Scala analysis: xen18-erlich-magic-19
3L 16s MOS for Magic, L=86.40, 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: 176.640 cents 176.640000 4: 263.040 cents 263.040000 5: 321.920 cents 321.920000 6: 380.800 cents 380.800000 7: 439.680 cents 439.680000 8: 498.560 cents 498.560000 9: 557.440 cents 557.440000 10: 643.840 cents 643.840000 11: 702.720 cents 702.720000 12: 761.600 cents 761.600000 13: 820.480 cents 820.480000 14: 879.360 cents 879.360000 15: 938.240 cents 938.240000 16: 1024.640 cents 1024.640000 17: 1083.520 cents 1083.520000 18: 1142.400 cents 1142.400000 19: 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: 86.4000 cents 86.4000 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: 86.4000 cents 86.4000 11: 58.8800 cents 58.8800 12: 58.8800 cents 58.8800 13: 58.8800 cents 58.8800 14: 58.8800 cents 58.8800 15: 58.8800 cents 58.8800 16: 86.4000 cents 86.4000 17: 58.8800 cents 58.8800 18: 58.8800 cents 58.8800 19: 58.8800 cents 58.8800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 16 58.88000 cents 1: 3 86.40000 cents 2: 13 117.76000 cents 2: 6 145.28000 cents 3: 10 176.64000 cents 3: 9 204.16000 cents 4: 7 235.52000 cents 4: 12 263.04000 cents 5: 4 294.40000 cents 5: 15 321.92000 cents 6: 1 353.28000 cents 6: 18 380.80000 cents 7: 17 439.68000 cents 7: 2 467.20000 cents 8: 14 498.56000 cents 8: 5 526.08000 cents 9: 11 557.44000 cents 9: 8 584.96000 cents 10: 8 616.32000 cents 10: 11 643.84000 cents 11: 5 675.20000 cents 11: 14 702.72000 cents 12: 2 734.08000 cents 12: 17 761.60000 cents 13: 18 820.48000 cents 13: 1 848.00000 cents 14: 15 879.36000 cents 14: 4 906.88000 cents 15: 12 938.24000 cents 15: 7 965.76000 cents 16: 9 997.12000 cents 16: 10 1024.64000 cents 17: 6 1056.00000 cents 17: 13 1083.52000 cents 18: 3 1114.88000 cents 18: 16 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 17 18 19 0.0 : 58.9 117.8 176.6 263.0 321.9 380.8 439.7 498.6 557.4 643.8 702.7 761.6 820.5 879.4 938.2 1024.6 1083.5 1142.4 1201.3 58.9 : 58.9 117.8 204.2 263.0 321.9 380.8 439.7 498.6 585.0 643.8 702.7 761.6 820.5 879.4 965.8 1024.6 1083.5 1142.4 1201.3 117.8 : 58.9 145.3 204.2 263.0 321.9 380.8 439.7 526.1 585.0 643.8 702.7 761.6 820.5 906.9 965.8 1024.6 1083.5 1142.4 1201.3 176.6 : 86.4 145.3 204.2 263.0 321.9 380.8 467.2 526.1 585.0 643.8 702.7 761.6 848.0 906.9 965.8 1024.6 1083.5 1142.4 1201.3 263.0 : 58.9 117.8 176.6 235.5 294.4 380.8 439.7 498.6 557.4 616.3 675.2 761.6 820.5 879.4 938.2 997.1 1056.0 1114.9 1201.3 321.9 : 58.9 117.8 176.6 235.5 321.9 380.8 439.7 498.6 557.4 616.3 702.7 761.6 820.5 879.4 938.2 997.1 1056.0 1142.4 1201.3 380.8 : 58.9 117.8 176.6 263.0 321.9 380.8 439.7 498.6 557.4 643.8 702.7 761.6 820.5 879.4 938.2 997.1 1083.5 1142.4 1201.3 439.7 : 58.9 117.8 204.2 263.0 321.9 380.8 439.7 498.6 585.0 643.8 702.7 761.6 820.5 879.4 938.2 1024.6 1083.5 1142.4 1201.3 498.6 : 58.9 145.3 204.2 263.0 321.9 380.8 439.7 526.1 585.0 643.8 702.7 761.6 820.5 879.4 965.8 1024.6 1083.5 1142.4 1201.3 557.4 : 86.4 145.3 204.2 263.0 321.9 380.8 467.2 526.1 585.0 643.8 702.7 761.6 820.5 906.9 965.8 1024.6 1083.5 1142.4 1201.3 643.8 : 58.9 117.8 176.6 235.5 294.4 380.8 439.7 498.6 557.4 616.3 675.2 734.1 820.5 879.4 938.2 997.1 1056.0 1114.9 1201.3 702.7 : 58.9 117.8 176.6 235.5 321.9 380.8 439.7 498.6 557.4 616.3 675.2 761.6 820.5 879.4 938.2 997.1 1056.0 1142.4 