Scala analysis: meanquar_19
19 of 1/4-comma meantone scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.049 cents 76.049000 2: 117.108 cents 117.107860 3: 193.157 cents 193.156860 4: 269.206 cents 269.205860 5: 310.265 cents 310.264710 6: 5/4 386.313714 major third 7: 462.363 cents 462.362710 8: 503.422 cents 503.421570 9: 579.471 cents 579.470570 10: 620.529 cents 620.529430 11: 696.578 cents 696.578430 12: 25/16 772.627428 classic augmented fifth 13: 8/5 813.686286 minor sixth 14: 889.735 cents 889.735290 15: 965.784 cents 965.784280 16: 1006.843 cents 1006.843140 17: 1082.892 cents 1082.892140 18: 125/64 1158.941142 classic augmented seventh, octave - minor diesis 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 128/125 41.0589 minor diesis, diesis 1: 76.0490 cents 76.0490 2: 41.0589 cents 41.0589 3: 76.0490 cents 76.0490 4: 76.0490 cents 76.0490 5: 41.0588 cents 41.0588 6: 76.0490 cents 76.0490 7: 76.0490 cents 76.0490 8: 41.0589 cents 41.0589 9: 76.0490 cents 76.0490 10: 41.0589 cents 41.0589 11: 76.0490 cents 76.0490 12: 76.0490 cents 76.0490 13: 128/125 41.0589 minor diesis, diesis 14: 76.0490 cents 76.0490 15: 76.0490 cents 76.0490 16: 41.0589 cents 41.0589 17: 76.0490 cents 76.0490 18: 76.0490 cents 76.0490 19: 128/125 41.0589 minor diesis, diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 41.05886 cents 1: 12 76.04900 cents 2: 14 117.10786 cents 2: 5 152.09800 cents 3: 2 158.16672 cents 3: 17 193.15686 cents 4: 9 234.21571 cents 4: 10 269.20586 cents 5: 16 310.26471 cents 5: 3 345.25485 cents 6: 4 351.32357 cents 6: 15 5/4 386.314 cents major third 7: 11 427.37257 cents 7: 8 462.36271 cents 8: 18 503.42157 cents 8: 1 538.41171 cents 9: 6 544.48043 cents 9: 13 579.47057 cents 10: 13 620.52943 cents 10: 6 655.51957 cents 11: 1 661.58829 cents 11: 18 696.57843 cents 12: 8 737.63729 cents 12: 11 25/16 772.627 cents classic augmented fifth 13: 15 8/5 813.686 cents minor sixth 13: 4 848.67642 cents 14: 3 854.74515 cents 14: 16 889.73529 cents 15: 10 930.79414 cents 15: 9 965.78428 cents 16: 17 1006.84314 cents 16: 2 1041.83328 cents 17: 5 1047.90200 cents 17: 14 1082.89214 cents 18: 12 1123.95100 cents 18: 7 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 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 : 76.0 117.1 193.2 269.2 310.3 386.3 462.4 503.4 579.5 620.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1158.9 1200.0 76.0 : 41.1 117.1 193.2 234.2 310.3 386.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 117.1 : 76.0 152.1 193.2 269.2 345.3 386.3 462.4 503.4 579.5 655.5 696.6 772.6 848.7 889.7 965.8 1041.8 1082.9 1158.9 1200.0 193.2 : 76.0 117.1 193.2 269.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1124.0 1200.0 269.2 : 41.1 117.1 193.2 234.2 310.3 351.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1047.9 1124.0 1200.0 310.3 : 76.0 152.1 193.2 269.2 310.3 386.3 462.4 503.4 579.5 655.5 696.6 772.6 848.7 889.7 965.8 1006.8 1082.9 1158.9 1200.0 386.3 : 76.0 117.1 193.2 234.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 772.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 462.4 : 41.1 117.1 158.2 234.2 310.3 351.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 854.7 930.8 1006.8 1047.9 1124.0 1200.0 503.4 : 76.0 117.1 193.2 269.2 310.3 386.3 462.4 503.4 579.5 655.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1158.9 1200.0 579.5 : 41.1 117.1 193.2 234.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 620.5 : 76.0 152.1 193.2 269.2 345.3 386.3 462.4 538.4 579.5 655.5 696.6 772.6 848.7 889.7 965.8 1041.8 1082.9 1158.9 1200.0 696.6 : 76.0 117.1 193.2 269.2 310.3 386.3 462.4 503.4 579.5 620.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1124.0 1200.0 772.6 : 41.1 117.1 193.2 234.2 310.3 386.