Scala analysis: lemba16
16 note lemba scale in 270 tuning (poptimal)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 93.333 cents 93.333333 2: 137.778 cents 137.777778 3: 231.111 cents 231.111111 4: 324.444 cents 324.444444 5: 368.889 cents 368.888889 6: 462.222 cents 462.222222 7: 506.667 cents 506.666667 8: 600.000 cents 600.000000 9: 693.333 cents 693.333333 10: 737.778 cents 737.777778 11: 831.111 cents 831.111111 12: 924.444 cents 924.444444 13: 968.889 cents 968.888889 14: 1062.222 cents 1062.222222 15: 1106.667 cents 1106.666667 16: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 93.3333 cents 93.3333 1: 93.3333 cents 93.3333 2: 44.4444 cents 44.4444 3: 93.3333 cents 93.3333 4: 93.3333 cents 93.3333 5: 44.4444 cents 44.4444 6: 93.3333 cents 93.3333 7: 44.4444 cents 44.4444 8: 93.3333 cents 93.3333 9: 93.3333 cents 93.3333 10: 44.4444 cents 44.4444 11: 93.3333 cents 93.3333 12: 93.3333 cents 93.3333 13: 44.4444 cents 44.4444 14: 93.3333 cents 93.3333 15: 44.4444 cents 44.4444 16: 93.3333 cents 93.3333
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 44.44445 cents 1: 10 93.33333 cents 2: 12 137.77778 cents 2: 4 186.66667 cents 3: 2 182.22222 cents 3: 14 231.11111 cents 4: 8 275.55556 cents 4: 8 324.44444 cents 5: 14 368.88889 cents 5: 2 417.77778 cents 6: 4 413.33333 cents 6: 12 462.22222 cents 7: 10 506.66667 cents 7: 6 555.55555 cents 8: 16 600.00000 cents 9: 6 644.44444 cents 9: 10 693.33333 cents 10: 12 737.77778 cents 10: 4 786.66667 cents 11: 2 782.22222 cents 11: 14 831.11111 cents 12: 8 875.55556 cents 12: 8 924.44444 cents 13: 14 968.88889 cents 13: 2 1017.77778 cents 14: 4 1013.33333 cents 14: 12 1062.22222 cents 15: 10 1106.66667 cents 15: 6 1155.55555 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.93333 = 29/15
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 93.3 137.8 231.1 324.4 368.9 462.2 506.7 600.0 693.3 737.8 831.1 924.4 968.9 1062.2 1106.7 1200.0 93.3 : 44.4 137.8 231.1 275.6 368.9 413.3 506.7 600.0 644.4 737.8 831.1 875.6 968.9 1013.3 1106.7 1200.0 137.8 : 93.3 186.7 231.1 324.4 368.9 462.2 555.6 600.0 693.3 786.7 831.1 924.4 968.9 1062.2 1155.6 1200.0 231.1 : 93.3 137.8 231.1 275.6 368.9 462.2 506.7 600.0 693.3 737.8 831.1 875.6 968.9 1062.2 1106.7 1200.0 324.4 : 44.4 137.8 182.2 275.6 368.9 413.3 506.7 600.0 644.4 737.8 782.2 875.6 968.9 1013.3 1106.7 1200.0 368.9 : 93.3 137.8 231.1 324.4 368.9 462.2 555.6 600.0 693.3 737.8 831.1 924.4 968.9 1062.2 1155.6 1200.0 462.2 : 44.4 137.8 231.1 275.6 368.9 462.2 506.7 600.0 644.4 737.8 831.1 875.6 968.9 1062.2 1106.7 1200.0 506.7 : 93.3 186.7 231.1 324.4 417.8 462.2 555.6 600.0 693.3 786.7 831.1 924.4 1017.8 1062.2 1155.6 1200.0 600.0 : 93.3 137.8 231.1 324.4 368.9 462.2 506.7 600.0 693.3 737.8 831.1 924.4 968.9 1062.2 1106.7 1200.0 693.3 : 44.4 137.8 231.1 275.6 368.9 413.3 506.7 600.0 644.4 737.8 831.1 875.6 968.9 1013.3 1106.7 1200.0 737.8 : 93.3 186.7 231.1 324.4 368.9 462.2 555.6 600.0 693.3 786.7 831.1 924.4 968.9 1062.2 1155.6 1200.0 831.1 : 93.3 137.8 231.1 275.6 368.9 462.2 506.7 600.0 693.3 737.8 831.1 875.6 968.9 1062.2 1106.7 1200.0 924.4 : 44.4 137.8 182.2 275.6 368.9 413.3 506.7 600.0 644.4 737.8 782.2 875.6 968.9 1013.3 1106.7 1200.0 968.9 : 93.3 137.8 231.1 324.4 368.9 462.2 555.6 600.0 693.3 737.8 831.1 924.4 968.9 1062.2 1155.6 1200.0 1062.2: 44.4 137.8 231.1 275.6 368.9 462.2 506.7 600.0 644.4 737.8 831.1 875.6 968.9 1062.2 1106.7 1200.0 1106.7: 93.3 186.7 231.1 324.4 417.8 462.2 555.6 600.0 693.3 786.7 831.1 924.4 1017.8 1062.2 1155.