Scala analysis: xen18-erlich-meantone-19
12L 7s MOS for Meantone, L=76.19, s=41.06
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.190 cents 76.190000 2: 117.250 cents 117.250000 3: 193.440 cents 193.440000 4: 269.630 cents 269.630000 5: 310.690 cents 310.690000 6: 386.880 cents 386.880000 7: 427.940 cents 427.940000 8: 504.130 cents 504.130000 9: 580.320 cents 580.320000 10: 621.380 cents 621.380000 11: 697.570 cents 697.570000 12: 773.760 cents 773.760000 13: 814.820 cents 814.820000 14: 891.010 cents 891.010000 15: 932.070 cents 932.070000 16: 1008.260 cents 1008.260000 17: 1084.450 cents 1084.450000 18: 1125.510 cents 1125.510000 19: 1201.700 cents 1201.700000
SHOW/INTERVAL
0: 76.1900 cents 76.1900 1: 76.1900 cents 76.1900 2: 41.0600 cents 41.0600 3: 76.1900 cents 76.1900 4: 76.1900 cents 76.1900 5: 41.0600 cents 41.0600 6: 76.1900 cents 76.1900 7: 41.0600 cents 41.0600 8: 76.1900 cents 76.1900 9: 76.1900 cents 76.1900 10: 41.0600 cents 41.0600 11: 76.1900 cents 76.1900 12: 76.1900 cents 76.1900 13: 41.0600 cents 41.0600 14: 76.1900 cents 76.1900 15: 41.0600 cents 41.0600 16: 76.1900 cents 76.1900 17: 76.1900 cents 76.1900 18: 41.0600 cents 41.0600 19: 76.1900 cents 76.1900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 41.06000 cents 1: 12 76.19000 cents 2: 14 117.25000 cents 2: 5 152.38000 cents 3: 2 158.31000 cents 3: 17 193.44000 cents 4: 9 234.50000 cents 4: 10 269.63000 cents 5: 16 310.69000 cents 5: 3 345.82000 cents 6: 4 351.75000 cents 6: 15 386.88000 cents 7: 11 427.94000 cents 7: 8 463.07000 cents 8: 18 504.13000 cents 8: 1 539.26000 cents 9: 6 545.19000 cents 9: 13 580.32000 cents 10: 13 621.38000 cents 10: 6 656.51000 cents 11: 1 662.44000 cents 11: 18 697.57000 cents 12: 8 738.63000 cents 12: 11 773.76000 cents 13: 15 814.82000 cents 13: 4 849.95000 cents 14: 3 855.88000 cents 14: 16 891.01000 cents 15: 10 932.07000 cents 15: 9 967.20000 cents 16: 17 1008.26000 cents 16: 2 1043.39000 cents 17: 5 1049.32000 cents 17: 14 1084.45000 cents 18: 12 1125.51000 cents 18: 7 1160.64000 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 : 76.2 117.3 193.4 269.6 310.7 386.9 427.9 504.1 580.3 621.4 697.6 773.8 814.8 891.0 932.1 1008.3 1084.5 1125.5 1201.7 76.2 : 41.1 117.3 193.4 234.5 310.7 351.8 427.9 504.1 545.2 621.4 697.6 738.6 814.8 855.9 932.1 1008.3 1049.3 1125.5 1201.7 117.3 : 76.2 152.4 193.4 269.6 310.7 386.9 463.1 504.1 580.3 656.5 697.6 773.8 814.8 891.0 967.2 1008.3 1084.4 1160.6 1201.7 193.4 : 76.2 117.3 193.4 234.5 310.7 386.9 427.9 504.1 580.3 621.4 697.6 738.6 814.8 891.0 932.1 1008.3 1084.4 1125.5 1201.7 269.6 : 41.1 117.3 158.3 234.5 310.7 351.8 427.9 504.1 545.2 621.4 662.4 738.6 814.8 855.9 932.1 1008.3 1049.3 1125.5 1201.7 310.7 : 76.2 117.3 193.4 269.6 