Scala analysis: xen18-erlich-luna-25
6L 19s MOS for Luna, L=70.784, s=40.804
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40.804 cents 40.804000 2: 81.608 cents 81.608000 3: 152.392 cents 152.392000 4: 193.196 cents 193.196000 5: 234.000 cents 234.000000 6: 274.804 cents 274.804000 7: 345.588 cents 345.588000 8: 386.392 cents 386.392000 9: 427.196 cents 427.196000 10: 468.000 cents 468.000000 11: 538.784 cents 538.784000 12: 579.588 cents 579.588000 13: 620.392 cents 620.392000 14: 661.196 cents 661.196000 15: 731.980 cents 731.980000 16: 772.784 cents 772.784000 17: 813.588 cents 813.588000 18: 854.392 cents 854.392000 19: 925.176 cents 925.176000 20: 965.980 cents 965.980000 21: 1006.784 cents 1006.784000 22: 1047.588 cents 1047.588000 23: 1118.372 cents 1118.372000 24: 1159.176 cents 1159.176000 25: 1199.980 cents 1199.980000
SHOW/INTERVAL
0: 40.8040 cents 40.8040 1: 40.8040 cents 40.8040 2: 40.8040 cents 40.8040 3: 70.7840 cents 70.7840 4: 40.8040 cents 40.8040 5: 40.8040 cents 40.8040 6: 40.8040 cents 40.8040 7: 70.7840 cents 70.7840 8: 40.8040 cents 40.8040 9: 40.8040 cents 40.8040 10: 40.8040 cents 40.8040 11: 70.7840 cents 70.7840 12: 40.8040 cents 40.8040 13: 40.8040 cents 40.8040 14: 40.8040 cents 40.8040 15: 70.7840 cents 70.7840 16: 40.8040 cents 40.8040 17: 40.8040 cents 40.8040 18: 40.8040 cents 40.8040 19: 70.7840 cents 70.7840 20: 40.8040 cents 40.8040 21: 40.8040 cents 40.8040 22: 40.8040 cents 40.8040 23: 70.7840 cents 70.7840 24: 40.8040 cents 40.8040 25: 40.8040 cents 40.8040
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 19 40.80400 cents 1: 6 70.78400 cents 2: 13 81.60800 cents 2: 12 111.58800 cents 3: 7 122.41200 cents 3: 18 152.39200 cents 4: 1 163.21600 cents 4: 24 193.19600 cents 5: 20 234.00000 cents 5: 5 263.98000 cents 6: 14 274.80400 cents 6: 11 304.78400 cents 7: 8 315.60800 cents 7: 17 345.58800 cents 8: 2 356.41200 cents 8: 23 386.39200 cents 9: 21 427.19600 cents 9: 4 457.17600 cents 10: 15 468.00000 cents 10: 10 497.98000 cents 11: 9 508.80400 cents 11: 16 538.78400 cents 12: 3 549.60800 cents 12: 22 579.58800 cents 13: 22 620.39200 cents 13: 3 650.37200 cents 14: 16 661.19600 cents 14: 9 691.17600 cents 15: 10 702.00000 cents 15: 15 731.98000 cents 16: 4 742.80400 cents 16: 21 772.78400 cents 17: 23 813.58800 cents 17: 2 843.56800 cents 18: 17 854.39200 cents 18: 8 884.37200 cents 19: 11 895.19600 cents 19: 14 925.17600 cents 20: 5 936.00000 cents 20: 20 965.98000 cents 21: 24 1006.78400 cents 21: 1 1036.76400 cents 22: 18 1047.58800 cents 22: 7 1077.56800 cents 23: 12 1088.39200 cents 23: 13 1118.37200 cents 24: 6 1129.19600 cents 24: 19 1159.17600 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 0.0 : 40.8 81.6 152.4 193.2 234.0 274.8 345.6 386.4 427.2 468.0 538.8 579.6 620.4 661.2 732.0 772.8 813.6 854.4 925.2 966.0 1006.8 1047.6 1118.4 