Scala analysis: xen18-erlich-magic-16
3L 13s MOS for Magic, L=145.28, s=58.88
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: 263.040 cents 263.040000 4: 321.920 cents 321.920000 5: 380.800 cents 380.800000 6: 439.680 cents 439.680000 7: 498.560 cents 498.560000 8: 557.440 cents 557.440000 9: 702.720 cents 702.720000 10: 761.600 cents 761.600000 11: 820.480 cents 820.480000 12: 879.360 cents 879.360000 13: 938.240 cents 938.240000 14: 1083.520 cents 1083.520000 15: 1142.400 cents 1142.400000 16: 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: 145.2800 cents 145.2800 4: 58.8800 cents 58.8800 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: 145.2800 cents 145.2800 10: 58.8800 cents 58.8800 11: 58.8800 cents 58.8800 12: 58.8800 cents 58.8800 13: 58.8800 cents 58.8800 14: 145.2800 cents 145.2800 15: 58.8800 cents 58.8800 16: 58.8800 cents 58.8800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 58.88000 cents 1: 3 145.28000 cents 2: 10 117.76000 cents 2: 6 204.16000 cents 3: 7 176.64000 cents 3: 9 263.04000 cents 4: 4 235.52000 cents 4: 12 321.92000 cents 5: 1 294.40000 cents 5: 15 380.80000 cents 6: 14 439.68000 cents 6: 2 526.08000 cents 7: 11 498.56000 cents 7: 5 584.96000 cents 8: 8 557.44000 cents 8: 8 643.84000 cents 9: 5 616.32000 cents 9: 11 702.72000 cents 10: 2 675.20000 cents 10: 14 761.60000 cents 11: 15 820.48000 cents 11: 1 906.88000 cents 12: 12 879.36000 cents 12: 4 965.76000 cents 13: 9 938.24000 cents 13: 7 1024.64000 cents 14: 6 997.12000 cents 14: 10 1083.52000 cents 15: 3 1056.00000 cents 15: 13 1142.40000 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 0.0 : 58.9 117.8 263.0 321.9 380.8 439.7 498.6 557.4 702.7 761.6 820.5 879.4 938.2 1083.5 1142.4 1201.3 58.9 : 58.9 204.2 263.0 321.9 380.8 439.7 498.6 643.8 702.7 761.6 820.5 879.4 1024.6 1083.5 1142.4 1201.3 117.8 : 145.3 204.2 263.0 321.9 380.8 439.7 585.0 643.8 702.7 761.6 820.5 965.8 1024.6 1083.5 1142.4 1201.3 263.0 : 58.9 117.8 176.6 235.5 294.4 439.7 498.6 557.4 616.3 675.2 820.5 879.4 938.2 997.1 1056.0 1201.3 321.9 : 58.9 117.8 176.6 235.5 380.8 439.7 498.6 557.4 616.3 761.6 820.5 879.4 938.2 997.1 1142.4 1201.3 380.8 : 58.9 117.8 176.6 321.9 380.8 439.7 498.6 557.4 702.7 761.6 820.5 879.4 938.2 1083.5 1142.4 1201.3 439.7 : 58.9 117.8 263.0 321.9 380.8 439.7 498.6 643.8 702.7 761.6 820.5 879.4 1024.6 1083.5 1142.4 1201.3 498.6 : 58.9 204.2 263.0 321.9 380.8 439.7 585.0 643.8 702.7 761.6 820.5 965.8 1024.6 1083.5 1142.4 1201.3 557.4 : 145.3 204.2 263.0 321.9 380.8 526.1 585.0 643.8 702.7 761.6 906.9 965.8 1024.6 1083.5 1142.4 1201.3 702.7 : 58.9 117.8 176.6 235.5 380.8 439.7 498.6 557.4 616.3 761.6 820.5 879.4 938.2 997.1 1056.0 1201.3 761.6 : 58.9 117.8 176.6 321.9 380.8 439.7 498.6 557.4 702.7 761.6 820.5 879.4 938.2 997.1 1142.4 1201.3 820.5 : 58.9 117.8 263.0 321.9 380.8 439.7 498.6 643.8 702.7 761.6 820.5 879.4 938.2 1083.5 1142.4 1201.3 879.4 : 58.9 204.2 263.0 321.9 380.8 439.7 585.0 643.8 702.7 761.6 820.5 879.4 1024.6 1083.5 1142.4 1201.3 938.2 : 145.3 204.2 263.0 321.9 380.8 526.1 585.0 643.8 702.7 761.6 820.5 965.8 1024.6 1083.5 1142.4 1201.3 1083.5: 58.9 117.8 176.6 235.5 380.8 439.7 498.6 557.4 616.3 675.2 820.5 879.4 938.2 997.1 1056.0 1201.3 1142.4: 58.9 117.8 176.6 321.9 380.8 439.7 498.6 557.4 616.3 761.6 820.5 879.4 938.2 997.1 1142.4 1201.3 1201.