Scala analysis: xen15-gilson-generalized-pythagorean-11-8-37
Generalized Pythagorean Scale, 11/8 stacked 37=17+20 times
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 31.631 cents 31.630617 2: 64.497 cents 64.497366 3: 96.128 cents 96.127983 4: 128.995 cents 128.994732 5: 161.861 cents 161.861481 6: 193.492 cents 193.492098 7: 226.359 cents 226.358847 8: 19487171/16777216 259.225597 9: 290.856 cents 290.856213 10: 323.723 cents 323.722963 11: 161051/131072 356.589712 12: 388.220 cents 388.220329 13: 421.087 cents 421.087078 14: 1331/1024 453.953827 15: 485.584 cents 485.584444 16: 518.451 cents 518.451193 17: 11/8 551.317942 undecimal semi-augmented fourth 18: 582.949 cents 582.948559 19: 615.815 cents 615.815308 20: 647.446 cents 647.445925 21: 680.313 cents 680.312674 22: 713.179 cents 713.179424 23: 744.810 cents 744.810040 24: 777.677 cents 777.676790 25: 214358881/134217728 810.543539 26: 842.174 cents 842.174156 27: 875.041 cents 875.040905 28: 1771561/1048576 907.907654 29: 939.538 cents 939.538271 30: 972.405 cents 972.405020 31: 14641/8192 1005.271769 32: 1036.902 cents 1036.902386 33: 1069.769 cents 1069.769135 34: 121/64 1102.635885 two (undecimal semi-augmented fourth) 35: 1134.267 cents 1134.266501 36: 1167.133 cents 1167.133251 37: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32.8667 cents 32.8667 1: 31.6306 cents 31.6306 2: 32.8667 cents 32.8667 3: 31.6306 cents 31.6306 4: 32.8667 cents 32.8667 5: 32.8667 cents 32.8667 6: 31.6306 cents 31.6306 7: 32.8667 cents 32.8667 8: 32.8667 cents 32.8667 9: 31.6306 cents 31.6306 10: 32.8667 cents 32.8667 11: 32.8667 cents 32.8667 12: 31.6306 cents 31.6306 13: 32.8667 cents 32.8667 14: 32.8667 cents 32.8667 15: 31.6306 cents 31.6306 16: 32.8667 cents 32.8667 17: 32.8667 cents 32.8667 18: 31.6306 cents 31.6306 19: 32.8667 cents 32.8667 20: 31.6306 cents 31.6306 21: 32.8667 cents 32.8667 22: 32.8668 cents 32.8668 23: 31.6306 cents 31.6306 24: 32.8668 cents 32.8668 25: 32.8667 cents 32.8667 26: 31.6306 cents 31.6306 27: 32.8667 cents 32.8667 28: 32.8667 cents 32.8667 29: 31.6306 cents 31.6306 30: 32.8667 cents 32.8667 31: 32.8667 cents 32.8667 32: 31.6306 cents 31.6306 33: 32.8667 cents 32.8667 34: 32.8667 cents 32.8667 35: 31.6306 cents 31.6306 36: 32.8667 cents 32.8667 37: 32.8667 cents 32.8667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 13 31.63062 cents 1: 24 32.86675 cents 2: 26 64.49737 cents 2: 11 65.73350 cents 3: 2 96.12798 cents 3: 35 97.36412 cents 4: 15 128.99473 cents 4: 22 130.23086 cents 5: 28 161.86148 cents 5: 9 163.09761 cents 6: 4 193.49210 cents 6: 33 194.72823 cents 7: 17 226.35885 cents 7: 20 227.59498 cents 8: 30 19487171/16777216 259.226 cents 8: 7 260.46173 cents 9: 6 290.85621 cents 9: 31 292.09235 cents 10: 19 323.72296 cents 10: 18 324.95909 cents 11: 32 161051/131072 356.590 cents 11: 5 357.82584 cents 12: 8 388.22033 cents 12: 29 389.45646 cents 13: 21 421.08708 cents 13: 16 422.32321 cents 14: 34 1331/1024 453.954 cents 14: 3 455.18996 cents 15: 