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1047.9 1124.0 1200.0 813.7 : 76.0 152.1 193.2 269.2 345.3 386.3 462.4 503.4 579.5 655.5 696.6 772.6 848.7 889.7 965.8 1006.8 1082.9 1158.9 1200.0 889.7 : 76.0 117.1 193.2 269.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 772.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 965.8 : 41.1 117.1 193.2 234.2 310.3 351.3 427.4 503.4 544.5 620.5 696.6 737.6 813.7 854.7 930.8 1006.8 1047.9 1124.0 1200.0 1006.8: 76.0 152.1 193.2 269.2 310.3 386.3 462.4 503.4 579.5 655.5 696.6 772.6 813.7 889.7 965.8 1006.8 1082.9 1158.9 1200.0 1082.9: 76.0 117.1 193.2 234.2 310.3 386.3 427.4 503.4 579.5 620.5 696.6 737.6 813.7 889.7 930.8 1006.8 1082.9 1124.0 1200.0 1158.9: 41.1 117.1 158.2 234.2 310.3 351.3 427.4 503.4 544.5 620.5 661.6 737.6 813.7 854.7 930.8 1006.8 1047.9 1124.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 76.0490 cents 34.99014 cents 41.05886 cents 2: 117.1079 .. 152.0980 cents 34.99014 cents 41.05886 cents 3: 158.1667 .. 193.1569 cents 34.99014 cents 6.06872 cents 4: 234.2157 .. 269.2059 cents 34.99015 cents 41.05885 cents 5: 310.2647 .. 345.2548 cents 34.99014 cents 41.05885 cents 6: 351.3236 .. 386.3137 cents 34.99014 cents 6.06872 cents 7: 427.3726 .. 462.3627 cents 34.99014 cents 41.05886 cents 8: 503.4216 .. 538.4117 cents 34.99014 cents 41.05886 cents 9: 544.4804 .. 579.4706 cents 34.99014 cents 6.06872 cents 10: 620.5294 .. 655.5196 cents 34.99014 cents 41.05886 cents 11: 661.5883 .. 696.5784 cents 34.99014 cents 6.06872 cents 12: 737.6373 .. 772.6274 cents 34.99014 cents 41.05886 cents 13: 813.6863 .. 848.6764 cents 34.99013 cents 128/125, 41.0589 cents 14: 854.7452 .. 889.7353 cents 34.99014 cents 6.06873 cents 15: 930.7941 .. 965.7843 cents 34.99014 cents 41.05885 cents 16: 1006.8431 .. 1041.8333 cents 34.99014 cents 41.05886 cents 17: 1047.9020 .. 1082.8921 cents 34.99014 cents 6.06872 cents 18: 1123.9510 .. 1158.9411 cents 34.99014 cents 41.05886 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 41.05885 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 76.04900 cents Average / Smallest step : 1.538229 Largest / Average step : 1.204109 Largest / Smallest step : 1.852195 Median interval of one step : 76.04900 cents, amount: 12 Most common interval of one step : 76.04900 cents, amount: 12 Least squares average step : 63.62537 cents, oct.: 1208.88211 cents Scale is strictly proper Scale has Myhill's property chromas: 34.99014 cents and 6.06872 cents, ratio: 5.765654 generators: 8 of 503.42157 cents and 11 of 696.57843 cents ET pair of linear temperament : 12&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 789-tone equal temperament with octave 2/1 degrees: 50 77 127 177 204 254 304 331 381 408 458 508 535 585 635 662 712 762 789 generators: 331 and 458 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABABAABAABAAB Step pattern size order : LSLLSLLSLSLLSLLSLLS Scale is a Constant Structure, by a margin of 6.06872 cents Ratio Whole / Half tone : 1.649393 Scale diversity : 1.183334 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.475148 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 : 6.06872 cents Most common intervals : 503.42157 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 503.422 1006.843 cents Most common triad is 0.0 503.422 696.578 cents, amount: 17 Number of recognisable fifths : 18, average 696.5784 cents Scale contains two identical disjunct "tetrachords" of 9 notes Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 5 Formal octave complements present : 13 = 68.4211% Limited inverse transpositions : 9 Inversional symmetry on degrees : 14 Inversional symmetry on intervals : 4-5 -- Rational properties -- Prime limit : 5 (not all pitches rational)
