Scala analysis: xen18-erlich-keemun-19
15L 4s MOS for Keemun, L=68.17, s=45.16
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68.170 cents 68.170000 2: 136.340 cents 136.340000 3: 181.500 cents 181.500000 4: 249.670 cents 249.670000 5: 317.840 cents 317.840000 6: 386.010 cents 386.010000 7: 454.180 cents 454.180000 8: 499.340 cents 499.340000 9: 567.510 cents 567.510000 10: 635.680 cents 635.680000 11: 703.850 cents 703.850000 12: 749.010 cents 749.010000 13: 817.180 cents 817.180000 14: 885.350 cents 885.350000 15: 953.520 cents 953.520000 16: 1021.690 cents 1021.690000 17: 1066.850 cents 1066.850000 18: 1135.020 cents 1135.020000 19: 1203.190 cents 1203.190000
SHOW/INTERVAL
0: 68.1700 cents 68.1700 1: 68.1700 cents 68.1700 2: 68.1700 cents 68.1700 3: 45.1600 cents 45.1600 4: 68.1700 cents 68.1700 5: 68.1700 cents 68.1700 6: 68.1700 cents 68.1700 7: 68.1700 cents 68.1700 8: 45.1600 cents 45.1600 9: 68.1700 cents 68.1700 10: 68.1700 cents 68.1700 11: 68.1700 cents 68.1700 12: 45.1600 cents 45.1600 13: 68.1700 cents 68.1700 14: 68.1700 cents 68.1700 15: 68.1700 cents 68.1700 16: 68.1700 cents 68.1700 17: 45.1600 cents 45.1600 18: 68.1700 cents 68.1700 19: 68.1700 cents 68.1700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 45.16000 cents 1: 15 68.17000 cents 2: 8 113.33000 cents 2: 11 136.34000 cents 3: 12 181.50000 cents 3: 7 204.51000 cents 4: 16 249.67000 cents 4: 3 272.68000 cents 5: 1 294.83000 cents 5: 18 317.84000 cents 6: 5 363.00000 cents 6: 14 386.01000 cents 7: 9 431.17000 cents 7: 10 454.18000 cents 8: 13 499.34000 cents 8: 6 522.35000 cents 9: 17 567.51000 cents 9: 2 590.52000 cents 10: 2 612.67000 cents 10: 17 635.68000 cents 11: 6 680.84000 cents 11: 13 703.85000 cents 12: 10 749.01000 cents 12: 9 772.02000 cents 13: 14 817.18000 cents 13: 5 840.19000 cents 14: 18 885.35000 cents 14: 1 908.36000 cents 15: 3 930.51000 cents 15: 16 953.52000 cents 16: 7 998.68000 cents 16: 12 1021.69000 cents 17: 11 1066.85000 cents 17: 8 1089.86000 cents 18: 15 1135.02000 cents 18: 4 1158.03000 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 : 68.2 136.3 181.5 249.7 317.8 386.0 454.2 499.3 567.5 635.7 703.8 749.0 817.2 885.3 953.5 1021.7 1066.8 1135.0 1203.2 68.2 : 68.2 113.3 181.5 249.7 317.8 386.0 431.2 499.3 567.5 635.7 680.8 749.0 817.2 885.3 953.5 998.7 1066.8 1135.0 1203.2 136.3 : 45.2 113.3 181.5 249.7 317.8 363.0 431.2 499.3 567.5 612.7 680.8 749.0 817.2 885.3 930.5 998.7 1066.8 1135.0 1203.2 181.5 : 68.2 136.3 204.5 272.7 317.8 386.0 454.2 522.4 567.5 635.7 703.8 772.0 840.2 885.3 953.5 1021.7 1089.9 1158.0 1203.2 249.7 : 68.2 136.3 204.5 249.7 317.8 386.0 454.2 499.3 567.5 635.7 703.8 772.0 817.2 885.4 953.5 1021.7 1089.9 1135.0 1203.2 317.8 : 68.2 136.3 181.5 249.7 317.8 386.0 431.2 499.3 567.5 635.7 703.8 749.0 817.2 885.3 953.5 1021.7 