Scala analysis: tenn41b
41&53 Tenney reduced fifths from -20 to 20
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/54 31.766654 telepathma 2: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 81/77 87.676155 4: 15/14 119.442808 major diatonic semitone 5: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 6: 10/9 182.403712 minor whole tone 7: 9/8 203.910002 major whole tone 8: 8/7 231.174094 septimal whole tone 9: 7/6 266.870906 septimal minor third 10: 25/21 301.846520 BP second, quasi-equal minor third 11: 6/5 315.641287 minor third 12: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 13: 5/4 386.313714 major third 14: 63/50 400.108480 quasi-equal major third 15: 9/7 435.084095 septimal major third, BP third 16: 21/16 470.780907 narrow fourth 17: 4/3 498.044999 perfect fourth 18: 27/20 519.551289 acute fourth 19: 25/18 568.717426 classic augmented fourth 20: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 21: 10/7 617.487807 Euler's tritone 22: 36/25 631.282574 classic diminished fifth 23: 40/27 680.448711 grave fifth 24: 3/2 701.955001 perfect fifth 25: 32/21 729.219093 wide fifth 26: 14/9 764.915905 septimal minor sixth 27: 100/63 799.891520 quasi-equal minor sixth 28: 8/5 813.686286 minor sixth 29: 44/27 845.452940 neutral sixth 30: 5/3 884.358713 major sixth, BP sixth 31: 27/16 905.865003 Pythagorean major sixth 32: 12/7 933.129094 septimal major sixth 33: 7/4 968.825906 harmonic seventh 34: 16/9 996.089998 Pythagorean minor seventh 35: 9/5 1017.596288 just minor seventh, BP seventh 36: 50/27 1066.762425 grave major seventh 37: 15/8 1088.268715 classic major seventh 38: 154/81 1112.323845 39: 27/14 1137.039096 septimal major seventh 40: 49/25 1165.024385 BP eighth 41: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 1: 55/54 31.7667 telepathma 2: 45/44 38.9058 1/5-tone 3: 1944/1925 17.0037 4: 55/54 31.7667 telepathma 5: 126/125 13.7948 septimal semicomma, Starling comma 6: 250/243 49.1661 maximal diesis, Porcupine comma 7: 81/80 21.5063 syntonic comma, Didymus comma 8: 64/63 27.2641 septimal comma, Archytas' comma 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 11: 126/125 13.7948 septimal semicomma, Starling comma 12: 45/44 38.9058 1/5-tone 13: 55/54 31.7667 telepathma 14: 126/125 13.7948 septimal semicomma, Starling comma 15: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 16: 49/48 35.6968 slendro diesis, septimal 1/6-tone 17: 64/63 27.2641 septimal comma, Archytas' comma 18: 81/80 21.5063 syntonic comma, Didymus comma 19: 250/243 49.1661 maximal diesis, Porcupine comma 20: 126/125 13.7948 septimal semicomma, Starling comma 21: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 22: 126/125 13.7948 septimal semicomma, Starling comma 23: 250/243 49.1661 maximal diesis, Porcupine comma 24: 81/80 21.5063 syntonic comma, Didymus comma 25: 64/63 27.2641 septimal comma, Archytas' comma 26: 49/48 35.6968 slendro diesis, septimal 1/6-tone 27: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 28: 126/125 13.7948 septimal semicomma, Starling comma 29: 55/54 31.7667 telepathma 30: 45/44 38.9058 