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.4444 .. 93.3333 cents 48.88889 cents 44.44445 cents 2: 137.7778 .. 186.6667 cents 48.88889 cents 44.44445 cents 3: 182.2222 .. 231.1111 cents 48.88889 cents -4.44444 cents 4: 275.5556 .. 324.4444 cents 48.88889 cents 44.44444 cents 5: 368.8889 .. 417.7778 cents 48.88889 cents 44.44444 cents 6: 413.3333 .. 462.2222 cents 48.88889 cents -4.44444 cents 7: 506.6667 .. 555.5556 cents 48.88889 cents 44.44445 cents 8: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 44.44444 cents 9: 644.4444 .. 693.3333 cents 48.88889 cents 44.44444 cents 10: 737.7778 .. 786.6667 cents 48.88889 cents 44.44444 cents 11: 782.2222 .. 831.1111 cents 48.88889 cents -4.44444 cents 12: 875.5556 .. 924.4444 cents 48.88889 cents 44.44444 cents 13: 968.8889 .. 1017.7778 cents 48.88889 cents 44.44444 cents 14: 1013.3333 .. 1062.2222 cents 48.88889 cents -4.44444 cents 15: 1106.6667 .. 1155.5556 cents 48.88889 cents 44.44444 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 44.44444 cents, class 1 Average step (divided formal octave): 75.0000 cents Largest one step interval : 93.33333 cents Average / Smallest step : 1.687500 Largest / Average step : 1.244444 Largest / Smallest step : 2.100000 Median interval of one step : 93.33333 cents, amount: 10 Most common interval of one step : 93.33333 cents, amount: 10 Least squares average step : 75.16340 cents, oct.: 1202.61438 cents Scale is not proper Scale has 2 repeating blocks of 8 notes Blocks have Myhill's property chromas: 48.88889 cents and 4.44444 cents, ratio: 11.000003 generators: 3 of 231.11111 cents and 5 of 368.88889 cents ET pair of linear temperament : 26&270 Scale is distributional even Scale is a mode of a 270-tone equal temperament with octave 1200.000 cents degrees: 21 31 52 73 83 104 114 135 156 166 187 208 218 239 249 270 Least number of segments generator : 137 of 608.889 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 187 of 831.111 cents and inv. generated superset size: 143 = 127 more = 893.750% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABAABABA Step pattern size order : LSLLSLSLLSLLSLSL Scale is a Constant Structure, by a margin of 4.44444 cents Scale diversity : 1.184736 Lumma stability : 0.444444 Lumma impropriety factor : 0.014815 Number of different interval sizes : 29 = 1.93333 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.93333 = 29/15 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 4.44444 cents Most common intervals : 600.00000 cents & inv., amount: 16 Number of recognisable fifths : 10, average 693.3333 cents Scale contains two identical disjunct "tetrachords" of 8 notes Best major thirds form a closed circle Formal octave complements present : 14 = 87.5000% Limited transpositions : 8 Limited inverse transpositions : 3 11 Inversional symmetry on intervals : 1-2 5-6 9-10 13-14 -- Rational properties --
