Scala analysis: xen18-erlich-doublewide-18
4L 14s MOS for Doublewide, L=108.40, s=54.64
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: 217.680 cents 217.680000 4: 272.320 cents 272.320000 5: 326.960 cents 326.960000 6: 381.600 cents 381.600000 7: 490.000 cents 490.000000 8: 544.640 cents 544.640000 9: 599.280 cents 599.280000 10: 653.920 cents 653.920000 11: 708.560 cents 708.560000 12: 816.960 cents 816.960000 13: 871.600 cents 871.600000 14: 926.240 cents 926.240000 15: 980.880 cents 980.880000 16: 1089.280 cents 1089.280000 17: 1143.920 cents 1143.920000 18: 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: 108.4000 cents 108.4000 4: 54.6400 cents 54.6400 5: 54.6400 cents 54.6400 6: 54.6400 cents 54.6400 7: 108.4000 cents 108.4000 8: 54.6400 cents 54.6400 9: 54.6400 cents 54.6400 10: 54.6400 cents 54.6400 11: 54.6400 cents 54.6400 12: 108.4000 cents 108.4000 13: 54.6400 cents 54.6400 14: 54.6400 cents 54.6400 15: 54.6400 cents 54.6400 16: 108.4000 cents 108.4000 17: 54.6400 cents 54.6400 18: 54.6400 cents 54.6400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 14 54.64000 cents 1: 4 108.40000 cents 2: 10 109.28000 cents 2: 8 163.04000 cents 3: 6 163.92000 cents 3: 12 217.68000 cents 4: 2 218.56000 cents 4: 16 272.32000 cents 5: 16 326.96000 cents 5: 2 380.72000 cents 6: 12 381.60000 cents 6: 6 435.36000 cents 7: 8 436.24000 cents 7: 10 490.00000 cents 8: 4 490.88000 cents 8: 14 544.64000 cents 9: 18 599.28000 cents 10: 14 653.92000 cents 10: 4 707.68000 cents 11: 10 708.56000 cents 11: 8 762.32000 cents 12: 6 763.20000 cents 12: 12 816.96000 cents 13: 2 817.84000 cents 13: 16 871.60000 cents 14: 16 926.24000 cents 14: 2 980.00000 cents 15: 12 980.88000 cents 15: 6 1034.64000 cents 16: 8 1035.52000 cents 16: 10 1089.28000 cents 17: 4 1090.16000 cents 17: 14 1143.92000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.94118 = 33/17
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 0.0 : 54.6 109.3 217.7 272.3 327.0 381.6 490.0 544.6 599.3 653.9 708.6 817.0 871.6 926.2 980.9 1089.3 1143.9 1198.6 54.6 : 54.6 163.0 217.7 272.3 327.0 435.4 490.0 544.6 599.3 653.9 762.3 817.0 871.6 926.2 1034.6 1089.3 1143.9 1198.6 109.3 : 108.4 163.0 217.7 272.3 380.7 435.4 490.0 544.6 599.3 707.7 762.3 817.0 871.6 980.0 1034.6 1089.3 1143.9 1198.6 217.7 : 54.6 109.3 163.9 272.3 327.0 381.6 436.2 490.9 599.3 653.9 708.6 763.2 871.6 926.2 980.9 1035.5 1090.2 1198.6 272.3 : 54.6 109.3 217.7 272.3 327.0 381.6 436.2 544.6 599.3 653.9 708.6 817.0 871.6 926.2 980.9 1035.5 1143.9 1198.6 327.0 : 54.6 163.0 217.7 272.3 327.0 381.6 490.0 544.6 599.3 653.9 762.3 817.0 871.6 926.2 980.9 1089.3 1143.9 1198.6 381.6 : 108.4 163.0 217.7 272.3 327.0 435.4 490.0 544.6 599.3 707.7 762.3 817.0 871.6 926.2 1034.6 1089.3 1143.9 1198.6 490.0 : 54.6 109.3 163.9 218.6 327.0 381.6 436.2 490.9 599.3 653.9 708.6 763.2 817.8 926.2 980.9 1035.5 1090.2 1198.6 544.6 : 54.6 109.3 163.9 272.3 327.0 381.6 436.2 544.6 599.3 653.9 708.6 763.2 871.6 926.2 980.9 1035.5 1143.9 1198.6 599.3 : 54.6 109.3 217.7 272.3 327.0 381.6 490.0 544.6 599.3 653.9 708.6 817.0 871.6 926.2 980.9 1089.3 1143.9 