10 485.58444 cents 15: 27 486.82058 cents 16: 23 518.45119 cents 16: 14 519.68733 cents 17: 36 11/8 551.318 cents undecimal semi-augmented fourth 17: 1 552.55407 cents 18: 12 582.94856 cents 18: 25 584.18469 cents 19: 25 615.81531 cents 19: 12 617.05144 cents 20: 1 647.44593 cents 20: 36 648.68206 cents 21: 14 680.31267 cents 21: 23 681.54881 cents 22: 27 713.17942 cents 22: 10 714.41556 cents 23: 3 744.81004 cents 23: 34 746.04617 cents 24: 16 777.67679 cents 24: 21 778.91292 cents 25: 29 214358881/134217728 810.544 cents 25: 8 811.77967 cents 26: 5 842.17416 cents 26: 32 843.41029 cents 27: 18 875.04090 cents 27: 19 876.27704 cents 28: 31 1771561/1048576 907.908 cents 28: 6 909.14379 cents 29: 7 939.53827 cents 29: 30 940.77440 cents 30: 20 972.40502 cents 30: 17 973.64115 cents 31: 33 14641/8192 1005.272 cents 31: 4 1006.50790 cents 32: 9 1036.90239 cents 32: 28 1038.13852 cents 33: 22 1069.76913 cents 33: 15 1071.00527 cents 34: 35 121/64 1102.636 cents two (undecimal semi-augmented fourth) 34: 2 1103.87202 cents 35: 11 1134.26650 cents 35: 26 1135.50263 cents 36: 24 1167.13325 cents 36: 13 1168.36938 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
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 25 26 27 28 29 30 31 32 33 34 35 36 37 0.0 : 31.6 64.5 96.1 129.0 161.9 193.5 226.4 259.2 290.9 323.7 356.6 388.2 421.1 454.0 485.6 518.5 551.3 582.9 615.8 647.4 680.3 713.2 744.8 777.7 810.5 842.2 875.0 907.9 939.5 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 31.6 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 64.5 : 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 96.1 : 32.9 65.7 97.4 130.2 163.1 194.7 227.6 260.5 292.1 325.0 357.8 389.5 422.3 455.2 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 811.8 843.4 876.3 909.1 940.8 973.6 1006.5 1038.1 1071.0 1103.9 1135.5 1168.4 1200.0 129.0 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1167.1 1200.0 161.9 : 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1134.3 1167.1 1200.0 193.5 : 32.9 65.7 97.4 130.2 163.1 194.7 227.6 260.5 292.1 325.0 357.8 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 811.8 843.4 876.3 909.1 940.8 973.6 1006.5 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 226.4 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 259.2 : 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 388.2 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 290.9 : 32.9 65.7 97.4 130.2 163.1 194.7 227.6 260.5 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 811.8 843.4 876.3 909.1 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 323.7 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 356.6 : 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 290.9 323.7 356.6 388.2 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 939.5 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 388.2 : 32.9 65.7 97.4 130.2 163.1 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 811.8 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 