Scala analysis: xen18-erlich-pajara-22
12L 10s MOS for Pajara, L=65.60, s=40.97
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65.600 cents 65.600000 2: 106.570 cents 106.570000 3: 172.170 cents 172.170000 4: 213.140 cents 213.140000 5: 278.740 cents 278.740000 6: 319.710 cents 319.710000 7: 385.310 cents 385.310000 8: 426.280 cents 426.280000 9: 491.880 cents 491.880000 10: 532.850 cents 532.850000 11: 598.450 cents 598.450000 12: 664.050 cents 664.050000 13: 705.020 cents 705.020000 14: 770.620 cents 770.620000 15: 811.590 cents 811.590000 16: 877.190 cents 877.190000 17: 918.160 cents 918.160000 18: 983.760 cents 983.760000 19: 1024.730 cents 1024.730000 20: 1090.330 cents 1090.330000 21: 1131.300 cents 1131.300000 22: 1196.900 cents 1196.900000
SHOW/INTERVAL
0: 65.6000 cents 65.6000 1: 65.6000 cents 65.6000 2: 40.9700 cents 40.9700 3: 65.6000 cents 65.6000 4: 40.9700 cents 40.9700 5: 65.6000 cents 65.6000 6: 40.9700 cents 40.9700 7: 65.6000 cents 65.6000 8: 40.9700 cents 40.9700 9: 65.6000 cents 65.6000 10: 40.9700 cents 40.9700 11: 65.6000 cents 65.6000 12: 65.6000 cents 65.6000 13: 40.9700 cents 40.9700 14: 65.6000 cents 65.6000 15: 40.9700 cents 40.9700 16: 65.6000 cents 65.6000 17: 40.9700 cents 40.9700 18: 65.6000 cents 65.6000 19: 40.9700 cents 40.9700 20: 65.6000 cents 65.6000 21: 40.9700 cents 40.9700 22: 65.6000 cents 65.6000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 40.97000 cents 1: 12 65.60000 cents 2: 20 106.57000 cents 2: 2 131.20000 cents 3: 8 147.54000 cents 3: 14 172.17000 cents 4: 18 213.14000 cents 4: 4 237.77000 cents 5: 6 254.11000 cents 5: 16 278.74000 cents 6: 16 319.71000 cents 6: 6 344.34000 cents 7: 4 360.68000 cents 7: 18 385.31000 cents 8: 14 426.28000 cents 8: 8 450.91000 cents 9: 2 467.25000 cents 9: 20 491.88000 cents 10: 12 532.85000 cents 10: 10 557.48000 cents 11: 22 598.45000 cents 12: 10 639.42000 cents 12: 12 664.05000 cents 13: 20 705.02000 cents 13: 2 729.65000 cents 14: 8 745.99000 cents 14: 14 770.62000 cents 15: 18 811.59000 cents 15: 4 836.22000 cents 16: 6 852.56000 cents 16: 16 877.19000 cents 17: 16 918.16000 cents 17: 6 942.79000 cents 18: 4 959.13000 cents 18: 18 983.76000 cents 19: 14 1024.73000 cents 19: 8 1049.36000 cents 20: 2 1065.70000 cents 20: 20 1090.33000 cents 21: 12 1131.30000 cents 21: 10 1155.93000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.95238 = 41/21
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 0.0 : 65.6 106.6 172.2 213.1 278.7 319.7 385.3 426.3 491.9 532.8 598.4 664.0 705.0 770.6 811.6 877.2 918.2 983.8 1024.7 1090.3 1131.3 1196.9 65.6 : 41.0 106.6 147.5 213.1 254.1 319.7 360.7 426.3 467.2 532.8 598.4 639.4 705.0 746.0 811.6 852.6 918.2 959.1 1024.7 1065.7 1131.3 1196.9 106.6 : 65.6 106.6 172.2 213.1 278.7 319.7 385.3 426.3 491.9 557.5 598.4 664.0 705.0 770.6 811.6 877.2 918.2 983.8 1024.7 1090.3 1155.9 1196.9 172.2 : 41.0 106.6 147.5 213.1 254.1 319.7 360.7 426.3 491.9 532.9 598.4 639.4 705.0 746.0 811.6 852.6 918.2 959.1 1024.7 1090.3 1131.3 1196.9 213.1 : 65.6 106.6 172.2 213.1 278.7 319.7 385.3 450.9 491.9 557.5 598.4 664.1 705.0 770.6 811.6 877.2 918.2 983.8 1049.4 1090.3 1155.9 1196.9 278.7 : 41.0 106.6 147.5 213.1 254.1 319.7 385.3 426.3 491.9 532.8 598.4 639.4 705.0 746.0 811.6 852.6 918.2 983.8 1024.7 1090.3 1131.3 1196.9 319.7 : 65.6 106.6 172.2 213.1 278.7 344.3 385.3 450.9 491.9 557.5 598.4 664.1 705.0 770.6 811.6 877.2 942.8 983.8 1049.4 1090.3 1155.9 1196.9 385.3 : 41.0 106.6 147.5 213.1 278.7 319.7 385.3 426.3 491.9 532.9 598.4 639.4 705.0 746.0 811.6 877.2 918.2 983.8 1024.7 1090.3 1131.3 1196.9 426.3 : 65.6 106.6 172.2 237.8 278.7 344.3 385.3 450.9 491.9 557.5 598.4 664.0 705.0 770.6 836.2 877.2 942.8 983.8 1049.4 1090.3 1155.9 1196.9 491.9 : 41.0 106.6 172.2 213.1 278.7 319.7 385.3 426.3 491.9 532.9 598.4 639.4 705.0 770.6 811.6 877.2 918.2 983.8 1024.7 1090.3 1131.3 1196.9 532.8 : 65.6 131.2 172.2 237.8 278.7 344.3 385.3 450.9 491.9 557.5 598.4 664.1 729.7 770.6 836.2 877.2 942.8 983.8 1049.4 1090.3 1155.9 1196.9 598.4 : 65.6 106.6 172.2 213.1 278.7 319.7 385.3 426.3 491.9 532.8 598.4 664.1 705.0 770.6 811.6 877.2 918.2 983.8 1024.7 1090.3 1131.3 1196.9 664.0 : 41.0 106.6 147.5 213.1 254.1 319.7 360.7 426.3 467.3 532.9 598.5 639.4 705.0 746.0 811.6 852.6 918.2 959.1 1024.7 1065.7 1131.3 1196.9 705.0 : 65.6 106.6 172.2 213.1 278.7 319.7 385.3 426.3 491.9 557.5 598.4 664.1 705.0 770.6 811.6 877.2 918.2 983.8 1024.7 1090.3 1155.9 1196.9 770.6 : 41.0 106.6 147.5 213.1 254.1 319.7 360.7 426.3 491.9 532.9 598.5 639.4 705.0 746.0 811.6 852.6 918.2 959.1 1024.7 1090.3 1131.3 1196.9 811.6 : 65.6 106.6 172.2 213.1 278.7 319.7 385.3 450.9 491.9 557.5 598.5 664.1 705.0 770.6 811.6 877.2 918.2 983.8 1049.4 1090.3 1155.9 1196.9 877.2 : 41.0 106.6 147.5 213.1 254.1 319.7 385.3 426.3 491.9 532.9 598.4 639.4 705.0 746.0 811.6 852.6 918.2 983.8 1024.7 1090.3 1131.3 1196.9 918.2 : 65.6 106.6 172.2 213.1 278.7 344.3 385.3 450.9 491.9 557.5 598.4 664.1 705.0 770.6 811.6 877.2 942.8 983.8 1049.4 1090.3 1155.9 1196.9 983.8 : 41.0 106.6 147.5 213.1 278.7 319.7 385.3 426.3 491.9 532.8 598.4 639.4 705.0 746.0 811.6 877.2 918.2 983.8 1024.7 1090.3 1131.3 1196.9 1024.7: 65.6 106.6 172.2 237.8 278.7 344.3 385.3 450.9 491.9 557.5 598.4 664.1 705.0 770.6 836.2 877.2 942.8 983.8 1049.4 1090.3 1155.9 1196.9 1090.3: 41.0 106.6 172.2 213.1 278.7 319.7 385.3 426.3 491.9 532.9 598.5 639.4 705.0 770.6 811.6 877.2 918.2 983.8 1024.7 1090.3 1131.3 1196.9 1131.3: 65.6 131.2 172.2 237.8 278.7 344.3 385.3 450.9 491.9 557.5 598.4 664.1 729.6 770.6 836.2 877.2 942.8 983.8 1049.4 1090.3 1155.9 1196.9 1196.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.9700 .. 65.6000 cents 24.63000 cents 40.97000 cents 2: 106.5700 .. 131.2000 cents 24.63000 cents 40.97000 cents 3: 147.5400 .. 172.1700 cents 24.63000 cents 16.34000 cents 4: 213.1400 .. 237.7700 cents 24.63000 cents 40.97000 cents 5: 254.1100 .. 278.7400 cents 24.63000 cents 16.34000 cents 6: 319.7100 .. 344.3400 cents 24.63000 cents 40.97000 cents 7: 360.6800 .. 