Scala analysis: xen18-erlich-cynder-21
5L 16s MOS for Cynder, L=115.22, s=39.10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39.100 cents 39.100000 2: 78.200 cents 78.200000 3: 193.420 cents 193.420000 4: 232.520 cents 232.520000 5: 271.620 cents 271.620000 6: 310.720 cents 310.720000 7: 425.940 cents 425.940000 8: 465.040 cents 465.040000 9: 504.140 cents 504.140000 10: 543.240 cents 543.240000 11: 658.460 cents 658.460000 12: 697.560 cents 697.560000 13: 736.660 cents 736.660000 14: 775.760 cents 775.760000 15: 890.980 cents 890.980000 16: 930.080 cents 930.080000 17: 969.180 cents 969.180000 18: 1008.280 cents 1008.280000 19: 1123.500 cents 1123.500000 20: 1162.600 cents 1162.600000 21: 1201.700 cents 1201.700000
SHOW/INTERVAL
0: 39.1000 cents 39.1000 1: 39.1000 cents 39.1000 2: 39.1000 cents 39.1000 3: 115.2200 cents 115.2200 4: 39.1000 cents 39.1000 5: 39.1000 cents 39.1000 6: 39.1000 cents 39.1000 7: 115.2200 cents 115.2200 8: 39.1000 cents 39.1000 9: 39.1000 cents 39.1000 10: 39.1000 cents 39.1000 11: 115.2200 cents 115.2200 12: 39.1000 cents 39.1000 13: 39.1000 cents 39.1000 14: 39.1000 cents 39.1000 15: 115.2200 cents 115.2200 16: 39.1000 cents 39.1000 17: 39.1000 cents 39.1000 18: 39.1000 cents 39.1000 19: 115.2200 cents 115.2200 20: 39.1000 cents 39.1000 21: 39.1000 cents 39.1000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 16 39.10000 cents 1: 5 115.22000 cents 2: 11 78.20000 cents 2: 10 154.32000 cents 3: 6 117.30000 cents 3: 15 193.42000 cents 4: 1 156.40000 cents 4: 20 232.52000 cents 5: 17 271.62000 cents 5: 4 347.74000 cents 6: 12 310.72000 cents 6: 9 386.84000 cents 7: 7 349.82000 cents 7: 14 425.94000 cents 8: 2 388.92000 cents 8: 19 465.04000 cents 9: 18 504.14000 cents 9: 3 580.26000 cents 10: 13 543.24000 cents 10: 8 619.36000 cents 11: 8 582.34000 cents 11: 13 658.46000 cents 12: 3 621.44000 cents 12: 18 697.56000 cents 13: 19 736.66000 cents 13: 2 812.78000 cents 14: 14 775.76000 cents 14: 7 851.88000 cents 15: 9 814.86000 cents 15: 12 890.98000 cents 16: 4 853.96000 cents 16: 17 930.08000 cents 17: 20 969.18000 cents 17: 1 1045.30000 cents 18: 15 1008.28000 cents 18: 6 1084.40000 cents 19: 10 1047.38000 cents 19: 11 1123.50000 cents 20: 5 1086.48000 cents 20: 16 1162.60000 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 0.0 : 39.1 78.2 193.4 232.5 271.6 310.7 425.9 465.0 504.1 543.2 658.5 697.6 736.7 775.8 891.0 930.1 969.2 1008.3 1123.5 1162.6 1201.7 39.1 : 39.1 154.3 193.4 232.5 271.6 386.8 425.9 465.0 504.1 619.4 658.5 697.6 736.7 851.9 891.0 930.1 969.2 1084.4 1123.5 1162.6 1201.7 78.2 : 115.2 154.3 193.4 232.5 347.7 386.8 425.9 465.0 580.3 