421.1 : 32.9 64.5 97.4 130.2 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 454.0 : 31.6 64.5 97.4 129.0 161.9 193.5 226.4 259.2 290.9 323.7 356.6 388.2 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 842.2 875.0 907.9 939.5 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 485.6 : 32.9 65.7 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 518.5 : 32.9 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 551.3 : 31.6 64.5 96.1 129.0 161.9 193.5 226.4 259.2 290.9 323.7 356.6 388.2 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 744.8 777.7 810.5 842.2 875.0 907.9 939.5 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 582.9 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 615.8 : 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 647.4 : 32.9 65.7 97.4 130.2 163.1 194.7 227.6 260.5 292.1 325.0 357.8 389.5 422.3 455.2 486.8 519.7 552.6 584.2 617.1 648.7 681.5 714.4 746.0 778.9 811.8 843.4 876.3 909.1 940.8 973.6 1006.5 1038.1 1071.0 1103.9 1135.5 1168.4 1200.0 680.3 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1167.1 1200.0 713.2 : 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1134.3 1167.1 1200.0 744.8 : 32.9 65.7 97.4 130.2 163.1 194.7 227.6 260.5 292.1 325.0 357.8 389.5 422.3 455.2 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 811.8 843.4 876.3 909.1 940.8 973.6 1006.5 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 777.7 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 810.5 : 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 842.2 : 32.9 65.7 97.4 130.2 163.1 194.7 227.6 260.5 292.1 325.0 357.8 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 811.8 843.4 876.3 909.1 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 875.0 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 907.9 : 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 388.2 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 939.5 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 939.5 : 32.9 65.7 97.4 130.2 163.1 194.7 227.6 260.5 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 811.8 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 972.4 : 32.9 64.5 97.4 130.2 161.9 194.7 227.6 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 778.9 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 1005.3: 31.6 64.5 97.4 129.0 161.9 194.7 226.4 259.2 290.9 323.7 356.6 388.2 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 746.0 777.7 810.5 842.2 875.0 907.9 939.5 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 1036.9: 32.9 65.7 97.4 130.2 163.1 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 714.4 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 1069.8: 32.9 64.5 97.4 130.2 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 681.5 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 1102.6: 31.6 64.5 97.4 129.0 161.9 193.5 226.4 259.2 290.9 323.7 356.6 388.2 421.1 454.0 485.6 518.5 551.3 582.9 615.8 648.7 680.3 713.2 744.8 777.7 810.5 842.2 875.0 907.9 939.5 972.4 