Scala analysis: met24-semineutral17_Fs
17-CS semineutral sixth from two large major thirds (~63:81:104)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57.422 cents 57.421870 2: 139.453 cents 139.453130 3: 207.422 cents 207.421870 4: 264.844 cents 264.843750 5: 370.312 cents 370.312500 6: 427.734 cents 427.734370 7: 496.875 cents 496.875000 8: 577.734 cents 577.734380 9: 635.156 cents 635.156250 10: 704.297 cents 704.296870 11: 761.719 cents 761.718750 12: 867.188 cents 867.187500 13: 924.609 cents 924.609370 14: 992.578 cents 992.578120 15: 1074.609 cents 1074.609370 16: 1132.031 cents 1132.031250 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 67.9687 cents 67.9687 1: 57.4219 cents 57.4219 2: 82.0313 cents 82.0313 3: 67.9687 cents 67.9687 4: 57.4219 cents 57.4219 5: 105.4687 cents 105.4687 6: 57.4219 cents 57.4219 7: 69.1406 cents 69.1406 8: 80.8594 cents 80.8594 9: 57.4219 cents 57.4219 10: 69.1406 cents 69.1406 11: 57.4219 cents 57.4219 12: 105.4687 cents 105.4687 13: 57.4219 cents 57.4219 14: 67.9687 cents 67.9687 15: 82.0312 cents 82.0312 16: 57.4219 cents 57.4219 17: 67.9687 cents 67.9687
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 57.42187 cents 1: 3 67.96874 cents 1: 2 69.14063 cents 1: 1 80.85938 cents 1: 2 82.03126 cents 1: 2 105.46875 cents 2: 4 125.39062 cents 2: 3 126.56250 cents 2: 1 138.28125 cents 2: 2 139.45313 cents 2: 3 150.00000 cents 2: 4 162.89063 cents 3: 1 182.81250 cents 3: 1 183.98437 cents 3: 9 207.42187 cents 3: 2 220.31250 cents 3: 2 230.85937 cents 3: 2 232.03125 cents 4: 6 264.84375 cents 4: 2 275.39063 cents 4: 1 276.56250 cents 4: 2 288.28124 cents 4: 3 289.45313 cents 4: 3 312.89063 cents 5: 4 332.81250 cents 5: 2 333.98437 cents 5: 2 346.87499 cents 5: 2 357.42187 cents 5: 7 370.31250 cents 6: 2 390.23437 cents 6: 1 391.40625 cents 6: 3 414.84374 cents 6: 4 427.73437 cents 6: 3 438.28125 cents 6: 4 439.45313 cents 7: 2 472.26563 cents 7: 1 482.81250 cents 7: 6 495.70312 cents 7: 7 496.87500 cents 7: 1 520.31251 cents 8: 2 540.23437 cents 8: 2 553.12500 cents 8: 3 554.29688 cents 8: 4 564.84374 cents 8: 5 577.73438 cents 8: 1 602.34375 cents 9: 1 597.65625 cents 9: 5 622.26562 cents 9: 4 635.15625 cents 9: 3 645.70312 cents 9: 2 646.87500 cents 9: 2 659.76563 cents 10: 1 679.68749 cents 10: 7 703.12500 cents 10: 6 704.29687 cents 10: 1 717.18750 cents 10: 2 727.73437 cents 11: 4 760.54687 cents 11: 3 761.71875 cents 11: 4 772.26563 cents 11: 3 785.15624 cents 11: 1 808.59375 cents 11: 2 809.76563 cents 12: 7 829.68750 cents 12: 2 842.57813 cents 12: 2 853.12499 cents 12: 2 866.01563 cents 12: 4 867.18750 cents 13: 3 887.10937 cents 13: 3 910.54687 cents 13: 2 911.71876 cents 13: 1 923.43750 cents 13: 2 924.60937 cents 13: 6 935.15625 cents 14: 2 967.96875 cents 14: 2 969.14063 cents 14: 2 979.68750 cents 14: 9 992.57812 cents 14: 1 1016.01563 cents 14: 1 1017.18750 cents 15: 4 1037.10937 cents 15: 3 1050.00000 cents 15: 2 1060.54687 cents 15: 1 1061.71875 cents 15: 3 1073.43750 cents 15: 4 1074.60937 cents 16: 2 1094.53125 cents 16: 2 