Scala analysis: xen18-erlich-magic-22
19L 3s MOS for Magic, L=58.88, s=27.52
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.880 cents 58.880000 2: 117.760 cents 117.760000 3: 176.640 cents 176.640000 4: 204.160 cents 204.160000 5: 263.040 cents 263.040000 6: 321.920 cents 321.920000 7: 380.800 cents 380.800000 8: 439.680 cents 439.680000 9: 498.560 cents 498.560000 10: 557.440 cents 557.440000 11: 616.320 cents 616.320000 12: 643.840 cents 643.840000 13: 702.720 cents 702.720000 14: 761.600 cents 761.600000 15: 820.480 cents 820.480000 16: 879.360 cents 879.360000 17: 938.240 cents 938.240000 18: 997.120 cents 997.120000 19: 1024.640 cents 1024.640000 20: 1083.520 cents 1083.520000 21: 1142.400 cents 1142.400000 22: 1201.280 cents 1201.280000
SHOW/INTERVAL
0: 58.8800 cents 58.8800 1: 58.8800 cents 58.8800 2: 58.8800 cents 58.8800 3: 58.8800 cents 58.8800 4: 27.5200 cents 27.5200 5: 58.8800 cents 58.8800 6: 58.8800 cents 58.8800 7: 58.8800 cents 58.8800 8: 58.8800 cents 58.8800 9: 58.8800 cents 58.8800 10: 58.8800 cents 58.8800 11: 58.8800 cents 58.8800 12: 27.5200 cents 27.5200 13: 58.8800 cents 58.8800 14: 58.8800 cents 58.8800 15: 58.8800 cents 58.8800 16: 58.8800 cents 58.8800 17: 58.8800 cents 58.8800 18: 58.8800 cents 58.8800 19: 27.5200 cents 27.5200 20: 58.8800 cents 58.8800 21: 58.8800 cents 58.8800 22: 58.8800 cents 58.8800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 27.52000 cents 1: 19 58.88000 cents 2: 6 86.40000 cents 2: 16 117.76000 cents 3: 9 145.28000 cents 3: 13 176.64000 cents 4: 12 204.16000 cents 4: 10 235.52000 cents 5: 15 263.04000 cents 5: 7 294.40000 cents 6: 18 321.92000 cents 6: 4 353.28000 cents 7: 21 380.80000 cents 7: 1 412.16000 cents 8: 2 408.32000 cents 8: 20 439.68000 cents 9: 5 467.20000 cents 9: 17 498.56000 cents 10: 8 526.08000 cents 10: 14 557.44000 cents 11: 11 584.96000 cents 11: 11 616.32000 cents 12: 14 643.84000 cents 12: 8 675.20000 cents 13: 17 702.72000 cents 13: 5 734.08000 cents 14: 20 761.60000 cents 14: 2 792.96000 cents 15: 1 789.12000 cents 15: 21 820.48000 cents 16: 4 848.00000 cents 16: 18 879.36000 cents 17: 7 906.88000 cents 17: 15 938.24000 cents 18: 10 965.76000 cents 18: 12 997.12000 cents 19: 13 1024.64000 cents 19: 9 1056.00000 cents 20: 16 1083.52000 cents 20: 6 1114.88000 cents 21: 19 1142.40000 cents 21: 3 1173.76000 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 20 21 22 0.0 : 58.9 117.8 176.6 204.2 263.0 321.9 380.8 439.7 498.6 557.4 616.3 643.8 702.7 761.6 820.5 879.4 938.2 997.1 1024.6 1083.5 1142.4 1201.3 58.9 : 58.9 117.8 145.3 204.2 263.0 321.9 380.8 439.7 498.6 557.4 