Scala analysis: xen18-erlich-doublewide-22
18L 4s MOS for Doublewide, L=54.64, s=53.76
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 54.640 cents 54.640000 2: 109.280 cents 109.280000 3: 163.040 cents 163.040000 4: 217.680 cents 217.680000 5: 272.320 cents 272.320000 6: 326.960 cents 326.960000 7: 381.600 cents 381.600000 8: 436.240 cents 436.240000 9: 490.000 cents 490.000000 10: 544.640 cents 544.640000 11: 599.280 cents 599.280000 12: 653.920 cents 653.920000 13: 708.560 cents 708.560000 14: 762.320 cents 762.320000 15: 816.960 cents 816.960000 16: 871.600 cents 871.600000 17: 926.240 cents 926.240000 18: 980.880 cents 980.880000 19: 1035.520 cents 1035.520000 20: 1089.280 cents 1089.280000 21: 1143.920 cents 1143.920000 22: 1198.560 cents 1198.560000
SHOW/INTERVAL
0: 54.6400 cents 54.6400 1: 54.6400 cents 54.6400 2: 54.6400 cents 54.6400 3: 53.7600 cents 53.7600 4: 54.6400 cents 54.6400 5: 54.6400 cents 54.6400 6: 54.6400 cents 54.6400 7: 54.6400 cents 54.6400 8: 54.6400 cents 54.6400 9: 53.7600 cents 53.7600 10: 54.6400 cents 54.6400 11: 54.6400 cents 54.6400 12: 54.6400 cents 54.6400 13: 54.6400 cents 54.6400 14: 53.7600 cents 53.7600 15: 54.6400 cents 54.6400 16: 54.6400 cents 54.6400 17: 54.6400 cents 54.6400 18: 54.6400 cents 54.6400 19: 54.6400 cents 54.6400 20: 53.7600 cents 53.7600 21: 54.6400 cents 54.6400 22: 54.6400 cents 54.6400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 53.76000 cents 1: 18 54.64000 cents 2: 8 108.40000 cents 2: 14 109.28000 cents 3: 12 163.04000 cents 3: 10 163.92000 cents 4: 16 217.68000 cents 4: 6 218.56000 cents 5: 20 272.32000 cents 5: 2 273.20000 cents 6: 2 326.08000 cents 6: 20 326.96000 cents 7: 6 380.72000 cents 7: 16 381.60000 cents 8: 10 435.36000 cents 8: 12 436.24000 cents 9: 14 490.00000 cents 9: 8 490.88000 cents 10: 18 544.64000 cents 10: 4 545.52000 cents 11: 22 599.28000 cents 12: 4 653.04000 cents 12: 18 653.92000 cents 13: 8 707.68000 cents 13: 14 708.56000 cents 14: 12 762.32000 cents 14: 10 763.20000 cents 15: 16 816.96000 cents 15: 6 817.84000 cents 16: 20 871.60000 cents 16: 2 872.48000 cents 17: 2 925.36000 cents 17: 20 926.24000 cents 18: 6 980.00000 cents 18: 16 980.88000 cents 19: 10 1034.64000 cents 19: 12 1035.52000 cents 20: 14 1089.28000 cents 20: 8 1090.16000 cents 21: 18 1143.92000 cents 21: 4 1144.80000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.95238 = 41/21
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 : 54.6 109.3 163.0 217.7 272.3 327.0 381.6 436.2 490.0 544.6 599.3 653.9 708.6 762.3 817.0 871.6 926.2 980.9 1035.5 1089.3 1143.9 1198.6 54.6 : 54.6 108.4 163.0 217.7 272.3 327.0 381.6 435.4 490.0 544.6 599.3 653.9 707.7 762.3 817.0 871.6 926.2 980.9 1034.6 1089.3 1143.9 1198.6 109.3 : 53.8 108.4 163.0 217.7 272.3 327.0 380.7 435.4 490.0 544.6 599.3 653.0 707.7 762.3 817.0 871.6 926.2 980.0 1034.6 1089.3 1143.9 1198.6 163.0 : 54.6 109.3 163.9 218.6 273.2 327.0 381.6 436.2 490.9 545.5 599.3 653.9 708.6 763.2 817.8 872.5 926.2 980.9 1035.5 1090.2 1144.8 1198.6 217.7 : 54.6 109.3 163.9 218.6 272.3 