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.8800 .. 145.2800 cents 86.40000 cents 58.88000 cents 2: 117.7600 .. 204.1600 cents 86.40000 cents -27.52000 cents 3: 176.6400 .. 263.0400 cents 86.40000 cents -27.52000 cents 4: 235.5200 .. 321.9200 cents 86.40000 cents -27.52000 cents 5: 294.4000 .. 380.8000 cents 86.40000 cents -27.52000 cents 6: 439.6800 .. 526.0800 cents 86.40000 cents 58.88000 cents 7: 498.5600 .. 584.9600 cents 86.40000 cents -27.52000 cents 8: 557.4400 .. 643.8400 cents 86.40000 cents -27.52000 cents 9: 616.3200 .. 702.7200 cents 86.40000 cents -27.52000 cents 10: 675.2000 .. 761.6000 cents 86.40000 cents -27.52000 cents 11: 820.4800 .. 906.8800 cents 86.40000 cents 58.88000 cents 12: 879.3600 .. 965.7600 cents 86.40000 cents -27.52000 cents 13: 938.2400 .. 1024.6400 cents 86.40000 cents -27.52000 cents 14: 997.1200 .. 1083.5200 cents 86.40000 cents -27.52000 cents 15: 1056.0000 .. 1142.4000 cents 86.40000 cents -27.52000 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 58.88000 cents, class 1 Average step (divided formal octave): 75.0800 cents Largest one step interval : 145.28000 cents Average / Smallest step : 1.275136 Largest / Average step : 1.935003 Largest / Smallest step : 2.467391 Median interval of one step : 58.88000 cents, amount: 13 Most common interval of one step : 58.88000 cents, amount: 13 Least squares average step : 74.93561 cents, oct.: 1198.96984 cents Scale is not proper Scale has Myhill's property chromas: 86.40000 cents and 27.52000 cents, ratio: 3.139535 generators: 5 of 380.80000 cents and 11 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: 77 154 344 421 498 575 652 729 919 996 1073 1150 1227 1417 1494 1571 generators: 498 and 1073 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAAABAAAABAA Step pattern size order : SSLSSSSSLSSSSLSS Scale is a Constant Structure, by a margin of 27.52000 cents Scale diversity : 1.193387 Lumma stability : 0.196058 Lumma impropriety factor : 0.274907 Rothenberg efficiency : 0.708333 redundancy: 0.291667 Efficiency x scale size : 11.333333 Number of different interval sizes : 30 = 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 : 27.52000 cents Most common intervals : 380.80000 cents & inv., amount: 15 Scale is a chain of 8 triads 0.0 263.040 820.480 cents Most common triad is 0.0 380.800 820.480 cents, amount: 14 Number of recognisable fifths : 11, average 702.7200 cents Number of recognisable fourths : 11, average 498.5600 cents Formal octave complements present : 15 = 93.7500% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 13-14 -- Rational properties --
FIT/MODE
