Scala analysis: neogeb24
Neo-Gothic e-based lineotuning (T/S or Blackwood's R=e, ~2.71828), 24 notes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55.283 cents 55.282890 2: 132.248 cents 132.248350 3: 187.531 cents 187.531250 4: 209.214 cents 209.213820 5: 264.497 cents 264.496710 6: 286.179 cents 286.179280 7: 341.462 cents 341.462170 8: 418.428 cents 418.427630 9: 473.711 cents 473.710520 10: 495.393 cents 495.393090 11: 550.676 cents 550.675980 12: 627.641 cents 627.641450 13: 682.924 cents 682.924340 14: 704.607 cents 704.606910 15: 759.890 cents 759.889800 16: 836.855 cents 836.855260 17: 892.138 cents 892.138150 18: 913.821 cents 913.820720 19: 969.104 cents 969.103620 20: 990.786 cents 990.786180 21: 1046.069 cents 1046.069080 22: 1123.035 cents 1123.034540 23: 1178.317 cents 1178.317430 24: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21.6826 cents 21.6826 1: 55.2829 cents 55.2829 2: 76.9655 cents 76.9655 3: 55.2829 cents 55.2829 4: 21.6826 cents 21.6826 5: 55.2829 cents 55.2829 6: 21.6826 cents 21.6826 7: 55.2829 cents 55.2829 8: 76.9655 cents 76.9655 9: 55.2829 cents 55.2829 10: 21.6826 cents 21.6826 11: 55.2829 cents 55.2829 12: 76.9655 cents 76.9655 13: 55.2829 cents 55.2829 14: 21.6826 cents 21.6826 15: 55.2829 cents 55.2829 16: 76.9655 cents 76.9655 17: 55.2829 cents 55.2829 18: 21.6826 cents 21.6826 19: 55.2829 cents 55.2829 20: 21.6826 cents 21.6826 21: 55.2829 cents 55.2829 22: 76.9655 cents 76.9655 23: 55.2829 cents 55.2829 24: 21.6826 cents 21.6826
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 21.68257 cents 1: 12 55.28289 cents 1: 5 76.96546 cents 2: 14 76.96547 cents 2: 10 132.24835 cents 3: 2 98.64803 cents 3: 7 132.24836 cents 3: 10 153.93093 cents 3: 5 187.53125 cents 4: 4 153.93093 cents 4: 20 209.21382 cents 5: 2 209.21382 cents 5: 9 230.89639 cents 5: 10 264.49671 cents 5: 3 286.17928 cents 6: 18 286.17928 cents 6: 6 341.46217 cents 7: 4 307.86184 cents 7: 9 341.46217 cents 7: 8 363.14474 cents 7: 3 396.74506 cents 8: 8 363.14474 cents 8: 16 418.42763 cents 9: 4 418.42763 cents 9: 11 440.11020 cents 9: 8 473.71052 cents 9: 1 495.39309 cents 10: 22 495.39309 cents 10: 2 550.67598 cents 11: 6 517.07566 cents 11: 11 550.67598 cents 11: 6 572.35856 cents 11: 1 605.95887 cents 12: 12 572.35856 cents 12: 12 627.64145 cents 13: 1 594.04113 cents 13: 6 627.64145 cents 13: 11 649.32402 cents 13: 6 682.92434 cents 14: 2 649.32402 cents 14: 22 704.60691 cents 15: 1 704.60691 cents 15: 8 726.28947 cents 15: 11 759.88980 cents 15: 4 781.57237 cents 16: 16 781.57237 cents 16: 8 836.85526 cents 17: 3 803.25493 cents 17: 8 836.85527 cents 17: 9 858.53783 cents 17: 4 892.13815 cents 18: 6 858.53783 cents 18: 18 913.82072 cents 19: 3 913.82073 cents 19: 10 935.50329 cents 19: 9 969.10362 cents 19: 2 990.78618 cents 20: 20 990.78618 cents 20: 4 1046.06907 cents 21: 5 1012.46875 cents 21: 10 1046.06908 cents 21: 7 1067.75165 cents 21: 2 1101.35197 cents 22: 10 1067.75165 cents 22: 14 1123.03454 cents 23: 5 1123.03454 cents 23: 12 1144.71711 cents 23: 7 1178.31743 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.95652 = 68/23