1117.96874 cents 16: 1 1119.14062 cents 16: 2 1130.85937 cents 16: 3 1132.03125 cents 16: 7 1142.57813 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.75000 = 23/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 57.4 139.5 207.4 264.8 370.3 427.7 496.9 577.7 635.2 704.3 761.7 867.2 924.6 992.6 1074.6 1132.0 1200.0 57.4 : 82.0 150.0 207.4 312.9 370.3 439.5 520.3 577.7 646.9 704.3 809.8 867.2 935.2 1017.2 1074.6 1142.6 1200.0 139.5 : 68.0 125.4 230.9 288.3 357.4 438.3 495.7 564.8 622.3 727.7 785.2 853.1 935.2 992.6 1060.5 1118.0 1200.0 207.4 : 57.4 162.9 220.3 289.5 370.3 427.7 496.9 554.3 659.8 717.2 785.2 867.2 924.6 992.6 1050.0 1132.0 1200.0 264.8 : 105.5 162.9 232.0 312.9 370.3 439.5 496.9 602.3 659.8 727.7 809.8 867.2 935.2 992.6 1074.6 1142.6 1200.0 370.3 : 57.4 126.6 207.4 264.8 334.0 391.4 496.9 554.3 622.3 704.3 761.7 829.7 887.1 969.1 1037.1 1094.5 1200.0 427.7 : 69.1 150.0 207.4 276.6 334.0 439.5 496.9 564.8 646.9 704.3 772.3 829.7 911.7 979.7 1037.1 1142.6 1200.0 496.9 : 80.9 138.3 207.4 264.8 370.3 427.7 495.7 577.7 635.2 703.1 760.5 842.6 910.5 968.0 1073.4 1130.9 1200.0 577.7 : 57.4 126.6 184.0 289.5 346.9 414.8 496.9 554.3 622.3 679.7 761.7 829.7 887.1 992.6 1050.0 1119.1 1200.0 635.2 : 69.1 126.6 232.0 289.5 357.4 439.5 496.9 564.8 622.3 704.3 772.3 829.7 935.2 992.6 1061.7 1142.6 1200.0 704.3 : 57.4 162.9 220.3 288.3 370.3 427.7 495.7 553.1 635.2 703.1 760.5 866.0 923.4 992.6 1073.4 1130.9 1200.0 761.7 : 105.5 162.9 230.9 312.9 370.3 438.3 495.7 577.7 645.7 703.1 808.6 866.0 935.2 1016.0 1073.4 1142.6 1200.0 867.2 : 57.4 125.4 207.4 264.8 332.8 390.2 472.3 540.2 597.7 703.1 760.5 829.7 910.5 968.0 1037.1 1094.5 1200.0 924.6 : 68.0 150.0 207.4 275.4 332.8 414.8 482.8 540.2 645.7 703.1 772.3 853.1 910.5 979.7 1037.1 1142.6 1200.0 992.6 : 82.0 139.5 207.4 264.8 346.9 414.8 472.3 577.7 635.2 704.3 785.2 842.6 911.7 969.1 1074.6 1132.0 1200.0 1074.6: 57.4 125.4 182.8 264.8 332.8 390.2 495.7 553.1 622.3 703.1 760.5 829.7 887.1 992.6 1050.0 1118.0 1200.0 1132.0: 68.0 125.4 207.4 275.4 332.8 438.3 495.7 564.8 645.7 703.1 772.3 829.7 935.2 992.6 1060.5 1142.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.4219 .. 105.4687 cents 48.04688 cents 57.42187 cents 2: 125.3906 .. 162.8906 cents 37.50001 cents 19.92187 cents 3: 182.8125 .. 232.0312 cents 49.21875 cents 19.92187 cents 4: 264.8438 .. 312.8906 cents 48.04688 cents 32.81250 cents 5: 332.8125 .. 370.3125 cents 37.50000 cents 19.92187 cents 6: 390.2344 .. 439.4531 cents 49.21876 cents 19.92187 cents 7: 472.2656 .. 520.3125 cents 48.04688 cents 32.81250 cents 8: 540.2344 .. 602.3437 cents 62.10938 cents 19.92186 cents 9: 597.6563 .. 659.7656 cents 62.10938 cents -4.68750 cents 10: 679.6875 .. 727.7344 cents 48.04688 cents 19.92186 cents 11: 760.5469 .. 809.7656 cents 49.21876 cents 32.81250 cents 12: 829.6875 .. 867.1875 cents 37.50000 cents 19.92187 cents 13: 887.1094 .. 935.1563 cents 48.04688 cents 19.92187 cents 14: 967.9687 .. 1017.1875 cents 49.21875 cents 32.81250 cents 15: 1037.1094 .. 1074.6094 cents 37.50000 cents 19.92187 cents 16: 1094.5313 .. 