Scala analysis: lemba22
Lemba[22] in 270-et (poptimal)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44.444 cents 44.444444 2: 93.333 cents 93.333333 3: 137.778 cents 137.777778 4: 231.111 cents 231.111111 5: 275.556 cents 275.555556 6: 324.444 cents 324.444444 7: 368.889 cents 368.888889 8: 462.222 cents 462.222222 9: 506.667 cents 506.666667 10: 555.556 cents 555.555556 11: 600.000 cents 600.000000 12: 644.444 cents 644.444444 13: 693.333 cents 693.333333 14: 737.778 cents 737.777778 15: 831.111 cents 831.111111 16: 875.556 cents 875.555556 17: 924.444 cents 924.444444 18: 968.889 cents 968.888889 19: 1062.222 cents 1062.222222 20: 1106.667 cents 1106.666667 21: 1155.556 cents 1155.555556 22: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 44.4444 cents 44.4444 1: 44.4444 cents 44.4444 2: 48.8889 cents 48.8889 3: 44.4444 cents 44.4444 4: 93.3333 cents 93.3333 5: 44.4444 cents 44.4444 6: 48.8889 cents 48.8889 7: 44.4444 cents 44.4444 8: 93.3333 cents 93.3333 9: 44.4444 cents 44.4444 10: 48.8889 cents 48.8889 11: 44.4444 cents 44.4444 12: 44.4444 cents 44.4444 13: 48.8889 cents 48.8889 14: 44.4444 cents 44.4444 15: 93.3333 cents 93.3333 16: 44.4444 cents 44.4444 17: 48.8889 cents 48.8889 18: 44.4444 cents 44.4444 19: 93.3333 cents 93.3333 20: 44.4444 cents 44.4444 21: 48.8889 cents 48.8889 22: 44.4444 cents 44.4444
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 12 44.44444 cents 1: 6 48.88889 cents 1: 4 93.33333 cents 2: 2 88.88889 cents 2: 12 93.33333 cents 2: 8 137.77778 cents 3: 10 137.77778 cents 3: 4 182.22222 cents 3: 8 186.66667 cents 4: 4 182.22222 cents 4: 2 186.66667 cents 4: 16 231.11111 cents 5: 4 231.11111 cents 5: 12 275.55556 cents 5: 4 280.00000 cents 5: 2 324.44444 cents 6: 2 275.55556 cents 6: 4 320.00000 cents 6: 12 324.44444 cents 6: 4 368.88889 cents 7: 16 368.88889 cents 7: 2 413.33333 cents 7: 4 417.77778 cents 8: 8 413.33333 cents 8: 4 417.77778 cents 8: 10 462.22222 cents 9: 8 462.22222 cents 9: 12 506.66667 cents 9: 2 511.11111 cents 10: 4 506.66667 cents 10: 6 551.11111 cents 10: 12 555.55556 cents 11: 22 600.00000 cents 12: 12 644.44444 cents 12: 6 648.88889 cents 12: 4 693.33333 cents 13: 2 688.88889 cents 13: 12 693.33333 cents 13: 8 737.77778 cents 14: 10 737.77778 cents 14: 4 782.22222 cents 14: 8 786.66667 cents 15: 4 782.22222 cents 15: 2 786.66667 cents 15: 16 831.11111 cents 16: 4 831.11111 cents 16: 12 875.55556 cents 16: 4 880.00000 cents 16: 2 924.44444 cents 17: 2 875.55556 cents 17: 4 920.00000 cents 17: 12 924.44444 cents 17: 4 968.88889 cents 18: 16 968.88889 cents 18: 2 1013.33333 cents 18: 4 1017.77778 cents 19: 8 1013.33333 cents 19: 4 1017.77778 cents 19: 10 1062.22222 cents 20: 8 1062.22222 cents 20: 12 1106.66667 cents 20: 2 1111.11111 cents 21: 4 1106.66667 cents 21: 6 1151.11111 cents 21: 12 1155.55556 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.09524 = 65/21
