: 13 700.00000 cents 12: 10 750.00000 cents 12: 9 766.66667 cents 13: 14 816.66667 cents 13: 5 833.33333 cents 14: 18 883.33333 cents 14: 1 900.00000 cents 15: 3 933.33333 cents 15: 16 950.00000 cents 16: 7 1000.00000 cents 16: 12 1016.66667 cents 17: 11 1066.66667 cents 17: 8 1083.33333 cents 18: 15 1133.33333 cents 18: 4 1150.00000 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 : 66.7 133.3 200.0 250.0 316.7 383.3 450.0 500.0 566.7 633.3 700.0 766.7 816.7 883.3 950.0 1016.7 1083.3 1133.3 1200.0 66.7 : 66.7 133.3 183.3 250.0 316.7 383.3 433.3 500.0 566.7 633.3 700.0 750.0 816.7 883.3 950.0 1016.7 1066.7 1133.3 1200.0 133.3 : 66.7 116.7 183.3 250.0 316.7 366.7 433.3 500.0 566.7 633.3 683.3 750.0 816.7 883.3 950.0 1000.0 1066.7 1133.3 1200.0 200.0 : 50.0 116.7 183.3 250.0 300.0 366.7 433.3 500.0 566.7 616.7 683.3 750.0 816.7 883.3 933.3 1000.0 1066.7 1133.3 1200.0 250.0 : 66.7 133.3 200.0 250.0 316.7 383.3 450.0 516.7 566.7 633.3 700.0 766.7 833.3 883.3 950.0 1016.7 1083.3 1150.0 1200.0 316.7 : 66.7 133.3 183.3 250.0 316.7 383.3 450.0 500.0 566.7 633.3 700.0 766.7 816.7 883.3 950.0 1016.7 1083.3 1133.3 1200.0 383.3 : 66.7 116.7 183.3 250.0 316.7 383.3 433.3 500.0 566.7 633.3 700.0 750.0 816.7 883.3 950.0 1016.7 1066.7 1133.3 1200.0 450.0 : 50.0 116.7 183.3 250.0 316.7 366.7 433.3 500.0 566.7 633.3 683.3 750.0 816.7 883.3 950.0 1000.0 1066.7 1133.3 1200.0 500.0 : 66.7 133.3 200.0 266.7 316.7 383.3 450.0 516.7 583.3 633.3 700.0 766.7 833.3 900.0 950.0 1016.7 1083.3 1150.0 1200.0 566.7 : 66.7 133.3 200.0 250.0 316.7 383.3 450.0 516.7 566.7 633.3 700.0 766.7 833.3 883.3 950.0 1016.7 1083.3 1133.3 1200.0 633.3 : 66.7 133.3 183.3 250.0 316.7 383.3 450.0 500.0 566.7 633.3 700.0 766.7 816.7 883.3 950.0 1016.7 1066.7 1133.3 1200.0 700.0 : 66.7 116.7 183.3 250.0 316.7 383.3 433.3 500.0 566.7 633.3 700.0 750.0 816.7 883.3 950.0 1000.0 1066.7 1133.3 1200.0 766.7 : 50.0 116.7 183.3 250.0 316.7 366.7 433.3 500.0 566.7 633.3 683.3 750.0 816.7 883.3 933.3 1000.0 1066.7 1133.3 1200.0 816.7 : 66.7 133.3 200.0 266.7 316.7 383.3 450.0 516.7 583.3 633.3 700.0 766.7 833.3 883.3 950.0 1016.7 1083.3 1150.0 1200.0 883.3 : 66.7 133.3 200.0 250.0 316.7 383.3 450.0 516.7 566.7 633.3 700.0 766.7 816.7 883.3 950.0 1016.7 1083.3 1133.3 1200.0 950.0 : 66.7 133.3 183.3 250.0 316.7 383.3 450.0 500.0 566.7 633.3 700.0 750.0 816.7 883.3 950.0 1016.7 1066.7 1133.3 1200.0 1016.7: 66.7 116.7 183.3 250.0 316.7 383.3 433.3 500.0 566.7 633.3 683.3 750.0 816.7 883.3 950.0 1000.0 1066.7 1133.3 1200.0 1083.3: 50.0 116.7 183.3 250.0 316.7 366.7 433.3 500.0 566.7 616.7 683.3 750.0 816.7 883.3 933.3 1000.0 1066.7 1133.3 1200.0 1133.3: 66.7 133.3 200.0 266.7 316.7 383.3 450.0 516.7 566.7 633.3 700.0 766.7 833.3 883.3 950.0 1016.7 1083.3 1150.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 50.0000 .. 