1142.5781 cents 48.04688 cents 19.92188 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 57.42187 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 105.46875 cents Average / Smallest step : 1.229292 Largest / Average step : 1.494141 Largest / Smallest step : 1.836735 Median interval of one step : 67.96874 cents, amount: 3 Most common interval of one step : 57.42187 cents, amount: 7 Least squares average step : 70.94013 cents, oct.: 1205.98214 cents Scale is not proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 49 119 177 226 316 365 424 493 542 601 650 740 789 847 917 966 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 831 of 973.828 cents and inv. generated superset size: 307 = 290 more = 1805.882% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCADAEFAEADACBAC Step pattern size order : AEBAFACDACAFABEAB Scale is a Constant Structure, by a margin of 4.68750 cents Scale diversity : 1.410455 Lumma stability : 0.371094 Lumma impropriety factor : 0.003906 Number of different interval sizes : 92 = 5.75000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.75000 = 23/4 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 1.17187 cents Most common intervals : 207.42187 cents & inv., amount: 9 Most common triad is 0.0 207.422 992.578 cents, amount: 2 Number of recognisable fifths : 14, average 704.6317 cents Number of appreciable fifths : 13, average 703.6659 cents Best fifths form a closed circle Formal octave complements present : 3 = 17.6471% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
17: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.7025 c. M: 20.1287 c. 22: 1 2 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 P M ME S SD: 12.1540 c. M:-24.1832 c. 29: 1 2 2 1 3 1 2 2 1 2 1 3 1 2 2 1 2 N D3 SD: 10.5457 c. M: 16.8912 c. 34: 2 2 2 2 2 2 2 2 2 2 2 3 1 2 2 2 2 P T3 SD: 10.2098 c. M:-17.5092 c. 35: 2 2 2 2 3 1 2 3 2 2 1 3 2 2 2 2 2 P D3 SD: 9.8679 c. M: 16.8750 c. 36: 2 2 2 2 3 2 2 2 2 2 2 3 2 2 2 2 2 P D3 S SD: 5.9445 c. M: 11.0677 c. 41: 2 3 2 2 4 2 2 3 2 2 2 4 2 2 3 2 2 N SD: 7.0853 c. M:-11.9760 c. 46: 2 3 3 2 4 2 3 3 2 3 2 4 2 3 3 2 3 P D3 SD: 6.3767 c. M: 11.5659 c. 51: 2 4 3 2 5 2 3 4 2 3 2 5 2 3 4 2 3 N SD: 5.7611 c. M:-10.5009 c. 58: 3 4 3 3 5 3 3 4 3 3 3 5 3 3 4 3 3 P SD: 3.8750 c. M:-6.7484 c. 68: 3 5 4 3 6 3 4 5 3 4 3 6 3 4 5 3 4 P SD: 3.2841 c. M: 6.9623 c. 83: 4 6 4 4 8 4 4 6 4 5 4 7 4 5 5 4 5 N SD: 4.0147 c. M:-6.0006 c. 85: 4 6 5 4 7 4 5 6 4 5 4 7 4 5 6 4 5 SP SD: 3.3196 c. M: 6.9623 c. 87: 4 6 5 4 8 4 5 6 4 5 4 8 4 5 6 4 5 N SD: 1.5218 c. M: 3.0981 c. 104: 5 7 6 5 9 5 6 7 5 6 5 9 5 6 7 5 6 P SD: 0.9258 c. M: 1.8029 c. 191: 9 13 11 9 17 9 11 13 9 11 9 17 9 11 13 9 11 N SD: 0.7496 c. M: 1.5093 c. 230: 11 16 13 11 20 11 13 16 11 13 11 20 11 13 16 11 13 P SD: 0.9291 c. M:-1.4164 c. 249: 12 17 14 12 22 12 14 17 12 14 12 22 12 14 17 12 14 N SD: 0.5573 c. M:-1.1813 c. 336: 16 23 19 16 30 16 19 23 16 19 16 30 16 19 23 16 19 N SD: 0.5957 c. M:-1.1161 c. 353: 17 24 20 17 31 17 20 24 17 20 17 31 17 20 24 17 20 N SD: 