Scala analysis: lin76-34
Two 12-note chains, ~704.160 cents, 34 4ths apart (32 4ths = 7:6)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.550 cents 58.550340 2: 129.122 cents 129.121990 3: 187.672 cents 187.672330 4: 208.321 cents 208.320570 5: 266.871 cents 266.870910 6: 287.519 cents 287.519150 7: 346.069 cents 346.069490 8: 416.641 cents 416.641140 9: 475.191 cents 475.191480 10: 495.840 cents 495.839720 11: 554.390 cents 554.390060 12: 624.962 cents 624.961710 13: 683.512 cents 683.512050 14: 704.160 cents 704.160290 15: 762.711 cents 762.710620 16: 833.282 cents 833.282280 17: 891.833 cents 891.832610 18: 912.481 cents 912.480860 19: 971.031 cents 971.031190 20: 991.679 cents 991.679430 21: 1050.230 cents 1050.229770 22: 1120.801 cents 1120.801420 23: 1179.352 cents 1179.351760 24: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 20.6482 cents 20.6482 1: 58.5503 cents 58.5503 2: 70.5717 cents 70.5717 3: 58.5503 cents 58.5503 4: 20.6482 cents 20.6482 5: 58.5503 cents 58.5503 6: 20.6482 cents 20.6482 7: 58.5503 cents 58.5503 8: 70.5717 cents 70.5717 9: 58.5503 cents 58.5503 10: 20.6482 cents 20.6482 11: 58.5503 cents 58.5503 12: 70.5717 cents 70.5717 13: 58.5503 cents 58.5503 14: 20.6482 cents 20.6482 15: 58.5503 cents 58.5503 16: 70.5717 cents 70.5717 17: 58.5503 cents 58.5503 18: 20.6482 cents 20.6482 19: 58.5503 cents 58.5503 20: 20.6482 cents 20.6482 21: 58.5503 cents 58.5503 22: 70.5717 cents 70.5717 23: 58.5503 cents 58.5503 24: 20.6482 cents 20.6482
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 20.64824 cents 1: 12 58.55034 cents 1: 5 70.57165 cents 2: 14 79.19858 cents 2: 10 129.12199 cents 3: 2 99.84682 cents 3: 7 137.74892 cents 3: 10 149.77023 cents 3: 5 187.67233 cents 4: 4 158.39716 cents 4: 20 208.32057 cents 5: 2 216.94750 cents 5: 9 228.96881 cents 5: 10 266.87091 cents 5: 3 278.89222 cents 6: 18 287.51915 cents 6: 6 337.44256 cents 7: 4 308.16739 cents 7: 9 346.06949 cents 7: 8 358.09080 cents 7: 3 395.99290 cents 8: 8 366.71773 cents 8: 16 416.64114 cents 9: 4 425.26807 cents 9: 11 437.28938 cents 9: 8 475.19148 cents 9: 1 487.21279 cents 10: 22 495.83972 cents 10: 2 545.76313 cents 11: 6 516.48796 cents 11: 11 554.39006 cents 11: 6 566.41137 cents 11: 1 604.31346 cents 12: 12 575.03830 cents 12: 12 624.96171 cents 13: 1 595.68654 cents 13: 6 633.58863 cents 13: 11 645.60995 cents 13: 6 683.51205 cents 14: 2 654.23687 cents 14: 22 704.16029 cents 15: 1 712.78721 cents 15: 8 724.80853 cents 15: 11 762.71062 cents 15: 4 774.73194 cents 16: 16 783.35887 cents 16: 8 833.28228 cents 17: 3 804.00710 cents 17: 8 841.90920 cents 17: 9 853.93052 cents 17: 4 891.83261 cents 18: 6 862.55744 cents 18: 18 912.48086 cents 19: 3 921.10778 cents 19: 10 933.12909 cents 19: 9 971.03119 cents 19: 2 983.05250 cents 20: 20 991.67943 cents 20: 4 1041.60284 cents 21: 5 1012.32767 cents 21: 10 1050.22977 cents 