1201.3 761.6 : 58.9 117.8 176.6 263.0 321.9 380.8 439.7 498.6 557.4 616.3 702.7 761.6 820.5 879.4 938.2 997.1 1083.5 1142.4 1201.3 820.5 : 58.9 117.8 204.2 263.0 321.9 380.8 439.7 498.6 557.4 643.8 702.7 761.6 820.5 879.4 938.2 1024.6 1083.5 1142.4 1201.3 879.4 : 58.9 145.3 204.2 263.0 321.9 380.8 439.7 498.6 585.0 643.8 702.7 761.6 820.5 879.4 965.8 1024.6 1083.5 1142.4 1201.3 938.2 : 86.4 145.3 204.2 263.0 321.9 380.8 439.7 526.1 585.0 643.8 702.7 761.6 820.5 906.9 965.8 1024.6 1083.5 1142.4 1201.3 1024.6: 58.9 117.8 176.6 235.5 294.4 353.3 439.7 498.6 557.4 616.3 675.2 734.1 820.5 879.4 938.2 997.1 1056.0 1114.9 1201.3 1083.5: 58.9 117.8 176.6 235.5 294.4 380.8 439.7 498.6 557.4 616.3 675.2 761.6 820.5 879.4 938.2 997.1 1056.0 1142.4 1201.3 1142.4: 58.9 117.8 176.6 235.5 321.9 380.8 439.7 498.6 557.4 616.3 702.7 761.6 820.5 879.4 938.2 997.1 1083.5 1142.4 1201.3 1201.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.8800 .. 86.4000 cents 27.52000 cents 58.88000 cents 2: 117.7600 .. 145.2800 cents 27.52000 cents 31.36000 cents 3: 176.6400 .. 204.1600 cents 27.52000 cents 31.36000 cents 4: 235.5200 .. 263.0400 cents 27.52000 cents 31.36000 cents 5: 294.4000 .. 321.9200 cents 27.52000 cents 31.36000 cents 6: 353.2800 .. 380.8000 cents 27.52000 cents 31.36000 cents 7: 439.6800 .. 467.2000 cents 27.52000 cents 58.88000 cents 8: 498.5600 .. 526.0800 cents 27.52000 cents 31.36000 cents 9: 557.4400 .. 584.9600 cents 27.52000 cents 31.36000 cents 10: 616.3200 .. 643.8400 cents 27.52000 cents 31.36000 cents 11: 675.2000 .. 702.7200 cents 27.52000 cents 31.36000 cents 12: 734.0800 .. 761.6000 cents 27.52000 cents 31.36000 cents 13: 820.4800 .. 848.0000 cents 27.52000 cents 58.88000 cents 14: 879.3600 .. 906.8800 cents 27.52000 cents 31.36000 cents 15: 938.2400 .. 965.7600 cents 27.52000 cents 31.36000 cents 16: 997.1200 .. 1024.6400 cents 27.52000 cents 31.36000 cents 17: 1056.0000 .. 1083.5200 cents 27.52000 cents 31.36000 cents 18: 1114.8800 .. 1142.4000 cents 27.52000 cents 31.36000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 58.88000 cents, class 1 Average step (divided formal octave): 63.2253 cents Largest one step interval : 86.40000 cents Average / Smallest step : 1.073799 Largest / Average step : 1.366542 Largest / Smallest step : 1.467391 Median interval of one step : 58.88000 cents, amount: 16 Most common interval of one step : 58.88000 cents, amount: 16 Least squares average step : 63.32554 cents, oct.: 1203.18523 cents Scale is strictly proper Scale has Myhill's property chromas: 27.52000 cents and 31.36000 cents, ratio: 1.139535 generators: 6 of 380.80000 cents and 13 of 820.48000 cents ET pair of linear temperament : 19&41 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1571-tone equal temperament with octave 1201.280 cents degrees: 77 154 231 344 421 498 575 652 729 842 919 996 1073 1150 1227 1340 1417 1494 1571 generators: 498 and 1073 Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABAAAAABAAAAABAAA Step pattern size order : SSSLSSSSSLSSSSSLSSS Scale is a Constant Structure, by a margin of 31.36000 cents Scale diversity : 1.197949 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.587640 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 : 27.52000 cents Most common intervals : 380.80000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 380.800 761.600 