1066.8 1135.0 1203.2 386.0 : 68.2 113.3 181.5 249.7 317.8 363.0 431.2 499.3 567.5 635.7 680.8 749.0 817.2 885.3 953.5 998.7 1066.8 1135.0 1203.2 454.2 : 45.2 113.3 181.5 249.7 294.8 363.0 431.2 499.3 567.5 612.7 680.8 749.0 817.2 885.4 930.5 998.7 1066.9 1135.0 1203.2 499.3 : 68.2 136.3 204.5 249.7 317.8 386.0 454.2 522.4 567.5 635.7 703.8 772.0 840.2 885.3 953.5 1021.7 1089.9 1158.0 1203.2 567.5 : 68.2 136.3 181.5 249.7 317.8 386.0 454.2 499.3 567.5 635.7 703.8 772.0 817.2 885.4 953.5 1021.7 1089.9 1135.0 1203.2 635.7 : 68.2 113.3 181.5 249.7 317.8 386.0 431.2 499.3 567.5 635.7 703.8 749.0 817.2 885.3 953.5 1021.7 1066.8 1135.0 1203.2 703.8 : 45.2 113.3 181.5 249.7 317.8 363.0 431.2 499.3 567.5 635.7 680.8 749.0 817.2 885.4 953.5 998.7 1066.8 1135.0 1203.2 749.0 : 68.2 136.3 204.5 272.7 317.8 386.0 454.2 522.4 590.5 635.7 703.8 772.0 840.2 908.4 953.5 1021.7 1089.9 1158.0 1203.2 817.2 : 68.2 136.3 204.5 249.7 317.8 386.0 454.2 522.4 567.5 635.7 703.8 772.0 840.2 885.3 953.5 1021.7 1089.9 1135.0 1203.2 885.3 : 68.2 136.3 181.5 249.7 317.8 386.0 454.2 499.3 567.5 635.7 703.9 772.0 817.2 885.3 953.5 1021.7 1066.9 1135.0 1203.2 953.5 : 68.2 113.3 181.5 249.7 317.8 386.0 431.2 499.3 567.5 635.7 703.8 749.0 817.2 885.4 953.5 998.7 1066.8 1135.0 1203.2 1021.7: 45.2 113.3 181.5 249.7 317.8 363.0 431.2 499.3 567.5 635.7 680.8 749.0 817.2 885.3 930.5 998.7 1066.8 1135.0 1203.2 1066.8: 68.2 136.3 204.5 272.7 317.8 386.0 454.2 522.4 590.5 635.7 703.8 772.0 840.2 885.4 953.5 1021.7 1089.9 1158.0 1203.2 1135.0: 68.2 136.3 204.5 249.7 317.8 386.0 454.2 522.3 567.5 635.7 703.8 772.0 817.2 885.3 953.5 1021.7 1089.9 1135.0 1203.2 1203.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 45.1600 .. 68.1700 cents 23.01000 cents 45.16000 cents 2: 113.3300 .. 136.3400 cents 23.01000 cents 45.16000 cents 3: 181.5000 .. 204.5100 cents 23.01000 cents 45.16000 cents 4: 249.6700 .. 272.6800 cents 23.01000 cents 45.16000 cents 5: 294.8300 .. 317.8400 cents 23.01000 cents 22.15000 cents 6: 363.0000 .. 386.0100 cents 23.01000 cents 45.16000 cents 7: 431.1700 .. 454.1800 cents 23.01000 cents 45.16000 cents 8: 499.3400 .. 522.3500 cents 23.01000 cents 45.16000 cents 9: 567.5100 .. 590.5200 cents 23.01000 cents 45.16000 cents 10: 612.6700 .. 635.6800 cents 23.01000 cents 22.15000 cents 11: 680.8400 .. 703.8500 cents 23.01000 cents 45.16000 cents 12: 749.0100 .. 772.0200 cents 23.01000 cents 45.16000 cents 13: 817.1800 .. 840.1900 cents 23.01000 cents 45.16000 cents 14: 885.3500 .. 908.3600 cents 23.01000 cents 45.16000 cents 15: 930.5100 .. 953.5200 cents 23.01000 cents 22.15000 cents 16: 998.6800 .. 1021.6900 cents 23.01000 cents 45.16000 cents 17: 1066.8500 .. 1089.8600 cents 23.01000 cents 45.16000 cents 18: 1135.0200 .. 