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 0.0 : 44.4 93.3 137.8 231.1 275.6 324.4 368.9 462.2 506.7 555.6 600.0 644.4 693.3 737.8 831.1 875.6 924.4 968.9 1062.2 1106.7 1155.6 1200.0 44.4 : 48.9 93.3 186.7 231.1 280.0 324.4 417.8 462.2 511.1 555.6 600.0 648.9 693.3 786.7 831.1 880.0 924.4 1017.8 1062.2 1111.1 1155.6 1200.0 93.3 : 44.4 137.8 182.2 231.1 275.6 368.9 413.3 462.2 506.7 551.1 600.0 644.4 737.8 782.2 831.1 875.6 968.9 1013.3 1062.2 1106.7 1151.1 1200.0 137.8 : 93.3 137.8 186.7 231.1 324.4 368.9 417.8 462.2 506.7 555.6 600.0 693.3 737.8 786.7 831.1 924.4 968.9 1017.8 1062.2 1106.7 1155.6 1200.0 231.1 : 44.4 93.3 137.8 231.1 275.6 324.4 368.9 413.3 462.2 506.7 600.0 644.4 693.3 737.8 831.1 875.6 924.4 968.9 1013.3 1062.2 1106.7 1200.0 275.6 : 48.9 93.3 186.7 231.1 280.0 324.4 368.9 417.8 462.2 555.6 600.0 648.9 693.3 786.7 831.1 880.0 924.4 968.9 1017.8 1062.2 1155.6 1200.0 324.4 : 44.4 137.8 182.2 231.1 275.6 320.0 368.9 413.3 506.7 551.1 600.0 644.4 737.8 782.2 831.1 875.6 920.0 968.9 1013.3 1106.7 1151.1 1200.0 368.9 : 93.3 137.8 186.7 231.1 275.6 324.4 368.9 462.2 506.7 555.6 600.0 693.3 737.8 786.7 831.1 875.6 924.4 968.9 1062.2 1106.7 1155.6 1200.0 462.2 : 44.4 93.3 137.8 182.2 231.1 275.6 368.9 413.3 462.2 506.7 600.0 644.4 693.3 737.8 782.2 831.1 875.6 968.9 1013.3 1062.2 1106.7 1200.0 506.7 : 48.9 93.3 137.8 186.7 231.1 324.4 368.9 417.8 462.2 555.6 600.0 648.9 693.3 737.8 786.7 831.1 924.4 968.9 1017.8 1062.2 1155.6 1200.0 555.6 : 44.4 88.9 137.8 182.2 275.6 320.0 368.9 413.3 506.7 551.1 600.0 644.4 688.9 737.8 782.2 875.6 920.0 968.9 1013.3 1106.7 1151.1 1200.0 600.0 : 44.4 93.3 137.8 231.1 275.6 324.4 368.9 462.2 506.7 555.6 600.0 644.4 693.3 737.8 831.1 875.6 924.4 968.9 1062.2 1106.7 1155.6 1200.0 644.4 : 48.9 93.3 186.7 231.1 280.0 324.4 417.8 462.2 511.1 555.6 600.0 648.9 693.3 786.7 831.1 880.0 924.4 1017.8 1062.2 1111.1 1155.6 1200.0 693.3 : 44.4 137.8 182.2 231.1 275.6 368.9 413.3 462.2 506.7 551.1 600.0 644.4 737.8 782.2 831.1 875.6 968.9 1013.3 1062.2 1106.7 1151.1 1200.0 737.8 : 93.3 137.8 186.7 231.1 324.4 368.9 417.8 462.2 506.7 555.6 600.0 693.3 737.8 786.7 831.1 924.4 968.9 1017.8 1062.2 1106.7 1155.6 1200.0 831.1 : 44.4 93.3 137.8 231.1 275.6 324.4 368.9 413.3 462.2 506.7 600.0 644.4 693.3 737.8 831.1 875.6 924.4 968.9 1013.3 1062.2 1106.7 1200.0 875.6 : 48.9 93.3 186.7 231.1 280.0 324.4 368.9 417.8 462.2 555.6 600.0 648.9 693.3 786.7 831.1 880.0 924.4 968.9 1017.8 1062.2 1155.6 1200.0 924.4 : 44.4 137.8 182.2 231.1 275.6 320.0 368.9 413.3 506.7 551.1 600.0 644.4 737.8 782.2 831.1 875.6 920.0 968.9 1013.3 1106.7 1151.1 1200.0 968.9 : 93.3 137.8 186.7 231.1 275.6 324.4 368.9 462.2 506.7 555.6 600.0 693.3 737.8 786.7 831.1 875.6 924.4 968.9 1062.2 1106.7 1155.6 1200.0 1062.2: 44.4 93.3 137.8 182.2 231.1 275.6 368.9 413.3 462.2 506.7 600.0 644.4 693.3 737.8 782.2 831.1 875.6 968.9 1013.3 1062.2 1106.7 1200.0 1106.7: 48.9 93.3 137.8 186.7 231.1 324.4 368.9 417.8 462.2 555.6 600.0 648.9 693.3 737.8 786.7 831.1 924.4 968.9 1017.8 1062.2 1155.6 1200.0 1155.6: 44.4 88.9 137.8 182.2 275.6 320.0 368.9 413.3 506.7 551.1 600.0 644.4 688.9 737.8 782.2 875.6 920.0 968.9 1013.3 1106.7 1151.1 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 44.44444 cents 2: 88.8889 .. 137.7778 cents 48.88889 cents -4.44444 cents 3: 137.7778 .. 