16: 1 0 2 1 1 1 0 1 2 1 1 0 1 2 1 1 N T3 SD: 29.4641 c. M: 53.4800 c. 17: 1 1 2 1 0 1 1 1 2 1 1 0 1 2 1 1 N SD: 19.7256 c. M:-31.3976 c. 18: 1 1 2 1 0 1 1 1 2 1 1 1 1 2 1 1 N T3 SD: 23.2039 c. M: 47.1111 c. 19: 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 P M ME SD: 6.7161 c. M:-11.5874 c. 22: 1 1 3 1 1 1 1 1 3 1 1 1 1 3 1 1 N M DE SD: 6.6096 c. M: 11.4036 c. 41: 2 2 5 2 2 2 2 2 5 2 2 2 2 5 2 2 N M DE SD: 0.4343 c. M: 0.7493 c. 183: 9 9 22 9 9 9 9 9 22 9 9 9 9 22 9 9 N M DE SD: 0.3081 c. M:-0.5316 c. 224: 11 11 27 11 11 11 11 11 27 11 11 11 11 27 11 11 N M DE SD: 0.1722 c. M:-0.2971 c. 265: 13 13 32 13 13 13 13 13 32 13 13 13 13 32 13 13 N M DE SD: 0.0784 c. M:-0.1352 c. 306: 15 15 37 15 15 15 15 15 37 15 15 15 15 37 15 15 N M DE SD: 0.0097 c. M:-0.0167 c. 959: 47 47 116 47 47 47 47 47 116 47 47 47 47 116 47 47 N M DE SD: 0.0093 c. M: 0.0160 c. 1265: 62 62 153 62 62 62 62 62 153 62 62 62 62 153 62 62 N M DE SD: 0.0047 c. M: 0.0081 c. 1571: 77 77 190 77 77 77 77 77 190 77 77 77 77 190 77 77 N M DE SD: 0.0019 c. M: 0.0033 c. 1877: 92 92 227 92 92 92 92 92 227 92 92 92 92 227 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: 7.7787 cents 5 .. 10 match: 5 H SD: 14.2292 cents 6 .. 12 match: 6 H SD: 5.7948 cents 7 .. 14 match: 7 H SD: 10.3472 cents 8 .. 16 match: 8 H SD: 8.7736 cents 9 .. 18 match: 7 SD: 10.2753 cents 10 .. 20 match: 9 SD: 7.2944 cents 11 .. 22 match: 9 SD: 7.0694 cents 12 .. 24 match: 12 H SD: 6.2157 cents 13 .. 26 match: 11 S SD: 5.0963 cents 14 .. 28 match: 12 SD: 4.6381 cents 15 .. 30 match: 13 SD: 5.1071 cents 16 .. 32 match: 13 SD: 4.7372 cents 17 .. 34 match: 12 SD: 4.7334 cents 18 .. 36 match: 14 SD: 3.2486 cents 19 .. 38 match: 14 SD: 5.6509 cents 20 .. 40 match: 15 SD: 3.9863 cents 21 .. 42 match: 15 SD: 4.1116 cents 22 .. 44 match: 15 SD: 4.8483 cents 23 .. 46 match: 16 SD: 4.1978 cents 24 .. 48 match: 16 SD: 2.5636 cents 29 .. 58 match: 16 SD: 2.4020 cents 30 .. 60 match: 16 SD: 2.3569 cents 36 .. 72 match: 16 SD: 2.3331 cents 38 .. 76 match: 16 SD: 2.2267 cents 42 .. 84 match: 16 SD: 2.0295 cents 44 .. 88 match: 16 SD: 1.8631 cents 45 .. 90 match: 16 SD: 1.7967 cents 48 .. 96 match: 16 SD: 1.6660 cents 53 .. 106 match: 16 SD: 1.4602 cents 54 .. 108 match: 16 SD: 1.3619 cents 56 .. 112 match: 16 SD: 1.2285 cents 60 .. 120 match: 16 SD: 1.0902 cents 74 .. 148 match: 16 SD: 1.0378 cents 82 .. 164 match: 16 SD: 1.0156 cents 84 .. 168 match: 16 SD: 0.8754 cents 86 .. 172 match: 16 SD: 0.8295 cents 97 .. 194 match: 16 SD: 0.8259 cents 98 .. 196 match: 16 SD: 0.8162 cents 110 .. 220 match: 16 SD: 0.6772 cents 114 .. 228 match: 16 SD: 0.5487 cents 142 .. 284 match: 16 SD: 0.4641 cents 170 .. 340 match: 16 SD: 0.3933 cents 195 .. 390 match: 16 SD: 0.3701 cents 200 .. 400 match: 16 SD: 0.3154 cents 224 .. 448 match: 16 SD: 0.3064 cents 231 .. 462 match: 16 SD: 0.2700 cents 260 .. 520 match: 16 SD: 0.2664 cents 284 .. 568 match: 16 SD: 0.2259 cents 342 .. 685 match: 16 SD: 0.1928 cents 353 .. 707 match: 16 SD: 0.1583 cents 440 .. 881 match: 16 SD: 0.1552 cents 456 .. 913 match: 16 SD: 0.1481 cents 485 .. 971 match: 16 SD: 0.1411 cents 523 .. 1047 match: 16 SD: 0.1328 cents 553 .. 1107 match: 16 SD: 0.1139 cents 581 .. 1163 match: 16 SD: 0.1122 cents