Scala analysis: xen05-secor-high-tolerance-19
Secor 15-limit high tolerance temperament, 19-tone subset
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28.000 cents 28.000000 2: 86.110 cents 86.110000 3: 168.197 cents 168.197000 4: 207.157 cents 207.157000 5: 317.264 cents 317.264000 6: 375.354 cents 375.354000 7: 457.461 cents 457.461000 8: 524.422 cents 524.422000 9: 582.512 cents 582.512000 10: 664.618 cents 664.618000 11: 703.578 cents 703.578000 12: 789.669 cents 789.669000 13: 813.686 cents 813.686000 14: 871.776 cents 871.776000 15: 910.736 cents 910.736000 16: 1020.843 cents 1020.843000 17: 1078.933 cents 1078.933000 18: 1161.040 cents 1161.040000 19: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 38.9600 cents 38.9600 1: 28.0000 cents 28.0000 2: 58.1100 cents 58.1100 3: 82.0870 cents 82.0870 4: 38.9600 cents 38.9600 5: 110.1070 cents 110.1070 6: 58.0900 cents 58.0900 7: 82.1070 cents 82.1070 8: 66.9610 cents 66.9610 9: 58.0900 cents 58.0900 10: 82.1060 cents 82.1060 11: 38.9600 cents 38.9600 12: 86.0910 cents 86.0910 13: 24.0170 cents 24.0170 14: 58.0900 cents 58.0900 15: 38.9600 cents 38.9600 16: 110.1070 cents 110.1070 17: 58.0900 cents 58.0900 18: 82.1070 cents 82.1070 19: 38.9600 cents 38.9600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24.01700 cents 1: 1 28.00000 cents 1: 4 38.96000 cents 1: 4 58.09000 cents 1: 1 58.11000 cents 1: 1 66.96100 cents 1: 1 82.08700 cents 1: 1 82.10600 cents 1: 2 82.10700 cents 1: 1 86.09100 cents 1: 2 110.10700 cents 2: 1 66.96000 cents 2: 1 82.10700 cents 2: 1 86.11000 cents 2: 1 97.05000 cents 2: 1 110.10800 cents 2: 1 121.04700 cents 2: 1 121.06600 cents 2: 1 121.06700 cents 2: 2 125.05100 cents 2: 1 140.19600 cents 2: 3 140.19700 cents 2: 2 149.06700 cents 2: 1 149.06800 cents 2: 2 168.19700 cents 3: 1 121.06700 cents 3: 1 125.07000 cents 3: 1 149.06700 cents 3: 1 149.06800 cents 3: 1 168.19700 cents 3: 1 168.19800 cents 3: 1 179.15600 cents 3: 2 179.15700 cents 3: 5 207.15700 cents 3: 2 207.15800 cents 3: 1 231.15400 cents 3: 2 250.30400 cents 4: 3 207.15700 cents 4: 2 207.15800 cents 4: 1 207.17700 cents 4: 2 231.17400 cents 4: 1 246.11700 cents 4: 2 265.24700 cents 4: 1 265.24800 cents 4: 1 289.24400 cents 4: 5 289.26400 cents 4: 1 317.26500 cents 5: 1 246.11700 cents 5: 1 246.11800 cents 5: 1 265.26700 cents 5: 4 289.26400 cents 5: 2 317.26400 cents 5: 1 317.26500 cents 5: 2 328.22400 cents 5: 1 332.20800 cents 5: 3 347.35400 cents 5: 1 356.22500 cents 5: 1 371.35100 cents 5: 1 375.35500 cents 6: 2 328.22400 cents 6: 2 347.35400 cents 6: 2 356.22400 cents 6: 2 356.22500 cents 6: 1 371.37100 cents 6: 1 375.35400 cents 6: 