1198.6 653.9 : 54.6 163.0 217.7 272.3 327.0 435.4 490.0 544.6 599.3 653.9 762.3 817.0 871.6 926.2 1034.6 1089.3 1143.9 1198.6 708.6 : 108.4 163.0 217.7 272.3 380.7 435.4 490.0 544.6 599.3 707.7 762.3 817.0 871.6 980.0 1034.6 1089.3 1143.9 1198.6 817.0 : 54.6 109.3 163.9 272.3 327.0 381.6 436.2 490.9 599.3 653.9 708.6 763.2 871.6 926.2 980.9 1035.5 1090.2 1198.6 871.6 : 54.6 109.3 217.7 272.3 327.0 381.6 436.2 544.6 599.3 653.9 708.6 817.0 871.6 926.2 980.9 1035.5 1143.9 1198.6 926.2 : 54.6 163.0 217.7 272.3 327.0 381.6 490.0 544.6 599.3 653.9 762.3 817.0 871.6 926.2 980.9 1089.3 1143.9 1198.6 980.9 : 108.4 163.0 217.7 272.3 327.0 435.4 490.0 544.6 599.3 707.7 762.3 817.0 871.6 926.2 1034.6 1089.3 1143.9 1198.6 1089.3: 54.6 109.3 163.9 218.6 327.0 381.6 436.2 490.9 599.3 653.9 708.6 763.2 817.8 926.2 980.9 1035.5 1090.2 1198.6 1143.9: 54.6 109.3 163.9 272.3 327.0 381.6 436.2 544.6 599.3 653.9 708.6 763.2 871.6 926.2 980.9 1035.5 1143.9 1198.6 1198.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.6400 .. 108.4000 cents 53.76000 cents 54.64000 cents 2: 109.2800 .. 163.0400 cents 53.76000 cents 0.88000 cents 3: 163.9200 .. 217.6800 cents 53.76000 cents 0.88000 cents 4: 218.5600 .. 272.3200 cents 53.76000 cents 0.88000 cents 5: 326.9600 .. 380.7200 cents 53.76000 cents 54.64000 cents 6: 381.6000 .. 435.3600 cents 53.76000 cents 0.88000 cents 7: 436.2400 .. 490.0000 cents 53.76000 cents 0.88000 cents 8: 490.8800 .. 544.6400 cents 53.76000 cents 0.88000 cents 9: 599.2800 .. 599.2800 cents 1/1, 0.0000 cents 54.64000 cents 10: 653.9200 .. 707.6800 cents 53.76000 cents 54.64000 cents 11: 708.5600 .. 762.3200 cents 53.76000 cents 0.88000 cents 12: 763.2000 .. 816.9600 cents 53.76000 cents 0.88000 cents 13: 817.8400 .. 871.6000 cents 53.76000 cents 0.88000 cents 14: 926.2400 .. 980.0000 cents 53.76000 cents 54.64000 cents 15: 980.8800 .. 1034.6400 cents 53.76000 cents 0.88000 cents 16: 1035.5200 .. 1089.2800 cents 53.76000 cents 0.88000 cents 17: 1090.1600 .. 1143.9200 cents 53.76000 cents 0.88000 cents
SHOW DATA
Number of notes : 18 -- Interval properties -- Smallest interval : 54.64000 cents, class 1 Average step (divided formal octave): 66.5867 cents Largest one step interval : 108.40000 cents Average / Smallest step : 1.218643 Largest / Average step : 1.627954 Largest / Smallest step : 1.983895 Median interval of one step : 54.64000 cents, amount: 14 Most common interval of one step : 54.64000 cents, amount: 14 Least squares average step : 66.72262 cents, oct.: 1201.00711 cents Scale is strictly proper Scale has 2 repeating blocks of 9 notes Blocks have Myhill's property chromas: 53.76000 cents and 0.88000 cents, ratio: 61.090909 generators: 4 of 272.32000 cents and 5 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 1338-tone equal temperament with octave 1198.560 cents degrees: 61 122 243 304 365 426 547 608 669 730 791 912 973 1034 1095 1216 1277 1338 Least number of segments generator : 671 of 601.072 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 973 of 871.599 cents and inv. generated superset size: 678 = 660 more = 3766.