1005.3 1036.9 1069.8 1102.6 1134.3 1167.1 1200.0 1134.3: 32.9 65.7 97.4 130.2 161.9 194.7 227.6 259.2 292.1 325.0 356.6 389.5 422.3 454.0 486.8 519.7 551.3 584.2 617.1 648.7 681.5 713.2 746.0 778.9 810.5 843.4 876.3 907.9 940.8 973.6 1005.3 1038.1 1071.0 1102.6 1135.5 1168.4 1200.0 1167.1: 32.9 64.5 97.4 129.0 161.9 194.7 226.4 259.2 292.1 323.7 356.6 389.5 421.1 454.0 486.8 518.5 551.3 584.2 615.8 648.7 680.3 713.2 746.0 777.7 810.5 843.4 875.0 907.9 940.8 972.4 1005.3 1038.1 1069.8 1102.6 1135.5 1167.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.6306 .. 32.8667 cents 1.23613 cents 31.63062 cents 2: 64.4974 .. 65.7335 cents 1.23613 cents 31.63062 cents 3: 96.1280 .. 97.3641 cents 1.23613 cents 30.39449 cents 4: 128.9947 .. 130.2309 cents 1.23613 cents 31.63062 cents 5: 161.8615 .. 163.0976 cents 1.23613 cents 31.63062 cents 6: 193.4921 .. 194.7282 cents 1.23613 cents 30.39448 cents 7: 226.3588 .. 227.5950 cents 1.23613 cents 31.63062 cents 8: 259.2256 .. 260.4617 cents 1.23613 cents 31.63062 cents 9: 290.8562 .. 292.0923 cents 1.23613 cents 30.39448 cents 10: 323.7230 .. 324.9591 cents 1.23613 cents 31.63062 cents 11: 356.5897 .. 357.8258 cents 1.23613 cents 31.63062 cents 12: 388.2203 .. 389.4565 cents 1.23613 cents 30.39448 cents 13: 421.0871 .. 422.3232 cents 1.23613 cents 31.63062 cents 14: 453.9538 .. 455.1900 cents 1.23613 cents 31.63062 cents 15: 485.5844 .. 486.8206 cents 1.23613 cents 30.39448 cents 16: 518.4512 .. 519.6873 cents 1.23613 cents 31.63062 cents 17: 551.3179 .. 552.5541 cents 1.23613 cents 31.63062 cents 18: 582.9486 .. 584.1847 cents 1.23613 cents 30.39448 cents 19: 615.8153 .. 617.0514 cents 1.23613 cents 31.63062 cents 20: 647.4459 .. 648.6821 cents 1.23613 cents 30.39448 cents 21: 680.3127 .. 681.5488 cents 1.23613 cents 31.63062 cents 22: 713.1794 .. 714.4156 cents 1.23613 cents 31.63062 cents 23: 744.8100 .. 746.0462 cents 1.23613 cents 30.39448 cents 24: 777.6768 .. 778.9129 cents 1.23613 cents 31.63062 cents 25: 810.5435 .. 811.7797 cents 1.23613 cents 31.63062 cents 26: 842.1742 .. 843.4103 cents 1.23613 cents 30.39448 cents 27: 875.0409 .. 876.2770 cents 1.23613 cents 31.63062 cents 28: 907.9077 .. 909.1438 cents 1.23613 cents 31.63062 cents 29: 939.5383 .. 940.7744 cents 1.23613 cents 30.39448 cents 30: 972.4050 .. 973.6412 cents 1.23613 cents 31.63062 cents 31: 1005.2718 .. 1006.5079 cents 1.23613 cents 31.63062 cents 32: 1036.9024 .. 1038.1385 cents 1.23613 cents 30.39448 cents 33: 1069.7691 .. 1071.0053 cents 1.23613 cents 31.63062 cents 34: 1102.6359 .. 1103.8720 cents 1.23613 cents 31.63062 cents 35: 1134.2665 .. 1135.5026 cents 1.23613 cents 30.39448 cents 36: 1167.1333 .. 1168.3694 cents 1.23613 cents 31.63062 cents
SHOW DATA