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 0.0 : 55.3 132.2 187.5 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 836.9 892.1 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 55.3 : 77.0 132.2 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 132.2 : 55.3 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1200.0 187.5 : 21.7 77.0 98.6 153.9 230.9 286.2 307.9 363.1 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 803.3 858.5 935.5 990.8 1012.5 1067.8 1144.7 1200.0 209.2 : 55.3 77.0 132.2 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 264.5 : 21.7 77.0 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 286.2 : 55.3 132.2 187.5 209.2 264.5 341.5 396.7 418.4 473.7 550.7 606.0 627.6 682.9 704.6 759.9 836.9 892.1 913.8 969.1 1046.1 1101.4 1123.0 1178.3 1200.0 341.5 : 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1144.7 1200.0 418.4 : 55.3 77.0 132.2 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1067.8 1123.0 1200.0 473.7 : 21.7 77.0 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1012.5 1067.8 1144.7 1200.0 495.4 : 55.3 132.2 187.5 209.2 264.5 341.5 396.7 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 836.9 892.1 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 550.7 : 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 627.6 : 55.3 77.0 132.2 209.2 264.5 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1200.0 682.9 : 21.7 77.0 153.9 209.2 230.9 286.2 307.9 363.1 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 803.3 858.5 935.5 990.8 1012.5 1067.8 1144.7 1200.0 704.6 : 55.3 132.2 187.5 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 759.9 : 77.0 132.2 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 836.9 : 55.3 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1200.0 892.1 : 21.7 77.0 98.6 153.9 230.9 286.2 307.9 363.1 440.1 495.4 517.1 572.4 594.0 649.3 726.3 781.6 803.3 858.5 935.5 990.8 1012.5 1067.8 1144.7 1200.0 913.8 : 55.3 77.0 132.2 209.2 264.5 286.2 341.5 418.4 473.7 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1123.0 1178.3 1200.0 969.1 : 21.7 77.0 153.9 209.2 230.9 286.2 363.1 418.4 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1067.8 1123.0 1144.7 1200.0 990.8 : 55.3 132.2 187.5 209.2 264.5 341.5 396.7 418.4 473.7 495.4 550.7 627.6 682.9 704.6 759.9 836.9 892.1 913.8 969.1 1046.1 1101.4 1123.0 1178.3 1200.0 1046.1: 77.0 132.2 153.9 209.2 286.2 341.5 363.1 418.4 440.1 495.4 572.4 627.6 649.3 704.6 781.6 836.9 858.5 913.8 990.8 1046.1 1067.8 1123.0 1144.7 1200.0 1123.0: 55.3 77.0 132.2 209.2 264.5 286.2 341.5 363.1 418.4 495.4 550.7 572.4 627.6 704.6 759.9 781.6 836.9 913.8 969.1 990.8 1046.1 1067.8 1123.0 1200.0 1178.3: 21.7 77.0 153.9 209.2 230.9 286.2 307.9 363.1 440.1 495.4 517.1 572.4 649.3 704.6 726.3 781.6 858.5 913.8 935.5 990.8 1012.5 1067.8 1144.