619.4 658.5 697.6 812.8 851.9 891.0 930.1 1045.3 1084.4 1123.5 1162.6 1201.7 193.4 : 39.1 78.2 117.3 232.5 271.6 310.7 349.8 465.0 504.1 543.2 582.3 697.6 736.7 775.8 814.9 930.1 969.2 1008.3 1047.4 1086.5 1201.7 232.5 : 39.1 78.2 193.4 232.5 271.6 310.7 425.9 465.0 504.1 543.2 658.5 697.6 736.7 775.8 891.0 930.1 969.2 1008.3 1047.4 1162.6 1201.7 271.6 : 39.1 154.3 193.4 232.5 271.6 386.8 425.9 465.0 504.1 619.4 658.5 697.6 736.7 851.9 891.0 930.1 969.2 1008.3 1123.5 1162.6 1201.7 310.7 : 115.2 154.3 193.4 232.5 347.7 386.8 425.9 465.0 580.3 619.4 658.5 697.6 812.8 851.9 891.0 930.1 969.2 1084.4 1123.5 1162.6 1201.7 425.9 : 39.1 78.2 117.3 232.5 271.6 310.7 349.8 465.0 504.1 543.2 582.3 697.6 736.7 775.8 814.9 854.0 969.2 1008.3 1047.4 1086.5 1201.7 465.0 : 39.1 78.2 193.4 232.5 271.6 310.7 425.9 465.0 504.1 543.2 658.5 697.6 736.7 775.8 814.9 930.1 969.2 1008.3 1047.4 1162.6 1201.7 504.1 : 39.1 154.3 193.4 232.5 271.6 386.8 425.9 465.0 504.1 619.4 658.5 697.6 736.7 775.8 891.0 930.1 969.2 1008.3 1123.5 1162.6 1201.7 543.2 : 115.2 154.3 193.4 232.5 347.7 386.8 425.9 465.0 580.3 619.4 658.5 697.6 736.7 851.9 891.0 930.1 969.2 1084.4 1123.5 1162.6 1201.7 658.5 : 39.1 78.2 117.3 232.5 271.6 310.7 349.8 465.0 504.1 543.2 582.3 621.4 736.7 775.8 814.9 854.0 969.2 1008.3 1047.4 1086.5 1201.7 697.6 : 39.1 78.2 193.4 232.5 271.6 310.7 425.9 465.0 504.1 543.2 582.3 697.6 736.7 775.8 814.9 930.1 969.2 1008.3 1047.4 1162.6 1201.7 736.7 : 39.1 154.3 193.4 232.5 271.6 386.8 425.9 465.0 504.1 543.2 658.5 697.6 736.7 775.8 891.0 930.1 969.2 1008.3 1123.5 1162.6 1201.7 775.8 : 115.2 154.3 193.4 232.5 347.7 386.8 425.9 465.0 504.1 619.4 658.5 697.6 736.7 851.9 891.0 930.1 969.2 1084.4 1123.5 1162.6 1201.7 891.0 : 39.1 78.2 117.3 232.5 271.6 310.7 349.8 388.9 504.1 543.2 582.3 621.4 736.7 775.8 814.9 854.0 969.2 1008.3 1047.4 1086.5 1201.7 930.1 : 39.1 78.2 193.4 232.5 271.6 310.7 349.8 465.0 504.1 543.2 582.3 697.6 736.7 775.8 814.9 930.1 969.2 1008.3 1047.4 1162.6 1201.7 969.2 : 39.1 154.3 193.4 232.5 271.6 310.7 425.9 465.0 504.1 543.2 658.5 697.6 736.7 775.8 891.0 930.1 969.2 1008.3 1123.5 1162.6 1201.7 1008.3: 115.2 154.3 193.4 232.5 271.6 386.8 425.9 465.0 504.1 619.4 658.5 697.6 736.7 851.9 891.0 930.1 969.2 1084.4 1123.5 1162.6 1201.7 1123.5: 39.1 78.2 117.3 156.4 271.6 310.7 349.8 388.9 504.1 543.2 582.3 621.4 736.7 775.8 814.9 854.0 969.2 1008.3 1047.4 1086.5 1201.7 1162.6: 39.1 78.2 117.3 232.5 271.6 310.7 349.8 465.0 504.1 543.2 582.3 697.6 736.7 775.8 814.9 930.1 969.2 1008.3 1047.4 1162.6 1201.7 1201.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 39.1000 .. 115.2200 cents 76.12000 cents 39.10000 cents 2: 78.2000 .. 