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: 11.5007 c. M: 22.0990 c. 27: 2 1 1 2 1 2 1 1 2 1 2 1 1 2 2 1 1 2 1 P D3 S SD: 12.0151 c. M: 17.9183 c. 29: 2 1 2 2 1 1 2 1 2 1 2 2 1 2 1 1 2 2 1 P D3 SD: 11.9439 c. M:-20.7698 c. 30: 2 1 2 2 1 2 2 1 2 1 1 2 1 2 2 1 2 2 1 N D3 S SD: 11.8367 c. M:-20.5294 c. 31: 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 2 2 1 P M ME S SD: 1.2226 c. M:-2.3492 c. 112: 7 4 7 7 4 7 7 4 7 4 7 7 4 7 7 4 7 7 4 SP M DE S SD: 0.9359 c. M: 1.7983 c. 143: 9 5 9 9 5 9 9 5 9 5 9 9 5 9 9 5 9 9 5 SP M DE S SD: 0.4679 c. M: 0.8992 c. 174: 11 6 11 11 6 11 11 6 11 6 11 11 6 11 11 6 11 11 6 SP M DE S SD: 0.1668 c. M: 0.3205 c. 205: 13 7 13 13 7 13 13 7 13 7 13 13 7 13 13 7 13 13 7 SP M DE S SD: 0.0433 c. M:-0.0832 c. 584: 37 20 37 37 20 37 37 20 37 20 37 37 20 37 37 20 37 37 20 SP M DE S SD: 0.0193 c. M: 0.0370 c. 789: 50 27 50 50 27 50 50 27 50 27 50 50 27 50 50 27 50 50 27 SP M DE S SD: 0.0030 c. M: 0.0058 c. 1783: 113 61 113 113 61 113 113 61 113 61 113 113 61 113 113 61 113 113 61 SP M DE S SD: 0.0023 c. M:-0.0045 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 2.6883 cents 3 .. 6 match: 3 H SD: 2.5345 cents 4 .. 8 match: 4 H SD: 1.5443 cents 5 .. 10 match: 5 H SD: 2.4802 cents 6 .. 12 match: 6 H SD: 5.8128 cents 7 .. 14 match: 7 H SD: 8.4365 cents 8 .. 16 match: 8 H SD: 5.1474 cents 9 .. 18 match: 9 H SD: 5.3478 cents 10 .. 20 match: 10 H SD: 5.1755 cents 11 .. 22 match: 11 H SD: 8.4639 cents 12 .. 24 match: 12 H SD: 4.8494 cents 13 .. 26 match: 13 H SD: 5.8999 cents 14 .. 28 match: 14 H SD: 5.6404 cents 15 .. 30 match: 15 H SD: 4.2204 cents 16 .. 32 match: 16 H SD: 3.4839 cents 17 .. 34 match: 14 SD: 4.5693 cents 18 .. 36 match: 16 S SD: 3.7426 cents 19 .. 38 match: 15 SD: 4.0354 cents 20 .. 40 match: 18 SD: 3.3701 cents 21 .. 42 match: 17 SD: 4.0030 cents 22 .. 44 match: 16 SD: 4.4180 cents 23 .. 46 match: 19 SD: 3.1611 cents 24 .. 48 match: 17 SD: 2.6784 cents 25 .. 50 match: 18 SD: 2.4746 cents 27 .. 54 match: 18 SD: 2.6432 cents 28 .. 56 match: 17 SD: 2.4134 cents 33 .. 66 match: 18 SD: 2.6467 cents 34 .. 68 match: 18 SD: 2.9249 cents 35 .. 70 match: 18 SD: 2.1792 cents 39 .. 78 match: 19 SD: 2.1203 cents 40 .. 80 match: 19 SD: 1.7943 cents 41 .. 82 match: 19 SD: 1.7771 cents 42 .. 84 match: 19 SD: 1.5772 cents 48 .. 96 match: 19 SD: 1.4599 cents 53 .. 106 match: 19 SD: 1.4510 cents 58 .. 116 match: 19 SD: 1.4361 cents 59 .. 118 match: 19 SD: 1.3371 cents 60 .. 120 match: 19 SD: 1.0269 cents 68 .. 136 match: 19 SD: 0.9834 cents 71 .. 142 match: 19 SD: 0.9061 cents 83 .. 166 match: 19 SD: 0.7887 cents 85 .. 170 match: 19 SD: 0.7245 cents 95 .. 190 match: 19 SD: 0.7239 cents 101 .. 202 match: 19 SD: 0.7004 cents 107 .. 214 match: 19 SD: 0.6816 cents 111 .. 222 match: 19 SD: 0.6804 cents 112 .. 224 match: 19 SD: 0.6169 cents 113 .. 226 match: 19 SD: 0.5757 cents 127 .. 254 match: 19 SD: 0.5571 cents 128 .. 256 match: 19 SD: 0.4831 cents 137 .. 274 match: 19 SD: 0.4700 cents 143 .. 286 match: 19 SD: 0.4684 cents 153 .. 306 match: 19 SD: 0.3786 cents 183 .. 366 match: 19 SD: 0.3677 cents 202 .. 404 match: 19 SD: 0.3565 cents 204 .. 408 match: 19 SD: 0.3247 cents 213 .. 426 match: 19 SD: 0.3126 cents 228 .. 456 match: 19 SD: 0.2695 cents 244 .. 488 match: 19 SD: 0.2445 cents 272 .. 544 match: 19 SD: 0.2391 cents 285 .. 570 match: 19 SD: 0.2272 cents 297 .. 594 match: 19 SD: 0.2006 cents 327 .. 654 match: 19 SD: 0.1946 cents 332 .. 664 match: 19 SD: 0.1832 cents 356 .. 712 match: 19 SD: 0.1813 cents 357 .. 714 match: 19 SD: 0.1669 cents 427 .. 854 match: 19 SD: 0.1501 cents 448 .. 896 match: 19 SD: 0.1358 cents 468 .. 936 match: 19 SD: 0.1306 cents 515 .. 1030 match: 19 SD: 0.1203 cents 533 .. 1066 match: 19 SD: 0.1202 cents 559 .. 1118 match: 19 SD: 0.1179 cents 576 .. 1152 match: 19 SD: 0.1130 cents