Scala analysis: xen18-erlich-cynder-26
5L 21s MOS for Cynder, L=76.12, 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: 154.320 cents 154.320000 4: 193.420 cents 193.420000 5: 232.520 cents 232.520000 6: 271.620 cents 271.620000 7: 310.720 cents 310.720000 8: 386.840 cents 386.840000 9: 425.940 cents 425.940000 10: 465.040 cents 465.040000 11: 504.140 cents 504.140000 12: 543.240 cents 543.240000 13: 619.360 cents 619.360000 14: 658.460 cents 658.460000 15: 697.560 cents 697.560000 16: 736.660 cents 736.660000 17: 775.760 cents 775.760000 18: 814.860 cents 814.860000 19: 890.980 cents 890.980000 20: 930.080 cents 930.080000 21: 969.180 cents 969.180000 22: 1008.280 cents 1008.280000 23: 1047.380 cents 1047.380000 24: 1123.500 cents 1123.500000 25: 1162.600 cents 1162.600000 26: 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: 76.1200 cents 76.1200 4: 39.1000 cents 39.1000 5: 39.1000 cents 39.1000 6: 39.1000 cents 39.1000 7: 39.1000 cents 39.1000 8: 76.1200 cents 76.1200 9: 39.1000 cents 39.1000 10: 39.1000 cents 39.1000 11: 39.1000 cents 39.1000 12: 39.1000 cents 39.1000 13: 76.1200 cents 76.1200 14: 39.1000 cents 39.1000 15: 39.1000 cents 39.1000 16: 39.1000 cents 39.1000 17: 39.1000 cents 39.1000 18: 39.1000 cents 39.1000 19: 76.1200 cents 76.1200 20: 39.1000 cents 39.1000 21: 39.1000 cents 39.1000 22: 39.1000 cents 39.1000 23: 39.1000 cents 39.1000 24: 76.1200 cents 76.1200 25: 39.1000 cents 39.1000 26: 39.1000 cents 39.1000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 21 39.10000 cents 1: 5 76.12000 cents 2: 16 78.20000 cents 2: 10 115.22000 cents 3: 11 117.30000 cents 3: 15 154.32000 cents 4: 6 156.40000 cents 4: 20 193.42000 cents 5: 1 195.50000 cents 5: 25 232.52000 cents 6: 22 271.62000 cents 6: 4 308.64000 cents 7: 17 310.72000 cents 7: 9 347.74000 cents 8: 12 349.82000 cents 8: 14 386.84000 cents 9: 7 388.92000 cents 9: 19 425.94000 cents 10: 2 428.02000 cents 10: 24 465.04000 cents 11: 23 504.14000 cents 11: 3 541.16000 cents 12: 18 543.24000 cents 12: 8 580.26000 cents 13: 13 582.34000 cents 13: 13 619.36000 cents 14: 8 621.44000 cents 14: 18 658.46000 cents 15: 3 660.54000 cents 15: 23 697.56000 cents 16: 24 736.66000 cents 16: 2 773.68000 cents 17: 19 775.76000 cents 17: 7 812.78000 cents 18: 14 814.86000 cents 18: 12 851.88000 cents 19: 9 853.96000 cents 19: 17 890.98000 cents 20: 4 893.06000 cents 20: 22 930.08000 cents 21: 25 969.18000 cents 21: 1 1006.20000 cents 22: 20 1008.28000 cents 22: 6 1045.30000 cents 23: 15 1047.38000 cents 23: 11 1084.40000 cents 24: 10 1086.48000 cents 24: 16 1123.50000 cents 25: 5 1125.58000 cents 25: 21 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 22 23 24 25 26 0.0 : 39.1 78.2 154.3 193.4 232.5 271.6 310.7 386.8 425.9 465.0 504.1 543.2 619.4 658.5 697.6 736.7 775.8 814.9 891.0 930.1 969.2 1008.3 1047.4 1123.5 1162.6 1201.7 39.1 : 39.1 115.2 154.3 193.4 232.5 271.6 347.7 386.8 425.9 465.0 504.1 580.3 619.4 658.5 697.6 736.7 775.8 851.9 891.0 930.1 969.2 1008.3 1084.4 1123.5 1162.6 1201.7 78.2 : 76.1 115.2 154.3 193.4 232.5 