Scala analysis: Tolerant-Secor-17
Tolerant temperament (rank 3: 324:325, 351:352, 363:364), Secor 17 "triple delight" mapping
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28.760 cents 28.760230 2: 138.678 cents 138.678030 3: 207.537 cents 207.536970 4: 265.057 cents 265.057420 5: 346.215 cents 346.215000 6: 5/4 386.313714 major third 7: 496.232 cents 496.231520 8: 553.752 cents 553.751970 9: 611.272 cents 611.272420 10: 703.768 cents 703.768490 11: 732.529 cents 732.528710 12: 842.447 cents 842.446510 13: 882.545 cents 882.545230 14: 7/4 968.825906 harmonic seventh 15: 1049.983 cents 1049.983480 16: 1090.082 cents 1090.082200 17: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 109.9178 cents 109.9178 1: 28.7602 cents 28.7602 2: 109.9178 cents 109.9178 3: 68.8589 cents 68.8589 4: 57.5205 cents 57.5205 5: 81.1576 cents 81.1576 6: 40.0987 cents 40.0987 7: 109.9178 cents 109.9178 8: 57.5205 cents 57.5205 9: 57.5205 cents 57.5205 10: 92.4961 cents 92.4961 11: 28.7602 cents 28.7602 12: 109.9178 cents 109.9178 13: 40.0987 cents 40.0987 14: 86.2807 cents 86.2807 15: 81.1576 cents 81.1576 16: 40.0987 cents 40.0987 17: 109.9178 cents 109.9178
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28.76023 cents 1: 3 40.09871 cents 1: 3 57.52045 cents 1: 1 68.85894 cents 1: 2 81.15758 cents 1: 1 86.28068 cents 1: 1 92.49607 cents 1: 4 109.91780 cents 2: 1 115.04090 cents 2: 3 121.25629 cents 2: 2 126.37939 cents 2: 4 138.67803 cents 2: 4 150.01652 cents 2: 2 167.43826 cents 2: 1 178.77674 cents 3: 4 178.77674 cents 3: 6 207.53697 cents 3: 1 224.95871 cents 3: 3 231.17410 cents 3: 2 236.29719 cents 3: 1 248.59583 cents 4: 1 236.29719 cents 4: 2 247.63568 cents 4: 1 259.93432 cents 4: 3 265.05742 cents 4: 1 271.27281 cents 4: 4 288.69455 cents 4: 5 317.45477 cents 5: 1 328.79326 cents 5: 7 346.21500 cents 5: 7 357.55348 cents 5: 1 369.85212 cents 5: 1 374.97522 cents 6: 5 5/4 386.314 cents major third 6: 1 403.73545 cents 6: 3 415.07394 cents 6: 3 438.71107 cents 6: 3 456.13280 cents 6: 2 467.47129 cents 7: 1 467.47129 cents 7: 2 472.59439 cents 7: 1 478.80978 cents 7: 11 496.23152 cents 7: 2 524.99174 cents 8: 2 524.99174 cents 8: 3 536.33023 cents 8: 2 553.75197 cents 8: 2 565.09046 cents 8: 2 577.38909 cents 8: 3 582.51219 cents 8: 1 588.72758 cents 8: 2 606.14932 cents 9: 2 593.85068 cents 9: 1 611.27242 cents 9: 3 617.48781 cents 9: 2 622.61091 cents 9: 2 634.90954 cents 9: 2 646.24803 cents 9: 3 663.66977 cents 9: 2 675.00826 cents 10: 2 675.00826 cents 10: 11 703.76849 cents 10: 1 721.19022 cents 10: 2 727.40561 cents 10: 1 732.52871 cents 11: 2 732.52871 cents 11: 3 743.86720 cents 11: 3 761.28894 cents 11: 3 784.92606 cents 11: 1 796.26455 cents 11: 5 813.68628 cents 12: 1 825.02478 cents 12: 1 830.14788 cents 12: 7 842.44651 cents 12: 7 853.78500 cents 12: 1 871.20674 cents 13: 5 882.54523 cents 13: 4 911.30545 cents 13: 1 928.72719 cents 13: 3 934.94258 cents 13: 1 940.06568 cents 13: 2 952.36432 