Scala analysis: lemba26
26 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: 44.444 cents 44.444444 2: 93.333 cents 93.333333 3: 137.778 cents 137.777778 4: 186.667 cents 186.666667 5: 231.111 cents 231.111111 6: 275.556 cents 275.555556 7: 324.444 cents 324.444444 8: 368.889 cents 368.888889 9: 413.333 cents 413.333333 10: 462.222 cents 462.222222 11: 506.667 cents 506.666667 12: 555.556 cents 555.555556 13: 600.000 cents 600.000000 14: 644.444 cents 644.444444 15: 693.333 cents 693.333333 16: 737.778 cents 737.777778 17: 786.667 cents 786.666667 18: 831.111 cents 831.111111 19: 875.556 cents 875.555556 20: 924.444 cents 924.444444 21: 968.889 cents 968.888889 22: 1013.333 cents 1013.333333 23: 1062.222 cents 1062.222222 24: 1106.667 cents 1106.666667 25: 1155.556 cents 1155.555556 26: 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: 48.8889 cents 48.8889 5: 44.4444 cents 44.4444 6: 44.4444 cents 44.4444 7: 48.8889 cents 48.8889 8: 44.4444 cents 44.4444 9: 44.4444 cents 44.4444 10: 48.8889 cents 48.8889 11: 44.4444 cents 44.4444 12: 48.8889 cents 48.8889 13: 44.4444 cents 44.4444 14: 44.4444 cents 44.4444 15: 48.8889 cents 48.8889 16: 44.4444 cents 44.4444 17: 48.8889 cents 48.8889 18: 44.4444 cents 44.4444 19: 44.4444 cents 44.4444 20: 48.8889 cents 48.8889 21: 44.4444 cents 44.4444 22: 44.4444 cents 44.4444 23: 48.8889 cents 48.8889 24: 44.4444 cents 44.4444 25: 48.8889 cents 48.8889 26: 44.4444 cents 44.4444
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 16 44.44444 cents 1: 10 48.88889 cents 2: 6 88.88889 cents 2: 20 93.33333 cents 3: 22 137.77778 cents 3: 4 142.22222 cents 4: 12 182.22222 cents 4: 14 186.66667 cents 5: 2 226.66667 cents 5: 24 231.11111 cents 6: 18 275.55556 cents 6: 8 280.00000 cents 7: 8 320.00000 cents 7: 18 324.44444 cents 8: 24 368.88889 cents 8: 2 373.33333 cents 9: 14 413.33333 cents 9: 12 417.77778 cents 10: 4 457.77778 cents 10: 22 462.22222 cents 11: 20 506.66667 cents 11: 6 511.11111 cents 12: 10 551.11111 cents 12: 16 555.55556 cents 13: 26 600.00000 cents 14: 16 644.44444 cents 14: 10 648.88889 cents 15: 6 688.88889 cents 15: 20 693.33333 cents 16: 22 737.77778 cents 16: 4 742.22222 cents 17: 12 782.22222 cents 17: 14 786.66667 cents 18: 2 826.66667 cents 18: 24 831.11111 cents 19: 18 875.55556 cents 19: 8 880.00000 cents 20: 8 920.00000 cents 20: 18 924.44444 cents 21: 24 968.88889 cents 21: 2 973.33333 cents 22: 14 1013.33333 cents 22: 12 1017.77778 cents 23: 4 1057.77778 cents 23: 22 1062.22222 cents 24: 20 1106.66667 cents 24: 6 1111.11111 cents 25: 10 1151.11111 cents 25: 16 1155.55556 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.96000 = 49/25