1159.2 1200.0 40.8 : 40.8 111.6 152.4 193.2 234.0 304.8 345.6 386.4 427.2 498.0 538.8 579.6 620.4 691.2 732.0 772.8 813.6 884.4 925.2 966.0 1006.8 1077.6 1118.4 1159.2 1200.0 81.6 : 70.8 111.6 152.4 193.2 264.0 304.8 345.6 386.4 457.2 498.0 538.8 579.6 650.4 691.2 732.0 772.8 843.6 884.4 925.2 966.0 1036.8 1077.6 1118.4 1159.2 1200.0 152.4 : 40.8 81.6 122.4 193.2 234.0 274.8 315.6 386.4 427.2 468.0 508.8 579.6 620.4 661.2 702.0 772.8 813.6 854.4 895.2 966.0 1006.8 1047.6 1088.4 1129.2 1200.0 193.2 : 40.8 81.6 152.4 193.2 234.0 274.8 345.6 386.4 427.2 468.0 538.8 579.6 620.4 661.2 732.0 772.8 813.6 854.4 925.2 966.0 1006.8 1047.6 1088.4 1159.2 1200.0 234.0 : 40.8 111.6 152.4 193.2 234.0 304.8 345.6 386.4 427.2 498.0 538.8 579.6 620.4 691.2 732.0 772.8 813.6 884.4 925.2 966.0 1006.8 1047.6 1118.4 1159.2 1200.0 274.8 : 70.8 111.6 152.4 193.2 264.0 304.8 345.6 386.4 457.2 498.0 538.8 579.6 650.4 691.2 732.0 772.8 843.6 884.4 925.2 966.0 1006.8 1077.6 1118.4 1159.2 1200.0 345.6 : 40.8 81.6 122.4 193.2 234.0 274.8 315.6 386.4 427.2 468.0 508.8 579.6 620.4 661.2 702.0 772.8 813.6 854.4 895.2 936.0 1006.8 1047.6 1088.4 1129.2 1200.0 386.4 : 40.8 81.6 152.4 193.2 234.0 274.8 345.6 386.4 427.2 468.0 538.8 579.6 620.4 661.2 732.0 772.8 813.6 854.4 895.2 966.0 1006.8 1047.6 1088.4 1159.2 1200.0 427.2 : 40.8 111.6 152.4 193.2 234.0 304.8 345.6 386.4 427.2 498.0 538.8 579.6 620.4 691.2 732.0 772.8 813.6 854.4 925.2 966.0 1006.8 1047.6 1118.4 1159.2 1200.0 468.0 : 70.8 111.6 152.4 193.2 264.0 304.8 345.6 386.4 457.2 498.0 538.8 579.6 650.4 691.2 732.0 772.8 813.6 884.4 925.2 966.0 1006.8 1077.6 1118.4 1159.2 1200.0 538.8 : 40.8 81.6 122.4 193.2 234.0 274.8 315.6 386.4 427.2 468.0 508.8 579.6 620.4 661.2 702.0 742.8 813.6 854.4 895.2 936.0 1006.8 1047.6 1088.4 1129.2 1200.0 579.6 : 40.8 81.6 152.4 193.2 234.0 274.8 345.6 386.4 427.2 468.0 538.8 579.6 620.4 661.2 702.0 772.8 813.6 854.4 895.2 966.0 1006.8 1047.6 1088.4 1159.2 1200.0 620.4 : 40.8 111.6 152.4 193.2 234.0 304.8 345.6 386.4 427.2 498.0 538.8 579.6 620.4 661.2 732.0 772.8 813.6 854.4 925.2 966.0 1006.8 1047.6 1118.4 1159.2 1200.0 661.2 : 70.8 111.6 152.4 193.2 264.0 304.8 345.6 386.4 457.2 498.0 538.8 579.6 620.4 691.2 732.0 772.8 813.6 884.4 925.2 966.0 1006.8 1077.6 1118.4 1159.2 1200.0 732.0 : 40.8 81.6 122.4 193.2 234.0 274.8 315.6 386.4 427.2 468.0 508.8 549.6 620.4 661.2 702.0 742.8 813.6 854.4 895.2 936.0 1006.8 1047.6 1088.4 1129.2 1200.0 772.8 : 40.8 81.6 152.4 193.2 234.0 274.8 345.6 386.4 427.2 468.0 508.8 579.6 620.4 661.2 702.0 772.8 813.6 854.4 895.2 966.0 1006.8 1047.6 1088.4 1159.2 1200.0 813.6 : 40.8 111.6 152.4 193.2 234.0 304.8 345.6 386.4 427.2 468.0 538.8 579.6 620.4 661.2 732.0 772.8 813.6 854.4 925.2 966.0 1006.8 1047.6 1118.4 1159.2 1200.0 854.4 : 70.8 111.6 152.4 193.2 264.0 304.8 345.6 386.4 427.2 498.0 538.8 579.6 620.4 691.2 732.0 