cents 13: 1 963.70281 cents 14: 1 951.40417 cents 14: 2 963.70281 cents 14: 3 7/4 968.826 cents harmonic seventh 14: 1 975.04129 cents 14: 6 992.46303 cents 14: 4 1021.22325 cents 15: 1 1021.22326 cents 15: 2 1032.56174 cents 15: 4 1049.98348 cents 15: 4 1061.32197 cents 15: 2 1073.62061 cents 15: 3 1078.74371 cents 15: 1 1084.95910 cents 16: 4 1090.08220 cents 16: 1 1107.50393 cents 16: 1 1113.71932 cents 16: 2 1118.84242 cents 16: 1 1131.14106 cents 16: 3 1142.47955 cents 16: 3 1159.90129 cents 16: 2 1171.23977 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.50000 = 13/2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 0.0 : 28.8 138.7 207.5 265.1 346.2 386.3 496.2 553.8 611.3 703.8 732.5 842.4 882.5 968.8 1050.0 1090.1 1200.0 28.8 : 109.9 178.8 236.3 317.5 357.6 467.5 525.0 582.5 675.0 703.8 813.7 853.8 940.1 1021.2 1061.3 1171.2 1200.0 138.7 : 68.9 126.4 207.5 247.6 357.6 415.1 472.6 565.1 593.9 703.8 743.9 830.1 911.3 951.4 1061.3 1090.1 1200.0 207.5 : 57.5 138.7 178.8 288.7 346.2 403.7 496.2 525.0 634.9 675.0 761.3 842.4 882.5 992.5 1021.2 1131.1 1200.0 265.1 : 81.2 121.3 231.2 288.7 346.2 438.7 467.5 577.4 617.5 703.8 784.9 825.0 934.9 963.7 1073.6 1142.5 1200.0 346.2 : 40.1 150.0 207.5 265.1 357.6 386.3 496.2 536.3 622.6 703.8 743.9 853.8 882.5 992.5 1061.3 1118.8 1200.0 386.3 : 109.9 167.4 225.0 317.5 346.2 456.1 496.2 582.5 663.7 703.8 813.7 842.4 952.4 1021.2 1078.7 1159.9 1200.0 496.2 : 57.5 115.0 207.5 236.3 346.2 386.3 472.6 553.8 593.9 703.8 732.5 842.4 911.3 968.8 1050.0 1090.1 1200.0 553.8 : 57.5 150.0 178.8 288.7 328.8 415.1 496.2 536.3 646.2 675.0 784.9 853.8 911.3 992.5 1032.6 1142.5 1200.0 611.3 : 92.5 121.3 231.2 271.3 357.6 438.7 478.8 588.7 617.5 727.4 796.3 853.8 934.9 975.0 1085.0 1142.5 1200.0 703.8 : 28.8 138.7 178.8 265.1 346.2 386.3 496.2 525.0 634.9 703.8 761.3 842.4 882.5 992.5 1050.0 1107.5 1200.0 732.5 : 109.9 150.0 236.3 317.5 357.6 467.5 496.2 606.1 675.0 732.5 813.7 853.8 963.7 1021.2 1078.7 1171.2 1200.0 842.4 : 40.1 126.4 207.5 247.6 357.6 386.3 496.2 565.1 622.6 703.8 743.9 853.8 911.3 968.8 1061.3 1090.1 1200.0 882.5 : 86.3 167.4 207.5 317.5 346.2 456.1 525.0 582.5 663.7 703.8 813.7 871.2 928.7 1021.2 1050.0 1159.9 1200.0 968.8 : 81.2 121.3 231.2 259.9 369.9 438.7 496.2 577.4 617.5 727.4 784.9 842.4 934.9 963.7 1073.6 1113.7 1200.0 1050.0: 40.1 150.0 178.8 288.7 357.6 415.1 496.2 536.3 646.2 703.8 761.3 853.8 882.5 992.5 1032.6 1118.8 1200.0 1090.1: 109.9 138.7 248.6 317.5 375.0 456.1 496.2 606.1 663.7 721.2 813.7 842.4 952.4 992.5 1078.7 1159.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 28.7602 .. 109.9178 cents 81.15757 cents 28.76023 cents 2: 115.0409 .. 178.7767 cents 63.73584 cents 5.12310 cents 3: 178.7767 .. 248.5958 cents 69.81909 cents 0.00000 cents 4: 236.2972 .. 317.4548 cents 81.15758 cents -12.29864 cents 5: 328.7933 .. 374.9752 cents 46.18196 cents 11.33849 cents 6: 386.3137 .. 467.4713 cents 81.15758 cents 11.33849 cents 7: 467.4713 .. 