186.6667 cents 48.88889 cents 1/1, 0.0000 cents 4: 182.2222 .. 231.1111 cents 48.88889 cents -4.44444 cents 5: 231.1111 .. 324.4444 cents 93.33333 cents 1/1, 0.0000 cents 6: 275.5556 .. 368.8889 cents 93.33333 cents -48.88889 cents 7: 368.8889 .. 417.7778 cents 48.88889 cents 1/1, 0.0000 cents 8: 413.3333 .. 462.2222 cents 48.88889 cents -4.44444 cents 9: 462.2222 .. 511.1111 cents 48.88889 cents 1/1, 0.0000 cents 10: 506.6667 .. 555.5556 cents 48.88889 cents -4.44445 cents 11: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 44.44444 cents 12: 644.4444 .. 693.3333 cents 48.88889 cents 44.44444 cents 13: 688.8889 .. 737.7778 cents 48.88889 cents -4.44444 cents 14: 737.7778 .. 786.6667 cents 48.88889 cents 1/1, 0.0000 cents 15: 782.2222 .. 831.1111 cents 48.88889 cents -4.44444 cents 16: 831.1111 .. 924.4444 cents 93.33333 cents 1/1, 0.0000 cents 17: 875.5556 .. 968.8889 cents 93.33333 cents -48.88889 cents 18: 968.8889 .. 1017.7778 cents 48.88889 cents 1/1, 0.0000 cents 19: 1013.3333 .. 1062.2222 cents 48.88889 cents -4.44444 cents 20: 1062.2222 .. 1111.1111 cents 48.88889 cents 1/1, 0.0000 cents 21: 1106.6667 .. 1155.5556 cents 48.88889 cents -4.44444 cents
SHOW DATA
Number of notes : 22 -- Interval properties -- Smallest interval : 44.44444 cents, class 1 Average step (divided formal octave): 54.5455 cents Largest one step interval : 93.33333 cents Average / Smallest step : 1.227273 Largest / Average step : 1.711111 Largest / Smallest step : 2.100000 Median interval of one step : 44.44444 cents, amount: 12 Most common interval of one step : 44.44444 cents, amount: 12 Least squares average step : 54.69770 cents, oct.: 1203.34944 cents Scale is not proper Scale has 2 repeating blocks of 11 notes Scale is a mode of a 270-tone equal temperament with octave 1200.000 cents degrees: 10 21 31 52 62 73 83 104 114 125 135 145 156 166 187 197 208 218 239 249 260 270 Least number of segments generator : 187 of 831.111 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 187 of 831.111 cents and inv. generated superset size: 146 = 124 more = 663.636% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABACABAABACABACABA Step pattern size order : SMSLSMSLSMSSMSLSMSLSMS Scale is not a Constant Structure Scale diversity : 1.090894 Lumma stability : 0.148148 Lumma impropriety factor : 0.111111 Number of different interval sizes : 41 = 1.95238 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.09524 = 65/21 Median interval variety : 3 Lowest interval variety : 1 Smallest interval difference : 4.44444 cents Most common intervals : 600.00000 cents & inv., amount: 22 Number of recognisable fifths : 18, average 692.8395 cents Number of appreciable fifths : 16, average 693.3333 cents Scale contains two identical disjunct "tetrachords" of 10 notes Formal octave complements present : 22 = 100.0000% Limited transpositions : 11 Limited inverse transpositions : 11 Inversional symmetry on degrees : 0 11 Inversional symmetry on intervals : 5-6 16-17 -- Rational properties --
FIT/MODE