308.6 347.7 386.8 425.9 465.0 541.2 580.3 619.4 658.5 697.6 736.7 812.8 851.9 891.0 930.1 969.2 1045.3 1084.4 1123.5 1162.6 1201.7 154.3 : 39.1 78.2 117.3 156.4 232.5 271.6 310.7 349.8 388.9 465.0 504.1 543.2 582.3 621.4 660.5 736.7 775.8 814.9 854.0 893.1 969.2 1008.3 1047.4 1086.5 1125.6 1201.7 193.4 : 39.1 78.2 117.3 193.4 232.5 271.6 310.7 349.8 425.9 465.0 504.1 543.2 582.3 621.4 697.6 736.7 775.8 814.9 854.0 930.1 969.2 1008.3 1047.4 1086.5 1162.6 1201.7 232.5 : 39.1 78.2 154.3 193.4 232.5 271.6 310.7 386.8 425.9 465.0 504.1 543.2 582.3 658.5 697.6 736.7 775.8 814.9 891.0 930.1 969.2 1008.3 1047.4 1123.5 1162.6 1201.7 271.6 : 39.1 115.2 154.3 193.4 232.5 271.6 347.7 386.8 425.9 465.0 504.1 543.2 619.4 658.5 697.6 736.7 775.8 851.9 891.0 930.1 969.2 1008.3 1084.4 1123.5 1162.6 1201.7 310.7 : 76.1 115.2 154.3 193.4 232.5 308.6 347.7 386.8 425.9 465.0 504.1 580.3 619.4 658.5 697.6 736.7 812.8 851.9 891.0 930.1 969.2 1045.3 1084.4 1123.5 1162.6 1201.7 386.8 : 39.1 78.2 117.3 156.4 232.5 271.6 310.7 349.8 388.9 428.0 504.1 543.2 582.3 621.4 660.5 736.7 775.8 814.9 854.0 893.1 969.2 1008.3 1047.4 1086.5 1125.6 1201.7 425.9 : 39.1 78.2 117.3 193.4 232.5 271.6 310.7 349.8 388.9 465.0 504.1 543.2 582.3 621.4 697.6 736.7 775.8 814.9 854.0 930.1 969.2 1008.3 1047.4 1086.5 1162.6 1201.7 465.0 : 39.1 78.2 154.3 193.4 232.5 271.6 310.7 349.8 425.9 465.0 504.1 543.2 582.3 658.5 697.6 736.7 775.8 814.9 891.0 930.1 969.2 1008.3 1047.4 1123.5 1162.6 1201.7 504.1 : 39.1 115.2 154.3 193.4 232.5 271.6 310.7 386.8 425.9 465.0 504.1 543.2 619.4 658.5 697.6 736.7 775.8 851.9 891.0 930.1 969.2 1008.3 1084.4 1123.5 1162.6 1201.7 543.2 : 76.1 115.2 154.3 193.4 232.5 271.6 347.7 386.8 425.9 465.0 504.1 580.3 619.4 658.5 697.6 736.7 812.8 851.9 891.0 930.1 969.2 1045.3 1084.4 1123.5 1162.6 1201.7 619.4 : 39.1 78.2 117.3 156.4 195.5 271.6 310.7 349.8 388.9 428.0 504.1 543.2 582.3 621.4 660.5 736.7 775.8 814.9 854.0 893.1 969.2 1008.3 1047.4 1086.5 1125.6 1201.7 658.5 : 39.1 78.2 117.3 156.4 232.5 271.6 310.7 349.8 388.9 465.0 504.1 543.2 582.3 621.4 697.6 736.7 775.8 814.9 854.0 930.1 969.2 1008.3 1047.4 1086.5 1162.6 1201.7 697.6 : 39.1 78.2 117.3 193.4 232.5 271.6 310.7 349.8 425.9 465.0 504.1 543.2 582.3 658.5 697.6 736.7 775.8 814.9 891.0 930.1 969.2 1008.3 1047.4 1123.5 1162.6 1201.7 736.7 : 39.1 78.2 154.3 193.4 232.5 271.6 310.7 386.8 425.9 465.0 504.1 543.2 619.4 658.5 697.6 736.7 775.8 851.9 891.0 930.1 969.2 1008.3 1084.4 1123.5 1162.6 1201.7 775.8 : 39.1 115.2 154.3 193.4 232.5 271.6 347.7 386.8 425.9 465.0 504.1 580.3 619.4 658.5 697.6 736.7 812.8 851.9 891.0 930.1 969.2 1045.3 1084.4 1123.5 1162.6 1201.7 814.9 : 76.1 115.2 154.3 193.4 232.5 308.6 347.7 386.8 425.9 465.0 541.2 580.3 619.4 658.5 697.6 773.7 812.8 851.9 891.0 930.1 1006.2 1045.3 1084.4 1123.5 1162.6 1201.7 891.0 : 39.1 78.2 117.3 156.4 232.5 271.6 310.7 349.8 388.9 465.0 504.1 543.2 582.3 621.4 697.6 736.7 775.8 814.9 854.0 930.1 969.2 1008.3 1047.4 1086.5 1125.6 1201.7 930.1 : 39.1 78.2 117.3 193.4 232.5 271.6 310.7 349.8 425.9 465.0 504.1 543.2 