327.0 381.6 436.2 490.9 544.6 599.3 653.9 708.6 763.2 817.8 871.6 926.2 980.9 1035.5 1090.2 1143.9 1198.6 272.3 : 54.6 109.3 163.9 217.7 272.3 327.0 381.6 436.2 490.0 544.6 599.3 653.9 708.6 763.2 817.0 871.6 926.2 980.9 1035.5 1089.3 1143.9 1198.6 327.0 : 54.6 109.3 163.0 217.7 272.3 327.0 381.6 435.4 490.0 544.6 599.3 653.9 708.6 762.3 817.0 871.6 926.2 980.9 1034.6 1089.3 1143.9 1198.6 381.6 : 54.6 108.4 163.0 217.7 272.3 327.0 380.7 435.4 490.0 544.6 599.3 653.9 707.7 762.3 817.0 871.6 926.2 980.0 1034.6 1089.3 1143.9 1198.6 436.2 : 53.8 108.4 163.0 217.7 272.3 326.1 380.7 435.4 490.0 544.6 599.3 653.0 707.7 762.3 817.0 871.6 925.4 980.0 1034.6 1089.3 1143.9 1198.6 490.0 : 54.6 109.3 163.9 218.6 272.3 327.0 381.6 436.2 490.9 545.5 599.3 653.9 708.6 763.2 817.8 871.6 926.2 980.9 1035.5 1090.2 1144.8 1198.6 544.6 : 54.6 109.3 163.9 217.7 272.3 327.0 381.6 436.2 490.9 544.6 599.3 653.9 708.6 763.2 817.0 871.6 926.2 980.9 1035.5 1090.2 1143.9 1198.6 599.3 : 54.6 109.3 163.0 217.7 272.3 327.0 381.6 436.2 490.0 544.6 599.3 653.9 708.6 762.3 817.0 871.6 926.2 980.9 1035.5 1089.3 1143.9 1198.6 653.9 : 54.6 108.4 163.0 217.7 272.3 327.0 381.6 435.4 490.0 544.6 599.3 653.9 707.7 762.3 817.0 871.6 926.2 980.9 1034.6 1089.3 1143.9 1198.6 708.6 : 53.8 108.4 163.0 217.7 272.3 327.0 380.7 435.4 490.0 544.6 599.3 653.0 707.7 762.3 817.0 871.6 926.2 980.0 1034.6 1089.3 1143.9 1198.6 762.3 : 54.6 109.3 163.9 218.6 273.2 327.0 381.6 436.2 490.9 545.5 599.3 653.9 708.6 763.2 817.8 872.5 926.2 980.9 1035.5 1090.2 1144.8 1198.6 817.0 : 54.6 109.3 163.9 218.6 272.3 327.0 381.6 436.2 490.9 544.6 599.3 653.9 708.6 763.2 817.8 871.6 926.2 980.9 1035.5 1090.2 1143.9 1198.6 871.6 : 54.6 109.3 163.9 217.7 272.3 327.0 381.6 436.2 490.0 544.6 599.3 653.9 708.6 763.2 817.0 871.6 926.2 980.9 1035.5 1089.3 1143.9 1198.6 926.2 : 54.6 109.3 163.0 217.7 272.3 327.0 381.6 435.4 490.0 544.6 599.3 653.9 708.6 762.3 817.0 871.6 926.2 980.9 1034.6 1089.3 1143.9 1198.6 980.9 : 54.6 108.4 163.0 217.7 272.3 327.0 380.7 435.4 490.0 544.6 599.3 653.9 707.7 762.3 817.0 871.6 926.2 980.0 1034.6 1089.3 1143.9 1198.6 1035.5: 53.8 108.4 163.0 217.7 272.3 326.1 380.7 435.4 490.0 544.6 599.3 653.0 707.7 762.3 817.0 871.6 925.4 980.0 1034.6 1089.3 1143.9 1198.6 1089.3: 54.6 109.3 163.9 218.6 272.3 327.0 381.6 436.2 490.9 545.5 599.3 653.9 708.6 763.2 817.8 871.6 926.2 980.9 1035.5 1090.2 1144.8 1198.6 1143.9: 54.6 109.3 163.9 217.7 272.3 327.0 381.6 436.2 490.9 544.6 599.3 653.9 708.6 763.2 817.0 871.6 926.2 980.9 1035.5 1090.2 1143.9 1198.6 1198.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.7600 .. 54.6400 cents 0.88000 cents 53.76000 cents 2: 108.4000 .. 109.2800 cents 0.88000 cents 53.76000 cents 3: 163.0400 .. 163.9200 cents 0.88000 cents 53.76000 cents 4: 217.6800 .. 218.5600 cents 0.88000 cents 53.76000 cents 5: 272.3200 .. 273.2000 cents 0.88000 cents 53.76000 cents 6: 326.0800 .. 326.9600 cents 0.88000 cents 52.88000 cents 7: 380.7200 .. 381.6000 cents 0.88000 cents 53.76000 cents 8: 435.3600 .. 436.2400 cents 0.88000 cents 53.76000 cents 9: 490.0000 .. 