Number of notes : 37 -- Interval properties -- Smallest interval : 31.63062 cents, class 1 Average step (divided formal octave): 32.4324 cents Largest one step interval : 32.86675 cents Average / Smallest step : 1.025349 Largest / Average step : 1.013391 Largest / Smallest step : 1.039080 Median interval of one step : 32.86675 cents, amount: 24 Most common interval of one step : 32.86675 cents, amount: 24 Least squares average step : 32.40985 cents, oct.: 1199.16463 cents Scale is strictly proper Scale has Myhill's property chromas: 1.23613 cents and 30.39448 cents, ratio: 24.588381 generators: 17 of 551.31794 cents and 648.68206 cents ET pair of linear temperament : 11&13 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1935-tone equal temperament with octave 2/1 degrees: 51 104 155 208 261 312 365 418 469 522 575 626 679 732 783 836 889 940 993 1044 1097 1150 1201 1254 1307 1358 1411 1464 1515 1568 1621 1672 1725 1778 1829 1882 1935 generators: 889 and 1046 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABBABBABBABBABBABABBABBABBABBABBABB Step pattern size order : SLSLLSLLSLLSLLSLLSLSLLSLLSLLSLLSLLSLL Scale is a Constant Structure, by a margin of 30.39448 cents Scale diversity : 1.020414 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.962916 Rothenberg efficiency : 0.684685 redundancy: 0.315315 Efficiency x scale size : 25.333333 Number of different interval sizes : 72 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 1.23613 cents Most common intervals : 11/8, 551.3179 cents & inv., amount: 36 Scale is a chain of 18 triads 0.0 551.318 1102.636 cents Most common triad is 0.0 551.318 648.682 cents, amount: 35 Number of recognisable fifths : 37, average 713.5135 cents Number of appreciable fifths : 27, average 713.1794 cents Scale contains two identical disjunct "tetrachords" of 16 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 2.7027% Limited transpositions with margin 1.2361 cents: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 Limited inverse transpositions : 20 Inversional symmetry on degrees : 10 Inversional symmetry on intervals : 28-29 -- Rational properties -- Prime limit : 11 (not all pitches rational)
FIT/MODE
37: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 0.6992 c. M:-1.2027 c. 486: 13 13 13 13 14 12 14 13 13 13 13 13 14 13 13 13 13 13 13 13 14 13 13 13 13 13 13 14 13 13 13 13 13 14 12 14 13 SP D3 SD: 0.6984 c. M:-1.2025 c. 487: 13 13 13 13 14 13 13 13 13 13 14 13 13 13 13 13 14 13 13 13 13 13 13 14 13 13 13 13 13 14 13 13 13 13 13 14 13 SP M ME S SD: 0.6971 c. M: 1.1985 c. 489: 13 13 13 14 13 13 13 14 13 13 13 13 14 13 13 13 14 13 13 13 13 14 13 13 13 13 14 13 13 13 14 13 13 13 13 14 13 SP M ME S SD: 0.6957 c. M:-1.2022 c. 491: 13 13 13 14 13 13 14 13 13 13 14 13 13 14 13 13 14 13 13 13 13 14 13 13 14 13 13 13 13 14 13 13 14 13 13 14 13 SP D3 SD: 0.6912 c. M: 1.1867 c. 495: 13 14 13 13 14 13 13 14 13 14 13 13 14 13 13 14 13 13 14 13 14 13 13 14 13 13 14 14 13 13 14 13 13 14 13 13 14 SP D3 SD: 0.6858 c. M:-1.1833 c. 496: 13 14 13 13 14 13 14 13 13 14 13 13 14 14 13 13 14 13 14 13 13 14 13 13 14 13 14 13 13 14 14 13 13 14 13 13 14 SP D3 S SD: 0.6851 c. M:-1.1798 c. 497: 13 14 13 13 14 13 14 13 13 14 14 13 13 14 13 14 13 13 14 13 14 13 13 14 14 13 13 14 13 14 13 13 14 14 