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 26 0.0 : 44.4 93.3 137.8 186.7 231.1 275.6 324.4 368.9 413.3 462.2 506.7 555.6 600.0 644.4 693.3 737.8 786.7 831.1 875.6 924.4 968.9 1013.3 1062.2 1106.7 1155.6 1200.0 44.4 : 48.9 93.3 142.2 186.7 231.1 280.0 324.4 368.9 417.8 462.2 511.1 555.6 600.0 648.9 693.3 742.2 786.7 831.1 880.0 924.4 968.9 1017.8 1062.2 1111.1 1155.6 1200.0 93.3 : 44.4 93.3 137.8 182.2 231.1 275.6 320.0 368.9 413.3 462.2 506.7 551.1 600.0 644.4 693.3 737.8 782.2 831.1 875.6 920.0 968.9 1013.3 1062.2 1106.7 1151.1 1200.0 137.8 : 48.9 93.3 137.8 186.7 231.1 275.6 324.4 368.9 417.8 462.2 506.7 555.6 600.0 648.9 693.3 737.8 786.7 831.1 875.6 924.4 968.9 1017.8 1062.2 1106.7 1155.6 1200.0 186.7 : 44.4 88.9 137.8 182.2 226.7 275.6 320.0 368.9 413.3 457.8 506.7 551.1 600.0 644.4 688.9 737.8 782.2 826.7 875.6 920.0 968.9 1013.3 1057.8 1106.7 1151.1 1200.0 231.1 : 44.4 93.3 137.8 182.2 231.1 275.6 324.4 368.9 413.3 462.2 506.7 555.6 600.0 644.4 693.3 737.8 782.2 831.1 875.6 924.4 968.9 1013.3 1062.2 1106.7 1155.6 1200.0 275.6 : 48.9 93.3 137.8 186.7 231.1 280.0 324.4 368.9 417.8 462.2 511.1 555.6 600.0 648.9 693.3 737.8 786.7 831.1 880.0 924.4 968.9 1017.8 1062.2 1111.1 1155.6 1200.0 324.4 : 44.4 88.9 137.8 182.2 231.1 275.6 320.0 368.9 413.3 462.2 506.7 551.1 600.0 644.4 688.9 737.8 782.2 831.1 875.6 920.0 968.9 1013.3 1062.2 1106.7 1151.1 1200.0 368.9 : 44.4 93.3 137.8 186.7 231.1 275.6 324.4 368.9 417.8 462.2 506.7 555.6 600.0 644.4 693.3 737.8 786.7 831.1 875.6 924.4 968.9 1017.8 1062.2 1106.7 1155.6 1200.0 413.3 : 48.9 93.3 142.2 186.7 231.1 280.0 324.4 373.3 417.8 462.2 511.1 555.6 600.0 648.9 693.3 742.2 786.7 831.1 880.0 924.4 973.3 1017.8 1062.2 1111.1 1155.6 1200.0 462.2 : 44.4 93.3 137.8 182.2 231.1 275.6 324.4 368.9 413.3 462.2 506.7 551.1 600.0 644.4 693.3 737.8 782.2 831.1 875.6 924.4 968.9 1013.3 1062.2 1106.7 1151.1 1200.0 506.7 : 48.9 93.3 137.8 186.7 231.1 280.0 324.4 368.9 417.8 462.2 506.7 555.6 600.0 648.9 693.3 737.8 786.7 831.1 880.0 924.4 968.9 1017.8 1062.2 1106.7 1155.6 1200.0 555.6 : 44.4 88.9 137.8 182.2 231.1 275.6 320.0 368.9 413.3 457.8 506.7 551.1 600.0 644.4 688.9 737.8 782.2 831.1 875.6 920.0 968.9 1013.3 1057.8 1106.7 1151.1 1200.0 600.0 : 44.4 93.3 137.8 186.7 231.1 275.6 324.4 368.9 413.3 462.2 506.7 555.6 600.0 644.4 693.3 737.8 786.7 831.1 875.6 924.4 968.9 1013.3 1062.2 1106.7 1155.6 1200.0 644.4 : 48.9 93.3 142.2 186.7 231.1 280.0 324.4 368.9 417.8 462.2 511.1 555.6 600.0 648.9 693.3 742.2 786.7 831.1 880.0 924.4 968.9 1017.8 1062.2 1111.1 1155.6 1200.0 693.3 : 44.4 93.3 137.8 182.2 231.1 275.6 320.0 368.9 413.3 462.2 506.7 551.1 600.0 644.4 693.3 737.8 782.2 831.1 875.6 920.0 968.9 1013.3 1062.2 1106.7 1151.1 1200.0 737.8 : 48.9 93.3 137.8 186.7 231.1 275.6 324.4 368.9 417.8 462.2 506.7 555.6 600.0 