FIT/MODE
16: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 14.3318 c. M: 24.4444 c. 25: 2 1 2 2 1 2 1 1 2 1 2 2 1 2 1 2 N D3 SD: 13.9488 c. M: 24.0000 c. 26: 2 1 2 2 1 2 1 2 2 1 2 2 1 2 1 2 P B ME SD: 0.8018 c. M: 1.3675 c. 140: 11 5 11 11 5 11 5 11 11 5 11 11 5 11 5 11 N B DE SD: 0.7445 c. M:-1.2698 c. 166: 13 6 13 13 6 13 6 13 13 6 13 13 6 13 6 13 N B DE SD: 0.5023 c. M:-0.8568 c. 192: 15 7 15 15 7 15 7 15 15 7 15 15 7 15 7 15 N B DE SD: 0.3257 c. M:-0.5556 c. 218: 17 8 17 17 8 17 8 17 17 8 17 17 8 17 8 17 N B DE SD: 0.1913 c. M:-0.3262 c. 244: 19 9 19 19 9 19 9 19 19 9 19 19 9 19 9 19 N B DE SD: 0.0854 c. M:-0.1457 c. 270: 21 10 21 21 10 21 10 21 21 10 21 21 10 21 10 21 N B DE SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 4.3108 cents 3 .. 6 match: 3 H SD: 13.6675 cents 4 .. 8 match: 4 H SD: 4.8603 cents 5 .. 10 match: 5 H SD: 10.3507 cents 6 .. 12 match: 6 H SD: 9.4276 cents 7 .. 14 match: 7 H SD: 8.0900 cents 8 .. 16 match: 8 H SD: 7.4359 cents 9 .. 18 match: 9 H SD: 9.2849 cents 10 .. 20 match: 10 H SD: 6.0103 cents 11 .. 22 match: 11 H SD: 8.3360 cents 12 .. 24 match: 12 H SD: 5.9879 cents 13 .. 26 match: 13 H SD: 5.0888 cents 14 .. 28 match: 13 SD: 5.5384 cents 15 .. 30 match: 12 S SD: 5.5723 cents 16 .. 32 match: 13 SD: 5.3503 cents 17 .. 34 match: 14 SD: 4.7778 cents 18 .. 36 match: 13 SD: 5.3564 cents 19 .. 38 match: 15 SD: 4.6176 cents 20 .. 40 match: 16 SD: 3.2676 cents 22 .. 44 match: 14 SD: 4.0364 cents 23 .. 46 match: 15 SD: 3.7219 cents 24 .. 48 match: 16 SD: 3.3227 cents 26 .. 52 match: 16 SD: 3.1834 cents 27 .. 54 match: 15 SD: 3.4542 cents 28 .. 56 match: 15 SD: 3.2256 cents 29 .. 58 match: 15 SD: 2.6637 cents 30 .. 60 match: 15 SD: 2.9604 cents 32 .. 64 match: 16 SD: 2.8763 cents 33 .. 66 match: 16 SD: 2.4380 cents 34 .. 68 match: 16 SD: 2.1194 cents 38 .. 76 match: 16 SD: 2.0658 cents 39 .. 78 match: 16 SD: 1.8845 cents 47 .. 94 match: 16 SD: 1.7034 cents 49 .. 98 match: 16 SD: 1.4943 cents 55 .. 110 match: 16 SD: 1.3679 cents 58 .. 116 match: 16 SD: 1.2683 cents 68 .. 136 match: 16 SD: 1.0773 cents 71 .. 142 match: 16 SD: 0.9840 cents 84 .. 168 match: 16 SD: 0.9492 cents 85 .. 170 match: 16 SD: 0.8004 cents 92 .. 184 match: 16 SD: 0.6937 cents 106 .. 212 match: 16 SD: 0.6755 cents 111 .. 222 match: 16 SD: 0.6204 cents 126 .. 252 match: 16 SD: 0.5981 cents 130 .. 260 match: 16 SD: 0.5726 cents 132 .. 264 match: 16 SD: 0.5475 cents 144 .. 288 match: 16 SD: 0.5277 cents 147 .. 294 match: 16 SD: 0.4839 cents 156 .. 312 match: 16 SD: 0.4284 cents 160 .. 320 match: 16 SD: 0.4164 cents 180 .. 360 match: 16 SD: 0.3896 cents 183 .. 366 match: 16 SD: 0.3677 cents 203 .. 406 match: 16 SD: 0.2527 cents 252 .. 504 match: 16 SD: 0.2490 cents 268 .. 536 match: 16 SD: 0.2322 cents 323 .. 646 match: 16 SD: 0.2246 cents 324 .. 648 match: 16 SD: 0.2105 cents 329 .. 658 match: 16 SD: 0.2104 cents 341 .. 682 match: 16 SD: 0.2002 cents 359 .. 718 match: 16 SD: 0.1851 cents 399 .. 798 match: 16 SD: 0.1712 cents 412 .. 824 match: 16 SD: 0.1173 cents 568 .. 1136 match: 16 SD: 0.1159 cents 581 .. 1162 match: 16 SD: 0.1106 cents