585.0 643.8 702.7 761.6 820.5 879.4 938.2 965.8 1024.6 1083.5 1142.4 1201.3 117.8 : 58.9 86.4 145.3 204.2 263.0 321.9 380.8 439.7 498.6 526.1 585.0 643.8 702.7 761.6 820.5 879.4 906.9 965.8 1024.6 1083.5 1142.4 1201.3 176.6 : 27.5 86.4 145.3 204.2 263.0 321.9 380.8 439.7 467.2 526.1 585.0 643.8 702.7 761.6 820.5 848.0 906.9 965.8 1024.6 1083.5 1142.4 1201.3 204.2 : 58.9 117.8 176.6 235.5 294.4 353.3 412.2 439.7 498.6 557.4 616.3 675.2 734.1 793.0 820.5 879.4 938.2 997.1 1056.0 1114.9 1173.8 1201.3 263.0 : 58.9 117.8 176.6 235.5 294.4 353.3 380.8 439.7 498.6 557.4 616.3 675.2 734.1 761.6 820.5 879.4 938.2 997.1 1056.0 1114.9 1142.4 1201.3 321.9 : 58.9 117.8 176.6 235.5 294.4 321.9 380.8 439.7 498.6 557.4 616.3 675.2 702.7 761.6 820.5 879.4 938.2 997.1 1056.0 1083.5 1142.4 1201.3 380.8 : 58.9 117.8 176.6 235.5 263.0 321.9 380.8 439.7 498.6 557.4 616.3 643.8 702.7 761.6 820.5 879.4 938.2 997.1 1024.6 1083.5 1142.4 1201.3 439.7 : 58.9 117.8 176.6 204.2 263.0 321.9 380.8 439.7 498.6 557.4 585.0 643.8 702.7 761.6 820.5 879.4 938.2 965.8 1024.6 1083.5 1142.4 1201.3 498.6 : 58.9 117.8 145.3 204.2 263.0 321.9 380.8 439.7 498.6 526.1 585.0 643.8 702.7 761.6 820.5 879.4 906.9 965.8 1024.6 1083.5 1142.4 1201.3 557.4 : 58.9 86.4 145.3 204.2 263.0 321.9 380.8 439.7 467.2 526.1 585.0 643.8 702.7 761.6 820.5 848.0 906.9 965.8 1024.6 1083.5 1142.4 1201.3 616.3 : 27.5 86.4 145.3 204.2 263.0 321.9 380.8 408.3 467.2 526.1 585.0 643.8 702.7 761.6 789.1 848.0 906.9 965.8 1024.6 1083.5 1142.4 1201.3 643.8 : 58.9 117.8 176.6 235.5 294.4 353.3 380.8 439.7 498.6 557.4 616.3 675.2 734.1 761.6 820.5 879.4 938.2 997.1 1056.0 1114.9 1173.8 1201.3 702.7 : 58.9 117.8 176.6 235.5 294.4 321.9 380.8 439.7 498.6 557.4 616.3 675.2 702.7 761.6 820.5 879.4 938.2 997.1 1056.0 1114.9 1142.4 1201.3 761.6 : 58.9 117.8 176.6 235.5 263.0 321.9 380.8 439.7 498.6 557.4 616.3 643.8 702.7 761.6 820.5 879.4 938.2 997.1 1056.0 1083.5 1142.4 1201.3 820.5 : 58.9 117.8 176.6 204.2 263.0 321.9 380.8 439.7 498.6 557.4 585.0 643.8 702.7 761.6 820.5 879.4 938.2 997.1 1024.6 1083.5 1142.4 1201.3 879.4 : 58.9 117.8 145.3 204.2 263.0 321.9 380.8 439.7 498.6 526.1 585.0 643.8 702.7 761.6 820.5 879.4 938.2 965.8 1024.6 1083.5 1142.4 1201.3 938.2 : 58.9 86.4 145.3 204.2 263.0 321.9 380.8 439.7 467.2 526.1 585.0 643.8 702.7 761.6 820.5 879.4 906.9 965.8 1024.6 1083.5 1142.4 1201.3 997.1 : 27.5 86.4 145.3 204.2 263.0 321.9 380.8 408.3 467.2 526.1 585.0 643.8 702.7 761.6 820.5 848.0 906.9 965.8 1024.6 1083.5 1142.4 1201.3 1024.6: 58.9 117.8 176.6 235.5 294.4 353.3 380.8 439.7 498.6 557.4 616.3 675.2 734.1 793.0 820.5 879.4 938.2 997.1 1056.0 1114.9 1173.8 1201.3 1083.5: 58.9 117.8 176.6 235.5 294.4 321.9 380.8 439.7 498.6 557.4 616.3 675.2 734.1 761.6 820.5 879.4 938.2 997.1 1056.0 1114.9 1142.4 1201.3 1142.4: 58.9 117.8 176.6 235.5 263.0 321.9 380.8 439.7 498.6 557.4 616.3 675.2 702.7 761.6 820.5 879.4 938.2 997.1 1056.0 1083.5 1142.4 1201.3 1201.