582.3 658.5 697.6 736.7 775.8 814.9 891.0 930.1 969.2 1008.3 1047.4 1086.5 1162.6 1201.7 969.2 : 39.1 78.2 154.3 193.4 232.5 271.6 310.7 386.8 425.9 465.0 504.1 543.2 619.4 658.5 697.6 736.7 775.8 851.9 891.0 930.1 969.2 1008.3 1047.4 1123.5 1162.6 1201.7 1008.3: 39.1 115.2 154.3 193.4 232.5 271.6 347.7 386.8 425.9 465.0 504.1 580.3 619.4 658.5 697.6 736.7 812.8 851.9 891.0 930.1 969.2 1008.3 1084.4 1123.5 1162.6 1201.7 1047.4: 76.1 115.2 154.3 193.4 232.5 308.6 347.7 386.8 425.9 465.0 541.2 580.3 619.4 658.5 697.6 773.7 812.8 851.9 891.0 930.1 969.2 1045.3 1084.4 1123.5 1162.6 1201.7 1123.5: 39.1 78.2 117.3 156.4 232.5 271.6 310.7 349.8 388.9 465.0 504.1 543.2 582.3 621.4 697.6 736.7 775.8 814.9 854.0 893.1 969.2 1008.3 1047.4 1086.5 1125.6 1201.7 1162.6: 39.1 78.2 117.3 193.4 232.5 271.6 310.7 349.8 425.9 465.0 504.1 543.2 582.3 658.5 697.6 736.7 775.8 814.9 854.0 930.1 969.2 1008.3 1047.4 1086.5 1162.6 1201.7 1201.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 39.1000 .. 76.1200 cents 37.02000 cents 39.10000 cents 2: 78.2000 .. 115.2200 cents 37.02000 cents 2.08000 cents 3: 117.3000 .. 154.3200 cents 37.02000 cents 2.08000 cents 4: 156.4000 .. 193.4200 cents 37.02000 cents 2.08000 cents 5: 195.5000 .. 232.5200 cents 37.02000 cents 2.08000 cents 6: 271.6200 .. 308.6400 cents 37.02000 cents 39.10000 cents 7: 310.7200 .. 347.7400 cents 37.02000 cents 2.08000 cents 8: 349.8200 .. 386.8400 cents 37.02000 cents 2.08000 cents 9: 388.9200 .. 425.9400 cents 37.02000 cents 2.08000 cents 10: 428.0200 .. 465.0400 cents 37.02000 cents 2.08000 cents 11: 504.1400 .. 541.1600 cents 37.02000 cents 39.10000 cents 12: 543.2400 .. 580.2600 cents 37.02000 cents 2.08000 cents 13: 582.3400 .. 619.3600 cents 37.02000 cents 2.08000 cents 14: 621.4400 .. 658.4600 cents 37.02000 cents 2.08000 cents 15: 660.5400 .. 697.5600 cents 37.02000 cents 2.08000 cents 16: 736.6600 .. 773.6800 cents 37.02000 cents 39.10000 cents 17: 775.7600 .. 812.7800 cents 37.02000 cents 2.08000 cents 18: 814.8600 .. 851.8800 cents 37.02000 cents 2.08000 cents 19: 853.9600 .. 890.9800 cents 37.02000 cents 2.08000 cents 20: 893.0600 .. 930.0800 cents 37.02000 cents 2.08000 cents 21: 969.1800 .. 1006.2000 cents 37.02000 cents 39.10000 cents 22: 1008.2800 .. 1045.3000 cents 37.02000 cents 2.08000 cents 23: 1047.3800 .. 1084.4000 cents 37.02000 cents 2.08000 cents 24: 1086.4800 .. 1123.5000 cents 37.02000 cents 2.08000 cents 25: 1125.5800 .. 1162.6000 cents 37.02000 cents 2.08000 cents
SHOW DATA
Number of notes : 26 -- Interval properties -- Smallest interval : 39.10000 cents, class 1 Average step (divided formal octave): 46.2192 cents Largest one step interval : 76.12000 cents Average / Smallest step : 1.182078 Largest / Average step : 1.646934 Largest / Smallest step : 1.946803 Median interval of one step : 39.10000 cents, amount: 21 Most common interval of one step : 39.10000 cents, amount: 21 Least squares average step : 46.25804 cents, oct.: 1202.70893 cents Scale is strictly proper Scale has Myhill's property chromas: 37.02000 cents and 2.08000 