154.3200 cents 76.12000 cents -37.02000 cents 3: 117.3000 .. 193.4200 cents 76.12000 cents -37.02000 cents 4: 156.4000 .. 232.5200 cents 76.12000 cents -37.02000 cents 5: 271.6200 .. 347.7400 cents 76.12000 cents 39.10000 cents 6: 310.7200 .. 386.8400 cents 76.12000 cents -37.02000 cents 7: 349.8200 .. 425.9400 cents 76.12000 cents -37.02000 cents 8: 388.9200 .. 465.0400 cents 76.12000 cents -37.02000 cents 9: 504.1400 .. 580.2600 cents 76.12000 cents 39.10000 cents 10: 543.2400 .. 619.3600 cents 76.12000 cents -37.02000 cents 11: 582.3400 .. 658.4600 cents 76.12000 cents -37.02000 cents 12: 621.4400 .. 697.5600 cents 76.12000 cents -37.02000 cents 13: 736.6600 .. 812.7800 cents 76.12000 cents 39.10000 cents 14: 775.7600 .. 851.8800 cents 76.12000 cents -37.02000 cents 15: 814.8600 .. 890.9800 cents 76.12000 cents -37.02000 cents 16: 853.9600 .. 930.0800 cents 76.12000 cents -37.02000 cents 17: 969.1800 .. 1045.3000 cents 76.12000 cents 39.10000 cents 18: 1008.2800 .. 1084.4000 cents 76.12000 cents -37.02000 cents 19: 1047.3800 .. 1123.5000 cents 76.12000 cents -37.02000 cents 20: 1086.4800 .. 1162.6000 cents 76.12000 cents -37.02000 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 39.10000 cents, class 1 Average step (divided formal octave): 57.2238 cents Largest one step interval : 115.22000 cents Average / Smallest step : 1.463525 Largest / Average step : 2.013498 Largest / Smallest step : 2.946803 Median interval of one step : 39.10000 cents, amount: 16 Most common interval of one step : 39.10000 cents, amount: 16 Least squares average step : 57.49203 cents, oct.: 1207.33256 cents Scale is not proper Scale has Myhill's property chromas: 76.12000 cents and 37.02000 cents, ratio: 2.056186 generators: 4 of 232.52000 cents and 17 of 969.18000 cents ET pair of linear temperament : 26&31 Scale is distributional even Scale is a mode of a 1721-tone equal temperament with octave 1201.700 cents degrees: 56 112 277 333 389 445 610 666 722 778 943 999 1055 1111 1276 1332 1388 1444 1609 1665 1721 generators: 333 and 1388 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAAABAAABAAABAA Step pattern size order : SSLSSSLSSSLSSSLSSSLSS Scale is a Constant Structure, by a margin of 2.08000 cents Scale diversity : 1.137843 Lumma stability : 0.195223 Lumma impropriety factor : 0.462095 Rothenberg efficiency : 0.698413 redundancy: 0.301587 Efficiency x scale size : 14.666667 Number of different interval sizes : 40 = 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 : 2.08000 cents Most common intervals : 232.52000 cents & inv., amount: 20 Scale is a chain of 10 triads 0.0 232.520 465.040 cents Most common triad is 0.0 232.520 969.180 cents, amount: 19 Number of recognisable fifths : 18, average 697.5600 cents Number of recognisable fourths : 18, average 504.1400 cents Scale contains two identical disjunct "tetrachords" of 10 notes Formal octave complements present : 21 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 10-11 -- Rational properties --