1 375.35500 cents 6: 1 375.37400 cents 6: 2 386.31400 cents 6: 2 414.31500 cents 6: 1 429.46100 cents 6: 1 438.31200 cents 6: 1 457.46100 cents 7: 2 386.31400 cents 7: 1 410.33100 cents 7: 2 414.31400 cents 7: 2 414.31500 cents 7: 1 414.33400 cents 7: 2 438.33100 cents 7: 1 438.33200 cents 7: 2 457.46100 cents 7: 1 457.46200 cents 7: 1 472.40500 cents 7: 1 496.40200 cents 7: 2 496.42100 cents 7: 1 496.42200 cents 8: 1 438.33100 cents 8: 1 453.27500 cents 8: 1 472.42400 cents 8: 7 496.42100 cents 8: 4 496.42200 cents 8: 1 524.42200 cents 8: 1 535.38100 cents 8: 1 554.51200 cents 8: 1 578.50800 cents 8: 1 582.51200 cents 9: 1 496.44100 cents 9: 1 524.42200 cents 9: 1 535.38100 cents 9: 2 535.38200 cents 9: 3 554.51100 cents 9: 1 554.51200 cents 9: 2 563.38200 cents 9: 2 578.52800 cents 9: 1 582.51200 cents 9: 1 606.52800 cents 9: 1 606.52900 cents 9: 1 617.46800 cents 9: 1 621.47200 cents 9: 1 636.61800 cents 10: 1 563.38200 cents 10: 1 578.52800 cents 10: 1 582.53200 cents 10: 1 593.47100 cents 10: 1 593.47200 cents 10: 1 617.48800 cents 10: 2 621.47200 cents 10: 2 636.61800 cents 10: 1 645.48800 cents 10: 3 645.48900 cents 10: 2 664.61800 cents 10: 1 664.61900 cents 10: 1 675.57800 cents 10: 1 703.55900 cents 11: 1 617.48800 cents 11: 1 621.49200 cents 11: 1 645.48800 cents 11: 1 664.61900 cents 11: 1 675.57800 cents 11: 4 703.57800 cents 11: 7 703.57900 cents 11: 1 727.57600 cents 11: 1 746.72500 cents 11: 1 761.66900 cents 12: 1 703.57800 cents 12: 2 703.57900 cents 12: 1 703.59800 cents 12: 1 727.59500 cents 12: 1 742.53800 cents 12: 2 742.53900 cents 12: 1 761.66800 cents 12: 2 761.66900 cents 12: 1 785.66600 cents 12: 2 785.68500 cents 12: 2 785.68600 cents 12: 1 789.66900 cents 12: 2 813.68600 cents 13: 1 742.53900 cents 13: 1 761.68800 cents 13: 1 770.53900 cents 13: 2 785.68500 cents 13: 2 813.68600 cents 13: 1 824.62600 cents 13: 1 824.64500 cents 13: 1 824.64600 cents 13: 1 828.62900 cents 13: 2 843.77500 cents 13: 2 843.77600 cents 13: 2 852.64600 cents 13: 2 871.77600 cents 14: 1 824.64500 cents 14: 1 828.64900 cents 14: 1 843.77500 cents 14: 3 852.64600 cents 14: 1 867.79200 cents 14: 2 871.77600 cents 14: 1 882.73500 cents 14: 2 882.73600 cents 14: 4 910.73600 cents 14: 1 934.73300 cents 14: 1 953.88200 cents 14: 1 953.88300 cents 15: 1 882.73500 cents 15: 5 910.73600 cents 15: 1 910.75600 cents 15: 1 934.75200 cents 15: 2 934.75300 cents 15: 1 953.88300 cents 15: 2 968.82600 cents 15: 1 992.82300 cents 15: 2 992.84200 cents 15: 3 992.84300 cents 16: 2 949.69600 cents 16: 1 968.84600 cents 16: 2 992.84200 cents 16: 5 992.84300 cents 16: 2 1020.84300 cents 16: 1 1020.84400 cents 