524.9917 cents 57.52045 cents 1/1, 0.0000 cents 8: 524.9917 .. 606.1493 cents 81.15758 cents 1/1, 0.0000 cents 9: 593.8507 .. 675.0083 cents 81.15758 cents -12.29864 cents 10: 675.0083 .. 732.5287 cents 57.52045 cents 1/1, 0.0000 cents 11: 732.5287 .. 813.6863 cents 81.15757 cents 1/1, 0.0000 cents 12: 825.0248 .. 871.2067 cents 46.18196 cents 11.33850 cents 13: 882.5452 .. 963.7028 cents 81.15758 cents 11.33849 cents 14: 951.4042 .. 1021.2233 cents 69.81908 cents -12.29864 cents 15: 1021.2233 .. 1084.9591 cents 63.73584 cents 0.00001 cents 16: 1090.0822 .. 1171.2398 cents 81.15757 cents 5.12310 cents
SHOW DATA
Number of notes : 17 -- Interval properties -- Smallest interval : 28.76022 cents, class 1 Average step (divided formal octave): 70.5882 cents Largest one step interval : 109.91780 cents Average / Smallest step : 2.454370 Largest / Average step : 1.557169 Largest / Smallest step : 3.821869 Median interval of one step : 68.85894 cents, amount: 1 Most common interval of one step : 109.91780 cents, amount: 4 Least squares average step : 69.06195 cents, oct.: 1174.05314 cents Scale is not proper Step pattern alph. order: ABCDEFBDDGABFHEFB Step pattern size order : AHDCEBHCCGAHBFEBH Scale is not a Constant Structure Scale diversity : 1.519377 Lumma stability : 0.094267 Lumma impropriety factor : 0.030747 Number of different interval sizes : 96 = 6.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 6.50000 = 13/2 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.96015 cents Most common intervals : 496.23152 cents & inv., amount: 11 Most common triad is 0.0 496.232 703.768 cents, amount: 6 Number of recognisable fifths : 11, average 703.7685 cents Formal octave complements present : 3 = 17.6471% -- Rational properties -- Prime limit : 7 (not all pitches rational)
FIT/MODE
17: 0 2 1 1 1 0 2 1 1 1 0 2 1 1 1 0 2 N T3 SD: 19.4191 c. M:-35.1018 c. 22: 0 2 2 1 1 1 2 1 1 2 0 2 1 2 1 1 2 N D3 SD: 15.5218 c. M: 29.5871 c. 23: 1 2 1 1 2 1 2 1 1 2 0 2 1 2 1 1 2 N D3 SD: 16.9102 c. M:-31.0776 c. 24: 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 P M ME S SD: 11.7668 c. M:-21.2398 c. 27: 1 2 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 P M ME S SD: 13.1674 c. M:-24.0258 c. 31: 1 3 1 2 2 1 3 1 2 2 1 3 1 2 2 1 3 N D3 S SD: 8.0992 c. M:-16.1607 c. 34: 1 3 2 2 2 1 3 2 1 3 1 3 1 3 2 1 3 P T3 SD: 8.5341 c. M:-19.4094 c. 37: 1 3 2 2 3 1 3 2 2 3 1 3 1 3 2 2 3 P D3 S SD: 8.3447 c. M:-13.4172 c. 41: 1 4 2 2 3 1 4 2 2 3 1 4 1 3 3 1 4 N SD: 4.0774 c. M:-7.6634 c. 63: 1 6 4 3 4 2 6 3 3 5 1 6 2 5 4 2 6 N SD: 4.4928 c. M: 9.7126 c. 72: 2 6 4 4 5 2 7 3 4 5 2 7 2 5 5 2 7 N SD: 4.2854 c. M:-7.5535 c. 75: 2 7 4 4 5 2 7 4 3 6 2 7 2 6 5 2 7 N SD: 4.3201 c. M:-7.1741 c. 77: 2 7 4 4 5 3 7 4 3 6 2 7 3 5 5 3 7 N SD: 3.4952 c. M:-7.2870 c. 79: 2 7 5 3 6 2 8 3 4 6 2 7 3 6 5 3 7 N SD: 4.4393 c. M: 7.0035 c. 80: 2 7 5 4 5 3 7 4 4 6 2 7 3 6 5 3 7 P SD: 3.0634 c. M:-6.1741 c. 87: 2 8 5 4 6 3 8 4 4 7 2 8 3 6 6 3 8 