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAAAABAAABAA Step pattern size order : SSLSSSLSSSSLSSSLSS Scale is a Constant Structure, by a margin of 0.88000 cents Scale diversity : 1.076320 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.282339 Number of different interval sizes : 33 = 1.94118 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.94118 = 33/17 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 0.88000 cents Most common intervals : 599.28000 cents & inv., amount: 18 Number of recognisable fifths : 14, average 708.3086 cents Number of recognisable fourths : 14, average 490.2514 cents Scale contains two identical disjunct "tetrachords" of 8 notes Formal octave complements present : 18 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 9 Limited inverse transpositions : 9 Inversional symmetry on degrees : 0 9 Inversional symmetry on intervals : 4-5 13-14 -- Rational properties --
FIT/MODE
18: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 15.4231 c. M:-23.8933 c. 22: 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 P B ME I SD: 0.2066 c. M: 0.3200 c. 700: 32 32 63 32 32 32 63 32 32 32 32 63 32 32 32 63 32 32 SP B DE I SD: 0.1953 c. M: 0.3026 c. 722: 33 33 65 33 33 33 65 33 33 33 33 65 33 33 33 65 33 33 SP B DE I SD: 0.1831 c. M:-0.2837 c. 744: 34 34 67 34 34 34 67 34 34 34 34 67 34 34 34 67 34 34 SP B DE I SD: 0.1716 c. M: 0.2658 c. 766: 35 35 69 35 35 35 69 35 35 35 35 69 35 35 35 69 35 35 SP B DE I SD: 0.1607 c. M: 0.2490 c. 788: 36 36 71 36 36 36 71 36 36 36 36 71 36 36 36 71 36 36 SP B DE I SD: 0.1505 c. M:-0.2331 c. 810: 37 37 73 37 37 37 73 37 37 37 37 73 37 37 37 73 37 37 SP B DE I SD: 0.1408 c. M: 0.2181 c. 832: 38 38 75 38 38 38 75 38 38 38 38 75 38 38 38 75 38 38 SP B DE I SD: 0.1316 c. M:-0.2038 c. 854: 39 39 77 39 39 39 77 39 39 39 39 77 39 39 39 77 39 39 SP B DE I SD: 0.1229 c. M:-0.1904 c. 876: 40 40 79 40 40 40 79 40 40 40 40 79 40 40 40 79 40 40 SP B DE I SD: 0.1146 c. M: 0.1775 c. 898: 41 41 81 41 41 41 81 41 41 41 41 81 41 41 41 81 41 41 SP B DE I SD: 0.1067 c. M: 0.1653 c. 920: 42 42 83 42 42 42 83 42 42 42 42 83 42 42 42 83 42 42 SP B DE I SD: 0.0992 c. M: 0.1537 c. 942: 43 43 85 43 43 43 85 43 43 43 43 85 43 43 43 85 43 43 SP B DE I SD: 0.0921 c. M: 0.1427 c. 964: 44 44 87 44 44 44 87 44 44 44 44 87 44 44 44 87 44 44 SP B DE I SD: 0.0853 c. M:-0.1321 c. 986: 45 45 89 45 45 45 89 45 45 45 45 89 45 45 45 89 45 45 SP B DE I SD: 0.0788 c. M: 0.1220 c. 1008: 46 46 91 46 46 46 91 46 46 46 46 91 46 46 46 91 46 46 SP B DE I SD: 0.0725 c. M: 0.1124 c. 1030: 47 47 93 47 47 47 93 47 47 47 47 93 47 47 47 93 47 47 SP B DE I SD: 0.0666 c. M: 0.1031 c. 1052: 48 48 95 48 48 48 95 48 48 48 48 95 48 48 48 95 48 48 SP B DE I SD: 0.0609 c. M: 0.0943 c. 1074: 49 49 97 49 49 49 97 49 49 49 49 97 49 49 49 97 49 49 SP B DE I SD: 0.0554 c. M:-0.0858 c. 1096: 50 50 99 50 50 50 99 50 50 50 50 99 50 50 50 99 50 50 SP B DE I SD: 0.0501 c. M: 0.0777 c. 1118: 51 51 101 51 51 51 101 51 51 51 51 101 51 51 51 101 51 51 SP B DE I SD: 0.0451 c. M:-0.0698 c. 1140: 52 52 103 52 52 52 103 52 52 52 52 103 52 52 52 103 52 52 SP B DE I SD: 0.0402 c. M:-0.0623 c. 1162: 