310.7 386.9 463.1 504.1 580.3 621.4 697.6 773.8 814.8 891.0 967.2 1008.3 1084.4 1160.6 1201.7 386.9 : 41.1 117.3 193.4 234.5 310.7 386.9 427.9 504.1 545.2 621.4 697.6 738.6 814.8 891.0 932.1 1008.3 1084.5 1125.5 1201.7 427.9 : 76.2 152.4 193.4 269.6 345.8 386.9 463.1 504.1 580.3 656.5 697.6 773.8 849.9 891.0 967.2 1043.4 1084.4 1160.6 1201.7 504.1 : 76.2 117.3 193.4 269.6 310.7 386.9 427.9 504.1 580.3 621.4 697.6 773.8 814.8 891.0 967.2 1008.3 1084.4 1125.5 1201.7 580.3 : 41.1 117.3 193.4 234.5 310.7 351.7 427.9 504.1 545.2 621.4 697.6 738.6 814.8 891.0 932.1 1008.3 1049.3 1125.5 1201.7 621.4 : 76.2 152.4 193.4 269.6 310.7 386.9 463.1 504.1 580.3 656.5 697.6 773.8 849.9 891.0 967.2 1008.3 1084.4 1160.6 1201.7 697.6 : 76.2 117.3 193.4 234.5 310.7 386.9 427.9 504.1 580.3 621.4 697.6 773.8 814.8 891.0 932.1 1008.3 1084.4 1125.5 1201.7 773.8 : 41.1 117.3 158.3 234.5 310.7 351.7 427.9 504.1 545.2 621.4 697.6 738.6 814.8 855.9 932.1 1008.3 1049.3 1125.5 1201.7 814.8 : 76.2 117.3 193.4 269.6 310.7 386.9 463.1 504.1 580.3 656.5 697.6 773.8 814.8 891.0 967.2 1008.3 1084.4 1160.6 1201.7 891.0 : 41.1 117.2 193.4 234.5 310.7 386.9 427.9 504.1 580.3 621.4 697.6 738.6 814.8 891.0 932.1 1008.3 1084.4 1125.5 1201.7 932.1 : 76.2 152.4 193.4 269.6 345.8 386.9 463.1 539.3 580.3 656.5 697.6 773.8 849.9 891.0 967.2 1043.4 1084.4 1160.6 1201.7 1008.3: 76.2 117.3 193.4 269.6 310.7 386.9 463.1 504.1 580.3 621.4 697.6 773.8 814.8 891.0 967.2 1008.3 1084.5 1125.5 1201.7 1084.5: 41.1 117.2 193.4 234.5 310.7 386.9 427.9 504.1 545.2 621.4 697.6 738.6 814.8 891.0 932.1 1008.3 1049.3 1125.5 1201.7 1125.5: 76.2 152.4 193.4 269.6 345.8 386.9 463.1 504.1 580.3 656.5 697.6 773.8 849.9 891.0 967.2 1008.3 1084.4 1160.6 1201.7 1201.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0600 .. 76.1900 cents 35.13000 cents 41.06000 cents 2: 117.2500 .. 152.3800 cents 35.13000 cents 41.06000 cents 3: 158.3100 .. 193.4400 cents 35.13000 cents 5.93000 cents 4: 234.5000 .. 269.6300 cents 35.13000 cents 41.06000 cents 5: 310.6900 .. 345.8200 cents 35.13000 cents 41.06000 cents 6: 351.7500 .. 386.8800 cents 35.13000 cents 5.93000 cents 7: 427.9400 .. 463.0700 cents 35.13000 cents 41.06000 cents 8: 504.1300 .. 539.2600 cents 35.13000 cents 41.06000 cents 9: 545.1900 .. 580.3200 cents 35.13000 cents 5.93000 cents 10: 621.3800 .. 656.5100 cents 35.13000 cents 41.06000 cents 11: 662.4400 .. 697.5700 cents 35.13000 cents 5.93000 cents 12: 738.6300 .. 773.7600 cents 35.13000 cents 41.06000 cents 13: 814.8200 .. 849.9500 cents 35.13000 cents 41.06000 cents 14: 855.8800 .. 891.0100 cents 35.13000 cents 5.93000 cents 15: 932.0700 .. 967.2000 cents 35.13000 cents 41.06000 cents 16: 1008.2600 .. 1043.3900 cents 35.13000 cents 41.06000 cents 17: 1049.3200 .. 