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.6826 .. 76.9655 cents 55.28289 cents 21.68257 cents 2: 76.9655 .. 132.2483 cents 55.28288 cents 0.00001 cents 3: 98.6480 .. 187.5312 cents 88.88322 cents -33.60032 cents 4: 153.9309 .. 209.2138 cents 55.28289 cents -33.60032 cents 5: 209.2138 .. 286.1793 cents 76.96546 cents 1/1, 0.0000 cents 6: 286.1793 .. 341.4622 cents 55.28289 cents 1/1, 0.0000 cents 7: 307.8618 .. 396.7451 cents 88.88322 cents -33.60033 cents 8: 363.1447 .. 418.4276 cents 55.28289 cents -33.60032 cents 9: 418.4276 .. 495.3931 cents 76.96546 cents 1/1, 0.0000 cents 10: 495.3931 .. 550.6760 cents 55.28289 cents 1/1, 0.0000 cents 11: 517.0757 .. 605.9589 cents 88.88321 cents -33.60032 cents 12: 572.3586 .. 627.6415 cents 55.28289 cents -33.60031 cents 13: 594.0411 .. 682.9243 cents 88.88321 cents -33.60032 cents 14: 649.3240 .. 704.6069 cents 55.28289 cents -33.60032 cents 15: 704.6069 .. 781.5724 cents 76.96546 cents 1/1, 0.0000 cents 16: 781.5724 .. 836.8553 cents 55.28289 cents 1/1, 0.0000 cents 17: 803.2549 .. 892.1381 cents 88.88322 cents -33.60033 cents 18: 858.5378 .. 913.8207 cents 55.28289 cents -33.60032 cents 19: 913.8207 .. 990.7862 cents 76.96545 cents 0.00001 cents 20: 990.7862 .. 1046.0691 cents 55.28289 cents 1/1, 0.0000 cents 21: 1012.4688 .. 1101.3520 cents 88.88322 cents -33.60032 cents 22: 1067.7517 .. 1123.0345 cents 55.28289 cents -33.60032 cents 23: 1123.0345 .. 1178.3174 cents 55.28289 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 21.68256 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 76.96546 cents Average / Smallest step : 2.306001 Largest / Average step : 1.539309 Largest / Smallest step : 3.549648 Median interval of one step : 55.28289 cents, amount: 12 Most common interval of one step : 55.28289 cents, amount: 12 Least squares average step : 50.86791 cents, oct.: 1220.82991 cents Scale is not proper Scale is a mode of a 1107-tone equal temperament with octave 2/1 degrees: 51 122 173 193 244 264 315 386 437 457 508 579 630 650 701 772 823 843 894 914 965 1036 1087 1107 Least number of segments generator : 554 of 600.542 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 650 of 704.607 cents and inv. generated superset size: 24 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACACABACABACABACACABAC Step pattern size order : MLMSMSMLMSMLMSMLMSMSMLMS Scale is not a Constant Structure Scale diversity : 1.194766 Lumma stability : 0.036138 Lumma impropriety factor : 0.326072 Rothenberg efficiency : 0.694444 redundancy: 0.305556 Efficiency x scale size : 16.666667 Number of different interval sizes : 46 = 2.00000 