N SD: 1.7846 c. M: 4.3759 c. 121: 3 11 7 6 8 4 11 6 6 9 3 11 4 9 8 4 11 N SD: 1.5266 c. M:-3.6036 c. 128: 3 12 7 6 9 4 12 6 6 10 3 12 4 9 9 4 12 N SD: 1.5965 c. M: 3.2009 c. 162: 4 15 9 8 11 5 15 8 8 12 4 15 5 12 11 5 15 N SD: 1.5626 c. M:-3.5424 c. 167: 4 15 10 8 11 6 15 8 8 13 4 15 6 12 11 6 15 N SD: 1.1657 c. M: 2.1511 c. 208: 5 19 12 10 14 7 19 10 10 16 5 19 7 15 14 7 19 N SD: 0.1962 c. M:-0.4049 c. 711: 17 65 41 34 48 24 65 34 34 55 17 65 24 51 48 24 65 N SD: 0.1667 c. M: 0.3020 c. 752: 18 69 43 36 51 25 69 36 36 58 18 69 25 54 51 25 69 N SD: 0.1102 c. M: 0.2089 c. 960: 23 88 55 46 65 32 88 46 46 74 23 88 32 69 65 32 88 N SD: 0.0453 c. M: 0.0822 c. 1168: 28 107 67 56 79 39 107 56 56 90 28 107 39 84 79 39 107 N SD: 0.0138 c. M:-0.0289 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.9067 cents 3 .. 6 match: 3 H SD: 0.8549 cents 4 .. 8 match: 4 H SD: 0.4534 cents 5 .. 10 match: 5 H SD: 12.0631 cents 6 .. 12 match: 6 H SD: 0.6133 cents 7 .. 14 match: 7 H SD: 12.0241 cents 8 .. 16 match: 8 H SD: 0.6771 cents 9 .. 18 match: 9 H SD: 6.2800 cents 10 .. 20 match: 10 H SD: 8.8593 cents 11 .. 22 match: 11 H SD: 6.7602 cents 12 .. 24 match: 11 S SD: 3.3956 cents 13 .. 26 match: 12 S SD: 6.1172 cents 14 .. 28 match: 11 SD: 7.0002 cents 15 .. 30 match: 12 SD: 5.4977 cents 16 .. 32 match: 14 S SD: 4.5831 cents 17 .. 34 match: 12 SD: 5.3233 cents 18 .. 36 match: 14 SD: 4.5770 cents 19 .. 38 match: 14 SD: 4.1386 cents 20 .. 40 match: 13 SD: 5.5132 cents 21 .. 42 match: 13 SD: 5.1565 cents 22 .. 44 match: 17 SD: 4.8962 cents 23 .. 46 match: 16 SD: 4.0614 cents 24 .. 48 match: 17 SD: 2.9380 cents 25 .. 50 match: 15 SD: 4.0477 cents 26 .. 52 match: 17 SD: 3.8985 cents 27 .. 54 match: 16 SD: 3.9044 cents 28 .. 56 match: 17 SD: 3.7216 cents 29 .. 58 match: 16 SD: 3.6229 cents 30 .. 60 match: 17 SD: 3.3068 cents 31 .. 62 match: 16 SD: 3.0168 cents 32 .. 64 match: 17 SD: 2.5083 cents 33 .. 66 match: 16 SD: 2.9886 cents 35 .. 70 match: 16 SD: 2.6507 cents 36 .. 72 match: 17 SD: 2.0816 cents 37 .. 74 match: 16 SD: 2.3136 cents 40 .. 80 match: 17 SD: 1.7679 cents 47 .. 94 match: 17 SD: 1.7156 cents 48 .. 96 match: 17 SD: 1.0555 cents 72 .. 144 match: 17 SD: 0.6827 cents 104 .. 208 match: 17 SD: 0.6725 cents 108 .. 216 match: 17 SD: 0.5031 cents 132 .. 264 match: 17 SD: 0.4615 cents 156 .. 312 match: 17 SD: 0.4503 cents 168 .. 336 match: 17 SD: 0.4470 cents 172 .. 344 match: 17 SD: 0.4368 cents 175 .. 350 match: 17 SD: 0.4152 cents 180 .. 360 match: 17 SD: 0.2748 cents 236 .. 472 match: 17 SD: 0.2424 cents 241 .. 482 match: 17 SD: 0.2390 cents 284 .. 568 match: 17 SD: 0.2347 cents 289 .. 578 match: 17 SD: 0.1994 cents 361 .. 722 match: 17 SD: 0.1415 cents 416 .. 832 match: 17 SD: 0.1328 cents 480 .. 960 match: 17 SD: 0.1293 cents 488 .. 976 match: 17 SD: 0.1243 cents 528 .. 1056 match: 17 SD: 0.1150 cents 552 .. 1104 match: 17 SD: 0.1133 cents 588 .. 1176 match: 17 SD: 0.1079 cents 600 .. 1200 match: 17 SD: 0.0935 cents