16: 1 1031.80200 cents 16: 1 1031.80300 cents 16: 1 1050.93200 cents 16: 1 1050.93300 cents 16: 1 1074.93000 cents 16: 1 1078.93300 cents 17: 2 1031.80300 cents 17: 1 1050.93200 cents 17: 2 1050.93300 cents 17: 3 1059.80300 cents 17: 1 1059.80400 cents 17: 2 1074.94900 cents 17: 1 1078.93300 cents 17: 1 1078.93400 cents 17: 1 1078.95300 cents 17: 1 1089.89200 cents 17: 1 1102.95000 cents 17: 1 1113.89000 cents 17: 1 1117.89300 cents 17: 1 1133.04000 cents 18: 2 1089.89300 cents 18: 1 1113.90900 cents 18: 2 1117.89300 cents 18: 1 1117.89400 cents 18: 1 1117.91300 cents 18: 1 1133.03900 cents 18: 1 1141.89000 cents 18: 4 1141.91000 cents 18: 4 1161.04000 cents 18: 1 1172.00000 cents 18: 1 1175.98300 cents Highest number of different intervals for one interval class: 14 Average number of different intervals per interval class: 12.11111 = 109/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 28.0 86.1 168.2 207.2 317.3 375.4 457.5 524.4 582.5 664.6 703.6 789.7 813.7 871.8 910.7 1020.8 1078.9 1161.0 1200.0 28.0 : 58.1 140.2 179.2 289.3 347.4 429.5 496.4 554.5 636.6 675.6 761.7 785.7 843.8 882.7 992.8 1050.9 1133.0 1172.0 1200.0 86.1 : 82.1 121.0 231.2 289.2 371.4 438.3 496.4 578.5 617.5 703.6 727.6 785.7 824.6 934.7 992.8 1074.9 1113.9 1141.9 1200.0 168.2 : 39.0 149.1 207.2 289.3 356.2 414.3 496.4 535.4 621.5 645.5 703.6 742.5 852.6 910.7 992.8 1031.8 1059.8 1117.9 1200.0 207.2 : 110.1 168.2 250.3 317.3 375.4 457.5 496.4 582.5 606.5 664.6 703.6 813.7 871.8 953.9 992.8 1020.8 1079.0 1161.0 1200.0 317.3 : 58.1 140.2 207.2 265.2 347.4 386.3 472.4 496.4 554.5 593.5 703.6 761.7 843.8 882.7 910.7 968.8 1050.9 1089.9 1200.0 375.4 : 82.1 149.1 207.2 289.3 328.2 414.3 438.3 496.4 535.4 645.5 703.6 785.7 824.6 852.6 910.8 992.8 1031.8 1141.9 1200.0 457.5 : 67.0 125.1 207.2 246.1 332.2 356.2 414.3 453.3 563.4 621.5 703.6 742.5 770.5 828.6 910.7 949.7 1059.8 1117.9 1200.0 524.4 : 58.1 140.2 179.2 265.2 289.3 347.4 386.3 496.4 554.5 636.6 675.6 703.6 761.7 843.8 882.7 992.8 1050.9 1133.0 1200.0 582.5 : 82.1 121.1 207.2 231.2 289.3 328.2 438.3 496.4 578.5 617.5 645.5 703.6 785.7 824.6 934.8 992.8 1074.9 1141.9 1200.0 664.6 : 39.0 125.1 149.1 207.2 246.1 356.2 414.3 496.4 535.4 563.4 621.5 703.6 742.5 852.6 910.7 992.8 1059.8 1117.9 1200.0 703.6 : 86.1 110.1 168.2 207.2 317.3 375.4 457.5 496.4 524.4 582.5 664.6 703.6 813.7 871.8 953.9 1020.8 1078.9 1161.0 1200.0 789.7 : 24.0 82.1 121.1 231.2 289.3 371.4 410.3 438.3 496.4 578.5 617.5 727.6 785.7 867.8 934.8 992.8 1074.9 1113.9 1200.0 813.7 : 58.1 97.0 207.2 265.2 347.4 386.3 414.3 472.4 554.5 593.5 703.6 761.7 843.8 910.7 968.8 1050.9 1089.9 1176.0 1200.0 