648.9 693.3 737.8 786.7 831.1 875.6 924.4 968.9 1017.8 1062.2 1106.7 1155.6 1200.0 786.7 : 44.4 88.9 137.8 182.2 226.7 275.6 320.0 368.9 413.3 457.8 506.7 551.1 600.0 644.4 688.9 737.8 782.2 826.7 875.6 920.0 968.9 1013.3 1057.8 1106.7 1151.1 1200.0 831.1 : 44.4 93.3 137.8 182.2 231.1 275.6 324.4 368.9 413.3 462.2 506.7 555.6 600.0 644.4 693.3 737.8 782.2 831.1 875.6 924.4 968.9 1013.3 1062.2 1106.7 1155.6 1200.0 875.6 : 48.9 93.3 137.8 186.7 231.1 280.0 324.4 368.9 417.8 462.2 511.1 555.6 600.0 648.9 693.3 737.8 786.7 831.1 880.0 924.4 968.9 1017.8 1062.2 1111.1 1155.6 1200.0 924.4 : 44.4 88.9 137.8 182.2 231.1 275.6 320.0 368.9 413.3 462.2 506.7 551.1 600.0 644.4 688.9 737.8 782.2 831.1 875.6 920.0 968.9 1013.3 1062.2 1106.7 1151.1 1200.0 968.9 : 44.4 93.3 137.8 186.7 231.1 275.6 324.4 368.9 417.8 462.2 506.7 555.6 600.0 644.4 693.3 737.8 786.7 831.1 875.6 924.4 968.9 1017.8 1062.2 1106.7 1155.6 1200.0 1013.3: 48.9 93.3 142.2 186.7 231.1 280.0 324.4 373.3 417.8 462.2 511.1 555.6 600.0 648.9 693.3 742.2 786.7 831.1 880.0 924.4 973.3 1017.8 1062.2 1111.1 1155.6 1200.0 1062.2: 44.4 93.3 137.8 182.2 231.1 275.6 324.4 368.9 413.3 462.2 506.7 551.1 600.0 644.4 693.3 737.8 782.2 831.1 875.6 924.4 968.9 1013.3 1062.2 1106.7 1151.1 1200.0 1106.7: 48.9 93.3 137.8 186.7 231.1 280.0 324.4 368.9 417.8 462.2 506.7 555.6 600.0 648.9 693.3 737.8 786.7 831.1 880.0 924.4 968.9 1017.8 1062.2 1106.7 1155.6 1200.0 1155.6: 44.4 88.9 137.8 182.2 231.1 275.6 320.0 368.9 413.3 457.8 506.7 551.1 600.0 644.4 688.9 737.8 782.2 831.1 875.6 920.0 968.9 1013.3 1057.8 1106.7 1151.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.4444 .. 48.8889 cents 4.44444 cents 44.44444 cents 2: 88.8889 .. 93.3333 cents 4.44444 cents 40.00000 cents 3: 137.7778 .. 142.2222 cents 4.44444 cents 44.44445 cents 4: 182.2222 .. 186.6667 cents 4.44444 cents 40.00000 cents 5: 226.6667 .. 231.1111 cents 4.44444 cents 40.00000 cents 6: 275.5556 .. 280.0000 cents 4.44444 cents 44.44444 cents 7: 320.0000 .. 324.4444 cents 4.44444 cents 40.00000 cents 8: 368.8889 .. 373.3333 cents 4.44444 cents 44.44444 cents 9: 413.3333 .. 417.7778 cents 4.44444 cents 40.00000 cents 10: 457.7778 .. 462.2222 cents 4.44444 cents 40.00000 cents 11: 506.6667 .. 511.1111 cents 4.44444 cents 44.44445 cents 12: 551.1111 .. 555.5556 cents 4.44444 cents 40.00000 cents 13: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 44.44444 cents 14: 644.4444 .. 648.8889 cents 4.44444 cents 44.44444 cents 15: 688.8889 .. 693.3333 cents 4.44444 cents 40.00000 cents 16: 737.7778 .. 742.2222 cents 4.44444 cents 44.44444 cents 17: 782.2222 .. 786.6667 cents 4.44444 cents 40.00000 cents 18: 826.6667 .. 831.1111 cents 4.44445 cents 40.00000 cents 19: 875.5556 .. 880.0000 cents 4.44444 cents 44.44444 cents 20: 920.0000 .. 924.4444 cents 4.44444 cents 40.00000 cents 21: 968.8889 .. 973.3333 cents 4.44444 cents 44.44444 cents 22: 1013.3333 .. 1017.7778 cents 4.44444 cents 40.00000 cents 23: 1057.7778 .. 1062.2222 cents 4.44444 cents 40.00000 cents 24: 1106.6667 .. 1111.1111 cents 4.44444 cents 44.44444 cents 25: 1151.1111 .. 1155.5556 cents 4.44444 cents 40.00000 cents