490.8800 cents 0.88000 cents 53.76000 cents 10: 544.6400 .. 545.5200 cents 0.88000 cents 53.76000 cents 11: 599.2800 .. 599.2800 cents 1/1, 0.0000 cents 53.76000 cents 12: 653.0400 .. 653.9200 cents 0.88000 cents 53.76000 cents 13: 707.6800 .. 708.5600 cents 0.88000 cents 53.76000 cents 14: 762.3200 .. 763.2000 cents 0.88000 cents 53.76000 cents 15: 816.9600 .. 817.8400 cents 0.88000 cents 53.76000 cents 16: 871.6000 .. 872.4800 cents 0.88000 cents 53.76000 cents 17: 925.3600 .. 926.2400 cents 0.88000 cents 52.88000 cents 18: 980.0000 .. 980.8800 cents 0.88000 cents 53.76000 cents 19: 1034.6400 .. 1035.5200 cents 0.88000 cents 53.76000 cents 20: 1089.2800 .. 1090.1600 cents 0.88000 cents 53.76000 cents 21: 1143.9200 .. 1144.8000 cents 0.88000 cents 53.76000 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 53.76000 cents, class 1 Average step (divided formal octave): 54.4800 cents Largest one step interval : 54.64000 cents Average / Smallest step : 1.013393 Largest / Average step : 1.002937 Largest / Smallest step : 1.016369 Median interval of one step : 54.64000 cents, amount: 18 Most common interval of one step : 54.64000 cents, amount: 18 Least squares average step : 54.47954 cents, oct.: 1198.54980 cents Scale is strictly proper Scale is maximally even in 1360-tone equal temperament Scale has 2 repeating blocks of 11 notes Blocks have Myhill's property chromas: 0.88000 cents and 52.88000 cents, ratio: 60.090909 generators: 5 of 272.32000 cents and 6 of 326.96000 cents ET pair of linear temperament : 22&1360 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1360-tone equal temperament with octave 1198.560 cents degrees: 62 124 185 247 309 371 433 495 556 618 680 742 804 865 927 989 1051 1113 1175 1236 1298 1360 Least number of segments generator : 681 of 600.161 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 989 of 871.600 cents and inv. generated superset size: 691 = 669 more = 3140.909% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAAABAAAABAAAAABAA Step pattern size order : LLSLLLLLSLLLLSLLLLLSLL Scale is a Constant Structure, by a margin of 52.88000 cents Scale diversity : 1.010265 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.985316 Number of different interval sizes : 41 = 1.95238 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.95238 = 41/21 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 0.88000 cents Most common intervals : 599.28000 cents & inv., amount: 22 Number of recognisable fifths : 22, average 708.2400 cents Number of recognisable fourths : 22, average 490.3200 cents Scale contains two identical disjunct "tetrachords" of 10 notes Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 22 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 11 Limited inverse transpositions : 11 Inversional symmetry on degrees : 0 11 Inversional symmetry on intervals : 5-6 16-17 -- 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: 0.2530 c. M:-0.4000 c. 700: 32 32 31 32 32 32 32 32 31 32 32 32 32 31 32 32 32 32 32 31 32 32 SP B