1084.4500 cents 35.13000 cents 5.93000 cents 18: 1125.5100 .. 1160.6400 cents 35.13000 cents 41.06000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 41.06000 cents, class 1 Average step (divided formal octave): 63.2474 cents Largest one step interval : 76.19000 cents Average / Smallest step : 1.540365 Largest / Average step : 1.204635 Largest / Smallest step : 1.855577 Median interval of one step : 76.19000 cents, amount: 12 Most common interval of one step : 76.19000 cents, amount: 12 Least squares average step : 63.14781 cents, oct.: 1199.80838 cents Scale is strictly proper Scale has Myhill's property chromas: 35.13000 cents and 5.93000 cents, ratio: 5.924115 generators: 8 of 504.13000 cents and 11 of 697.57000 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 2224-tone equal temperament with octave 1201.700 cents degrees: 141 217 358 499 575 716 792 933 1074 1150 1291 1432 1508 1649 1725 1866 2007 2083 2224 generators: 933 and 1291 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABAABABAABA Step pattern size order : LSLLSLSLLSLLSLSLLSL Scale is a Constant Structure, by a margin of 5.93000 cents Scale diversity : 1.181917 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.473795 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 : 5.93000 cents Most common intervals : 504.13000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 504.130 1008.260 cents Most common triad is 0.0 504.130 697.570 cents, amount: 17 Number of recognisable fifths : 18, average 697.5700 cents Number of recognisable fourths : 18, average 504.1300 cents Scale contains two identical conjunct "tetrachords" of 9 notes Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 19 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- 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: 10.1271 c. M: 16.6405 c. 31: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2 P M ME I SD: 1.0477 c. M: 1.7216 c. 112: 7 4 7 7 4 7 4 7 7 4 7 7 4 7 4 7 7 4 7 SP M DE I SD: 0.8480 c. M: 1.3934 c. 143: 9 5 9 9 5 9 5 9 9 5 9 9 5 9 5 9 9 5 9 SP M DE I SD: 0.4370 c. M: 0.7181 c. 174: 11 6 11 11 6 11 6 11 11 6 11 11 6 11 6 11 11 6 11 SP M DE I SD: 0.1725 c. M: 0.2834 c. 205: 13 7 13 13 7 13 7 13 13 7 13 13 7 13 7 13 13 7 13 SP M DE I SD: 0.0120 c. M: 0.0198 c. 1404: 89 48 89 89 48 89 48 89 89 48 89 89 48 89 48 89 89 48 89 SP M DE I SD: 0.0108 c. M: 0.0178 c. 1609: 102 55 102 102 55 102 55 102 102 55 102 102 55 102 55 102 102 55 102 SP M DE I SD: 0.0079 c. M: 0.0130 c. 1814: 115 62 115 115 62 115 62 115 115 62 115 115 62 115 62 115 115 62 115 SP M DE I SD: 0.0057 c. M: 0.0093 c. 2019: 128 69 128 128 69 128 69 128 128 69 128 128 69 128 69 128 128 69 128 SP M DE I SD: 0.0039 c. M: 0.0064 c. 2224: 141 76 141 141 76 141 76 141 141 76 141 141 76 141 76 141 141 76 141 SP M DE I SD: 0.0024 c. M: 0.0040 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 1.7000 cents 2 .. 