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.5200 .. 58.8800 cents 31.36000 cents 27.52000 cents 2: 86.4000 .. 117.7600 cents 31.36000 cents 27.52000 cents 3: 145.2800 .. 176.6400 cents 31.36000 cents 27.52000 cents 4: 204.1600 .. 235.5200 cents 31.36000 cents 27.52000 cents 5: 263.0400 .. 294.4000 cents 31.36000 cents 27.52000 cents 6: 321.9200 .. 353.2800 cents 31.36000 cents 27.52000 cents 7: 380.8000 .. 412.1600 cents 31.36000 cents 27.52000 cents 8: 408.3200 .. 439.6800 cents 31.36000 cents -3.84000 cents 9: 467.2000 .. 498.5600 cents 31.36000 cents 27.52000 cents 10: 526.0800 .. 557.4400 cents 31.36000 cents 27.52000 cents 11: 584.9600 .. 616.3200 cents 31.36000 cents 27.52000 cents 12: 643.8400 .. 675.2000 cents 31.36000 cents 27.52000 cents 13: 702.7200 .. 734.0800 cents 31.36000 cents 27.52000 cents 14: 761.6000 .. 792.9600 cents 31.36000 cents 27.52000 cents 15: 789.1200 .. 820.4800 cents 31.36000 cents -3.84000 cents 16: 848.0000 .. 879.3600 cents 31.36000 cents 27.52000 cents 17: 906.8800 .. 938.2400 cents 31.36000 cents 27.52000 cents 18: 965.7600 .. 997.1200 cents 31.36000 cents 27.52000 cents 19: 1024.6400 .. 1056.0000 cents 31.36000 cents 27.52000 cents 20: 1083.5200 .. 1114.8800 cents 31.36000 cents 27.52000 cents 21: 1142.4000 .. 1173.7600 cents 31.36000 cents 27.52000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 27.52000 cents, class 1 Average step (divided formal octave): 54.6036 cents Largest one step interval : 58.88000 cents Average / Smallest step : 1.984144 Largest / Average step : 1.078316 Largest / Smallest step : 2.139535 Median interval of one step : 58.88000 cents, amount: 19 Most common interval of one step : 58.88000 cents, amount: 19 Least squares average step : 54.61603 cents, oct.: 1201.55270 cents Scale is not proper Scale has Myhill's property chromas: 31.36000 cents and 3.84000 cents, ratio: 8.166667 generators: 7 of 380.80000 cents and 15 of 820.48000 cents ET pair of linear temperament : 19&41 Scale is distributional even Scale is a mode of a 1571-tone equal temperament with octave 1201.280 cents degrees: 77 154 231 267 344 421 498 575 652 729 806 842 919 996 1073 1150 1227 1304 1340 1417 1494 1571 generators: 498 and 1073 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAAAABAAAAAABAAA Step pattern size order : LLLSLLLLLLLSLLLLLLSLLL Scale is a Constant Structure, by a margin of 3.84000 cents Scale diversity : 1.203243 Lumma stability : 0.458178 Lumma impropriety factor : 0.006393 Rothenberg efficiency : 0.696970 redundancy: 0.303030 Efficiency x scale size : 15.333333 Number of different interval sizes : 42 = 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 : 3.84000 cents Most common intervals : 380.80000 cents & inv., amount: 21 Scale is a chain of 11 triads 0.0 204.160 820.480 cents Most common triad is 0.0 380.800 820.480 cents, amount: 20 Number of recognisable fifths : 17, average 702.7200 cents Number of recognisable fourths : 17, average 498.5600 cents Best major thirds form a closed circle Formal octave complements present : 21 = 95.4545% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 15 Inversional symmetry on intervals : 7-8 18-19 -- 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: 9.0715 c. M: 15.6800 c. 37: 2 2 1 1 2 2 2 2 1 2 2 1 2 1 2 2 2 2 1 1 2 2 N D3 SD: 9.3232 c. M: 14.8584 c. 38: 2 2 2 0 2 2 2 2 2 2 1 1 2 2 2 2 2 2 0 2 2 2 N D3 I SD: 9.1980 c. M: 15.6800 c. 39: 2 2 2 1 2 1 2 2 2 2 2 1 2 2 2 2 1 2 1 2 2 2 P D3 SD: 8.8805 c. M: 14.1785 c. 40: 2 2 2 1 2 2 2 2 2 2 2 0 2 2 2 2 2 2 1 2 2 2 N T3 SD: 8.5766 c. M:-14.3520 c. 41: 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 P M ME SD: 0.5960 c. M: 1.0302 c. 183: 9 9 9 4 9 9 9 9 9 9 9 4 9 9 9 9 9 9 4 9 9 9 N M DE SD: 0.4229 c. M:-0.7309 c. 224: 11 11 11 5 11 11 11 11 11 11 11 5 11 11 11 11 11 11 5 11 11 11 N M DE SD: 0.2364 c. M:-0.4086 c. 265: 13 13 13 6 13 13 13 13 13 13 13 6 13 13 13 13 13 13 6 13 13 13 N M DE SD: 0.1076 c. M:-0.1860 c. 306: 15 15 15 7 15 15 15 15 15 15 15 7 15 15 15 15 15 15 7 15 15 15 N M DE SD: 0.0133 c. M:-0.0230 c. 959: 47 47 47 22 47 47 47 47 47 47 47 22 47 47 47 47 47 47 22 47 47 47 N M DE SD: 0.0127 c. M: 0.0220 c. 1265: 62 62 62 29 62 62 62 62 62 62 62 29 62 62 62 62 62 62 29 62 62 62 N M DE SD: 0.0064 c. M: 0.0111 c. 1571: 77 77 77 36 77 77 77 77 77 77 77 36 77 77 77 77 77 77 36 77 77 77 N M DE SD: 0.0026 c. M: 0.0045 c. 1877: 92 92 92 43 92 92 92 92 92 92 92 43 92 92 92 92 92 92 43 92 92 92 N M DE SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 1.2800 cents 2 .. 4 match: 2 H SD: 0.7456 cents 3 .. 6 match: 3 H SD: 1.7285 cents 4 .. 8 match: 4 H SD: 7.2162 cents 5 .. 10 match: 5 H SD: 5.5333 cents 6 .. 12 match: 6 H SD: 4.2602 cents 7 .. 14 match: 7 H SD: 5.2609 cents 8 .. 16 match: 8 H SD: 4.4986 cents 9 .. 18 match: 9 H SD: 3.6534 cents 10 .. 20 match: 10 H SD: 4.7570 cents 11 .. 22 match: 11 H SD: 5.5848 cents 12 .. 