21: 7 1062.25108 cents 21: 2 1100.15318 cents 22: 10 1070.87801 cents 22: 14 1120.80142 cents 23: 5 1129.42835 cents 23: 12 1141.44966 cents 23: 7 1179.35176 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 : 58.6 129.1 187.7 208.3 266.9 287.5 346.1 416.6 475.2 495.8 554.4 625.0 683.5 704.2 762.7 833.3 891.8 912.5 971.0 991.7 1050.2 1120.8 1179.4 1200.0 58.6 : 70.6 129.1 149.8 208.3 229.0 287.5 358.1 416.6 437.3 495.8 566.4 625.0 645.6 704.2 774.7 833.3 853.9 912.5 933.1 991.7 1062.3 1120.8 1141.4 1200.0 129.1 : 58.6 79.2 137.7 158.4 216.9 287.5 346.1 366.7 425.3 495.8 554.4 575.0 633.6 704.2 762.7 783.4 841.9 862.6 921.1 991.7 1050.2 1070.9 1129.4 1200.0 187.7 : 20.6 79.2 99.8 158.4 229.0 287.5 308.2 366.7 437.3 495.8 516.5 575.0 645.6 704.2 724.8 783.4 804.0 862.6 933.1 991.7 1012.3 1070.9 1141.4 1200.0 208.3 : 58.6 79.2 137.7 208.3 266.9 287.5 346.1 416.6 475.2 495.8 554.4 625.0 683.5 704.2 762.7 783.4 841.9 912.5 971.0 991.7 1050.2 1120.8 1179.4 1200.0 266.9 : 20.6 79.2 149.8 208.3 229.0 287.5 358.1 416.6 437.3 495.8 566.4 625.0 645.6 704.2 724.8 783.4 853.9 912.5 933.1 991.7 1062.3 1120.8 1141.4 1200.0 287.5 : 58.6 129.1 187.7 208.3 266.9 337.4 396.0 416.6 475.2 545.8 604.3 625.0 683.5 704.2 762.7 833.3 891.8 912.5 971.0 1041.6 1100.2 1120.8 1179.4 1200.0 346.1 : 70.6 129.1 149.8 208.3 278.9 337.4 358.1 416.6 487.2 545.8 566.4 625.0 645.6 704.2 774.7 833.3 853.9 912.5 983.1 1041.6 1062.3 1120.8 1141.4 1200.0 416.6 : 58.6 79.2 137.7 208.3 266.9 287.5 346.1 416.6 475.2 495.8 554.4 575.0 633.6 704.2 762.7 783.4 841.9 912.5 971.0 991.7 1050.2 1070.9 1129.4 1200.0 475.2 : 20.6 79.2 149.8 208.3 229.0 287.5 358.1 416.6 437.3 495.8 516.5 575.0 645.6 704.2 724.8 783.4 853.9 912.5 933.1 991.7 1012.3 1070.9 1141.4 1200.0 495.8 : 58.6 129.1 187.7 208.3 266.9 337.4 396.0 416.6 475.2 495.8 554.4 625.0 683.5 704.2 762.7 833.3 891.8 912.5 971.0 991.7 1050.2 1120.8 1179.4 1200.0 554.4 : 70.6 129.1 149.8 208.3 278.9 337.4 358.1 416.6 437.3 495.8 566.4 625.0 645.6 704.2 774.7 833.3 853.9 912.5 933.1 991.7 1062.3 1120.8 1141.4 1200.0 625.0 : 58.6 79.2 137.7 208.3 266.9 287.5 346.1 366.7 425.3 495.8 554.4 575.0 633.6 704.2 762.7 783.4 841.9 862.6 921.1 991.7 1050.2 1070.9 1129.4 1200.0 683.5 : 20.6 79.2 149.8 208.3 229.0 287.5 308.2 366.7 437.3 495.8 516.5 575.0 645.6 704.2 724.8 783.4 804.0 862.6 933.1 991.7 1012.3 1070.9 1141.4 1200.0 704.2 : 58.6 129.1 187.7 208.3 266.9 287.5 346.1 416.6 475.2 495.8 554.4 625.0 683.5 704.2 762.7 783.4 841.9 912.5 971.0 991.7 1050.2 1120.8 1179.4 1200.0 762.7 : 70.6 129.1 149.8 208.3 229.0 287.5 358.1 416.6 437.3 495.8 566.4 625.0 645.6 704.2 724.8 783.4 853.9 912.5 933.1 991.7 1062.3 1120.8 1141.4 1200.0 833.3 : 58.6 79.2 137.7 158.4 216.9 287.5 346.1 366.7 425.3 495.8 554.4 575.0 633.6 654.2 712.8 783.4 841.9 862.6 921.1 991.7 1050.2 1070.9 1129.4 1200.0 891.8 : 20.6 79.2 99.8 158.4 229.0 287.5 