871.8 : 39.0 149.1 207.2 289.3 328.2 356.2 414.3 496.4 535.4 645.5 703.6 785.7 852.6 910.7 992.8 1031.8 1117.9 1141.9 1200.0 910.7 : 110.1 168.2 250.3 289.3 317.3 375.4 457.5 496.4 606.5 664.6 746.7 813.7 871.8 953.9 992.8 1078.9 1103.0 1161.0 1200.0 1020.8: 58.1 140.2 179.2 207.2 265.3 347.4 386.3 496.4 554.5 636.6 703.6 761.7 843.8 882.7 968.8 992.8 1050.9 1089.9 1200.0 1078.9: 82.1 121.1 149.1 207.2 289.3 328.2 438.3 496.4 578.5 645.5 703.6 785.7 824.6 910.7 934.8 992.8 1031.8 1141.9 1200.0 1161.0: 39.0 67.0 125.1 207.2 246.1 356.2 414.3 496.4 563.4 621.5 703.6 742.5 828.6 852.6 910.7 949.7 1059.8 1117.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 24.0170 .. 110.1070 cents 86.09000 cents 24.01700 cents 2: 66.9600 .. 168.1970 cents 101.23700 cents -43.14700 cents 3: 121.0670 .. 250.3040 cents 129.23700 cents -47.13000 cents 4: 207.1570 .. 317.2650 cents 110.10800 cents -43.14700 cents 5: 246.1170 .. 375.3550 cents 129.23800 cents -71.14800 cents 6: 328.2240 .. 457.4610 cents 129.23700 cents -47.13100 cents 7: 386.3140 .. 496.4220 cents 110.10800 cents -71.14700 cents 8: 438.3310 .. 582.5120 cents 144.18100 cents -58.09100 cents 9: 496.4410 .. 636.6180 cents 140.17700 cents -86.07100 cents 10: 563.3820 .. 703.5590 cents 140.17700 cents -73.23600 cents 11: 617.4880 .. 761.6690 cents 144.18100 cents -86.07100 cents 12: 703.5780 .. 813.6860 cents 110.10800 cents -58.09100 cents 13: 742.5390 .. 871.7760 cents 129.23700 cents -71.14700 cents 14: 824.6450 .. 953.8830 cents 129.23800 cents -47.13100 cents 15: 882.7350 .. 992.8430 cents 110.10800 cents -71.14800 cents 16: 949.6960 .. 1078.9330 cents 129.23700 cents -43.14700 cents 17: 1031.8030 .. 1133.0400 cents 101.23700 cents -47.13000 cents 18: 1089.8930 .. 1175.9830 cents 86.09000 cents -43.14700 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 24.01700 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 110.10700 cents Average / Smallest step : 2.629716 Largest / Average step : 1.743361 Largest / Smallest step : 4.584544 Median interval of one step : 58.09000 cents, amount: 4 Least squares average step : 63.43787 cents, oct.: 1205.31962 cents Scale is not proper Step pattern alph. order: ABCDEFGHFIDJKFDEFGD Step pattern size order : BEGCKDIFDHCJADCKDIC Scale is not a Constant Structure Scale diversity : 1.440860 Lumma stability : 0.040028 Lumma impropriety factor : 0.768638 Number of different interval sizes : 166 = 9.22222 / class Number of one step interval sizes : 11 Highest interval variety : 14 Mean interval variety : 12.11111 = 109/9 Median interval variety : 10 Lowest interval variety : 10 Smallest interval difference : 0.00100 cents Most common triad is 0.0 289.264 496.421 cents, amount: 6 Number of recognisable fifths : 16, average 703.5786 cents Formal octave complements present : 1 = 5.2632% -- Rational properties --