66.6667 cents 16.66667 cents 50.00000 cents 2: 116.6667 .. 133.3333 cents 16.66667 cents 50.00000 cents 3: 183.3333 .. 200.0000 cents 16.66667 cents 50.00000 cents 4: 250.0000 .. 266.6667 cents 16.66667 cents 50.00000 cents 5: 300.0000 .. 316.6667 cents 16.66667 cents 33.33333 cents 6: 366.6667 .. 383.3333 cents 16.66667 cents 50.00000 cents 7: 433.3333 .. 450.0000 cents 16.66667 cents 50.00000 cents 8: 500.0000 .. 516.6667 cents 16.66667 cents 50.00000 cents 9: 566.6667 .. 583.3333 cents 16.66667 cents 50.00000 cents 10: 616.6667 .. 633.3333 cents 16.66667 cents 33.33333 cents 11: 683.3333 .. 700.0000 cents 16.66667 cents 50.00000 cents 12: 750.0000 .. 766.6667 cents 16.66667 cents 50.00000 cents 13: 816.6667 .. 833.3333 cents 16.66667 cents 50.00000 cents 14: 883.3333 .. 900.0000 cents 16.66667 cents 50.00000 cents 15: 933.3333 .. 950.0000 cents 16.66667 cents 33.33333 cents 16: 1000.0000 .. 1016.6667 cents 16.66667 cents 50.00000 cents 17: 1066.6667 .. 1083.3333 cents 16.66667 cents 50.00000 cents 18: 1133.3333 .. 1150.0000 cents 16.66667 cents 50.00000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 50.00000 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 66.66667 cents Average / Smallest step : 1.263158 Largest / Average step : 1.055556 Largest / Smallest step : 1.333333 Median interval of one step : 66.66667 cents, amount: 15 Most common interval of one step : 66.66667 cents, amount: 15 Least squares average step : 63.32659 cents, oct.: 1203.20513 cents Scale is strictly proper Scale has Myhill's property chromas: 16.66667 cents and 33.33333 cents, ratio: 2.000000 generators: 5 of 316.66667 cents and 14 of 883.33333 cents Scale is maximally even in 72-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 72-tone equal temperament with octave 1200.000 cents degrees: 4 8 12 15 19 23 27 30 34 38 42 46 49 53 57 61 65 68 72 generators: 19 and 53 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 72-tone equal temperament Step pattern alph. order: AAABAAABAAAABAAAABA Step pattern size order : LLLSLLLSLLLLSLLLLSL Interval vector is [ 0 0 4 15 0 0 8 11 0 0 12 7 0 0 16 3 0 1 18 0 0 5 14 0 0 9 10 0 0 13 6 0 0 17 2 0 ] Scale is a Constant Structure, by a margin of 33.33333 cents Scale diversity : 1.152775 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.750000 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 : 16.66667 cents Most common intervals : 316.66667 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 433.333 883.333 cents Most common triad is 0.0 316.667 883.333 cents, amount: 17 Number of recognisable fifths : 13, average 700.0000 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: 5.4781 c. M: 10.5263 c. 48: 3 2 3 2 3 2 3 2 3 2 3 3 2 2 3 3 2 2 3 SP D3 S SD: 6.6227 c. M: 8.3333 c. 50: 3 3 2 2 3 3 3 2 3 2 3 3 2 3 3 2 3 2 3 SP D3 S SD: 6.5266 c. M:-10.6667 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: 1.9638 c. M:-3.7736 c. 72: 4 4 4 3 4 4 4 3 4 4 4 4 3 4 4 4 4 3 4 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: 0.9775 cents 3 .. 