ME I SD: 0.2392 c. M: 0.3783 c. 722: 33 33 32 33 33 33 33 33 32 33 33 33 33 32 33 33 33 33 33 32 33 33 SP B ME I SD: 0.2243 c. M: 0.3546 c. 744: 34 34 33 34 34 34 34 34 33 34 34 34 34 33 34 34 34 34 34 33 34 34 SP B ME I SD: 0.2101 c. M:-0.3323 c. 766: 35 35 34 35 35 35 35 35 34 35 35 35 35 34 35 35 35 35 35 34 35 35 SP B ME I SD: 0.1968 c. M: 0.3112 c. 788: 36 36 35 36 36 36 36 36 35 36 36 36 36 35 36 36 36 36 36 35 36 36 SP B ME I SD: 0.1843 c. M:-0.2914 c. 810: 37 37 36 37 37 37 37 37 36 37 37 37 37 36 37 37 37 37 37 36 37 37 SP B ME I SD: 0.1724 c. M: 0.2726 c. 832: 38 38 37 38 38 38 38 38 37 38 38 38 38 37 38 38 38 38 38 37 38 38 SP B ME I SD: 0.1612 c. M:-0.2548 c. 854: 39 39 38 39 39 39 39 39 38 39 39 39 39 38 39 39 39 39 39 38 39 39 SP B ME I SD: 0.1505 c. M:-0.2379 c. 876: 40 40 39 40 40 40 40 40 39 40 40 40 40 39 40 40 40 40 40 39 40 40 SP B ME I SD: 0.1404 c. M: 0.2219 c. 898: 41 41 40 41 41 41 41 41 40 41 41 41 41 40 41 41 41 41 41 40 41 41 SP B ME I SD: 0.1307 c. M: 0.2067 c. 920: 42 42 41 42 42 42 42 42 41 42 42 42 42 41 42 42 42 42 42 41 42 42 SP B ME I SD: 0.1215 c. M: 0.1922 c. 942: 43 43 42 43 43 43 43 43 42 43 43 43 43 42 43 43 43 43 43 42 43 43 SP B ME I SD: 0.1128 c. M: 0.1783 c. 964: 44 44 43 44 44 44 44 44 43 44 44 44 44 43 44 44 44 44 44 43 44 44 SP B ME I SD: 0.1044 c. M: 0.1651 c. 986: 45 45 44 45 45 45 45 45 44 45 45 45 45 44 45 45 45 45 45 44 45 45 SP B ME I SD: 0.0965 c. M: 0.1525 c. 1008: 46 46 45 46 46 46 46 46 45 46 46 46 46 45 46 46 46 46 46 45 46 46 SP B ME I SD: 0.0888 c. M: 0.1405 c. 1030: 47 47 46 47 47 47 47 47 46 47 47 47 47 46 47 47 47 47 47 46 47 47 SP B ME I SD: 0.0815 c. M:-0.1289 c. 1052: 48 48 47 48 48 48 48 48 47 48 48 48 48 47 48 48 48 48 48 47 48 48 SP B ME I SD: 0.0745 c. M: 0.1179 c. 1074: 49 49 48 49 49 49 49 49 48 49 49 49 49 48 49 49 49 49 49 48 49 49 SP B ME I SD: 0.0678 c. M: 0.1073 c. 1096: 50 50 49 50 50 50 50 50 49 50 50 50 50 49 50 50 50 50 50 49 50 50 SP B ME I SD: 0.0614 c. M: 0.0971 c. 1118: 51 51 50 51 51 51 51 51 50 51 51 51 51 50 51 51 51 51 51 50 51 51 SP B ME I SD: 0.0552 c. M:-0.0873 c. 1140: 52 52 51 52 52 52 52 52 51 52 52 52 52 51 52 52 52 52 52 51 52 52 SP B ME I SD: 0.0493 c. M:-0.0779 c. 1162: 53 53 52 53 53 53 53 53 52 53 53 53 53 52 53 53 53 53 53 52 53 53 SP B ME I SD: 0.0435 c. M:-0.0688 c. 1184: 54 54 53 54 54 54 54 54 53 54 54 54 54 53 54 54 54 54 54 53 54 54 SP B ME I SD: 0.0380 c. M:-0.0601 c. 1206: 55 55 54 55 55 55 55 55 54 55 55 55 55 54 55 55 55 55 55 54 55 55 SP B ME I SD: 0.0327 c. M: 0.0517 c. 1228: 56 56 55 56 56 56 56 56 55 56 56 56 56 55 56 56 56 56 56 55 56 56 SP B ME I SD: 0.0276 c. M: 0.0436 c. 1250: 57 57 56 57 57 57 57 57 56 57 57 57 57 56 57 57 57 57 57 56 57 57 SP B ME I SD: 0.0227 c. M: 0.0358 c. 1272: 58 58 57 58 58 58 58 58 57 58 58 58 58 57 58 58 58 58 58 57 58 58 SP B ME I SD: 0.0179 c. M:-0.0283 c. 1294: 59 59 58 59 59 59 59 59 58 59 59 59 59 58 59 59 59 59 59 58 59 59 SP B ME I SD: 0.0133 c. M: 0.0210 c. 1316: 60 60 59 60 60 60 60 60 59 60 60 60 60 59 60 60 60 60 60 59 60 60 SP B ME I SD: 0.0088 c. M: 0.0140 c. 1338: 61 61 60 61 61 61 61 61 60 61 61 61 61 60 61 61 61 61 61 60 61 61 SP B ME I SD: 0.0045 c. M: 0.0072 c. 1360: 62 62 61 62 62 62 62 62 61 62 62 62 62 61 62 62 62 62 62 61 62 62 SP B ME I SD: 0.0004 c. M: 0.0006 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 1.4400 cents 2 .. 