1/5-tone 31: 81/80 21.5063 syntonic comma, Didymus comma 32: 64/63 27.2641 septimal comma, Archytas' comma 33: 49/48 35.6968 slendro diesis, septimal 1/6-tone 34: 64/63 27.2641 septimal comma, Archytas' comma 35: 81/80 21.5063 syntonic comma, Didymus comma 36: 250/243 49.1661 maximal diesis, Porcupine comma 37: 81/80 21.5063 syntonic comma, Didymus comma 38: 1232/1215 24.0551 sensmus 39: 2187/2156 24.7153 40: 686/675 27.9853 senga 41: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 126/125 13.795 cents septimal semicomma, Starling comma 1: 1 1944/1925 17.004 cents 1: 6 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 1232/1215 24.055 cents sensmus 1: 1 2187/2156 24.715 cents 1: 5 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 686/675 27.985 cents senga 1: 4 55/54 31.767 cents telepathma 1: 5 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 4 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 3 45/44 38.906 cents 1/5-tone 1: 4 250/243 49.166 cents maximal diesis, Porcupine comma 2: 4 77/75 45.561 cents 2: 12 36/35 48.770 cents septimal diesis, 1/4-tone 2: 2 567/550 52.701 cents 2: 1 4374/4235 55.910 cents 2: 1 729/704 60.412 cents undecimal major diesis 2: 9 28/27 62.961 cents Archytas' 1/3-tone 2: 1 1375/1323 66.742 cents 2: 11 25/24 70.672 cents classic chromatic semitone, minor chroma 3: 2 648/625 62.565 cents major diesis 3: 1 729/700 70.277 cents 3: 1 392/375 76.756 cents 3: 2 22/21 80.537 cents undecimal minor semitone 3: 14 21/20 84.467 cents minor semitone 3: 5 81/77 87.676 cents 3: 1 256/243 90.225 cents limma, Pythagorean minor second 3: 2 135/128 92.179 cents major chroma, major limma 3: 3 770/729 94.728 cents 3: 9 200/189 97.937 cents 3: 1 625/588 105.648 cents 4: 2 1323/1250 98.262 cents 4: 1 1458/1375 101.471 cents 4: 1 1701/1600 105.973 cents 4: 12 16/15 111.731 cents minor diatonic semitone 4: 4 77/72 116.234 cents undecimal secor 4: 13 15/14 119.443 cents major diatonic semitone 4: 1 4050/3773 122.652 cents 4: 2 189/176 123.373 cents 4: 5 175/162 133.633 cents 5: 12 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 5: 2 243/224 140.949 cents Archytas' 2/3-tone 5: 5 88/81 143.498 cents 2nd undecimal neutral second 5: 2 160/147 146.707 cents 5: 4 49/45 147.428 cents BP minor semitone 5: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 5: 1 375/343 154.418 cents BP major semitone, minor BP chroma 5: 5 35/32 155.140 cents septimal neutral second 5: 1 675/616 158.349 cents 5: 2 800/729 160.897 cents grave whole tone 5: 3 625/567 168.609 cents BP great semitone, major BP chroma 6: 3 192/175 160.502 cents septimal 4/5-tone 6: 3 11/10 165.004 cents Ptolemy's second, 4/5-tone 6: 4 54/49 168.213 cents Zalzal's mujannab 6: 4 441/400 168.934 cents two (minor semitone) 6: 3 243/220 172.143 cents 6: 1 6561/5929 175.352 cents 6: 1 567/512 176.646 cents 6: 2 539/486 179.195 cents 6: 20 10/9 182.404 cents minor whole tone 7: 11 28/25 196.198 cents middle second 7: 2 432/385 199.407 cents 7: 15 9/8 203.910 cents major whole tone 7: 1 2464/2187 206.459 cents 7: 1 1215/1078 207.119 cents 7: 2 640/567 