13 13 14 SP D3 S SD: 0.6779 c. M: 1.1481 c. 500: 13 14 13 14 13 14 13 14 13 14 14 13 13 14 13 14 14 13 14 13 13 14 13 14 14 13 14 13 13 14 14 13 14 13 14 13 14 SP D3 S SD: 0.6771 c. M: 1.1383 c. 504: 13 14 13 14 14 13 14 14 13 14 14 13 14 14 13 14 14 13 14 13 14 14 13 14 13 14 14 13 14 13 14 14 13 14 13 14 14 SP D3 S SD: 0.6752 c. M:-1.1929 c. 505: 13 14 13 14 14 13 14 14 13 14 14 13 14 14 13 14 14 13 14 13 14 14 13 14 14 13 14 14 13 14 14 13 14 14 13 14 14 SP M ME S SD: 0.6449 c. M: 1.1093 c. 511: 13 14 14 14 14 13 14 14 14 14 14 13 14 14 14 14 14 13 14 14 14 14 13 14 14 14 14 14 13 14 14 14 14 14 13 14 14 SP D3 SD: 0.6641 c. M: 1.1022 c. 512: 13 15 13 14 14 14 14 14 13 14 14 14 14 14 13 14 14 14 14 13 14 14 14 14 14 13 14 14 14 14 14 13 14 14 14 14 14 SP D3 SD: 0.6639 c. M: 1.1619 c. 513: 14 14 13 14 14 14 14 14 13 14 14 14 14 14 14 14 14 13 14 14 14 14 13 14 15 13 14 14 14 14 14 13 14 14 14 14 14 SP D3 SD: 0.6619 c. M:-1.1524 c. 515: 14 14 13 14 14 14 14 14 14 14 14 14 14 14 13 15 14 13 14 14 14 14 14 14 14 13 15 14 13 14 14 14 14 14 14 14 14 SP D3 SD: 0.6595 c. M:-1.1605 c. 517: 14 14 13 15 14 13 15 14 13 14 15 13 14 15 13 14 15 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 SP D3 SD: 0.6531 c. M:-1.1073 c. 519: 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 13 14 15 13 15 14 13 15 14 14 14 14 SP D3 S SD: 0.6532 c. M: 1.0642 c. 521: 14 14 14 14 14 14 14 15 13 15 14 14 14 14 14 14 14 14 14 14 14 15 13 15 14 14 14 14 14 14 14 14 14 15 13 15 14 SP D3 SD: 0.6494 c. M: 1.0611 c. 528: 14 14 14 15 14 14 15 14 14 14 15 14 14 15 14 14 15 13 15 14 14 15 14 14 15 14 14 14 14 15 14 14 15 14 14 15 14 SP D3 SD: 0.6447 c. M: 1.1304 c. 532: 14 15 14 14 15 14 14 15 14 15 14 14 15 14 14 15 14 14 15 14 15 14 14 15 14 14 15 15 14 14 15 14 14 15 14 14 15 SP D3 SD: 0.6409 c. M:-1.1149 c. 534: 14 15 14 14 15 14 15 14 14 15 15 14 14 15 14 15 14 14 15 14 15 14 14 15 15 14 14 15 14 15 14 14 15 15 14 14 15 SP D3 S SD: 0.6184 c. M: 0.9898 c. 542: 14 15 14 15 15 14 15 15 14 15 15 14 15 15 14 15 15 14 15 14 15 15 14 15 15 14 15 15 14 15 15 14 15 15 14 15 15 SP M ME S SD: 0.5531 c. M: 0.9515 c. 571: 15 16 15 15 16 15 16 15 15 16 16 15 15 16 15 16 15 15 16 15 16 15 15 16 16 15 15 16 15 16 15 15 16 16 15 15 16 SP D3 S SD: 0.5701 c. M: 0.8521 c. 579: 15 16 15 16 16 15 16 16 15 16 16 15 16 16 15 16 16 15 16 15 16 16 15 16 16 15 16 16 15 16 16 15 16 16 15 16 16 SP M ME S SD: 0.4731 c. M: 0.8138 c. 608: 16 17 16 16 17 16 17 16 16 17 17 16 16 17 16 17 16 16 17 16 17 16 16 17 17 16 16 17 16 17 16 16 17 17 16 16 17 SP D3 S SD: 0.5309 c. M: 0.7311 c. 616: 16 17 16 17 17 16 17 17 16 17 17 16 17 17 16 17 17 16 17 16 17 17 16 17 17 16 17 17 16 17 17 16 17 17 16 17 17 SP M ME S SD: 0.4027 c. M: 0.6927 c. 645: 17 18 17 17 18 17 18 17 17 18 18 17 17 18 17 18 17 17 18 17 18 17 17 18 18 17 17 18 17 18 17 17 18 18 17 17 18 SP D3 S SD: 0.4994 c. M: 0.6240 c. 653: 17 18 17 18 18 17 18 18 17 18 18 17 18 18 17 18 18 17 18 17 18 18 17 18 18 17 18 18 17 18 18 17 18 18 17 18 18 SP M ME