cents Most common triad is 0.0 380.800 820.480 cents, amount: 17 Number of recognisable fifths : 14, average 702.7200 cents Number of recognisable fourths : 14, average 498.5600 cents Best fifths form a closed circle 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: 7.9333 c. M: 13.0358 c. 22: 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 P M ME I SD: 7.8075 c. M: 12.8291 c. 41: 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 SP M ME I SD: 0.5130 c. M: 0.8429 c. 183: 9 9 9 13 9 9 9 9 9 13 9 9 9 9 9 13 9 9 9 SP M DE I SD: 0.3640 c. M: 0.5980 c. 224: 11 11 11 16 11 11 11 11 11 16 11 11 11 11 11 16 11 11 11 SP M DE I SD: 0.2034 c. M: 0.3343 c. 265: 13 13 13 19 13 13 13 13 13 19 13 13 13 13 13 19 13 13 13 SP M DE I SD: 0.0926 c. M: 0.1522 c. 306: 15 15 15 22 15 15 15 15 15 22 15 15 15 15 15 22 15 15 15 SP M DE I SD: 0.0115 c. M: 0.0188 c. 959: 47 47 47 69 47 47 47 47 47 69 47 47 47 47 47 69 47 47 47 SP M DE I SD: 0.0110 c. M: 0.0180 c. 1265: 62 62 62 91 62 62 62 62 62 91 62 62 62 62 62 91 62 62 62 SP M DE I SD: 0.0055 c. M: 0.0091 c. 1571: 77 77 77 113 77 77 77 77 77 113 77 77 77 77 77 113 77 77 77 SP M DE I SD: 0.0022 c. M: 0.0037 c. 1877: 92 92 92 135 92 92 92 92 92 135 92 92 92 92 92 135 92 92 92 SP M DE I 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: 5.5333 cents 6 .. 12 match: 6 H SD: 4.2602 cents 7 .. 14 match: 7 H SD: 6.9030 cents 8 .. 16 match: 8 H SD: 5.8279 cents 9 .. 18 match: 9 H SD: 4.8370 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: 5.6519 cents 13 .. 26 match: 12 S SD: 4.7983 cents 14 .. 28 match: 14 H SD: 4.6436 cents 15 .. 30 match: 15 H SD: 4.3623 cents 16 .. 32 match: 16 H SD: 4.3314 cents 17 .. 34 match: 15 SD: 4.3646 cents 18 .. 36 match: 17 SD: 3.0932 cents 19 .. 38 match: 17 S SD: 5.0330 cents 20 .. 40 match: 18 SD: 3.4069 cents 21 .. 42 match: 18 SD: 3.8766 cents 22 .. 44 match: 17 SD: 4.1656 cents 23 .. 46 match: 18 SD: 4.0005 cents 24 .. 48 match: 19 SD: 2.7554 cents 28 .. 56 match: 19 SD: 2.6543 cents 29 .. 58 match: 19 SD: 2.1764 cents 36 .. 72 match: 19 SD: 2.0260 cents 38 .. 76 match: 19 SD: 1.9408 cents 44 .. 88 match: 19 SD: 1.7561 cents 45 .. 90 match: 19 SD: 1.6319 cents 48 .. 96 match: 19 SD: 1.5328 cents 53 .. 106 match: 19 SD: 1.3415 cents 54 .. 108 match: 19 SD: 1.3013 cents 56 .. 112 match: 19 SD: 1.0826 cents 73 .. 146 match: 19 SD: 1.0782 cents 74 .. 148 match: 19 SD: 0.9376 cents 82 .. 164 match: 19 SD: 0.8865 cents 84 .. 168 match: 19 SD: 0.7552 cents 109 .. 218 match: 19 SD: 0.7472 cents 110 .. 220 match: 19 SD: 0.6457 cents 114 .. 228 match: 19 SD: 0.5326 cents 138 .. 276 match: 19 SD: 0.5050 cents 139 .. 278 match: 19 SD: 0.5035 cents 142 .. 284 match: 19 SD: 0.4366 cents 166 .. 332 match: 19 SD: 0.4118 cents 170 .. 340 match: 19 SD: 0.3936 cents 171 .. 342 match: 19 SD: 0.3812 cents 195 .. 390 match: 19 SD: 0.3355 cents 224 .. 448 match: 19 SD: 0.2627 cents 231 .. 462 match: 19 SD: 0.2609 cents 260 .. 520 match: 19 SD: 0.2282 cents 317 .. 634 match: 19 SD: 0.2027 cents 342 .. 685 match: 19 SD: 0.1754 cents 353 .. 707 match: 19 SD: 0.1347 cents 495 .. 991 match: 19 SD: 0.1292 cents 513 .. 1027 match: 19 SD: 0.1280 cents 523 .. 1047 match: 19 SD: 0.1269 cents 524 .. 1049 match: 19 SD: 0.1225 cents 553 .. 1107 match: 19 SD: 0.1213 cents 577 .. 1155 match: 19 SD: 0.1029 cents 597 .. 1195 match: 19 SD: 0.0971 cents