FIT/MODE
19: 0 1 1 1 2 1 1 1 1 1 1 1 1 1 0 2 1 1 1 N T3 SD: 20.5265 c. M: 41.8812 c. 20: 0 1 2 0 2 1 2 1 1 1 1 1 1 1 0 2 1 1 1 N SD: 18.3047 c. M:-28.2240 c. 21: 1 1 1 1 2 1 1 1 1 2 0 2 0 1 1 2 1 1 1 N T3 SD: 16.7357 c. M:-29.1429 c. 22: 1 1 1 1 2 1 2 1 1 1 1 2 0 1 1 2 1 1 1 N SD: 16.6239 c. M:-33.4481 c. 26: 1 1 2 0 3 1 2 1 2 1 1 2 1 1 1 2 1 2 1 N SD: 12.9117 c. M: 22.5416 c. 27: 1 1 2 1 2 1 2 2 1 2 1 2 0 2 0 3 1 2 1 N SD: 11.7105 c. M: 21.8471 c. 29: 1 1 2 1 3 1 2 2 1 2 1 2 1 1 1 3 1 2 1 N SD: 7.3084 c. M:-13.9002 c. 41: 1 2 3 1 4 2 3 2 2 3 1 3 1 2 1 4 2 3 1 N SD: 5.2638 c. M:-10.8317 c. 55: 1 3 4 1 6 2 4 3 3 3 2 4 1 3 2 5 2 4 2 N SD: 6.1677 c. M: 10.7934 c. 58: 1 3 4 2 5 3 4 3 3 4 2 4 1 3 2 5 3 4 2 N SD: 4.1872 c. M: 7.3103 c. 78: 2 4 5 2 8 3 6 4 4 5 3 5 2 4 2 7 4 5 3 N SD: 4.4051 c. M: 7.1938 c. 79: 2 4 5 3 7 4 5 5 3 6 2 6 2 3 3 7 4 5 3 N SD: 4.2188 c. M:-7.2236 c. 80: 2 4 5 3 7 4 5 5 4 5 3 6 1 4 3 7 4 5 3 N SD: 3.4785 c. M: 7.4610 c. 83: 2 4 6 2 8 4 6 4 4 6 3 6 1 4 3 8 4 5 3 N SD: 3.8575 c. M:-5.6630 c. 87: 2 4 6 3 8 4 6 5 4 6 3 6 2 4 3 8 4 6 3 N SD: 2.1118 c. M: 3.4621 c. 99: 2 5 7 3 9 5 7 5 5 7 3 7 2 5 3 9 5 7 3 N SD: 1.9476 c. M: 3.7576 c. 121: 3 6 8 4 11 6 8 7 6 8 4 9 2 6 4 11 6 8 4 N SD: 1.6170 c. M:-3.7194 c. 128: 3 6 9 4 12 6 9 7 6 9 4 9 3 6 4 12 6 9 4 N SD: 1.2025 c. M: 2.1690 c. 186: 4 9 13 6 17 9 13 10 9 13 6 13 4 9 6 17 9 13 6 N SD: 1.3399 c. M: 2.5722 c. 208: 5 10 14 7 19 10 14 12 10 14 7 15 4 10 7 19 10 14 7 N SD: 0.7423 c. M: 1.6918 c. 220: 5 11 15 7 20 11 15 12 11 15 7 16 4 11 7 20 11 15 7 N SD: 0.8421 c. M:-1.2401 c. 249: 6 12 17 8 23 12 17 14 12 17 8 18 5 12 8 23 12 17 8 N SD: 0.5846 c. M:-0.9157 c. 307: 7 15 21 10 28 15 21 17 15 21 10 22 6 15 10 28 15 21 10 N SD: 0.3425 c. M: 0.6567 c. 336: 8 16 23 11 31 16 23 19 16 23 11 24 7 16 11 31 16 23 11 N SD: 0.3951 c. M:-0.5997 c. 435: 10 21 30 14 40 21 30 24 21 30 14 31 9 21 14 40 21 30 14 N SD: 0.3314 c. M: 0.7035 c. 556: 13 27 38 18 51 27 38 31 27 38 18 40 11 27 18 51 27 38 18 N SD: 0.1336 c. M:-0.2591 c. 863: 20 42 59 28 79 42 59 48 42 59 28 62 17 42 28 79 42 59 28 N SD: 0.1267 c. M: 0.2445 c. 892: 21 43 61 29 82 43 61 50 43 61 29 64 18 43 29 82 43 61 29 N SD: 0.1225 c. M:-0.2511 c. 950: 22 46 65 31 87 46 65 53 46 65 31 68 19 46 31 87 46 65 31 N SD: 0.1804 c. M: 0.2153 c. 991: 23 48 68 32 91 48 68 55 48 68 32 71 20 48 32 91 48 68 32 N SD: 0.1208 c. M:-0.2585 c. 1199: 28 58 82 39 110 58 82 67 58 82 39 86 24 58 39 110 58 82 39 N SD: 0.0386 c. M: 0.0798 c. 1755: 41 85 120 57 161 85 120 98 85 120 57 126 35 85 57 161 85 120 57 N SD: 0.0306 c. M:-0.0746 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.8115 cents 3 .. 