0.3412 c. M: 0.6142 c. 457: 22 31 26 22 40 22 26 31 22 26 22 40 22 26 31 22 26 N SD: 0.3680 c. M: 0.6667 c. 544: 26 37 31 26 48 26 31 37 26 31 26 48 26 31 37 26 31 N SD: 0.3511 c. M: 0.6893 c. 567: 27 39 32 27 50 27 33 38 27 33 27 50 27 32 39 27 32 N SD: 0.2966 c. M:-0.5374 c. 584: 28 40 33 28 51 28 34 39 28 34 28 51 28 33 40 28 33 N SD: 0.2916 c. M:-0.6100 c. 671: 32 46 38 32 59 32 39 45 32 39 32 59 32 38 46 32 38 N SD: 0.1795 c. M:-0.3231 c. 775: 37 53 44 37 68 37 45 52 37 45 37 68 37 44 53 37 44 N SD: 0.1791 c. M: 0.3795 c. 833: 40 57 47 40 73 40 48 56 40 48 40 73 40 47 57 40 47 N SD: 0.1719 c. M:-0.3461 c. 920: 44 63 52 44 81 44 53 62 44 53 44 81 44 52 63 44 52 N SD: 0.1047 c. M:-0.2038 c. 1024: 49 70 58 49 90 49 59 69 49 59 49 90 49 58 70 49 58 N 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: 1.1709 cents 3 .. 6 match: 3 H SD: 5.7370 cents 4 .. 8 match: 4 H SD: 7.1837 cents 5 .. 10 match: 5 H SD: 15.4010 cents 6 .. 12 match: 6 H SD: 5.1186 cents 7 .. 14 match: 7 H SD: 5.4266 cents 8 .. 16 match: 8 H SD: 6.1659 cents 9 .. 18 match: 9 H SD: 5.1763 cents 10 .. 20 match: 10 H SD: 8.8084 cents 11 .. 22 match: 11 H SD: 6.4819 cents 12 .. 24 match: 12 H SD: 4.9863 cents 13 .. 26 match: 13 H SD: 5.0300 cents 14 .. 28 match: 14 H SD: 4.6512 cents 15 .. 30 match: 13 SD: 5.0304 cents 16 .. 32 match: 15 S SD: 5.1890 cents 17 .. 34 match: 15 S SD: 5.2034 cents 18 .. 36 match: 16 SD: 4.0319 cents 19 .. 38 match: 14 SD: 6.1691 cents 20 .. 40 match: 16 SD: 4.2426 cents 21 .. 42 match: 16 SD: 3.9507 cents 22 .. 44 match: 17 SD: 3.4051 cents 24 .. 48 match: 17 SD: 3.0083 cents 25 .. 50 match: 17 SD: 2.6215 cents 31 .. 62 match: 17 SD: 2.5731 cents 32 .. 64 match: 17 SD: 2.5441 cents 34 .. 68 match: 17 SD: 2.4224 cents 36 .. 72 match: 17 SD: 1.9599 cents 38 .. 76 match: 17 SD: 1.8560 cents 47 .. 94 match: 17 SD: 1.8265 cents 48 .. 96 match: 17 SD: 1.6686 cents 49 .. 98 match: 17 SD: 1.6294 cents 50 .. 100 match: 17 SD: 1.5858 cents 54 .. 108 match: 17 SD: 1.2502 cents 58 .. 116 match: 17 SD: 1.2481 cents 60 .. 120 match: 17 SD: 1.2093 cents 61 .. 122 match: 17 SD: 1.1867 cents 63 .. 126 match: 17 SD: 1.1123 cents 71 .. 142 match: 17 SD: 1.0807 cents 72 .. 144 match: 17 SD: 0.9933 cents 79 .. 158 match: 17 SD: 0.9275 cents 84 .. 168 match: 17 SD: 0.9060 cents 85 .. 170 match: 17 SD: 0.7728 cents 93 .. 186 match: 17 SD: 0.7581 cents 96 .. 192 match: 17 SD: 0.7088 cents 108 .. 216 match: 17 SD: 0.6563 cents 117 .. 234 match: 17 SD: 0.5947 cents 121 .. 242 match: 17 SD: 0.5713 cents 129 .. 258 match: 17 SD: 0.5648 cents 142 .. 284 match: 17 SD: 0.5144 cents 143 .. 286 match: 17 SD: 0.4886 cents 151 .. 302 match: 17 SD: 0.4592 cents 156 .. 312 match: 17 SD: 0.4145 cents 180 .. 360 match: 17 SD: 0.3939 cents 181 .. 362 match: 17 SD: 0.3019 cents 217 .. 434 match: 17 SD: 0.3013 cents 235 .. 470 match: 17 SD: 0.1807 cents 386 .. 772 match: 17 SD: 0.1721 cents 394 .. 788 match: 17 SD: 0.1594 cents 418 .. 836 match: 17 SD: 0.1512 cents 442 .. 884 match: 17 SD: 0.1317 cents 478 .. 956 match: 17 SD: 0.1022 cents