Scala analysis: xen18-erlich-luna-19
6L 13s MOS for Luna, L=111.588, 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: 152.392 cents 152.392000 3: 193.196 cents 193.196000 4: 234.000 cents 234.000000 5: 345.588 cents 345.588000 6: 386.392 cents 386.392000 7: 427.196 cents 427.196000 8: 538.784 cents 538.784000 9: 579.588 cents 579.588000 10: 620.392 cents 620.392000 11: 661.196 cents 661.196000 12: 772.784 cents 772.784000 13: 813.588 cents 813.588000 14: 854.392 cents 854.392000 15: 965.980 cents 965.980000 16: 1006.784 cents 1006.784000 17: 1047.588 cents 1047.588000 18: 1159.176 cents 1159.176000 19: 1199.980 cents 1199.980000
SHOW/INTERVAL
0: 40.8040 cents 40.8040 1: 40.8040 cents 40.8040 2: 111.5880 cents 111.5880 3: 40.8040 cents 40.8040 4: 40.8040 cents 40.8040 5: 111.5880 cents 111.5880 6: 40.8040 cents 40.8040 7: 40.8040 cents 40.8040 8: 111.5880 cents 111.5880 9: 40.8040 cents 40.8040 10: 40.8040 cents 40.8040 11: 40.8040 cents 40.8040 12: 111.5880 cents 111.5880 13: 40.8040 cents 40.8040 14: 40.8040 cents 40.8040 15: 111.5880 cents 111.5880 16: 40.8040 cents 40.8040 17: 40.8040 cents 40.8040 18: 111.5880 cents 111.5880 19: 40.8040 cents 40.8040
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 40.80400 cents 1: 6 111.58800 cents 2: 7 81.60800 cents 2: 12 152.39200 cents 3: 1 122.41200 cents 3: 18 193.19600 cents 4: 14 234.00000 cents 4: 5 304.78400 cents 5: 8 274.80400 cents 5: 11 345.58800 cents 6: 2 315.60800 cents 6: 17 386.39200 cents 7: 15 427.19600 cents 7: 4 497.98000 cents 8: 9 468.00000 cents 8: 10 538.78400 cents 9: 3 508.80400 cents 9: 16 579.58800 cents 10: 16 620.39200 cents 10: 3 691.17600 cents 11: 10 661.19600 cents 11: 9 731.98000 cents 12: 4 702.00000 cents 12: 15 772.78400 cents 13: 17 813.58800 cents 13: 2 884.37200 cents 14: 11 854.39200 cents 14: 8 925.17600 cents 15: 5 895.19600 cents 15: 14 965.98000 cents 16: 18 1006.78400 cents 16: 1 1077.56800 cents 17: 12 1047.58800 cents 17: 7 1118.37200 cents 18: 6 1088.39200 cents 18: 13 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 0.0 : 40.8 152.4 193.2 234.0 345.6 386.4 427.2 538.8 579.6 620.4 661.2 772.8 813.6 854.4 966.0 1006.8 1047.6 1159.2 1200.0 40.8 : 111.6 152.4 193.2 304.8 345.6 386.4 498.0 538.8 579.6 620.4 732.0 772.8 813.6 925.2 966.0 1006.8 1118.4 1159.2 1200.0 152.4 : 40.8 81.6 193.2 234.0 274.8 386.4 427.2 468.0 508.8 620.4 661.2 702.0 813.6 854.4 895.2 1006.8 1047.6 1088.4 1200.0 193.2 : 40.8 152.4 193.2 234.0 345.6 386.4 427.2 468.0 579.6 620.4 661.2 772.8 813.6 854.4 966.0 1006.8 1047.6 1159.2 1200.0 234.0 : 111.6 152.4 193.2 304.8 345.6 386.4 427.2 538.8 579.6 620.4 732.0 772.8 813.6 925.2 966.0 1006.8 1118.4 1159.2 1200.0 345.6 : 40.8 81.6 193.2 