772.8 813.6 884.4 925.2 966.0 1006.8 1077.6 1118.4 1159.2 1200.0 925.2 : 40.8 81.6 122.4 193.2 234.0 274.8 315.6 356.4 427.2 468.0 508.8 549.6 620.4 661.2 702.0 742.8 813.6 854.4 895.2 936.0 1006.8 1047.6 1088.4 1129.2 1200.0 966.0 : 40.8 81.6 152.4 193.2 234.0 274.8 315.6 386.4 427.2 468.0 508.8 579.6 620.4 661.2 702.0 772.8 813.6 854.4 895.2 966.0 1006.8 1047.6 1088.4 1159.2 1200.0 1006.8: 40.8 111.6 152.4 193.2 234.0 274.8 345.6 386.4 427.2 468.0 538.8 579.6 620.4 661.2 732.0 772.8 813.6 854.4 925.2 966.0 1006.8 1047.6 1118.4 1159.2 1200.0 1047.6: 70.8 111.6 152.4 193.2 234.0 304.8 345.6 386.4 427.2 498.0 538.8 579.6 620.4 691.2 732.0 772.8 813.6 884.4 925.2 966.0 1006.8 1077.6 1118.4 1159.2 1200.0 1118.4: 40.8 81.6 122.4 163.2 234.0 274.8 315.6 356.4 427.2 468.0 508.8 549.6 620.4 661.2 702.0 742.8 813.6 854.4 895.2 936.0 1006.8 1047.6 1088.4 1129.2 1200.0 1159.2: 40.8 81.6 122.4 193.2 234.0 274.8 315.6 386.4 427.2 468.0 508.8 579.6 620.4 661.2 702.0 772.8 813.6 854.4 895.2 966.0 1006.8 1047.6 1088.4 1159.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.8040 .. 70.7840 cents 29.98000 cents 40.80400 cents 2: 81.6080 .. 111.5880 cents 29.98000 cents 10.82400 cents 3: 122.4120 .. 152.3920 cents 29.98000 cents 10.82400 cents 4: 163.2160 .. 193.1960 cents 29.98000 cents 10.82400 cents 5: 234.0000 .. 263.9800 cents 29.98000 cents 40.80400 cents 6: 274.8040 .. 304.7840 cents 29.98000 cents 10.82400 cents 7: 315.6080 .. 345.5880 cents 29.98000 cents 10.82400 cents 8: 356.4120 .. 386.3920 cents 29.98000 cents 10.82400 cents 9: 427.1960 .. 457.1760 cents 29.98000 cents 40.80400 cents 10: 468.0000 .. 497.9800 cents 29.98000 cents 10.82400 cents 11: 508.8040 .. 538.7840 cents 29.98000 cents 10.82400 cents 12: 549.6080 .. 579.5880 cents 29.98000 cents 10.82400 cents 13: 620.3920 .. 650.3720 cents 29.98000 cents 40.80400 cents 14: 661.1960 .. 691.1760 cents 29.98000 cents 10.82400 cents 15: 702.0000 .. 731.9800 cents 29.98000 cents 10.82400 cents 16: 742.8040 .. 772.7840 cents 29.98000 cents 10.82400 cents 17: 813.5880 .. 843.5680 cents 29.98000 cents 40.80400 cents 18: 854.3920 .. 884.3720 cents 29.98000 cents 10.82400 cents 19: 895.1960 .. 925.1760 cents 29.98000 cents 10.82400 cents 20: 936.0000 .. 965.9800 cents 29.98000 cents 10.82400 cents 21: 1006.7840 .. 1036.7640 cents 29.98000 cents 40.80400 cents 22: 1047.5880 .. 1077.5680 cents 29.98000 cents 10.82400 cents 23: 1088.3920 .. 1118.3720 cents 29.98000 cents 10.82400 cents 24: 1129.1960 .. 