308.2 366.7 437.3 495.8 516.5 575.0 595.7 654.2 724.8 783.4 804.0 862.6 933.1 991.7 1012.3 1070.9 1141.4 1200.0 912.5 : 58.6 79.2 137.7 208.3 266.9 287.5 346.1 416.6 475.2 495.8 554.4 575.0 633.6 704.2 762.7 783.4 841.9 912.5 971.0 991.7 1050.2 1120.8 1179.4 1200.0 971.0 : 20.6 79.2 149.8 208.3 229.0 287.5 358.1 416.6 437.3 495.8 516.5 575.0 645.6 704.2 724.8 783.4 853.9 912.5 933.1 991.7 1062.3 1120.8 1141.4 1200.0 991.7 : 58.6 129.1 187.7 208.3 266.9 337.4 396.0 416.6 475.2 495.8 554.4 625.0 683.5 704.2 762.7 833.3 891.8 912.5 971.0 1041.6 1100.2 1120.8 1179.4 1200.0 1050.2: 70.6 129.1 149.8 208.3 278.9 337.4 358.1 416.6 437.3 495.8 566.4 625.0 645.6 704.2 774.7 833.3 853.9 912.5 983.1 1041.6 1062.3 1120.8 1141.4 1200.0 1120.8: 58.6 79.2 137.7 208.3 266.9 287.5 346.1 366.7 425.3 495.8 554.4 575.0 633.6 704.2 762.7 783.4 841.9 912.5 971.0 991.7 1050.2 1070.9 1129.4 1200.0 1179.4: 20.6 79.2 149.8 208.3 229.0 287.5 308.2 366.7 437.3 495.8 516.5 575.0 645.6 704.2 724.8 783.4 853.9 912.5 933.1 991.7 1012.3 1070.9 1141.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.6482 .. 70.5717 cents 49.92341 cents 20.64824 cents 2: 79.1986 .. 129.1220 cents 49.92341 cents 8.62693 cents 3: 99.8468 .. 187.6723 cents 87.82551 cents -29.27517 cents 4: 158.3972 .. 208.3206 cents 49.92341 cents -29.27517 cents 5: 216.9475 .. 278.8922 cents 61.94472 cents 8.62693 cents 6: 287.5191 .. 337.4426 cents 49.92341 cents 8.62693 cents 7: 308.1674 .. 395.9929 cents 87.82551 cents -29.27517 cents 8: 366.7177 .. 416.6411 cents 49.92341 cents -29.27517 cents 9: 425.2681 .. 487.2128 cents 61.94472 cents 8.62693 cents 10: 495.8397 .. 545.7631 cents 49.92341 cents 8.62693 cents 11: 516.4880 .. 604.3135 cents 87.82550 cents -29.27517 cents 12: 575.0383 .. 624.9617 cents 49.92341 cents -29.27516 cents 13: 595.6865 .. 683.5121 cents 87.82551 cents -29.27517 cents 14: 654.2369 .. 704.1603 cents 49.92342 cents -29.27518 cents 15: 712.7872 .. 774.7319 cents 61.94473 cents 8.62692 cents 16: 783.3589 .. 833.2823 cents 49.92341 cents 8.62693 cents 17: 804.0071 .. 891.8326 cents 87.82551 cents -29.27518 cents 18: 862.5574 .. 912.4809 cents 49.92342 cents -29.27517 cents 19: 921.1078 .. 983.0525 cents 61.94472 cents 8.62692 cents 20: 991.6794 .. 1041.6028 cents 49.92341 cents 8.62693 cents 21: 1012.3277 .. 1100.1532 cents 87.82551 cents -29.27517 cents 22: 1070.8780 .. 1120.8014 cents 49.92341 cents -29.27517 cents 23: 1129.4284 .. 1179.3518 cents 49.92341 cents 8.62693 cents
SHOW DATA