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 2.95652 = 68/23 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 11.91774 cents Most common intervals : 495.39309 cents & inv., amount: 23 Scale has Generated (pseudo-Myhill) property, generator: 704.607 cents and inv. Scale is a chain of 12 triads 0.0 55.283 704.607 cents Most common triad is 0.0 495.393 704.607 cents, amount: 22 Number of recognisable fifths : 23, average 704.6069 cents Scale contains two identical disjunct "tetrachords" of 11 notes Formal octave complements present : 7 = 29.1667% Limited inverse transpositions : 23 Inversional symmetry on intervals : 11-12 23-24 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
24: 1 2 1 0 1 1 1 1 1 1 1 2 1 0 1 2 1 0 1 1 1 1 2 0 N T3 SD: 14.1171 c. M: 23.7105 c. 25: 1 2 1 0 2 0 1 2 1 0 1 2 1 1 1 1 2 0 1 1 1 1 2 0 N SD: 13.9138 c. M:-23.5033 c. 27: 1 2 1 0 2 0 1 2 1 1 1 2 1 1 1 2 1 0 2 0 1 2 1 1 N SD: 16.5400 c. M: 31.4360 c. 28: 1 2 1 1 1 1 1 2 1 1 1 2 1 0 2 2 1 0 2 0 1 2 1 1 N SD: 12.4722 c. M: 21.1746 c. 29: 1 2 1 1 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 1 1 P D3 SD: 12.7010 c. M: 23.1726 c. 30: 1 2 2 0 2 0 2 1 2 0 2 2 1 1 1 2 1 1 1 1 1 2 1 1 N SD: 11.3508 c. M:-18.5378 c. 31: 1 2 2 0 2 0 2 2 1 1 1 2 2 0 2 2 1 1 1 1 1 2 1 1 N SD: 11.0514 c. M: 17.0271 c. 32: 1 3 1 1 1 1 1 2 2 0 2 2 1 1 1 2 2 0 2 0 2 2 1 1 N SD: 10.7734 c. M: 17.7829 c. 38: 2 2 2 1 1 1 2 2 2 1 1 3 2 0 2 3 1 1 2 0 2 3 1 1 N SD: 8.8631 c. M:-15.7763 c. 41: 2 2 2 1 2 1 1 3 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2 1 N SD: 9.2159 c. M: 19.5110 c. 42: 2 3 2 0 2 1 2 3 2 0 2 3 2 1 2 2 2 1 2 1 2 2 2 1 N SD: 7.8976 c. M:-12.4688 c. 46: 2 3 2 1 2 1 2 3 2 1 2 3 2 1 2 3 2 1 2 1 2 3 2 1 N SD: 2.8401 c. M: 5.1816 c. 63: 3 4 3 1 3 1 3 4 3 1 3 4 3 1 3 4 3 1 3 1 3 4 3 1 N G SD: 1.6991 c. M:-3.0999 c. 109: 5 7 5 2 5 2 5 7 5 2 5 7 5 2 5 7 5 2 5 2 5 7 5 2 N G SD: 0.2165 c. M: 0.3950 c. 281: 13 18 13 5 13 5 13 18 13 5 13 18 13 5 13 18 13 5 13 5 13 18 13 5 N G SD: 0.2130 c. M:-0.3885 c. 390: 18 25 18 7 18 7 18 25 18 7 18 25 18 7 18 25 18 7 18 7 18 25 18 7 N G SD: 0.0929 c. M:-0.1695 c. 499: 23 32 23 9 23 9 23 32 23 9 23 32 23 9 23 32 23 9 23 9 23 32 23 9 N G SD: 0.0253 c. M:-0.0462 c. 608: 28 39 28 11 28 11 28 39 28 11 28 39 28 11 28 39 28 11 28 11 28 39 28 11 N G SD: 0.0180 c. M: 0.0329 c. 1107: 51 71 51 20 51 20 51 71 51 20 51 71 51 20 51 71 51 20 51 20 51 71 51 20 N G SD: 0.0015 c. M:-0.0028 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.3260 cents 3 .. 6 match: 3 H SD: 2.7397 cents 4 .. 8 match: 4 H SD: 8.0561 cents 5 .. 10 match: 5 H SD: 10.8367 cents 6 .. 12 match: 6 H SD: 1.5905 cents 7 .. 14 match: 7 H SD: 7.0036 cents 8 .. 16 match: 8 H SD: 5.9806 cents 9 .. 18 match: 9 H SD: 3.0362 cents 10 .. 20 match: 10 H SD: 6.3196 cents 11 .. 22 match: 11 H SD: 3.9898 cents 12 .. 24 match: 12 H SD: 4.6042 cents 13 .. 