385.3100 cents 24.63000 cents 16.34000 cents 8: 426.2800 .. 450.9100 cents 24.63000 cents 40.97000 cents 9: 467.2500 .. 491.8800 cents 24.63000 cents 16.34000 cents 10: 532.8500 .. 557.4800 cents 24.63000 cents 40.97000 cents 11: 598.4500 .. 598.4500 cents 1/1, 0.0000 cents 40.97000 cents 12: 639.4200 .. 664.0500 cents 24.63000 cents 40.97000 cents 13: 705.0200 .. 729.6500 cents 24.63000 cents 40.97000 cents 14: 745.9900 .. 770.6200 cents 24.63000 cents 16.34000 cents 15: 811.5900 .. 836.2200 cents 24.63000 cents 40.97000 cents 16: 852.5600 .. 877.1900 cents 24.63000 cents 16.34000 cents 17: 918.1600 .. 942.7900 cents 24.63000 cents 40.97000 cents 18: 959.1300 .. 983.7600 cents 24.63000 cents 16.34000 cents 19: 1024.7300 .. 1049.3600 cents 24.63000 cents 40.97000 cents 20: 1065.7000 .. 1090.3300 cents 24.63000 cents 16.34000 cents 21: 1131.3000 .. 1155.9300 cents 24.63000 cents 40.97000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 40.97000 cents, class 1 Average step (divided formal octave): 54.4045 cents Largest one step interval : 65.60000 cents Average / Smallest step : 1.327912 Largest / Average step : 1.205782 Largest / Smallest step : 1.601172 Median interval of one step : 65.60000 cents, amount: 12 Most common interval of one step : 65.60000 cents, amount: 12 Least squares average step : 54.33964 cents, oct.: 1195.47217 cents Scale is strictly proper Scale has 2 repeating blocks of 11 notes Blocks have Myhill's property chromas: 24.63000 cents and 16.34000 cents, ratio: 1.507344 generators: 2 of 106.57000 cents and 9 of 491.88000 cents ET pair of linear temperament : 22&34 Scale is maximally even for L / S <= 2 Scale is distributional even Step pattern alph. order: ABABABABABAABABABABABA Step pattern size order : LSLSLSLSLSLLSLSLSLSLSL Scale is a Constant Structure, by a margin of 16.34000 cents Scale diversity : 1.178318 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.588437 Number of different interval sizes : 41 = 1.95238 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.95238 = 41/21 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 16.34000 cents Most common intervals : 598.45000 cents & inv., amount: 22 Number of recognisable fifths : 20, average 705.0200 cents Number of recognisable fourths : 20, average 491.8800 cents Scale contains two identical disjunct "tetrachords" of 10 notes Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 22 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 11 Limited inverse transpositions : 11 Inversional symmetry on degrees : 0 11 Inversional symmetry on intervals : 5-6 16-17 -- Rational properties --
FIT/MODE