Number of notes : 24 -- Interval properties -- Smallest interval : 20.64824 cents, class 1 Average step (divided formal octave): 50.0000 cents Largest one step interval : 70.57165 cents Average / Smallest step : 2.421514 Largest / Average step : 1.411433 Largest / Smallest step : 3.417805 Median interval of one step : 58.55034 cents, amount: 12 Most common interval of one step : 58.55034 cents, amount: 12 Least squares average step : 50.89485 cents, oct.: 1221.47630 cents Scale is not proper Step pattern alph. order: ABACACABACABACABACACABAC Step pattern size order : MLMSMSMLMSMLMSMLMSMSMLMS Scale is a Constant Structure, by a margin of 8.62692 cents Scale diversity : 1.249136 Lumma stability : 0.106305 Lumma impropriety factor : 0.285563 Number of different interval sizes : 68 = 2.95652 / 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 : 8.62692 cents Most common intervals : 495.83972 cents & inv., amount: 22 Most common triad is 0.0 495.840 704.160 cents, amount: 20 Number of recognisable fifths : 23, average 704.5354 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 1 2 0 1 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 1 1 N T3 SD: 17.8038 c. M: 33.5121 c. 25: 1 2 1 0 2 0 1 2 1 0 2 1 1 1 1 1 2 0 1 1 1 1 2 0 N SD: 13.5257 c. M:-21.6099 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: 13.6820 c. M: 22.8671 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: 11.2972 c. M: 19.3518 c. 32: 2 1 2 1 1 1 1 2 2 0 2 2 1 1 1 2 2 0 2 0 2 2 1 1 N SD: 10.6553 c. M: 16.8518 c. 38: 2 2 2 0 2 1 2 2 2 0 2 3 1 1 2 2 2 1 1 1 2 2 2 1 N SD: 11.8656 c. M: 23.6628 c. 39: 2 2 2 1 1 1 2 2 2 1 2 2 2 1 2 2 2 0 2 1 2 2 2 1 N SD: 10.0414 c. M: 20.7171 c. 40: 2 2 2 1 2 1 1 3 2 0 2 3 2 0 2 3 2 0 2 1 2 2 2 1 N SD: 9.3296 c. M: 16.0695 c. 41: 2 2 2 1 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 1 2 2 2 1 P D3 SD: 7.3405 c. M: 13.7838 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: 7.8802 c. M:-13.7352 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: 4.2401 c. M: 6.9391 c. 58: 3 3 3 1 3 1 3 3 3 1 3 3 3 1 3 3 3 1 3 1 3 3 3 1 N D3 SD: 3.0227 c. M: 5.6961 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: 2.3343 c. M:-4.8130 c. 96: 5 5 5 2 4 2 5 5 5 2 4 6 5 1 5 6 4 2 5 1 5 6 4 2 N SD: 3.4038 c. M: 4.3901 c. 101: 5 6 5 2 4 2 5 6 5 2 5 6 5 1 5 6 5 2 5 1 5 6 5 2 N SD: 3.3612 c. M:-5.5969 c. 102: 5 6 5 2 5 1 5 6 5 2 5 6 5 2 5 6 5 1 5 2 5 6 5 2 N SD: 3.3550 c. M: 6.5985 c. 104: 5 6 5 2 5 2 5 6 5 2 5 6 5 2 5 6 5 2 5 2 5 6 5 2 N SD: 1.6836 c. M: 3.3711 c. 121: 6 7 6 2 6 2 6 7 6 2 6 7 6 2 6 7 6 2 6 2 6 7 6 2 N SD: 0.6342 c. M:-1.0379 c. 288: 14 17 14 5 14 5 14 17 14 5 14 17 14 5 14 17 14 5 14 5 14 17 14 5 N SD: 0.1443 c. M: 0.2362 c. 409: 20 24 20 7 20 7 20 24 20 7 20 24 20 7 20 24 20 7 20 7 20 24 20 7 N SD: 0.0860 c. M:-0.1408 c. 697: 34 41 34 12 34 12 34 41 34 12 34 41 34 12 34 41 34 12 34 12 34 41 34 12 N SD: 0.0091 c. M: 0.0150 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 1.1026 cents 3 .. 6 match: 3 H SD: 2.5975 cents 4 .. 8 match: 4 H SD: 7.6218 cents 5 .. 10 match: 5 H SD: 10.2711 cents 6 .. 12 match: 6 H SD: 1.3575 cents 7 .. 14 match: 7 H SD: 6.6960 cents 8 .. 16 match: 8 H SD: 5.6861 cents 9 .. 18 match: 9 H SD: 2.8126 cents 10 .. 20 match: 10 H SD: 6.1044 cents 11 .. 