234.0 274.8 315.6 427.2 468.0 508.8 620.4 661.2 702.0 813.6 854.4 895.2 1006.8 1047.6 1088.4 1200.0 386.4 : 40.8 152.4 193.2 234.0 274.8 386.4 427.2 468.0 579.6 620.4 661.2 772.8 813.6 854.4 966.0 1006.8 1047.6 1159.2 1200.0 427.2 : 111.6 152.4 193.2 234.0 345.6 386.4 427.2 538.8 579.6 620.4 732.0 772.8 813.6 925.2 966.0 1006.8 1118.4 1159.2 1200.0 538.8 : 40.8 81.6 122.4 234.0 274.8 315.6 427.2 468.0 508.8 620.4 661.2 702.0 813.6 854.4 895.2 1006.8 1047.6 1088.4 1200.0 579.6 : 40.8 81.6 193.2 234.0 274.8 386.4 427.2 468.0 579.6 620.4 661.2 772.8 813.6 854.4 966.0 1006.8 1047.6 1159.2 1200.0 620.4 : 40.8 152.4 193.2 234.0 345.6 386.4 427.2 538.8 579.6 620.4 732.0 772.8 813.6 925.2 966.0 1006.8 1118.4 1159.2 1200.0 661.2 : 111.6 152.4 193.2 304.8 345.6 386.4 498.0 538.8 579.6 691.2 732.0 772.8 884.4 925.2 966.0 1077.6 1118.4 1159.2 1200.0 772.8 : 40.8 81.6 193.2 234.0 274.8 386.4 427.2 468.0 579.6 620.4 661.2 772.8 813.6 854.4 966.0 1006.8 1047.6 1088.4 1200.0 813.6 : 40.8 152.4 193.2 234.0 345.6 386.4 427.2 538.8 579.6 620.4 732.0 772.8 813.6 925.2 966.0 1006.8 1047.6 1159.2 1200.0 854.4 : 111.6 152.4 193.2 304.8 345.6 386.4 498.0 538.8 579.6 691.2 732.0 772.8 884.4 925.2 966.0 1006.8 1118.4 1159.2 1200.0 966.0 : 40.8 81.6 193.2 234.0 274.8 386.4 427.2 468.0 579.6 620.4 661.2 772.8 813.6 854.4 895.2 1006.8 1047.6 1088.4 1200.0 1006.8: 40.8 152.4 193.2 234.0 345.6 386.4 427.2 538.8 579.6 620.4 732.0 772.8 813.6 854.4 966.0 1006.8 1047.6 1159.2 1200.0 1047.6: 111.6 152.4 193.2 304.8 345.6 386.4 498.0 538.8 579.6 691.2 732.0 772.8 813.6 925.2 966.0 1006.8 1118.4 1159.2 1200.0 1159.2: 40.8 81.6 193.2 234.0 274.8 386.4 427.2 468.0 579.6 620.4 661.2 702.0 813.6 854.4 895.2 1006.8 1047.6 1088.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.8040 .. 111.5880 cents 70.78400 cents 40.80400 cents 2: 81.6080 .. 152.3920 cents 70.78400 cents -29.98000 cents 3: 122.4120 .. 193.1960 cents 70.78400 cents -29.98000 cents 4: 234.0000 .. 304.7840 cents 70.78400 cents 40.80400 cents 5: 274.8040 .. 345.5880 cents 70.78400 cents -29.98000 cents 6: 315.6080 .. 386.3920 cents 70.78400 cents -29.98000 cents 7: 427.1960 .. 497.9800 cents 70.78400 cents 40.80400 cents 8: 468.0000 .. 538.7840 cents 70.78400 cents -29.98000 cents 9: 508.8040 .. 579.5880 cents 70.78400 cents -29.98000 cents 10: 620.3920 .. 691.1760 cents 70.78400 cents 40.80400 cents 11: 661.1960 .. 731.9800 cents 70.78400 cents -29.98000 cents 12: 702.0000 .. 772.7840 cents 70.78400 cents -29.98000 cents 13: 813.5880 .. 884.3720 cents 70.78400 cents 40.80400 cents 14: 854.3920 .. 925.1760 cents 70.78400 cents -29.98000 cents 15: 895.1960 .. 965.9800 cents 70.78400 cents -29.98000 cents 16: 1006.7840 .. 