S SD: 0.3403 c. M: 0.5853 c. 690: 18 19 18 19 19 18 19 19 18 19 19 18 19 19 18 19 19 18 19 18 19 19 18 19 19 18 19 19 18 19 19 18 19 19 18 19 19 SP M ME S SD: 0.2845 c. M: 0.4894 c. 727: 19 20 19 20 20 19 20 20 19 20 20 19 20 20 19 20 20 19 20 19 20 20 19 20 20 19 20 20 19 20 20 19 20 20 19 20 20 SP M ME S SD: 0.2344 c. M: 0.4033 c. 764: 20 21 20 21 21 20 21 21 20 21 21 20 21 21 20 21 21 20 21 20 21 21 20 21 21 20 21 21 20 21 21 20 21 21 20 21 21 SP M ME S SD: 0.1892 c. M: 0.3255 c. 801: 21 22 21 22 22 21 22 22 21 22 22 21 22 22 21 22 22 21 22 21 22 22 21 22 22 21 22 22 21 22 22 21 22 22 21 22 22 SP M ME S SD: 0.1482 c. M: 0.2549 c. 838: 22 23 22 23 23 22 23 23 22 23 23 22 23 23 22 23 23 22 23 22 23 23 22 23 23 22 23 23 22 23 23 22 23 23 22 23 23 SP M ME S SD: 0.1108 c. M: 0.1906 c. 875: 23 24 23 24 24 23 24 24 23 24 24 23 24 24 23 24 24 23 24 23 24 24 23 24 24 23 24 24 23 24 24 23 24 24 23 24 24 SP M ME S SD: 0.0765 c. M: 0.1316 c. 912: 24 25 24 25 25 24 25 25 24 25 25 24 25 25 24 25 25 24 25 24 25 25 24 25 25 24 25 25 24 25 25 24 25 25 24 25 25 SP M ME S SD: 0.0451 c. M: 0.0775 c. 949: 25 26 25 26 26 25 26 26 25 26 26 25 26 26 25 26 26 25 26 25 26 26 25 26 26 25 26 26 25 26 26 25 26 26 25 26 26 SP M ME S SD: 0.0160 c. M: 0.0276 c. 986: 26 27 26 27 27 26 27 27 26 27 27 26 27 27 26 27 27 26 27 26 27 27 26 27 27 26 27 27 26 27 27 26 27 27 26 27 27 SP M ME S SD: 0.0108 c. M:-0.0186 c. 1935: 51 53 51 53 53 51 53 53 51 53 53 51 53 53 51 53 53 51 53 51 53 53 51 53 53 51 53 53 51 53 53 51 53 53 51 53 53 SP M DE S SD: 0.0024 c. M: 0.0041 c. 2921: 77 80 77 80 80 77 80 80 77 80 80 77 80 80 77 80 80 77 80 77 80 80 77 80 80 77 80 80 77 80 80 77 80 80 77 80 80 SP M DE S SD: 0.0021 c. M:-0.0036 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 5.6122 cents 3 .. 6 match: 3 H SD: 5.1864 cents 4 .. 8 match: 4 H SD: 2.9836 cents 5 .. 10 match: 5 H SD: 3.0151 cents 6 .. 12 match: 6 H SD: 4.0201 cents 7 .. 14 match: 7 H SD: 2.4323 cents 8 .. 16 match: 8 H SD: 2.6812 cents 9 .. 18 match: 9 H SD: 3.1745 cents 10 .. 20 match: 10 H SD: 2.3490 cents 11 .. 22 match: 11 H SD: 2.5761 cents 12 .. 24 match: 12 H SD: 2.8160 cents 13 .. 26 match: 13 H SD: 2.3684 cents 14 .. 28 match: 14 H SD: 2.2799 cents 15 .. 30 match: 15 H SD: 2.6170 cents 16 .. 32 match: 16 H SD: 2.1250 cents 17 .. 34 match: 17 H SD: 2.3028 cents 18 .. 36 match: 18 H SD: 2.3958 cents 19 .. 38 match: 19 H SD: 2.2570 cents 20 .. 40 match: 20 H SD: 1.8492 cents 21 .. 42 match: 21 H SD: 2.0770 cents 22 .. 44 match: 22 H SD: 1.8750 cents 23 .. 46 match: 23 H SD: 2.1301 cents 24 .. 48 match: 24 H SD: 1.8022 cents 25 .. 50 match: 25 H SD: 1.7333 cents 26 .. 52 match: 26 H SD: 1.6321 cents 27 .. 54 match: 27 H SD: 1.5779 cents 28 .. 56 match: 28 H SD: 1.5204 cents 29 .. 58 match: 29 H SD: 1.5538 cents 30 .. 60 match: 30 H SD: 1.6925 cents 31 .. 62 match: 30 S SD: 1.9444 cents 32 .. 64 match: 31 SD: 1.5187 cents 33 .. 66 match: 32 S SD: 1.4894 cents 34 .. 68 match: 32 SD: 1.7521 cents 35 .. 70 match: 33 SD: 1.3519 cents 36 .. 