SHOW DATA
Number of notes : 26 -- Interval properties -- Smallest interval : 44.44444 cents, class 1 Average step (divided formal octave): 46.1538 cents Largest one step interval : 48.88889 cents Average / Smallest step : 1.038462 Largest / Average step : 1.059259 Largest / Smallest step : 1.100000 Median interval of one step : 44.44444 cents, amount: 16 Most common interval of one step : 44.44444 cents, amount: 16 Least squares average step : 46.15528 cents, oct.: 1200.03727 cents Scale is strictly proper Scale is maximally even in 270-tone equal temperament Scale has 2 repeating blocks of 13 notes Blocks have Myhill's property chromas: 4.44444 cents and 40.00000 cents, ratio: 8.999999 generators: 5 of 231.11111 cents and 8 of 368.88889 cents ET pair of linear temperament : 26&270 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 270-tone equal temperament with octave 1200.000 cents degrees: 10 21 31 42 52 62 73 83 93 104 114 125 135 145 156 166 177 187 197 208 218 228 239 249 260 270 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: 148 = 122 more = 569.231% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAABAABABAABABAABAABABA Step pattern size order : SLSLSSLSSLSLSSLSLSSLSSLSLS Scale is a Constant Structure, by a margin of 40.00000 cents Scale diversity : 1.053153 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.911111 Number of different interval sizes : 49 = 1.96000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.96000 = 49/25 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 4.44444 cents Most common intervals : 600.00000 cents & inv., amount: 26 Number of recognisable fifths : 26, average 692.3077 cents Scale contains two identical disjunct "tetrachords" of 12 notes Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 26 = 100.0000% Limited transpositions : 13 Limited inverse transpositions : 13 Inversional symmetry on degrees : 0 13 Inversional symmetry on intervals : 6-7 19-20 -- Rational properties --
FIT/MODE