6 match: 3 H SD: 0.7359 cents 4 .. 8 match: 4 H SD: 4.7901 cents 5 .. 10 match: 5 H SD: 3.2365 cents 6 .. 12 match: 6 H SD: 6.1517 cents 7 .. 14 match: 7 H SD: 5.5298 cents 8 .. 16 match: 8 H SD: 4.3512 cents 9 .. 18 match: 9 H SD: 4.9821 cents 10 .. 20 match: 10 H SD: 5.2533 cents 11 .. 22 match: 11 H SD: 6.3541 cents 12 .. 24 match: 12 H SD: 4.6904 cents 13 .. 26 match: 13 H SD: 4.9077 cents 14 .. 28 match: 14 H SD: 4.3134 cents 15 .. 30 match: 15 H SD: 3.8606 cents 16 .. 32 match: 16 H SD: 3.7956 cents 17 .. 34 match: 16 SD: 5.6103 cents 18 .. 36 match: 17 S SD: 3.7967 cents 19 .. 38 match: 16 S SD: 5.0414 cents 20 .. 40 match: 18 SD: 3.3648 cents 21 .. 42 match: 18 SD: 3.5716 cents 22 .. 44 match: 17 SD: 4.1898 cents 23 .. 46 match: 19 SD: 3.2178 cents 24 .. 48 match: 19 SD: 2.5682 cents 25 .. 50 match: 19 SD: 2.4964 cents 30 .. 60 match: 19 SD: 2.4212 cents 33 .. 66 match: 19 SD: 2.3952 cents 34 .. 68 match: 19 SD: 2.3373 cents 36 .. 72 match: 19 SD: 2.0754 cents 39 .. 78 match: 19 SD: 2.0696 cents 40 .. 80 match: 19 SD: 1.8387 cents 41 .. 82 match: 19 SD: 1.7893 cents 45 .. 90 match: 19 SD: 1.7077 cents 48 .. 96 match: 19 SD: 1.4459 cents 50 .. 100 match: 19 SD: 1.2543 cents 60 .. 120 match: 19 SD: 1.2501 cents 64 .. 128 match: 19 SD: 1.1810 cents 65 .. 130 match: 19 SD: 1.1261 cents 70 .. 140 match: 19 SD: 1.0835 cents 72 .. 144 match: 19 SD: 1.0449 cents 74 .. 148 match: 19 SD: 0.9788 cents 75 .. 150 match: 19 SD: 0.8093 cents 84 .. 168 match: 19 SD: 0.8082 cents 90 .. 180 match: 19 SD: 0.7108 cents 98 .. 196 match: 19 SD: 0.6604 cents 101 .. 202 match: 19 SD: 0.6512 cents 104 .. 208 match: 19 SD: 0.5684 cents 124 .. 248 match: 19 SD: 0.5398 cents 129 .. 258 match: 19 SD: 0.4144 cents 149 .. 298 match: 19 SD: 0.3489 cents 174 .. 348 match: 19 SD: 0.3409 cents 179 .. 358 match: 19 SD: 0.3393 cents 199 .. 398 match: 19 SD: 0.3187 cents 229 .. 458 match: 19 SD: 0.3159 cents 230 .. 460 match: 19 SD: 0.2969 cents 239 .. 478 match: 19 SD: 0.2710 cents 253 .. 506 match: 19 SD: 0.2481 cents 263 .. 526 match: 19 SD: 0.2392 cents 279 .. 558 match: 19 SD: 0.2379 cents 287 .. 574 match: 19 SD: 0.2285 cents 302 .. 604 match: 19 SD: 0.2245 cents 303 .. 606 match: 19 SD: 0.2237 cents 310 .. 620 match: 19 SD: 0.2101 cents 323 .. 646 match: 19 SD: 0.1966 cents 335 .. 670 match: 19 SD: 0.1750 cents 398 .. 796 match: 19 SD: 0.1583 cents 400 .. 800 match: 19 SD: 0.1571 cents 424 .. 848 match: 19 SD: 0.1363 cents 488 .. 976 match: 19 SD: 0.1191 cents 508 .. 1016 match: 19 SD: 0.1169 cents 553 .. 1106 match: 19 SD: 0.1126 cents 562 .. 1124 match: 19 SD: 0.1068 cents