22: 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: 14.7350 c. M:-25.8586 c. 23: 1 1 1 1 1 1 1 2 1 1 0 1 1 1 2 1 1 1 1 1 1 1 N D3 SD: 14.6236 c. M: 26.0870 c. 24: 1 1 1 2 1 0 1 2 1 1 1 1 1 1 2 1 0 1 2 1 1 1 N B D3 I SD: 14.6412 c. M:-24.4444 c. 25: 1 1 1 2 1 1 1 2 1 1 0 1 1 1 2 1 1 1 2 1 1 1 N SD: 13.9198 c. M: 24.0000 c. 26: 1 1 1 2 1 1 1 2 1 1 1 1 1 1 2 1 1 1 2 1 1 1 N B D3 I SD: 1.0811 c. M: 1.7094 c. 140: 5 6 5 11 5 6 5 11 5 6 5 5 6 5 11 5 6 5 11 5 6 5 N B I SD: 1.0039 c. M: 1.5873 c. 166: 6 7 6 13 6 7 6 13 6 7 6 6 7 6 13 6 7 6 13 6 7 6 N B I SD: 0.6773 c. M: 1.0710 c. 192: 7 8 7 15 7 8 7 15 7 8 7 7 8 7 15 7 8 7 15 7 8 7 N B I SD: 0.4392 c. M: 0.6944 c. 218: 8 9 8 17 8 9 8 17 8 9 8 8 9 8 17 8 9 8 17 8 9 8 N B I SD: 0.2579 c. M: 0.4077 c. 244: 9 10 9 19 9 10 9 19 9 10 9 9 10 9 19 9 10 9 19 9 10 9 N B I SD: 0.1152 c. M: 0.1821 c. 270: 10 11 10 21 10 11 10 21 10 11 10 10 11 10 21 10 11 10 21 10 11 10 N B I 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: 4.1073 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: 3.6015 cents 7 .. 14 match: 7 H SD: 8.0900 cents 8 .. 16 match: 8 H SD: 4.9418 cents 9 .. 18 match: 9 H SD: 7.1785 cents 10 .. 20 match: 10 H SD: 6.0103 cents 11 .. 22 match: 11 H SD: 6.3025 cents 12 .. 24 match: 12 H SD: 4.1083 cents 13 .. 26 match: 13 H SD: 3.2962 cents 14 .. 28 match: 13 SD: 4.9018 cents 15 .. 30 match: 14 S SD: 4.6184 cents 16 .. 32 match: 15 S SD: 4.3129 cents 17 .. 34 match: 17 H SD: 3.9799 cents 18 .. 36 match: 16 SD: 3.4219 cents 19 .. 38 match: 17 SD: 4.1243 cents 20 .. 40 match: 19 SD: 2.7895 cents 21 .. 42 match: 19 SD: 2.9317 cents 22 .. 44 match: 18 SD: 3.4090 cents 23 .. 46 match: 19 SD: 2.9849 cents 24 .. 48 match: 21 SD: 2.6673 cents 25 .. 50 match: 19 SD: 3.3460 cents 26 .. 52 match: 20 SD: 2.5513 cents 27 .. 54 match: 20 SD: 2.6629 cents 28 .. 56 match: 21 SD: 2.8958 cents 29 .. 58 match: 21 SD: 2.1439 cents 30 .. 60 match: 21 SD: 2.6271 cents 32 .. 64 match: 22 SD: 2.5195 cents 33 .. 66 match: 22 SD: 2.1704 cents 34 .. 68 match: 22 SD: 1.8002 cents 38 .. 76 match: 22 SD: 1.7988 cents 39 .. 78 match: 22 SD: 1.6455 cents 47 .. 94 match: 22 SD: 1.3869 cents 53 .. 106 match: 22 SD: 1.3299 cents 58 .. 116 match: 22 SD: 1.1478 cents 68 .. 136 match: 22 SD: 0.9858 cents 71 .. 142 match: 22 SD: 0.8316 cents 85 .. 170 match: 22 SD: 0.7240 cents 104 .. 208 match: 22 SD: 0.6928 cents 105 .. 210 match: 22 SD: 0.6280 cents 106 .. 212 match: 22 SD: 0.5914 cents 111 .. 222 match: 22 SD: 0.4880 cents 140 .. 280 match: 22 SD: 0.4684 cents 146 .. 292 match: 22 SD: 0.4598 cents 156 .. 312 match: 22 SD: 0.3527 cents 180 .. 360 match: 22 SD: 0.3463 cents 193 .. 386 match: 22 SD: 0.3294 cents 203 .. 406 match: 22 SD: 0.2712 cents 232 .. 464 match: 22 SD: 0.2283 cents 268 .. 536 match: 22 SD: 0.2220 cents 301 .. 602 match: 22 SD: 0.2199 cents 302 .. 604 match: 22 SD: 0.2196 cents 307 .. 614 match: 22 SD: 0.2006 cents 341 .. 682 match: 22 SD: 0.1715 cents 359 .. 718 match: 22 SD: 0.1623 cents 399 .. 798 match: 22 SD: 0.1549 cents 412 .. 824 match: 22 SD: 0.1084 cents 544 .. 1088 match: 22 SD: 0.1035 cents 568 .. 1136 match: 22 SD: 0.0934 cents