209.668 cents 7: 4 275/243 214.170 cents 7: 3 500/441 217.379 cents 7: 2 25/22 221.309 cents undecimal acute whole tone 8: 3 567/500 217.705 cents 8: 2 2187/1925 220.914 cents 8: 1 729/640 225.416 cents acute major second 8: 4 154/135 227.965 cents 8: 15 8/7 231.174 cents septimal whole tone 8: 1 343/300 231.895 cents 8: 2 63/55 235.104 cents 8: 1 55/48 235.677 cents undecimal semi-augmented whole tone 8: 1 225/196 238.886 cents two (major diatonic semitone) 8: 2 147/128 239.607 cents 8: 1 405/352 242.816 cents 8: 3 280/243 245.365 cents 8: 5 125/108 253.076 cents semi-augmented whole tone 9: 4 144/125 244.969 cents classic diminished third 9: 6 81/70 252.680 cents Al-Hwarizmi's lute middle finger 9: 1 512/441 258.438 cents 9: 1 784/675 259.159 cents 9: 3 220/189 262.941 cents 9: 1 400/343 266.150 cents 9: 17 7/6 266.871 cents septimal minor third 9: 3 90/77 270.080 cents 9: 3 75/64 274.582 cents classic augmented second 9: 2 2000/1701 280.340 cents 10: 1 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 10: 2 88/75 276.736 cents 10: 3 147/125 280.666 cents 10: 2 324/275 283.875 cents 10: 6 189/160 288.377 cents 10: 3 729/616 291.586 cents 10: 9 32/27 294.135 cents Pythagorean minor third 10: 3 385/324 298.638 cents 10: 12 25/21 301.847 cents BP second, quasi-equal minor third 11: 2 539/450 312.432 cents 11: 18 6/5 315.641 cents minor third 11: 2 648/539 318.850 cents 11: 1 1323/1100 319.571 cents 11: 1 729/605 322.780 cents 11: 4 135/112 323.353 cents septimal wide minor third 11: 3 880/729 325.902 cents 11: 2 1600/1323 329.111 cents 11: 2 98/81 329.832 cents 11: 1 1250/1029 336.822 cents 11: 5 175/144 337.543 cents 12: 2 756/625 329.436 cents 12: 6 243/200 337.148 cents acute minor third 12: 3 128/105 342.905 cents septimal neutral third 12: 5 11/9 347.408 cents undecimal neutral third 12: 4 60/49 350.617 cents smaller approximation to neutral third 12: 4 49/40 351.338 cents larger approximation to neutral third 12: 5 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 12: 1 315/256 359.050 cents 12: 11 100/81 364.807 cents grave major third 13: 5 216/175 364.412 cents 13: 1 3087/2500 365.133 cents 13: 1 1701/1375 368.342 cents 13: 1 243/196 372.123 cents 13: 2 704/567 374.672 cents 13: 8 56/45 378.602 cents septimal narrow major third 13: 1 96/77 381.811 cents 13: 2 539/432 383.105 cents 13: 17 5/4 386.314 cents major third 13: 2 675/539 389.523 cents 13: 1 5000/3969 399.783 cents 14: 12 63/50 400.108 cents quasi-equal major third 14: 3 486/385 403.317 cents 14: 4 81/64 407.820 cents Pythagorean major third 14: 4 308/243 410.369 cents 14: 12 80/63 413.578 cents wide major third 14: 1 14/11 417.508 cents undecimal diminished fourth or major third 14: 1 275/216 418.080 cents 14: 1 125/98 421.289 cents 14: 1 225/176 425.219 cents 14: 2 625/486 435.480 cents 15: 7 32/25 427.373 cents classic diminished fourth 15: 3 77/60 431.875 cents 15: 13 9/7 435.084 cents septimal major third, BP third 15: 1 1029/800 435.805 cents 15: 1 567/440 439.014 cents 15: 2 2187/1694 442.223 cents 15: 2 2200/1701 445.344 cents 15: 10 