53 53 105 53 53 53 105 53 53 53 53 105 53 53 53 105 53 53 SP B DE I SD: 0.0356 c. M: 0.0551 c. 1184: 54 54 107 54 54 54 107 54 54 54 54 107 54 54 54 107 54 54 SP B DE I SD: 0.0311 c. M: 0.0481 c. 1206: 55 55 109 55 55 55 109 55 55 55 55 109 55 55 55 109 55 55 SP B DE I SD: 0.0267 c. M: 0.0414 c. 1228: 56 56 111 56 56 56 111 56 56 56 56 111 56 56 56 111 56 56 SP B DE I SD: 0.0225 c. M: 0.0349 c. 1250: 57 57 113 57 57 57 113 57 57 57 57 113 57 57 57 113 57 57 SP B DE I SD: 0.0185 c. M: 0.0287 c. 1272: 58 58 115 58 58 58 115 58 58 58 58 115 58 58 58 115 58 58 SP B DE I SD: 0.0146 c. M: 0.0226 c. 1294: 59 59 117 59 59 59 117 59 59 59 59 117 59 59 59 117 59 59 SP B DE I SD: 0.0109 c. M: 0.0168 c. 1316: 60 60 119 60 60 60 119 60 60 60 60 119 60 60 60 119 60 60 SP B DE I SD: 0.0072 c. M: 0.0112 c. 1338: 61 61 121 61 61 61 121 61 61 61 61 121 61 61 61 121 61 61 SP B DE I SD: 0.0037 c. M:-0.0057 c. 1360: 62 62 123 62 62 62 123 62 62 62 62 123 62 62 62 123 62 62 SP B DE I SD: 0.0003 c. M: 0.0005 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: 8.4146 cents 6 .. 12 match: 6 H SD: 7.2577 cents 7 .. 14 match: 7 H SD: 10.0211 cents 8 .. 16 match: 8 H SD: 3.9605 cents 9 .. 18 match: 9 H SD: 8.0660 cents 10 .. 20 match: 10 H SD: 8.0046 cents 11 .. 22 match: 10 SD: 8.2239 cents 12 .. 24 match: 11 SD: 4.1760 cents 13 .. 26 match: 13 H SD: 5.5661 cents 14 .. 28 match: 13 SD: 4.3961 cents 15 .. 30 match: 14 S SD: 4.0738 cents 16 .. 32 match: 14 S SD: 3.9774 cents 17 .. 34 match: 15 SD: 3.5449 cents 18 .. 36 match: 15 SD: 4.1155 cents 19 .. 38 match: 16 S SD: 4.5564 cents 20 .. 40 match: 15 SD: 3.8246 cents 21 .. 42 match: 16 SD: 3.9946 cents 22 .. 44 match: 16 SD: 3.5715 cents 24 .. 48 match: 18 S SD: 2.8350 cents 28 .. 56 match: 18 SD: 2.4522 cents 29 .. 58 match: 18 SD: 2.4504 cents 30 .. 60 match: 18 SD: 2.0301 cents 43 .. 86 match: 18 SD: 1.7656 cents 46 .. 92 match: 18 SD: 1.6603 cents 48 .. 96 match: 18 SD: 1.6141 cents 52 .. 104 match: 18 SD: 1.5300 cents 57 .. 114 match: 18 SD: 1.4080 cents 58 .. 116 match: 18 SD: 1.1103 cents 65 .. 130 match: 18 SD: 1.0711 cents 73 .. 146 match: 18 SD: 1.0565 cents 76 .. 152 match: 18 SD: 0.9794 cents 81 .. 162 match: 18 SD: 0.9506 cents 89 .. 178 match: 18 SD: 0.6829 cents 105 .. 210 match: 18 SD: 0.6619 cents 106 .. 212 match: 18 SD: 0.6510 cents 119 .. 238 match: 18 SD: 0.5825 cents 122 .. 244 match: 18 SD: 0.5743 cents 125 .. 250 match: 18 SD: 0.5699 cents 126 .. 252 match: 18 SD: 0.5663 cents 135 .. 270 match: 18 SD: 0.5228 cents 150 .. 300 match: 18 SD: 0.5120 cents 153 .. 306 match: 18 SD: 0.5031 cents 154 .. 308 match: 18 SD: 0.4112 cents 184 .. 368 match: 18 SD: 0.4030 cents 186 .. 372 match: 18 SD: 0.3394 cents 211 .. 422 match: 18 SD: 0.2953 cents 247 .. 494 match: 18 SD: 0.2644 cents 275 .. 550 match: 18 SD: 0.2393 cents 312 .. 623 match: 18 SD: 0.1985 cents 336 .. 671 match: 18 SD: 0.1830 cents 370 .. 739 match: 18 SD: 0.1606 cents 433 .. 865 match: 18 SD: 0.1453 cents 462 .. 923 match: 18 SD: 0.1344 cents 471 .. 941 match: 18 SD: 0.1138 cents 568 .. 1135 match: 18 SD: 0.1040 cents 597 .. 1193 match: 18 SD: 0.0909 cents