cents, ratio: 17.798077 generators: 5 of 232.52000 cents and 21 of 969.18000 cents ET pair of linear temperament : 26&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 2305-tone equal temperament with octave 1201.700 cents degrees: 75 150 296 371 446 521 596 742 817 892 967 1042 1188 1263 1338 1413 1488 1563 1709 1784 1859 1934 2009 2155 2230 2305 generators: 446 and 1859 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAABAAAABAAAAABAAAABAA Step pattern size order : SSLSSSSLSSSSLSSSSSLSSSSLSS Scale is a Constant Structure, by a margin of 2.08000 cents Scale diversity : 1.073896 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.229841 Rothenberg efficiency : 0.692308 redundancy: 0.307692 Efficiency x scale size : 18.000000 Number of different interval sizes : 50 = 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: 25 Scale is a chain of 13 triads 0.0 386.840 969.180 cents Most common triad is 0.0 232.520 969.180 cents, amount: 24 Number of recognisable fifths : 23, average 697.5600 cents Number of recognisable fourths : 23, average 504.1400 cents Formal octave complements present : 25 = 96.1538% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 15-16 -- Rational properties --
FIT/MODE
26: 1 1 1 1 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: 10.7026 c. M: 18.5100 c. 31: 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 P M ME SD: 0.5043 c. M:-0.8723 c. 305: 10 10 19 10 10 10 10 19 10 10 10 10 19 10 10 10 10 10 19 10 10 10 10 19 10 10 SP M DE SD: 0.4510 c. M: 0.7800 c. 336: 11 11 21 11 11 11 11 21 11 11 11 11 21 11 11 11 11 11 21 11 11 11 11 21 11 11 SP M DE SD: 0.3629 c. M: 0.6276 c. 367: 12 12 23 12 12 12 12 23 12 12 12 12 23 12 12 12 12 12 23 12 12 12 12 23 12 12 SP M DE SD: 0.2896 c. M: 0.5009 c. 398: 13 13 25 13 13 13 13 25 13 13 13 13 25 13 13 13 13 13 25 13 13 13 13 25 13 13 SP M DE SD: 0.2278 c. M: 0.3939 c. 429: 14 14 27 14 14 14 14 27 14 14 14 14 27 14 14 14 14 14 27 14 14 14 14 27 14 14 SP M DE SD: 0.1749 c. M: 0.3024 c. 460: 15 15 29 15 15 15 15 29 15 15 15 15 29 15 15 15 15 15 29 15 15 15 15 29 15 15 SP M DE SD: 0.1291 c. M: 0.2233 c. 491: 16 16 31 16 16 16 16 31 16 16 16 16 31 16 16 16 16 16 31 16 16 16 16 31 16 16 SP M DE SD: 0.0891 c. M: 0.1541 c. 522: 17 17 33 17 17 17 17 33 17 17 17 17 33 17 17 17 17 17 33 17 17 17 17 33 17 17 SP M DE SD: 0.0539 c. M: 0.0931 c. 553: 18 18 35 18 18 18 18 35 18 18 18 18 35 18 18 18 18 18 35 18 18 18 18 35 18 18 SP M DE SD: 0.0226 c. M: 0.0390 c. 584: 19 19 37 19 19 19 19 37 19 19 19 19 37 19 19 19 19 19 37 19 19 19 19 37 19 19 SP M DE SD: 0.0054 c. M:-0.0093 c. 1721: 56 56 109 56 56 56 56 109 56 56 56 56 109 56 56 56 56 56 109 56 56 56 56 109 56 56 SP M DE SD: 0.0036 c. M: 0.0062 c. 2305: 75 75 146 75 75 75 75 146 75 75 75 75 146 75 75 75 75 75 146 75 75 75 75 146 75 75 SP M DE SD: 0.0013 c. M: 0.0023 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: 1.1887 cents 5 .. 10 match: 5 H SD: 7.6760 cents 6 .. 12 match: 6 H SD: 1.8980 cents 7 .. 14 match: 7 H SD: 3.8808 cents 8 .. 16 match: 8 H SD: 5.7255 cents 9 .. 