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 15: 2 125/96 456.986 cents classic augmented third 16: 5 162/125 448.879 cents 16: 1 729/560 456.590 cents 16: 2 176/135 459.139 cents 16: 3 64/49 462.348 cents 2 septatones or septatonic major third 16: 4 98/75 463.069 cents 16: 2 72/55 466.278 cents undecimal semi-diminished fourth 16: 1 55/42 466.851 cents 16: 1 450/343 470.060 cents 16: 9 21/16 470.781 cents narrow fourth 16: 3 405/308 473.990 cents 16: 3 320/243 476.539 cents grave fourth 16: 2 1925/1458 481.041 cents 16: 5 250/189 484.250 cents 17: 1 1323/1000 484.576 cents 17: 5 729/550 487.785 cents 17: 1 968/729 490.906 cents 17: 2 539/405 494.836 cents 17: 24 4/3 498.045 cents perfect fourth 17: 1 385/288 502.548 cents 17: 7 75/56 505.757 cents marvelous fourth 18: 4 168/125 511.840 cents 18: 12 27/20 519.551 cents acute fourth 18: 2 729/539 522.760 cents 18: 3 256/189 525.309 cents 18: 5 110/81 529.812 cents 18: 4 200/147 533.021 cents 18: 5 49/36 533.742 cents Arabic lute acute fourth 18: 3 15/11 536.951 cents undecimal augmented fourth 18: 1 175/128 541.453 cents 18: 2 1000/729 547.211 cents 19: 2 1701/1250 533.346 cents 19: 3 308/225 543.606 cents 19: 8 48/35 546.815 cents septimal semi-augmented fourth 19: 1 343/250 547.537 cents 19: 1 378/275 550.746 cents 19: 2 11/8 551.318 cents undecimal semi-augmented fourth 19: 3 135/98 554.527 cents 19: 4 243/176 558.457 cents 19: 5 112/81 561.006 cents 19: 12 25/18 568.717 cents classic augmented fourth 20: 1 864/625 560.610 cents 20: 3 243/175 568.322 cents 20: 2 88/63 578.582 cents 20: 15 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 20: 5 108/77 585.721 cents 20: 6 45/32 590.224 cents diatonic tritone 20: 2 3080/2187 592.773 cents 20: 5 800/567 595.982 cents 20: 1 1375/972 600.484 cents 20: 1 625/441 603.693 cents two (BP second, quasi-equal minor third) 21: 1 882/625 596.307 cents 21: 1 1944/1375 599.516 cents 21: 5 567/400 604.018 cents 21: 2 2187/1540 607.227 cents 21: 6 64/45 609.776 cents 2nd tritone 21: 5 77/54 614.279 cents 21: 15 10/7 617.488 cents Euler's tritone 21: 2 63/44 621.418 cents 21: 3 350/243 631.678 cents 21: 1 625/432 639.390 cents 22: 12 36/25 631.283 cents classic diminished fifth 22: 5 81/56 638.994 cents 22: 4 352/243 641.543 cents 22: 3 196/135 645.473 cents 22: 2 16/11 648.682 cents undecimal semi-diminished fifth 22: 1 275/189 649.254 cents 22: 1 500/343 652.463 cents 22: 8 35/24 653.185 cents septimal semi-diminished fifth 22: 3 225/154 656.394 cents 22: 2 2500/1701 666.654 cents 23: 2 729/500 652.789 cents 23: 1 256/175 658.547 cents 23: 3 22/15 663.049 cents undecimal diminished fifth 23: 5 72/49 666.258 cents Arabic lute grave fifth 23: 4 147/100 666.979 cents 23: 5 81/55 670.188 cents 23: 3 189/128 674.691 cents 23: 2 1078/729 677.240 cents 23: 12 40/27 680.449 cents grave fifth 23: 4 125/84 688.160 cents 24: 7 112/75 694.243 cents marvelous fifth 24: 1 576/385 697.452 cents 24: 24 3/2 701.955 cents perfect fifth 24: 2 810/539 705.164 cents 24: 1 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 24: 5 1100/729 712.215 cents 24: 1 