1077.5680 cents 70.78400 cents 40.80400 cents 17: 1047.5880 .. 1118.3720 cents 70.78400 cents -29.98000 cents 18: 1088.3920 .. 1159.1760 cents 70.78400 cents -29.98000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 40.80400 cents, class 1 Average step (divided formal octave): 63.1568 cents Largest one step interval : 111.58800 cents Average / Smallest step : 1.547810 Largest / Average step : 1.766839 Largest / Smallest step : 2.734732 Median interval of one step : 40.80400 cents, amount: 13 Most common interval of one step : 40.80400 cents, amount: 13 Least squares average step : 63.07087 cents, oct.: 1198.34652 cents Scale is not proper Scale has Myhill's property chromas: 70.78400 cents and 29.98000 cents, ratio: 2.361041 generators: 3 of 193.19600 cents and 16 of 1006.78400 cents ET pair of linear temperament : 25&31 Scale is distributional even Scale is a mode of a 1441-tone equal temperament with octave 1199.980 cents degrees: 49 183 232 281 415 464 513 647 696 745 794 928 977 1026 1160 1209 1258 1392 1441 generators: 232 and 1209 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABAAABAABAABA Step pattern size order : SLSSLSSLSSSLSSLSSLS Scale is a Constant Structure, by a margin of 10.82400 cents Scale diversity : 1.191517 Lumma stability : 0.238027 Lumma impropriety factor : 0.299805 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 : 10.82400 cents Most common intervals : 193.19600 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 538.784 1006.784 cents Most common triad is 0.0 193.196 1006.784 cents, amount: 17 Number of recognisable fifths : 7, average 697.3611 cents Number of recognisable fourths : 7, average 502.6189 cents Scale contains two identical disjunct "tetrachords" of 9 notes 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: 0 2 1 0 2 1 0 2 1 0 1 2 0 1 2 0 1 2 1 N T3 SD: 34.5148 c. M: 59.4314 c. 20: 1 2 0 1 2 0 1 2 1 0 1 2 1 0 2 1 0 2 1 N I SD: 16.9041 c. M:-27.6050 c. 22: 1 2 1 0 2 1 1 2 1 0 1 2 1 1 2 0 1 2 1 N T3 I SD: 14.8351 c. M:-24.9822 c. 24: 1 2 1 1 2 1 1 2 1 0 1 2 1 1 2 1 1 2 1 N T3 I SD: 13.2121 c. M:-22.7965 c. 25: 1 2 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 1 P M ME I SD: 6.5683 c. M:-10.7928 c. 31: 1 3 1 1 3 1 1 3 1 1 1 3 1 1 3 1 1 3 1 N M DE I SD: 1.9124 c. M:-3.1425 c. 56: 2 5 2 2 5 2 2 5 2 2 2 5 2 2 5 2 2 5 2 N M DE I SD: 1.8736 c. M:-3.0786 c. 87: 3 8 3 3 8 3 3 8 3 3 3 8 3 3 8 3 3 8 3 N M DE I SD: 0.5246 c. M:-0.8619 c. 118: 4 11 4 4 11 4 4 11 4 4 4 11 4 4 11 4 4 11 4 N M DE I SD: 0.1157 c. M:-0.1901 c. 323: 11 30 11 11 30 11 11 30 11 11 11 30 11 11 30 11 11 30 11 N M DE I SD: 0.0568 c. M:-0.0933 c. 441: 15 41 15 15 41 15 15 41 15 15 15 41 15 15 41 15 15 41 15 N M DE I SD: 0.0106 c. M:-0.0175 c. 1000: 34 93 34 34 93 34 34 93 34 34 34 93 34 34 93 34 34 93 34 N M DE I SD: 0.0043 c. M:-0.0070 c. 1441: 49 134 49 49 134 49 49 134 49 49 49 134 49 49 134 49 49 134 49 N M DE I SD: 0.0003 c. M:-0.0005 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0200 cents 2 .. 