22: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.0806 c. M:-11.1955 c. 34: 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 P B ME I SD: 3.0395 c. M:-4.8059 c. 56: 3 2 3 2 3 2 3 2 3 2 3 3 2 3 2 3 2 3 2 3 2 3 SP B ME I SD: 0.9363 c. M:-1.4804 c. 90: 5 3 5 3 5 3 5 3 5 3 5 5 3 5 3 5 3 5 3 5 3 5 SP B DE I SD: 0.5657 c. M:-0.8944 c. 146: 8 5 8 5 8 5 8 5 8 5 8 8 5 8 5 8 5 8 5 8 5 8 SP B DE I SD: 0.0104 c. M:-0.0164 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 3.1000 cents 2 .. 4 match: 2 H SD: 2.1797 cents 3 .. 6 match: 3 H SD: 3.3168 cents 4 .. 8 match: 4 H SD: 3.8974 cents 5 .. 10 match: 5 H SD: 3.6631 cents 6 .. 12 match: 6 H SD: 4.8764 cents 7 .. 14 match: 7 H SD: 5.5085 cents 8 .. 16 match: 8 H SD: 4.8588 cents 9 .. 18 match: 9 H SD: 4.9973 cents 10 .. 20 match: 10 H SD: 3.9759 cents 11 .. 22 match: 11 H SD: 4.8428 cents 12 .. 24 match: 12 H SD: 4.0883 cents 13 .. 26 match: 13 H SD: 5.8163 cents 14 .. 28 match: 14 H SD: 3.7103 cents 15 .. 30 match: 15 H SD: 3.5780 cents 16 .. 32 match: 16 H SD: 3.7333 cents 17 .. 34 match: 17 H SD: 3.3242 cents 18 .. 36 match: 18 H SD: 3.9120 cents 19 .. 38 match: 16 S SD: 4.1546 cents 20 .. 40 match: 18 S SD: 3.4456 cents 21 .. 42 match: 20 S SD: 3.4322 cents 22 .. 44 match: 19 SD: 3.0728 cents 23 .. 46 match: 19 SD: 3.3707 cents 24 .. 48 match: 21 SD: 2.8091 cents 25 .. 50 match: 21 SD: 2.8513 cents 26 .. 52 match: 19 SD: 2.9858 cents 27 .. 54 match: 21 SD: 2.7589 cents 28 .. 56 match: 22 SD: 2.4175 cents 29 .. 58 match: 21 SD: 2.2926 cents 30 .. 60 match: 22 SD: 1.9468 cents 32 .. 64 match: 21 SD: 2.3018 cents 34 .. 68 match: 21 SD: 2.2773 cents 36 .. 72 match: 22 SD: 1.9028 cents 39 .. 78 match: 21 SD: 1.6755 cents 45 .. 90 match: 22 SD: 1.6655 cents 46 .. 92 match: 22 SD: 1.5412 cents 47 .. 94 match: 22 SD: 1.3777 cents 50 .. 100 match: 22 SD: 1.3734 cents 56 .. 112 match: 22 SD: 1.3294 cents 58 .. 116 match: 22 SD: 1.2585 cents 60 .. 120 match: 22 SD: 1.2106 cents 64 .. 128 match: 22 SD: 1.0108 cents 68 .. 136 match: 22 SD: 0.9738 cents 73 .. 146 match: 22 SD: 0.9718 cents 75 .. 150 match: 22 SD: 0.8348 cents 79 .. 158 match: 22 SD: 0.8318 cents 80 .. 160 match: 22 SD: 0.8305 cents 85 .. 170 match: 22 SD: 0.8279 cents 92 .. 184 match: 22 SD: 0.7770 cents 94 .. 188 match: 22 SD: 0.7363 cents 97 .. 194 match: 22 SD: 0.6090 cents 107 .. 214 match: 22 SD: 0.5869 cents 114 .. 228 match: 22 SD: 0.5699 cents 124 .. 248 match: 22 SD: 0.5299 cents 137 .. 274 match: 22 SD: 0.4965 cents 144 .. 287 match: 22 SD: 0.4789 cents 152 .. 303 match: 22 SD: 0.4609 cents 153 .. 305 match: 22 SD: 0.4064 cents 161 .. 321 match: 22 SD: 0.3929 cents 177 .. 353 match: 22 SD: 0.3700 cents 182 .. 363 match: 22 SD: 0.3640 cents 189 .. 377 match: 22 SD: 0.3152 cents 201 .. 401 match: 22 SD: 0.3148 cents 222 .. 443 match: 22 SD: 0.3122 cents 229 .. 457 match: 22 SD: 0.2940 cents 236 .. 471 match: 22 SD: 0.2903 cents 237 .. 473 match: 22 SD: 0.2528 cents 252 .. 503 match: 22 SD: 0.2467 cents 269 .. 537 match: 22 SD: 0.2307 cents 280 .. 559 match: 22 SD: 0.2162 cents 286 .. 571 match: 22 SD: 0.1881 cents 336 .. 671 match: 22 SD: 0.1750 cents 344 .. 687 match: 22 SD: 0.1376 cents 441 .. 880 match: 22 SD: 0.1327 cents 458 .. 914 match: 22 SD: 0.1287 cents 487 .. 972 match: 22 SD: 0.1255 cents 533 .. 1064 match: 22 SD: 0.1144 cents 565 .. 1128 match: 22 SD: 0.1101 cents 566 .. 1130 match: 22 SD: 0.1090 cents 567 .. 1132 match: 22 SD: 0.1011 cents