FIT/MODE
21: 0 1 2 1 0 1 2 1 0 1 2 1 1 0 2 1 1 0 2 1 1 N T3 SD: 26.4948 c. M: 46.3495 c. 22: 1 0 3 0 1 1 2 1 0 1 2 1 0 1 2 1 1 0 3 0 1 N I SD: 16.6409 c. M: 26.5645 c. 24: 1 0 3 0 1 1 2 1 1 1 2 1 0 1 3 0 1 1 2 1 1 N SD: 18.6822 c. M: 35.6683 c. 25: 1 0 3 1 0 1 3 0 1 1 2 1 1 1 2 1 1 1 2 1 1 N SD: 19.2915 c. M: 33.5760 c. 26: 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 P M ME I SD: 8.6218 c. M: 14.2385 c. 31: 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 1 3 1 1 N M DE I SD: 0.4063 c. M: 0.6710 c. 305: 10 10 29 10 10 10 29 10 10 10 29 10 10 10 29 10 10 10 29 10 10 N M DE I SD: 0.3633 c. M: 0.6000 c. 336: 11 11 32 11 11 11 32 11 11 11 32 11 11 11 32 11 11 11 32 11 11 N M DE I SD: 0.2923 c. M: 0.4827 c. 367: 12 12 35 12 12 12 35 12 12 12 35 12 12 12 35 12 12 12 35 12 12 N M DE I SD: 0.2333 c. M: 0.3853 c. 398: 13 13 38 13 13 13 38 13 13 13 38 13 13 13 38 13 13 13 38 13 13 N M DE I SD: 0.1835 c. M: 0.3030 c. 429: 14 14 41 14 14 14 41 14 14 14 41 14 14 14 41 14 14 14 41 14 14 N M DE I SD: 0.1409 c. M: 0.2326 c. 460: 15 15 44 15 15 15 44 15 15 15 44 15 15 15 44 15 15 15 44 15 15 N M DE I SD: 0.1040 c. M: 0.1717 c. 491: 16 16 47 16 16 16 47 16 16 16 47 16 16 16 47 16 16 16 47 16 16 N M DE I SD: 0.0718 c. M: 0.1185 c. 522: 17 17 50 17 17 17 50 17 17 17 50 17 17 17 50 17 17 17 50 17 17 N M DE I SD: 0.0434 c. M: 0.0716 c. 553: 18 18 53 18 18 18 53 18 18 18 53 18 18 18 53 18 18 18 53 18 18 N M DE I SD: 0.0182 c. M: 0.0300 c. 584: 19 19 56 19 19 19 56 19 19 19 56 19 19 19 56 19 19 19 56 19 19 N M DE I SD: 0.0044 c. M: 0.0072 c. 1721: 56 56 165 56 56 56 165 56 56 56 165 56 56 56 165 56 56 56 165 56 56 N M DE I SD: 0.0029 c. M: 0.0048 c. 2305: 75 75 221 75 75 75 221 75 75 75 221 75 75 75 221 75 75 75 221 75 75 N M DE I SD: 0.0011 c. M: 0.0017 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 1.7000 cents 2 .. 4 match: 2 H SD: 2.3562 cents 3 .. 6 match: 3 H SD: 3.0529 cents 4 .. 8 match: 4 H SD: 9.9768 cents 5 .. 10 match: 5 H SD: 11.1258 cents 6 .. 12 match: 6 H SD: 7.0976 cents 7 .. 14 match: 7 H SD: 9.5882 cents 8 .. 16 match: 8 H SD: 9.3161 cents 9 .. 18 match: 9 H SD: 5.8781 cents 10 .. 20 match: 10 H SD: 6.5732 cents 11 .. 22 match: 11 H SD: 6.4925 cents 12 .. 24 match: 10 SD: 7.1444 cents 13 .. 