1158.0300 cents 23.01000 cents 45.16000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 45.16000 cents, class 1 Average step (divided formal octave): 63.3258 cents Largest one step interval : 68.17000 cents Average / Smallest step : 1.402254 Largest / Average step : 1.076497 Largest / Smallest step : 1.509522 Median interval of one step : 68.17000 cents, amount: 15 Most common interval of one step : 68.17000 cents, amount: 15 Least squares average step : 63.26058 cents, oct.: 1201.95100 cents Scale is strictly proper Scale has Myhill's property chromas: 23.01000 cents and 22.15000 cents, ratio: 1.038826 generators: 5 of 317.84000 cents and 14 of 885.35000 cents ET pair of linear temperament : 15&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1359-tone equal temperament with octave 1203.190 cents degrees: 77 154 205 282 359 436 513 564 641 718 795 846 923 1000 1077 1154 1205 1282 1359 generators: 359 and 1000 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAAABAAABAAAABAA Step pattern size order : LLSLLLLSLLLSLLLLSLL Scale is a Constant Structure, by a margin of 22.15000 cents Scale diversity : 1.187005 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.655765 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 : 22.15000 cents Most common intervals : 317.84000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 454.180 885.350 cents Most common triad is 0.0 317.840 885.350 cents, amount: 17 Number of recognisable fifths : 13, average 703.8500 cents Number of recognisable fourths : 13, average 499.3400 cents Scale contains two identical disjunct "tetrachords" of 9 notes 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: 6.6332 c. M: 10.8995 c. 34: 2 2 1 2 2 2 2 1 2 2 2 1 2 2 2 2 1 2 2 P M ME I SD: 3.5683 c. M: 5.8632 c. 53: 3 3 2 3 3 3 3 2 3 3 3 2 3 3 3 3 2 3 3 SP M ME I SD: 0.0889 c. M: 0.1460 c. 723: 41 41 27 41 41 41 41 27 41 41 41 27 41 41 41 41 27 41 41 SP M DE I SD: 0.0831 c. M: 0.1366 c. 776: 44 44 29 44 44 44 44 29 44 44 44 29 44 44 44 44 29 44 44 SP M DE I SD: 0.0714 c. M: 0.1173 c. 829: 47 47 31 47 47 47 47 31 47 47 47 31 47 47 47 47 31 47 47 SP M DE I SD: 0.0611 c. M:-0.1004 c. 882: 50 50 33 50 50 50 50 33 50 50 50 33 50 50 50 50 33 50 50 SP M DE I SD: 0.0521 c. M:-0.0856 c. 935: 53 53 35 53 53 53 53 35 53 53 53 35 53 53 53 53 35 53 53 SP M DE I SD: 0.0441 c. M:-0.0725 c. 988: 56 56 37 56 56 56 56 37 56 56 56 37 56 56 56 56 37 56 56 SP M DE I SD: 0.0370 c. M: 0.0608 c. 1041: 59 59 39 59 59 59 59 39 59 59 59 39 59 59 59 59 39 59 59 SP M DE I SD: 0.0306 c. M: 0.0502 c. 1094: 62 62 41 62 62 62 62 41 62 62 62 41 62 62 62 62 41 62 62 SP M DE I SD: 0.0248 c. M: 0.0407 c. 1147: 65 65 43 65 65 65 65 43 65 65 65 43 65 65 65 65 43 65 65 SP M DE I SD: 0.0195 c. M: 0.0321 c. 1200: 68 68 45 68 68 68 68 45 68 68 68 45 68 68 68 68 45 68 68 SP M DE I SD: 0.0147 c. M: 0.0242 c. 1253: 71 71 47 71 71 71 