2000/1323 715.424 cents 25: 5 189/125 715.750 cents 25: 2 2916/1925 718.959 cents 25: 3 243/160 723.461 cents acute fifth 25: 3 616/405 726.010 cents 25: 9 32/21 729.219 cents wide fifth 25: 1 343/225 729.940 cents 25: 1 84/55 733.149 cents 25: 2 55/36 733.722 cents undecimal semi-augmented fifth 25: 4 75/49 736.931 cents BP fifth 25: 3 49/32 737.652 cents 25: 2 135/88 740.861 cents 25: 1 1120/729 743.410 cents 25: 5 125/81 751.121 cents 26: 2 192/125 743.014 cents classic diminished sixth 26: 10 54/35 750.725 cents septimal semi-augmented fifth 26: 2 1701/1100 754.656 cents 26: 2 3388/2187 757.777 cents 26: 1 880/567 760.986 cents 26: 1 1600/1029 764.195 cents 26: 13 14/9 764.916 cents septimal minor sixth 26: 3 120/77 768.125 cents 26: 7 25/16 772.627 cents classic augmented fifth 27: 2 972/625 764.520 cents 27: 1 352/225 774.781 cents 27: 1 196/125 778.711 cents 27: 1 432/275 781.920 cents 27: 1 11/7 782.492 cents undecimal augmented fifth 27: 12 63/40 786.422 cents narrow minor sixth 27: 4 243/154 789.631 cents 27: 4 128/81 792.180 cents Pythagorean minor sixth 27: 3 385/243 796.683 cents 27: 12 100/63 799.892 cents quasi-equal minor sixth 28: 1 3969/2500 800.217 cents two (quasi-equal major third) 28: 2 1078/675 810.477 cents 28: 17 8/5 813.686 cents minor sixth 28: 2 864/539 816.895 cents 28: 1 77/48 818.189 cents 28: 8 45/28 821.398 cents septimale wide minor sixth 28: 2 567/352 825.328 cents 28: 1 392/243 827.877 cents 28: 1 2750/1701 831.658 cents 28: 1 5000/3087 834.867 cents 28: 5 175/108 835.588 cents 29: 11 81/50 835.193 cents acute minor sixth 29: 1 512/315 840.950 cents 29: 5 44/27 845.453 cents neutral sixth 29: 4 80/49 848.662 cents smaller approximation to neutral sixth 29: 4 49/30 849.383 cents larger approximation to neutral sixth 29: 5 18/11 852.592 cents undecimal neutral sixth 29: 3 105/64 857.095 cents septimal neutral sixth 29: 6 400/243 862.852 cents grave major sixth 29: 2 625/378 870.564 cents 30: 5 288/175 862.457 cents 30: 1 1029/625 863.178 cents 30: 2 81/49 870.168 cents two (septimal major third, BP third) 30: 2 1323/800 870.889 cents 30: 3 729/440 874.098 cents 30: 4 224/135 876.647 cents narrow septimal major sixth 30: 1 1210/729 877.220 cents 30: 1 2200/1323 880.429 cents 30: 2 539/324 881.150 cents 30: 18 5/3 884.359 cents major sixth, BP sixth 30: 2 900/539 887.568 cents 31: 12 42/25 898.153 cents quasi-equal major sixth 31: 3 648/385 901.362 cents 31: 9 27/16 905.865 cents Pythagorean major sixth 31: 3 1232/729 908.414 cents 31: 6 320/189 911.623 cents 31: 2 275/162 916.125 cents 31: 3 250/147 919.334 cents 31: 2 75/44 923.264 cents 31: 1 1250/729 933.525 cents 32: 2 1701/1000 919.660 cents 32: 3 128/75 925.418 cents diminished seventh 32: 3 77/45 929.920 cents 32: 17 12/7 933.129 cents septimal major sixth 32: 1 343/200 933.850 cents 32: 3 189/110 937.059 cents 32: 1 675/392 940.841 cents 32: 1 441/256 941.562 cents two (narrow fourth) 32: 6 140/81 947.320 cents 32: 4 125/72 955.031 cents classic augmented sixth 33: 5 216/125 946.924 cents semi-augmented sixth 33: 3 243/140 954.635 cents 33: 