26 match: 11 SD: 7.2747 cents 14 .. 28 match: 13 SD: 5.7548 cents 15 .. 30 match: 13 SD: 4.8813 cents 16 .. 32 match: 14 SD: 4.8423 cents 17 .. 34 match: 13 SD: 4.3056 cents 18 .. 36 match: 16 S SD: 3.9433 cents 19 .. 38 match: 16 S SD: 3.3645 cents 20 .. 40 match: 16 SD: 3.3340 cents 21 .. 42 match: 17 SD: 3.0553 cents 22 .. 44 match: 15 SD: 2.8163 cents 23 .. 46 match: 17 SD: 3.4444 cents 24 .. 48 match: 18 SD: 2.1791 cents 25 .. 50 match: 17 SD: 2.3496 cents 26 .. 52 match: 18 SD: 2.7775 cents 27 .. 54 match: 18 SD: 2.7930 cents 28 .. 56 match: 19 SD: 2.5808 cents 29 .. 58 match: 20 SD: 2.8844 cents 30 .. 60 match: 19 SD: 2.2606 cents 31 .. 62 match: 18 SD: 3.0685 cents 32 .. 64 match: 19 SD: 2.0971 cents 33 .. 66 match: 20 SD: 2.5106 cents 35 .. 70 match: 21 SD: 1.9070 cents 36 .. 72 match: 21 SD: 1.7693 cents 41 .. 82 match: 21 SD: 1.5087 cents 48 .. 96 match: 21 SD: 1.4143 cents 49 .. 98 match: 21 SD: 1.3688 cents 57 .. 114 match: 21 SD: 1.3643 cents 58 .. 116 match: 21 SD: 1.3212 cents 60 .. 120 match: 21 SD: 1.2707 cents 62 .. 124 match: 21 SD: 1.1762 cents 65 .. 130 match: 21 SD: 1.1032 cents 68 .. 136 match: 21 SD: 1.0881 cents 71 .. 142 match: 21 SD: 0.9343 cents 76 .. 152 match: 21 SD: 0.8761 cents 82 .. 164 match: 21 SD: 0.8460 cents 83 .. 166 match: 21 SD: 0.7704 cents 91 .. 182 match: 21 SD: 0.7648 cents 92 .. 184 match: 21 SD: 0.7145 cents 101 .. 202 match: 21 SD: 0.6732 cents 104 .. 208 match: 21 SD: 0.6708 cents 111 .. 222 match: 21 SD: 0.6131 cents 117 .. 234 match: 21 SD: 0.5797 cents 125 .. 250 match: 21 SD: 0.5292 cents 133 .. 266 match: 21 SD: 0.5195 cents 136 .. 272 match: 21 SD: 0.4905 cents 147 .. 294 match: 21 SD: 0.4344 cents 166 .. 332 match: 21 SD: 0.4273 cents 168 .. 336 match: 21 SD: 0.3889 cents 172 .. 344 match: 21 SD: 0.3739 cents 177 .. 354 match: 21 SD: 0.3686 cents 187 .. 374 match: 21 SD: 0.3615 cents 195 .. 390 match: 21 SD: 0.3581 cents 208 .. 416 match: 21 SD: 0.3563 cents 211 .. 422 match: 21 SD: 0.3276 cents 214 .. 428 match: 21 SD: 0.3184 cents 218 .. 436 match: 21 SD: 0.2945 cents 230 .. 460 match: 21 SD: 0.2878 cents 236 .. 472 match: 21 SD: 0.2866 cents 260 .. 521 match: 21 SD: 0.2502 cents 264 .. 529 match: 21 SD: 0.2322 cents 301 .. 603 match: 21 SD: 0.2137 cents 304 .. 609 match: 21 SD: 0.2059 cents 305 .. 611 match: 21 SD: 0.1786 cents 347 .. 695 match: 21 SD: 0.1551 cents 432 .. 865 match: 21 SD: 0.1505 cents 437 .. 875 match: 21 SD: 0.1319 cents 473 .. 947 match: 21 SD: 0.1249 cents 520 .. 1041 match: 21 SD: 0.1212 cents 523 .. 1047 match: 21 SD: 0.1174 cents 559 .. 1119 match: 21 SD: 0.1164 cents 564 .. 1129 match: 21 SD: 0.0984 cents