71 47 71 71 71 47 71 71 71 71 47 71 71 SP M DE I SD: 0.0104 c. M: 0.0170 c. 1306: 74 74 49 74 74 74 74 49 74 74 74 49 74 74 74 74 49 74 74 SP M DE I SD: 0.0063 c. M: 0.0104 c. 1359: 77 77 51 77 77 77 77 51 77 77 77 51 77 77 77 77 51 77 77 SP M DE I SD: 0.0026 c. M: 0.0043 c. 1412: 80 80 53 80 80 80 80 53 80 80 80 53 80 80 80 80 53 80 80 SP M DE I SD: 0.0008 c. M: 0.0013 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 3.1900 cents 2 .. 4 match: 2 H SD: 1.8552 cents 3 .. 6 match: 3 H SD: 1.1942 cents 4 .. 8 match: 4 H SD: 3.9380 cents 5 .. 10 match: 5 H SD: 3.2805 cents 6 .. 12 match: 6 H SD: 4.1436 cents 7 .. 14 match: 7 H SD: 7.2959 cents 8 .. 16 match: 8 H SD: 5.6130 cents 9 .. 18 match: 9 H SD: 6.0363 cents 10 .. 20 match: 10 H SD: 4.7122 cents 11 .. 22 match: 11 H SD: 6.2301 cents 12 .. 24 match: 12 H SD: 4.1404 cents 13 .. 26 match: 13 H SD: 4.4704 cents 14 .. 28 match: 14 H SD: 5.0951 cents 15 .. 30 match: 15 H SD: 3.9801 cents 16 .. 32 match: 16 H SD: 4.3688 cents 17 .. 34 match: 15 SD: 5.6873 cents 18 .. 36 match: 17 SD: 3.9143 cents 19 .. 38 match: 16 SD: 4.3023 cents 20 .. 40 match: 18 SD: 2.7517 cents 21 .. 42 match: 17 S SD: 3.6128 cents 22 .. 44 match: 17 SD: 4.2484 cents 23 .. 46 match: 18 SD: 3.8085 cents 24 .. 48 match: 19 SD: 2.8067 cents 25 .. 50 match: 18 SD: 2.7858 cents 26 .. 52 match: 19 SD: 2.5182 cents 31 .. 62 match: 18 SD: 2.6763 cents 33 .. 66 match: 19 SD: 2.3653 cents 36 .. 72 match: 19 SD: 2.0519 cents 39 .. 78 match: 19 SD: 1.9982 cents 44 .. 88 match: 19 SD: 1.7747 cents 45 .. 90 match: 19 SD: 1.6192 cents 46 .. 92 match: 19 SD: 1.5652 cents 48 .. 96 match: 19 SD: 1.5489 cents 50 .. 100 match: 19 SD: 1.5485 cents 51 .. 102 match: 19 SD: 1.4979 cents 52 .. 104 match: 19 SD: 1.3995 cents 54 .. 108 match: 19 SD: 1.3924 cents 56 .. 112 match: 19 SD: 1.3044 cents 60 .. 120 match: 19 SD: 1.2362 cents 63 .. 126 match: 19 SD: 1.2075 cents 70 .. 140 match: 19 SD: 1.0351 cents 72 .. 144 match: 19 SD: 0.8717 cents 83 .. 166 match: 19 SD: 0.8074 cents 96 .. 192 match: 19 SD: 0.6983 cents 108 .. 216 match: 19 SD: 0.6097 cents 120 .. 240 match: 19 SD: 0.5971 cents 123 .. 246 match: 19 SD: 0.5800 cents 124 .. 248 match: 19 SD: 0.4973 cents 144 .. 289 match: 19 SD: 0.4067 cents 173 .. 347 match: 19 SD: 0.3619 cents 199 .. 399 match: 19 SD: 0.3454 cents 207 .. 415 match: 19 SD: 0.3072 cents 219 .. 439 match: 19 SD: 0.2734 cents 244 .. 489 match: 19 SD: 0.2445 cents 257 .. 515 match: 19 SD: 0.2444 cents 271 .. 543 match: 19 SD: 0.2438 cents 297 .. 595 match: 19 SD: 0.1820 cents 317 .. 635 match: 19 SD: 0.1755 cents 343 .. 687 match: 19 SD: 0.1600 cents 353 .. 707 match: 19 SD: 0.1449 cents 451 .. 904 match: 19 SD: 0.1196 cents 541 .. 1084 match: 19 SD: 0.1167 cents 572 .. 1146 match: 19 SD: 0.1063 cents 600 .. 1202 match: 19 SD: 0.1042 cents