6 match: 3 H SD: 9.7415 cents 4 .. 8 match: 4 H SD: 13.2960 cents 5 .. 10 match: 5 H SD: 0.7259 cents 6 .. 12 match: 6 H SD: 10.8135 cents 7 .. 14 match: 7 H SD: 7.7012 cents 8 .. 16 match: 8 H SD: 8.2633 cents 9 .. 18 match: 9 H SD: 7.3159 cents 10 .. 20 match: 10 H SD: 3.3766 cents 11 .. 22 match: 11 H SD: 8.0644 cents 12 .. 24 match: 11 S SD: 7.5335 cents 13 .. 26 match: 13 H SD: 6.9908 cents 14 .. 28 match: 14 H SD: 5.2549 cents 15 .. 30 match: 14 SD: 4.7833 cents 16 .. 32 match: 15 SD: 4.4991 cents 17 .. 34 match: 16 SD: 4.0977 cents 18 .. 36 match: 15 S SD: 5.1292 cents 19 .. 38 match: 16 SD: 4.2323 cents 20 .. 40 match: 17 SD: 2.7295 cents 21 .. 42 match: 18 SD: 3.8194 cents 22 .. 44 match: 17 SD: 3.5130 cents 23 .. 46 match: 18 SD: 3.3143 cents 24 .. 48 match: 17 SD: 3.4757 cents 25 .. 50 match: 17 SD: 3.0695 cents 26 .. 52 match: 17 SD: 2.8664 cents 27 .. 54 match: 16 SD: 3.8202 cents 28 .. 56 match: 18 SD: 3.1636 cents 29 .. 58 match: 17 SD: 2.9604 cents 30 .. 60 match: 19 SD: 2.6357 cents 34 .. 68 match: 18 SD: 2.8203 cents 35 .. 70 match: 18 SD: 2.7113 cents 36 .. 72 match: 19 SD: 2.3237 cents 37 .. 74 match: 19 SD: 2.1922 cents 38 .. 76 match: 19 SD: 2.0633 cents 39 .. 78 match: 18 SD: 2.1138 cents 40 .. 80 match: 19 SD: 1.3787 cents 55 .. 110 match: 19 SD: 1.3620 cents 56 .. 112 match: 19 SD: 1.3614 cents 57 .. 114 match: 19 SD: 1.3200 cents 58 .. 116 match: 19 SD: 1.3129 cents 60 .. 120 match: 19 SD: 1.0831 cents 62 .. 124 match: 19 SD: 1.0368 cents 70 .. 140 match: 19 SD: 0.9605 cents 78 .. 156 match: 19 SD: 0.9461 cents 79 .. 158 match: 19 SD: 0.8893 cents 90 .. 180 match: 19 SD: 0.8513 cents 95 .. 190 match: 19 SD: 0.7903 cents 100 .. 200 match: 19 SD: 0.7566 cents 110 .. 220 match: 19 SD: 0.6486 cents 115 .. 230 match: 19 SD: 0.6440 cents 116 .. 232 match: 19 SD: 0.5299 cents 118 .. 236 match: 19 SD: 0.5131 cents 133 .. 266 match: 19 SD: 0.4626 cents 156 .. 312 match: 19 SD: 0.4599 cents 158 .. 316 match: 19 SD: 0.4291 cents 173 .. 346 match: 19 SD: 0.3546 cents 175 .. 350 match: 19 SD: 0.3432 cents 178 .. 356 match: 19 SD: 0.3289 cents 195 .. 390 match: 19 SD: 0.2854 cents 235 .. 470 match: 19 SD: 0.2015 cents 313 .. 626 match: 19 SD: 0.1988 cents 353 .. 706 match: 19 SD: 0.1745 cents 393 .. 786 match: 19 SD: 0.1394 cents 433 .. 866 match: 19 SD: 0.1326 cents 472 .. 944 match: 19 SD: 0.1164 cents 568 .. 1136 match: 19 SD: 0.1154 cents 588 .. 1176 match: 19 SD: 0.1152 cents