1159.1760 cents 29.98000 cents 10.82400 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 40.80400 cents, class 1 Average step (divided formal octave): 47.9992 cents Largest one step interval : 70.78400 cents Average / Smallest step : 1.176336 Largest / Average step : 1.474691 Largest / Smallest step : 1.734732 Median interval of one step : 40.80400 cents, amount: 19 Most common interval of one step : 40.80400 cents, amount: 19 Least squares average step : 48.08602 cents, oct.: 1202.15050 cents Scale is strictly proper Scale has Myhill's property chromas: 29.98000 cents and 10.82400 cents, ratio: 2.769771 generators: 4 of 193.19600 cents and 21 of 1006.78400 cents ET pair of linear temperament : 25&31 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1441-tone equal temperament with octave 1199.980 cents degrees: 49 98 183 232 281 330 415 464 513 562 647 696 745 794 879 928 977 1026 1111 1160 1209 1258 1343 1392 1441 generators: 232 and 1209 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAAABAAABAAABAAABAA Step pattern size order : SSLSSSLSSSLSSSLSSSLSSSLSS Scale is a Constant Structure, by a margin of 10.82400 cents Scale diversity : 1.151813 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.400390 Rothenberg efficiency : 0.693333 redundancy: 0.306667 Efficiency x scale size : 17.333333 Number of different interval sizes : 48 = 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 : 10.82400 cents Most common intervals : 193.19600 cents & inv., amount: 24 Scale is a chain of 12 triads 0.0 193.196 386.392 cents Most common triad is 0.0 193.196 1006.784 cents, amount: 23 Number of recognisable fifths : 19, average 696.8728 cents Number of recognisable fourths : 19, average 503.1072 cents Scale contains two identical disjunct "tetrachords" of 11 notes Best major thirds form a closed circle Formal octave complements present : 25 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 12-13 -- Rational properties --
FIT/MODE
25: 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: 8.6476 c. M:-14.3904 c. 31: 1 1 2 1 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: 2.5178 c. M:-4.1899 c. 56: 2 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 2 2 3 2 2 SP M ME I SD: 2.4667 c. M:-4.1049 c. 87: 3 3 5 3 3 3 5 3 3 3 5 3 3 3 5 3 3 3 5 3 3 3 5 3 3 SP M DE I SD: 0.6906 c. M:-1.1492 c. 118: 4 4 7 4 4 4 7 4 4 4 7 4 4 4 7 4 4 4 7 4 4 4 7 4 4 SP M DE I SD: 0.1523 c. M:-0.2534 c. 323: 11 11 19 11 11 11 19 11 11 11 19 11 11 11 19 11 11 11 19 11 11 11 19 11 11 SP M DE I SD: 0.0747 c. M:-0.1244 c. 441: 15 15 26 15 15 15 26 15 15 15 26 15 15 15 26 15 15 15 26 15 15 15 26 15 15 SP M DE I SD: 0.0140 c. M:-0.0233 c. 1000: 34 34 59 34 34 34 59 34 34 34 59 34 34 34 59 34 34 34 59 34 34 34 59 34 34 SP M DE I SD: 0.0056 c. M:-0.0094 c. 1441: 49 49 85 49 49 49 85 49 49 49 85 49 49 49 85 49 49 49 85 49 49 49 85 49 49 SP M DE I SD: 0.0004 c. M:-0.0006 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0200 cents 2 .. 4 match: 2 H SD: 15.0125 cents 3 .. 6 match: 3 H SD: 14.1449 cents 4 .. 8 match: 4 H SD: 7.5399 cents 5 .. 10 match: 5 H SD: 6.3946 cents 6 .. 12 match: 6 H SD: 8.7691 cents 7 .. 14 match: 7 H SD: 4.0848 cents 8 .. 16 match: 8 H SD: 5.9686 cents 9 .. 