72 match: 33 SD: 1.7362 cents 37 .. 74 match: 34 SD: 1.3111 cents 38 .. 76 match: 34 SD: 1.5488 cents 39 .. 78 match: 35 SD: 1.4283 cents 40 .. 80 match: 35 SD: 1.2624 cents 41 .. 82 match: 35 SD: 1.5654 cents 42 .. 84 match: 36 SD: 1.4541 cents 43 .. 86 match: 36 SD: 1.1267 cents 44 .. 88 match: 36 SD: 1.2266 cents 45 .. 90 match: 36 SD: 1.4377 cents 46 .. 92 match: 36 SD: 1.5162 cents 47 .. 94 match: 37 SD: 1.3503 cents 48 .. 96 match: 37 SD: 1.1455 cents 49 .. 98 match: 37 SD: 1.0055 cents 57 .. 114 match: 37 SD: 0.9993 cents 61 .. 122 match: 37 SD: 0.9472 cents 62 .. 124 match: 37 SD: 0.9214 cents 64 .. 128 match: 37 SD: 0.9136 cents 65 .. 130 match: 37 SD: 0.9068 cents 67 .. 134 match: 37 SD: 0.8501 cents 69 .. 138 match: 37 SD: 0.8291 cents 70 .. 140 match: 37 SD: 0.8209 cents 72 .. 144 match: 37 SD: 0.8043 cents 73 .. 146 match: 37 SD: 0.7993 cents 74 .. 148 match: 37 SD: 0.7928 cents 75 .. 150 match: 37 SD: 0.7722 cents 77 .. 154 match: 37 SD: 0.7164 cents 80 .. 160 match: 37 SD: 0.7046 cents 83 .. 166 match: 37 SD: 0.6665 cents 91 .. 182 match: 37 SD: 0.6357 cents 92 .. 184 match: 37 SD: 0.6276 cents 93 .. 186 match: 37 SD: 0.5772 cents 99 .. 198 match: 37 SD: 0.5575 cents 100 .. 200 match: 37 SD: 0.5359 cents 102 .. 204 match: 37 SD: 0.4976 cents 104 .. 208 match: 37 SD: 0.4708 cents 117 .. 234 match: 37 SD: 0.4563 cents 123 .. 246 match: 37 SD: 0.4526 cents 126 .. 252 match: 37 SD: 0.4236 cents 137 .. 274 match: 37 SD: 0.4207 cents 141 .. 282 match: 37 SD: 0.3976 cents 143 .. 286 match: 37 SD: 0.3632 cents 152 .. 304 match: 37 SD: 0.3439 cents 154 .. 308 match: 37 SD: 0.3422 cents 155 .. 310 match: 37 SD: 0.3277 cents 157 .. 314 match: 37 SD: 0.3274 cents 160 .. 320 match: 37 SD: 0.3203 cents 171 .. 342 match: 37 SD: 0.3193 cents 178 .. 356 match: 37 SD: 0.3175 cents 179 .. 358 match: 37 SD: 0.2966 cents 192 .. 384 match: 37 SD: 0.2745 cents 203 .. 406 match: 37 SD: 0.2660 cents 206 .. 412 match: 37 SD: 0.2566 cents 210 .. 420 match: 37 SD: 0.2275 cents 229 .. 458 match: 37 SD: 0.2200 cents 235 .. 470 match: 37 SD: 0.2197 cents 243 .. 486 match: 37 SD: 0.2136 cents 257 .. 514 match: 37 SD: 0.2101 cents 258 .. 516 match: 37 SD: 0.2096 cents 262 .. 524 match: 37 SD: 0.2028 cents 263 .. 526 match: 37 SD: 0.1939 cents 272 .. 544 match: 37 SD: 0.1898 cents 283 .. 566 match: 37 SD: 0.1842 cents 287 .. 574 match: 37 SD: 0.1842 cents 297 .. 594 match: 37 SD: 0.1815 cents 310 .. 620 match: 37 SD: 0.1730 cents 315 .. 630 match: 37 SD: 0.1650 cents 322 .. 644 match: 37 SD: 0.1627 cents 335 .. 670 match: 37 SD: 0.1577 cents 337 .. 674 match: 37 SD: 0.1385 cents 370 .. 740 match: 37 SD: 0.1342 cents 389 .. 778 match: 37 SD: 0.1184 cents 441 .. 882 match: 37 SD: 0.1174 cents 447 .. 894 match: 37 SD: 0.1171 cents 450 .. 900 match: 37 SD: 0.1083 cents 490 .. 980 match: 37 SD: 0.1012 cents 530 .. 1060 match: 37 SD: 0.0963 cents 541 .. 1082 match: 37 SD: 0.0903 cents 573 .. 1146 match: 37 SD: 0.0871 cents 584 .. 1168 match: 37 SD: 0.0842 cents