26: 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 1 SP B ME I SD: 1.2792 c. M:-2.0513 c. 140: 5 6 5 6 5 5 6 5 5 6 5 6 5 5 6 5 6 5 5 6 5 5 6 5 6 5 SP B ME I SD: 1.1878 c. M:-1.9048 c. 166: 6 7 6 7 6 6 7 6 6 7 6 7 6 6 7 6 7 6 6 7 6 6 7 6 7 6 SP B ME I SD: 0.8014 c. M:-1.2851 c. 192: 7 8 7 8 7 7 8 7 7 8 7 8 7 7 8 7 8 7 7 8 7 7 8 7 8 7 SP B ME I SD: 0.5197 c. M:-0.8333 c. 218: 8 9 8 9 8 8 9 8 8 9 8 9 8 8 9 8 9 8 8 9 8 8 9 8 9 8 SP B ME I SD: 0.3051 c. M:-0.4893 c. 244: 9 10 9 10 9 9 10 9 9 10 9 10 9 9 10 9 10 9 9 10 9 9 10 9 10 9 SP B ME I SD: 0.1363 c. M:-0.2186 c. 270: 10 11 10 11 10 10 11 10 10 11 10 11 10 10 11 10 11 10 10 11 10 10 11 10 11 10 SP B ME 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: 5.3108 cents 6 .. 12 match: 6 H SD: 3.6015 cents 7 .. 14 match: 7 H SD: 4.4300 cents 8 .. 16 match: 8 H SD: 4.1841 cents 9 .. 18 match: 9 H SD: 4.2957 cents 10 .. 20 match: 10 H SD: 3.6974 cents 11 .. 22 match: 11 H SD: 4.5928 cents 12 .. 24 match: 12 H SD: 2.9410 cents 13 .. 26 match: 13 H SD: 3.2962 cents 14 .. 28 match: 14 H SD: 3.7024 cents 15 .. 30 match: 15 H SD: 3.3909 cents 16 .. 32 match: 16 H SD: 3.4171 cents 17 .. 34 match: 17 H SD: 2.8918 cents 18 .. 36 match: 18 H SD: 2.7394 cents 19 .. 38 match: 19 H SD: 2.7360 cents 20 .. 40 match: 20 H SD: 2.5275 cents 21 .. 42 match: 21 H SD: 2.6239 cents 22 .. 44 match: 20 S SD: 3.1820 cents 23 .. 46 match: 22 S SD: 2.7424 cents 24 .. 48 match: 23 SD: 2.2958 cents 25 .. 50 match: 23 SD: 2.9586 cents 26 .. 52 match: 24 SD: 2.1845 cents 27 .. 54 match: 24 SD: 2.5397 cents 28 .. 56 match: 25 SD: 2.6499 cents 29 .. 58 match: 25 SD: 2.0049 cents 30 .. 60 match: 25 SD: 2.4122 cents 31 .. 62 match: 25 SD: 2.6685 cents 32 .. 64 match: 26 SD: 2.4344 cents 33 .. 66 match: 26 SD: 1.9166 cents 34 .. 68 match: 26 SD: 1.6560 cents 44 .. 88 match: 26 SD: 1.5809 cents 45 .. 90 match: 26 SD: 1.4930 cents 47 .. 94 match: 26 SD: 1.3440 cents 53 .. 106 match: 26 SD: 1.2315 cents 58 .. 116 match: 26 SD: 1.1372 cents 59 .. 118 match: 26 SD: 1.1006 cents 63 .. 126 match: 26 SD: 1.0904 cents 64 .. 128 match: 26 SD: 1.0843 cents 68 .. 136 match: 26 SD: 0.9072 cents 71 .. 142 match: 26 SD: 0.7651 cents 85 .. 170 match: 26 SD: 0.6773 cents 97 .. 194 match: 26 SD: 0.6341 cents 104 .. 208 match: 26 SD: 0.6052 cents 105 .. 210 match: 26 SD: 0.6004 cents 106 .. 212 match: 26 SD: 0.5547 cents 111 .. 222 match: 26 SD: 0.4727 cents 140 .. 280 match: 26 SD: 0.4433 cents 146 .. 292 match: 26 SD: 0.4411 cents 155 .. 310 match: 26 SD: 0.4311 cents 156 .. 312 match: 26 SD: 0.3222 cents 193 .. 386 match: 26 SD: 0.2924 cents 203 .. 406 match: 26 SD: 0.2622 cents 219 .. 438 match: 26 SD: 0.2515 cents 237 .. 474 match: 26 SD: 0.2457 cents 256 .. 512 match: 26 SD: 0.2382 cents 266 .. 532 match: 26 SD: 0.2250 cents 273 .. 546 match: 26 SD: 0.2173 cents 300 .. 600 match: 26 SD: 0.2171 cents 301 .. 602 match: 26 SD: 0.2051 cents 307 .. 614 match: 26 SD: 0.1849 cents 341 .. 682 match: 26 SD: 0.1530 cents 412 .. 824 match: 26 SD: 0.0958 cents 544 .. 1088 match: 26 SD: 0.0939 cents 568 .. 1136 match: 26 SD: 0.0905 cents