4 match: 2 H SD: 20.3795 cents 3 .. 6 match: 3 H SD: 16.8578 cents 4 .. 8 match: 4 H SD: 10.2146 cents 5 .. 10 match: 5 H SD: 6.3946 cents 6 .. 12 match: 6 H SD: 12.1365 cents 7 .. 14 match: 7 H SD: 6.1171 cents 8 .. 16 match: 8 H SD: 7.6938 cents 9 .. 18 match: 8 S SD: 6.9788 cents 10 .. 20 match: 9 S SD: 8.4718 cents 11 .. 22 match: 11 H SD: 6.9246 cents 12 .. 24 match: 12 H SD: 7.0754 cents 13 .. 26 match: 12 SD: 5.8466 cents 14 .. 28 match: 14 H SD: 5.1983 cents 15 .. 30 match: 14 SD: 6.1614 cents 16 .. 32 match: 11 SD: 5.2294 cents 17 .. 34 match: 12 SD: 3.8069 cents 18 .. 36 match: 14 SD: 5.2410 cents 19 .. 38 match: 15 SD: 4.4763 cents 20 .. 40 match: 17 SD: 4.2620 cents 21 .. 42 match: 14 SD: 4.3129 cents 22 .. 44 match: 16 SD: 3.5713 cents 23 .. 46 match: 17 SD: 3.2300 cents 24 .. 48 match: 16 SD: 3.3378 cents 25 .. 50 match: 18 SD: 2.8860 cents 26 .. 52 match: 18 SD: 3.6798 cents 27 .. 54 match: 19 SD: 3.1638 cents 28 .. 56 match: 18 SD: 2.0589 cents 29 .. 58 match: 17 SD: 3.4361 cents 30 .. 60 match: 17 SD: 2.5347 cents 31 .. 62 match: 18 SD: 2.8584 cents 32 .. 64 match: 19 SD: 2.0782 cents 33 .. 66 match: 19 SD: 2.0647 cents 35 .. 70 match: 19 SD: 1.7266 cents 41 .. 82 match: 19 SD: 1.5904 cents 43 .. 86 match: 19 SD: 1.5560 cents 53 .. 106 match: 19 SD: 1.3675 cents 60 .. 120 match: 19 SD: 1.2363 cents 67 .. 134 match: 19 SD: 1.1112 cents 68 .. 136 match: 19 SD: 1.0068 cents 75 .. 150 match: 19 SD: 0.8865 cents 76 .. 152 match: 19 SD: 0.8599 cents 83 .. 166 match: 19 SD: 0.8260 cents 85 .. 170 match: 19 SD: 0.7828 cents 95 .. 190 match: 19 SD: 0.7645 cents 96 .. 192 match: 19 SD: 0.7292 cents 108 .. 216 match: 19 SD: 0.7041 cents 110 .. 220 match: 19 SD: 0.6690 cents 118 .. 236 match: 19 SD: 0.5076 cents 151 .. 302 match: 19 SD: 0.4646 cents 153 .. 306 match: 19 SD: 0.3867 cents 172 .. 344 match: 19 SD: 0.3401 cents 208 .. 416 match: 19 SD: 0.3036 cents 213 .. 426 match: 19 SD: 0.2905 cents 236 .. 472 match: 19 SD: 0.2866 cents 249 .. 498 match: 19 SD: 0.2508 cents 285 .. 570 match: 19 SD: 0.2406 cents 290 .. 580 match: 19 SD: 0.2233 cents 297 .. 594 match: 19 SD: 0.2183 cents 304 .. 608 match: 19 SD: 0.1554 cents 380 .. 760 match: 19 SD: 0.1402 cents 457 .. 914 match: 19 SD: 0.1364 cents 475 .. 950 match: 19 SD: 0.1332 cents 499 .. 998 match: 19 SD: 0.1325 cents 503 .. 1006 match: 19 SD: 0.1293 cents 533 .. 1066 match: 19 SD: 0.1166 cents 553 .. 1106 match: 19 SD: 0.1026 cents