18 match: 9 H SD: 5.7308 cents 10 .. 20 match: 10 H SD: 4.8652 cents 11 .. 22 match: 11 H SD: 3.3838 cents 12 .. 24 match: 12 H SD: 5.0402 cents 13 .. 26 match: 13 H SD: 3.9769 cents 14 .. 28 match: 14 H SD: 4.1521 cents 15 .. 30 match: 14 SD: 5.0141 cents 16 .. 32 match: 15 SD: 3.8883 cents 17 .. 34 match: 17 H SD: 3.2155 cents 18 .. 36 match: 17 SD: 3.4618 cents 19 .. 38 match: 19 H SD: 2.8660 cents 20 .. 40 match: 19 SD: 2.8370 cents 21 .. 42 match: 19 S SD: 3.2364 cents 22 .. 44 match: 19 S SD: 2.5207 cents 23 .. 46 match: 22 S SD: 2.1500 cents 24 .. 48 match: 20 SD: 2.5062 cents 25 .. 50 match: 22 SD: 2.2557 cents 26 .. 52 match: 22 SD: 3.0992 cents 27 .. 54 match: 23 SD: 2.7694 cents 28 .. 56 match: 23 SD: 1.9651 cents 29 .. 58 match: 22 SD: 2.8445 cents 30 .. 60 match: 22 SD: 2.1648 cents 31 .. 62 match: 24 SD: 2.6445 cents 32 .. 64 match: 25 SD: 2.1231 cents 33 .. 66 match: 25 SD: 2.0021 cents 35 .. 70 match: 25 SD: 1.5993 cents 41 .. 82 match: 25 SD: 1.3606 cents 53 .. 106 match: 25 SD: 1.3158 cents 55 .. 110 match: 25 SD: 1.2473 cents 58 .. 116 match: 25 SD: 1.1566 cents 63 .. 126 match: 25 SD: 1.1223 cents 64 .. 128 match: 25 SD: 1.0740 cents 65 .. 130 match: 25 SD: 1.0420 cents 67 .. 134 match: 25 SD: 1.0226 cents 68 .. 136 match: 25 SD: 0.8817 cents 75 .. 150 match: 25 SD: 0.8323 cents 76 .. 152 match: 25 SD: 0.7885 cents 83 .. 166 match: 25 SD: 0.7370 cents 85 .. 170 match: 25 SD: 0.7159 cents 88 .. 176 match: 25 SD: 0.7087 cents 99 .. 198 match: 25 SD: 0.6283 cents 110 .. 220 match: 25 SD: 0.5615 cents 118 .. 236 match: 25 SD: 0.4964 cents 123 .. 246 match: 25 SD: 0.4944 cents 128 .. 256 match: 25 SD: 0.4881 cents 139 .. 278 match: 25 SD: 0.4758 cents 144 .. 288 match: 25 SD: 0.4414 cents 151 .. 302 match: 25 SD: 0.4129 cents 161 .. 322 match: 25 SD: 0.3939 cents 164 .. 328 match: 25 SD: 0.3655 cents 167 .. 334 match: 25 SD: 0.3435 cents 185 .. 370 match: 25 SD: 0.3434 cents 186 .. 372 match: 25 SD: 0.3420 cents 194 .. 388 match: 25 SD: 0.3346 cents 203 .. 406 match: 25 SD: 0.3243 cents 204 .. 408 match: 25 SD: 0.3032 cents 208 .. 416 match: 25 SD: 0.2838 cents 213 .. 426 match: 25 SD: 0.2821 cents 228 .. 456 match: 25 SD: 0.2668 cents 249 .. 498 match: 25 SD: 0.2050 cents 290 .. 580 match: 25 SD: 0.1863 cents 304 .. 608 match: 25 SD: 0.1652 cents 348 .. 696 match: 25 SD: 0.1560 cents 372 .. 744 match: 25 SD: 0.1431 cents 415 .. 830 match: 25 SD: 0.1398 cents 435 .. 870 match: 25 SD: 0.1335 cents 455 .. 910 match: 25 SD: 0.1334 cents 457 .. 914 match: 25 SD: 0.1274 cents 458 .. 916 match: 25 SD: 0.1244 cents 498 .. 996 match: 25 SD: 0.1209 cents 499 .. 998 match: 25 SD: 0.1172 cents 535 .. 1070 match: 25 SD: 0.1150 cents 540 .. 1080 match: 25 SD: 0.1074 cents 553 .. 1106 match: 25 SD: 0.0970 cents 576 .. 1152 match: 25 SD: 0.0964 cents 583 .. 1166 match: 25 SD: 0.0948 cents