4 match: 2 H SD: 3.3801 cents 3 .. 6 match: 3 H SD: 5.0506 cents 4 .. 8 match: 4 H SD: 3.6505 cents 5 .. 10 match: 5 H SD: 5.4528 cents 6 .. 12 match: 6 H SD: 3.7063 cents 7 .. 14 match: 7 H SD: 5.1118 cents 8 .. 16 match: 8 H SD: 3.9605 cents 9 .. 18 match: 9 H SD: 4.5792 cents 10 .. 20 match: 10 H SD: 4.0646 cents 11 .. 22 match: 11 H SD: 4.3711 cents 12 .. 24 match: 12 H SD: 3.7660 cents 13 .. 26 match: 13 H SD: 4.8766 cents 14 .. 28 match: 14 H SD: 3.5616 cents 15 .. 30 match: 15 H SD: 3.6804 cents 16 .. 32 match: 16 H SD: 3.5588 cents 17 .. 34 match: 17 H SD: 3.1876 cents 18 .. 36 match: 18 H SD: 3.1821 cents 19 .. 38 match: 18 SD: 4.2702 cents 20 .. 40 match: 19 S SD: 3.3088 cents 21 .. 42 match: 20 SD: 3.3916 cents 22 .. 44 match: 20 SD: 3.1007 cents 23 .. 46 match: 21 SD: 3.7021 cents 24 .. 48 match: 21 S SD: 2.4973 cents 25 .. 50 match: 21 SD: 3.0303 cents 26 .. 52 match: 21 SD: 3.5304 cents 27 .. 54 match: 22 SD: 2.8404 cents 28 .. 56 match: 22 SD: 2.2795 cents 29 .. 58 match: 22 SD: 2.1718 cents 30 .. 60 match: 22 SD: 2.0713 cents 37 .. 74 match: 22 SD: 2.0672 cents 38 .. 76 match: 22 SD: 1.9904 cents 40 .. 80 match: 22 SD: 1.9400 cents 41 .. 82 match: 22 SD: 1.8620 cents 43 .. 86 match: 22 SD: 1.6040 cents 48 .. 96 match: 22 SD: 1.5109 cents 49 .. 98 match: 22 SD: 1.4727 cents 52 .. 104 match: 22 SD: 1.3383 cents 58 .. 116 match: 22 SD: 1.1112 cents 59 .. 118 match: 22 SD: 1.1077 cents 61 .. 122 match: 22 SD: 1.0728 cents 63 .. 126 match: 22 SD: 1.0479 cents 72 .. 144 match: 22 SD: 1.0271 cents 73 .. 146 match: 22 SD: 0.9405 cents 81 .. 162 match: 22 SD: 0.8207 cents 89 .. 178 match: 22 SD: 0.6918 cents 105 .. 210 match: 22 SD: 0.6013 cents 111 .. 222 match: 22 SD: 0.5972 cents 119 .. 238 match: 22 SD: 0.5307 cents 121 .. 242 match: 22 SD: 0.5210 cents 122 .. 244 match: 22 SD: 0.5155 cents 143 .. 286 match: 22 SD: 0.4833 cents 150 .. 300 match: 22 SD: 0.4319 cents 154 .. 308 match: 22 SD: 0.3607 cents 186 .. 372 match: 22 SD: 0.3350 cents 202 .. 404 match: 22 SD: 0.3347 cents 211 .. 422 match: 22 SD: 0.2942 cents 244 .. 488 match: 22 SD: 0.2632 cents 251 .. 502 match: 22 SD: 0.2616 cents 275 .. 550 match: 22 SD: 0.2074 cents 312 .. 623 match: 22 SD: 0.2065 cents 324 .. 647 match: 22 SD: 0.2038 cents 336 .. 671 match: 22 SD: 0.1647 cents 370 .. 739 match: 22 SD: 0.1646 cents 394 .. 787 match: 22 SD: 0.1591 cents 403 .. 805 match: 22 SD: 0.1558 cents 425 .. 849 match: 22 SD: 0.1477 cents 433 .. 865 match: 22 SD: 0.1451 cents 446 .. 891 match: 22 SD: 0.1448 cents 447 .. 893 match: 22 SD: 0.1424 cents 471 .. 941 match: 22 SD: 0.1324 cents 486 .. 971 match: 22 SD: 0.1201 cents 506 .. 1011 match: 22 SD: 0.1078 cents 568 .. 1135 match: 22 SD: 0.0917 cents 597 .. 1193 match: 22 SD: 0.0801 cents