24 match: 12 H SD: 4.5450 cents 13 .. 26 match: 13 H SD: 4.4875 cents 14 .. 28 match: 14 H SD: 3.8186 cents 15 .. 30 match: 15 H SD: 3.5496 cents 16 .. 32 match: 16 H SD: 3.8653 cents 17 .. 34 match: 17 H SD: 4.0461 cents 18 .. 36 match: 18 H SD: 2.9219 cents 19 .. 38 match: 18 S SD: 4.7124 cents 20 .. 40 match: 18 SD: 3.4069 cents 21 .. 42 match: 19 SD: 3.3965 cents 22 .. 44 match: 20 SD: 3.8260 cents 23 .. 46 match: 20 SD: 3.5301 cents 24 .. 48 match: 20 SD: 2.2924 cents 25 .. 50 match: 20 SD: 2.9149 cents 26 .. 52 match: 21 SD: 2.7502 cents 27 .. 54 match: 20 SD: 2.8491 cents 28 .. 56 match: 22 SD: 2.6187 cents 29 .. 58 match: 21 SD: 2.3207 cents 30 .. 60 match: 22 SD: 2.1904 cents 31 .. 62 match: 22 SD: 2.0954 cents 32 .. 64 match: 21 SD: 2.1878 cents 33 .. 66 match: 21 SD: 2.2528 cents 34 .. 68 match: 20 SD: 2.5583 cents 35 .. 70 match: 21 SD: 2.2188 cents 36 .. 72 match: 22 SD: 2.0835 cents 38 .. 76 match: 22 SD: 1.8333 cents 40 .. 80 match: 22 SD: 1.8024 cents 41 .. 82 match: 21 SD: 2.0721 cents 42 .. 84 match: 21 SD: 1.6488 cents 43 .. 86 match: 21 SD: 2.1264 cents 44 .. 88 match: 22 SD: 1.7421 cents 45 .. 90 match: 22 SD: 1.5496 cents 48 .. 96 match: 22 SD: 1.4743 cents 53 .. 106 match: 22 SD: 1.3232 cents 54 .. 108 match: 22 SD: 1.1709 cents 56 .. 112 match: 22 SD: 0.9845 cents 73 .. 146 match: 22 SD: 0.9584 cents 74 .. 148 match: 22 SD: 0.9140 cents 82 .. 164 match: 22 SD: 0.8024 cents 84 .. 168 match: 22 SD: 0.8006 cents 86 .. 172 match: 22 SD: 0.7313 cents 94 .. 188 match: 22 SD: 0.7214 cents 103 .. 206 match: 22 SD: 0.6799 cents 110 .. 220 match: 22 SD: 0.5920 cents 114 .. 228 match: 22 SD: 0.5103 cents 138 .. 276 match: 22 SD: 0.4826 cents 142 .. 284 match: 22 SD: 0.4270 cents 166 .. 332 match: 22 SD: 0.3758 cents 171 .. 342 match: 22 SD: 0.3732 cents 176 .. 352 match: 22 SD: 0.3566 cents 195 .. 390 match: 22 SD: 0.3433 cents 200 .. 400 match: 22 SD: 0.3368 cents 201 .. 402 match: 22 SD: 0.3364 cents 208 .. 416 match: 22 SD: 0.3313 cents 213 .. 426 match: 22 SD: 0.3257 cents 215 .. 430 match: 22 SD: 0.3133 cents 224 .. 448 match: 22 SD: 0.2503 cents 231 .. 462 match: 22 SD: 0.2336 cents 288 .. 576 match: 22 SD: 0.2275 cents 297 .. 594 match: 22 SD: 0.2087 cents 317 .. 634 match: 22 SD: 0.2050 cents 318 .. 636 match: 22 SD: 0.1971 cents 342 .. 685 match: 22 SD: 0.1681 cents 353 .. 707 match: 22 SD: 0.1224 cents 456 .. 913 match: 22 SD: 0.1210 cents 524 .. 1049 match: 22 SD: 0.1199 cents 529 .. 1059 match: 22 SD: 0.1195 cents 566 .. 1133 match: 22 SD: 0.1129 cents 577 .. 1155 match: 22 SD: 0.1008 cents 597 .. 1195 match: 22 SD: 0.0937 cents