4 match: 2 H SD: 2.3515 cents 3 .. 6 match: 3 H SD: 3.0579 cents 4 .. 8 match: 4 H SD: 9.2650 cents 5 .. 10 match: 5 H SD: 2.1969 cents 6 .. 12 match: 6 H SD: 6.1058 cents 7 .. 14 match: 7 H SD: 5.9467 cents 8 .. 16 match: 8 H SD: 6.8461 cents 9 .. 18 match: 9 H SD: 5.3149 cents 10 .. 20 match: 10 H SD: 4.4988 cents 11 .. 22 match: 11 H SD: 7.1668 cents 12 .. 24 match: 12 H SD: 5.1758 cents 13 .. 26 match: 13 H SD: 6.2717 cents 14 .. 28 match: 14 H SD: 4.6048 cents 15 .. 30 match: 15 H SD: 4.2821 cents 16 .. 32 match: 15 SD: 4.3157 cents 17 .. 34 match: 15 SD: 4.7325 cents 18 .. 36 match: 16 S SD: 3.4034 cents 19 .. 38 match: 14 SD: 4.8337 cents 20 .. 40 match: 18 S SD: 3.8316 cents 21 .. 42 match: 17 SD: 3.6713 cents 22 .. 44 match: 17 SD: 4.2341 cents 23 .. 46 match: 18 SD: 3.4568 cents 24 .. 48 match: 17 SD: 2.6124 cents 25 .. 50 match: 19 SD: 2.3694 cents 26 .. 52 match: 18 SD: 3.1328 cents 27 .. 54 match: 18 SD: 2.8961 cents 28 .. 56 match: 19 SD: 2.6184 cents 30 .. 60 match: 18 SD: 2.4484 cents 32 .. 64 match: 19 SD: 2.3535 cents 33 .. 66 match: 18 SD: 2.6935 cents 34 .. 68 match: 18 SD: 2.8280 cents 35 .. 70 match: 18 SD: 2.0246 cents 40 .. 80 match: 19 SD: 1.8390 cents 42 .. 84 match: 19 SD: 1.5963 cents 48 .. 96 match: 19 SD: 1.5398 cents 53 .. 106 match: 19 SD: 1.3804 cents 60 .. 120 match: 19 SD: 0.9865 cents 67 .. 134 match: 19 SD: 0.9847 cents 71 .. 142 match: 19 SD: 0.8472 cents 83 .. 166 match: 19 SD: 0.7160 cents 85 .. 170 match: 19 SD: 0.7115 cents 101 .. 202 match: 19 SD: 0.6814 cents 111 .. 222 match: 19 SD: 0.6276 cents 113 .. 226 match: 19 SD: 0.6054 cents 125 .. 250 match: 19 SD: 0.5957 cents 128 .. 256 match: 19 SD: 0.5312 cents 143 .. 286 match: 19 SD: 0.4505 cents 153 .. 306 match: 19 SD: 0.3341 cents 203 .. 406 match: 19 SD: 0.3320 cents 213 .. 426 match: 19 SD: 0.3277 cents 220 .. 440 match: 19 SD: 0.3263 cents 224 .. 448 match: 19 SD: 0.3213 cents 238 .. 476 match: 19 SD: 0.3108 cents 239 .. 478 match: 19 SD: 0.2969 cents 243 .. 486 match: 19 SD: 0.2693 cents 271 .. 543 match: 19 SD: 0.2529 cents 286 .. 573 match: 19 SD: 0.2402 cents 296 .. 593 match: 19 SD: 0.1774 cents 331 .. 663 match: 19 SD: 0.1725 cents 356 .. 713 match: 19 SD: 0.1626 cents 439 .. 879 match: 19 SD: 0.1591 cents 443 .. 887 match: 19 SD: 0.1534 cents 447 .. 895 match: 19 SD: 0.1385 cents 467 .. 935 match: 19 SD: 0.1315 cents 474 .. 949 match: 19 SD: 0.1272 cents 488 .. 977 match: 19 SD: 0.1266 cents 514 .. 1029 match: 19 SD: 0.1256 cents 556 .. 1113 match: 19 SD: 0.1202 cents 559 .. 1119 match: 19 SD: 0.1057 cents 600 .. 1201 match: 19 SD: 0.0916 cents