18 match: 9 H SD: 5.6868 cents 10 .. 20 match: 10 H SD: 4.4787 cents 11 .. 22 match: 11 H SD: 4.7005 cents 12 .. 24 match: 12 H SD: 2.6695 cents 13 .. 26 match: 13 H SD: 4.4703 cents 14 .. 28 match: 14 H SD: 4.5337 cents 15 .. 30 match: 14 SD: 4.4283 cents 16 .. 32 match: 15 SD: 3.4745 cents 17 .. 34 match: 16 SD: 3.7965 cents 18 .. 36 match: 18 H SD: 3.4793 cents 19 .. 38 match: 18 S SD: 3.0045 cents 20 .. 40 match: 19 SD: 2.6134 cents 21 .. 42 match: 20 S SD: 2.2836 cents 22 .. 44 match: 19 SD: 2.7504 cents 23 .. 46 match: 21 SD: 2.7160 cents 24 .. 48 match: 22 S SD: 2.0525 cents 25 .. 50 match: 22 S SD: 2.2545 cents 26 .. 52 match: 22 SD: 2.7589 cents 27 .. 54 match: 21 SD: 2.5315 cents 28 .. 56 match: 23 SD: 2.1901 cents 29 .. 58 match: 24 SD: 2.5964 cents 30 .. 60 match: 23 SD: 1.9344 cents 31 .. 62 match: 23 SD: 2.6005 cents 32 .. 64 match: 24 SD: 1.8019 cents 33 .. 66 match: 25 SD: 2.1503 cents 34 .. 68 match: 25 SD: 2.2904 cents 35 .. 70 match: 26 SD: 1.6520 cents 38 .. 76 match: 25 SD: 2.2629 cents 39 .. 78 match: 26 SD: 1.8010 cents 40 .. 80 match: 26 SD: 1.5956 cents 41 .. 82 match: 26 SD: 1.4068 cents 42 .. 84 match: 26 SD: 1.3969 cents 48 .. 96 match: 26 SD: 1.3461 cents 49 .. 98 match: 26 SD: 1.3369 cents 51 .. 102 match: 26 SD: 1.2542 cents 56 .. 112 match: 26 SD: 1.2412 cents 60 .. 120 match: 26 SD: 1.1193 cents 65 .. 130 match: 26 SD: 0.9226 cents 71 .. 142 match: 26 SD: 0.9113 cents 76 .. 152 match: 26 SD: 0.7610 cents 83 .. 166 match: 26 SD: 0.6892 cents 95 .. 190 match: 26 SD: 0.6548 cents 100 .. 200 match: 26 SD: 0.6220 cents 111 .. 222 match: 26 SD: 0.5676 cents 117 .. 234 match: 26 SD: 0.5253 cents 119 .. 238 match: 26 SD: 0.5238 cents 125 .. 250 match: 26 SD: 0.4875 cents 128 .. 256 match: 26 SD: 0.4595 cents 147 .. 294 match: 26 SD: 0.4009 cents 153 .. 306 match: 26 SD: 0.4008 cents 160 .. 320 match: 26 SD: 0.3996 cents 168 .. 336 match: 26 SD: 0.3535 cents 172 .. 344 match: 26 SD: 0.3171 cents 195 .. 390 match: 26 SD: 0.3039 cents 211 .. 422 match: 26 SD: 0.2990 cents 214 .. 428 match: 26 SD: 0.2876 cents 218 .. 436 match: 26 SD: 0.2810 cents 223 .. 446 match: 26 SD: 0.2738 cents 236 .. 472 match: 26 SD: 0.2544 cents 255 .. 511 match: 26 SD: 0.2532 cents 260 .. 521 match: 26 SD: 0.2183 cents 279 .. 559 match: 26 SD: 0.2134 cents 300 .. 601 match: 26 SD: 0.2086 cents 301 .. 603 match: 26 SD: 0.2000 cents 304 .. 609 match: 26 SD: 0.1920 cents 311 .. 623 match: 26 SD: 0.1865 cents 340 .. 681 match: 26 SD: 0.1838 cents 347 .. 695 match: 26 SD: 0.1601 cents 388 .. 777 match: 26 SD: 0.1588 cents 391 .. 783 match: 26 SD: 0.1477 cents 396 .. 793 match: 26 SD: 0.1416 cents 431 .. 863 match: 26 SD: 0.1397 cents 432 .. 865 match: 26 SD: 0.1349 cents 437 .. 875 match: 26 SD: 0.1289 cents 472 .. 945 match: 26 SD: 0.1287 cents 473 .. 947 match: 26 SD: 0.1247 cents 474 .. 949 match: 26 SD: 0.1182 cents 516 .. 1033 match: 26 SD: 0.1066 cents 523 .. 1047 match: 26 SD: 0.1049 cents 559 .. 1119 match: 26 SD: 0.1040 cents 564 .. 1129 match: 26 SD: 0.1003 cents 600 .. 1201 match: 26 SD: 0.0903 cents