26 match: 13 H SD: 3.5419 cents 14 .. 28 match: 14 H SD: 4.4963 cents 15 .. 30 match: 14 SD: 5.0369 cents 16 .. 32 match: 15 SD: 3.6175 cents 17 .. 34 match: 15 SD: 5.4108 cents 18 .. 36 match: 17 S SD: 3.4652 cents 19 .. 38 match: 17 SD: 3.7938 cents 20 .. 40 match: 17 SD: 4.7334 cents 21 .. 42 match: 20 S SD: 3.8160 cents 22 .. 44 match: 18 SD: 2.8366 cents 23 .. 46 match: 21 SD: 2.7899 cents 24 .. 48 match: 20 SD: 2.5907 cents 25 .. 50 match: 19 SD: 2.7774 cents 26 .. 52 match: 20 SD: 2.6081 cents 27 .. 54 match: 22 SD: 2.2921 cents 28 .. 56 match: 20 SD: 2.6737 cents 29 .. 58 match: 21 SD: 2.3493 cents 30 .. 60 match: 21 SD: 2.5346 cents 31 .. 62 match: 22 SD: 2.5205 cents 32 .. 64 match: 22 SD: 2.0863 cents 33 .. 66 match: 22 SD: 2.2292 cents 34 .. 68 match: 20 SD: 1.9398 cents 35 .. 70 match: 21 SD: 1.8901 cents 36 .. 72 match: 23 SD: 1.6452 cents 37 .. 74 match: 23 SD: 1.5619 cents 38 .. 76 match: 22 SD: 1.9535 cents 39 .. 78 match: 24 SD: 1.9444 cents 40 .. 80 match: 21 SD: 1.4717 cents 41 .. 82 match: 22 SD: 1.8583 cents 42 .. 84 match: 22 SD: 1.7825 cents 43 .. 86 match: 23 SD: 1.7304 cents 45 .. 90 match: 24 SD: 1.5876 cents 46 .. 92 match: 23 SD: 1.6880 cents 47 .. 94 match: 23 SD: 1.6449 cents 48 .. 96 match: 24 SD: 1.4629 cents 49 .. 98 match: 23 SD: 1.5319 cents 50 .. 100 match: 23 SD: 1.4394 cents 51 .. 102 match: 24 SD: 1.3854 cents 52 .. 104 match: 23 SD: 1.3417 cents 54 .. 108 match: 24 SD: 1.2052 cents 55 .. 110 match: 24 SD: 1.1786 cents 57 .. 114 match: 23 SD: 1.4821 cents 58 .. 116 match: 22 SD: 1.2433 cents 60 .. 120 match: 24 SD: 1.0087 cents 66 .. 132 match: 23 SD: 0.9915 cents 69 .. 138 match: 24 SD: 0.9836 cents 72 .. 144 match: 24 SD: 0.9265 cents 73 .. 146 match: 24 SD: 0.9057 cents 78 .. 156 match: 24 SD: 0.8398 cents 85 .. 170 match: 24 SD: 0.7389 cents 87 .. 174 match: 24 SD: 0.7206 cents 91 .. 182 match: 24 SD: 0.7183 cents 96 .. 192 match: 24 SD: 0.6243 cents 114 .. 228 match: 24 SD: 0.5452 cents 123 .. 246 match: 24 SD: 0.5064 cents 124 .. 248 match: 24 SD: 0.4494 cents 147 .. 294 match: 24 SD: 0.4193 cents 151 .. 302 match: 24 SD: 0.3934 cents 163 .. 326 match: 24 SD: 0.3880 cents 165 .. 330 match: 24 SD: 0.3546 cents 184 .. 368 match: 24 SD: 0.3459 cents 187 .. 374 match: 24 SD: 0.3056 cents 193 .. 386 match: 24 SD: 0.2931 cents 211 .. 422 match: 24 SD: 0.2376 cents 272 .. 544 match: 24 SD: 0.2308 cents 277 .. 554 match: 24 SD: 0.2202 cents 279 .. 558 match: 24 SD: 0.2147 cents 289 .. 578 match: 24 SD: 0.1760 cents 341 .. 682 match: 24 SD: 0.1612 cents 366 .. 732 match: 24 SD: 0.1579 cents 368 .. 736 match: 24 SD: 0.1384 cents 428 .. 856 match: 24 SD: 0.1260 cents 483 .. 966 match: 24 SD: 0.1255 cents 490 .. 980 match: 24 SD: 0.1180 cents 492 .. 984 match: 24 SD: 0.1172 cents 515 .. 1030 match: 24 SD: 0.1119 cents 528 .. 1056 match: 24 SD: 0.0981 cents 552 .. 1104 match: 24 SD: 0.0872 cents