22 match: 11 H SD: 4.6703 cents 12 .. 24 match: 12 H SD: 4.3076 cents 13 .. 26 match: 13 H SD: 3.4518 cents 14 .. 28 match: 14 H SD: 4.6016 cents 15 .. 30 match: 15 H SD: 5.0562 cents 16 .. 32 match: 15 SD: 3.5784 cents 17 .. 34 match: 15 S SD: 5.3680 cents 18 .. 36 match: 16 S SD: 2.9302 cents 19 .. 38 match: 18 S SD: 3.8659 cents 20 .. 40 match: 18 SD: 4.6555 cents 21 .. 42 match: 19 SD: 3.7823 cents 22 .. 44 match: 18 SD: 3.0682 cents 23 .. 46 match: 21 SD: 2.7212 cents 24 .. 48 match: 20 SD: 2.6934 cents 25 .. 50 match: 20 S SD: 3.0517 cents 26 .. 52 match: 20 SD: 2.4430 cents 27 .. 54 match: 21 SD: 2.1724 cents 28 .. 56 match: 20 SD: 2.6985 cents 29 .. 58 match: 21 SD: 2.3936 cents 30 .. 60 match: 21 SD: 2.4471 cents 31 .. 62 match: 22 SD: 2.3515 cents 32 .. 64 match: 22 SD: 2.1093 cents 33 .. 66 match: 22 SD: 2.2911 cents 34 .. 68 match: 20 SD: 2.1007 cents 35 .. 70 match: 21 SD: 2.0125 cents 36 .. 72 match: 24 SD: 1.8188 cents 37 .. 74 match: 23 SD: 1.6636 cents 38 .. 76 match: 22 SD: 2.1559 cents 39 .. 78 match: 23 SD: 1.8713 cents 40 .. 80 match: 21 SD: 1.5244 cents 41 .. 82 match: 21 SD: 1.7971 cents 42 .. 84 match: 22 SD: 1.7199 cents 43 .. 86 match: 23 SD: 1.8749 cents 44 .. 88 match: 24 SD: 1.6831 cents 45 .. 90 match: 23 SD: 1.5722 cents 46 .. 92 match: 22 SD: 1.7898 cents 47 .. 94 match: 23 SD: 1.6467 cents 48 .. 96 match: 24 SD: 1.3970 cents 49 .. 98 match: 23 SD: 1.4212 cents 50 .. 100 match: 23 SD: 1.3523 cents 51 .. 102 match: 23 SD: 1.4508 cents 52 .. 104 match: 23 SD: 1.3272 cents 53 .. 106 match: 24 SD: 1.2344 cents 54 .. 108 match: 24 SD: 1.1025 cents 55 .. 110 match: 24 SD: 1.1000 cents 57 .. 114 match: 22 SD: 1.4835 cents 58 .. 116 match: 22 SD: 1.1736 cents 60 .. 120 match: 24 SD: 1.0069 cents 63 .. 126 match: 23 SD: 1.0875 cents 66 .. 132 match: 23 SD: 0.9622 cents 69 .. 138 match: 23 SD: 1.0716 cents 72 .. 144 match: 24 SD: 0.9927 cents 76 .. 152 match: 24 SD: 0.8199 cents 78 .. 156 match: 24 SD: 0.7099 cents 85 .. 170 match: 24 SD: 0.6838 cents 89 .. 178 match: 24 SD: 0.6682 cents 108 .. 216 match: 24 SD: 0.6491 cents 113 .. 226 match: 24 SD: 0.6375 cents 114 .. 228 match: 24 SD: 0.5090 cents 132 .. 264 match: 24 SD: 0.4516 cents 150 .. 300 match: 24 SD: 0.4085 cents 157 .. 314 match: 24 SD: 0.3750 cents 172 .. 344 match: 24 SD: 0.3569 cents 177 .. 354 match: 24 SD: 0.3566 cents 180 .. 360 match: 24 SD: 0.3388 cents 181 .. 362 match: 24 SD: 0.2971 cents 209 .. 418 match: 24 SD: 0.2494 cents 235 .. 470 match: 24 SD: 0.2197 cents 283 .. 566 match: 24 SD: 0.2089 cents 289 .. 578 match: 24 SD: 0.2047 cents 295 .. 590 match: 24 SD: 0.1973 cents 320 .. 640 match: 24 SD: 0.1803 cents 343 .. 686 match: 24 SD: 0.1730 cents 349 .. 698 match: 24 SD: 0.1471 cents 437 .. 874 match: 24 SD: 0.1177 cents 500 .. 1000 match: 24 SD: 0.1161 cents 516 .. 1032 match: 24 SD: 0.0998 cents 582 .. 1164 match: 24 SD: 0.0976 cents