1 704/405 957.184 cents 33: 2 256/147 960.393 cents 33: 1 392/225 961.114 cents 33: 1 96/55 964.323 cents 33: 2 110/63 964.896 cents 33: 1 600/343 968.105 cents 33: 15 7/4 968.826 cents harmonic seventh 33: 4 135/77 972.035 cents 33: 1 1280/729 974.584 cents grave minor seventh 33: 2 3850/2187 979.086 cents 33: 3 1000/567 982.295 cents 34: 2 44/25 978.691 cents undecimal grave minor seventh 34: 3 441/250 982.621 cents 34: 4 486/275 985.830 cents 34: 2 567/320 990.332 cents 34: 1 2156/1215 992.881 cents 34: 1 2187/1232 993.541 cents 34: 15 16/9 996.090 cents Pythagorean minor seventh 34: 2 385/216 1000.593 cents 34: 11 25/14 1003.802 cents middle minor seventh 35: 20 9/5 1017.596 cents just minor seventh, BP seventh 35: 2 972/539 1020.805 cents 35: 1 1024/567 1023.354 cents 35: 1 11858/6561 1024.648 cents 35: 3 440/243 1027.857 cents 35: 4 800/441 1031.066 cents 35: 4 49/27 1031.787 cents 35: 3 20/11 1034.996 cents large minor seventh 35: 3 175/96 1039.498 cents 36: 3 1134/625 1031.391 cents 36: 2 729/400 1039.103 cents acute minor seventh 36: 1 1232/675 1041.651 cents 36: 5 64/35 1044.860 cents septimal neutral seventh 36: 1 686/375 1045.582 cents 36: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 36: 4 90/49 1052.572 cents 36: 2 147/80 1053.293 cents 36: 5 81/44 1056.502 cents 2nd undecimal neutral seventh 36: 2 448/243 1059.051 cents 36: 12 50/27 1066.762 cents grave major seventh 37: 5 324/175 1066.367 cents 37: 2 352/189 1076.627 cents 37: 1 3773/2025 1077.348 cents 37: 13 28/15 1080.557 cents grave major seventh 37: 4 144/77 1083.766 cents 37: 12 15/8 1088.269 cents classic major seventh 37: 1 3200/1701 1094.027 cents 37: 1 1375/729 1098.529 cents 37: 2 2500/1323 1101.738 cents 38: 1 1176/625 1094.352 cents 38: 9 189/100 1102.063 cents 38: 3 729/385 1105.272 cents 38: 2 256/135 1107.821 cents octave - major chroma 38: 1 243/128 1109.775 cents Pythagorean major seventh 38: 5 154/81 1112.324 cents 38: 14 40/21 1115.533 cents acute major seventh 38: 2 21/11 1119.463 cents undecimal major seventh 38: 1 375/196 1123.244 cents 38: 1 1400/729 1129.723 cents 38: 2 625/324 1137.435 cents octave - major diesis 39: 11 48/25 1129.328 cents classic diminished octave 39: 1 2646/1375 1133.258 cents 39: 9 27/14 1137.039 cents septimal major seventh 39: 1 1408/729 1139.588 cents 39: 1 4235/2187 1144.090 cents 39: 2 1100/567 1147.299 cents 39: 12 35/18 1151.230 cents septimal semi-diminished octave 39: 4 150/77 1154.439 cents 40: 4 243/125 1150.834 cents octave - maximal diesis 40: 3 88/45 1161.094 cents 40: 4 96/49 1164.303 cents 40: 5 49/25 1165.024 cents BP eighth 40: 4 108/55 1168.233 cents 40: 1 675/343 1172.015 cents 40: 5 63/32 1172.736 cents octave - septimal comma 40: 1 4312/2187 1175.285 cents 40: 1 1215/616 1175.945 cents 40: 6 160/81 1178.494 cents octave - syntonic comma 40: 1 1925/972 1182.996 cents 40: 6 125/63 1186.205 cents Highest number of different intervals for one interval class: 13 Average number of different intervals per interval class: 10.05000 = 201/20
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 38 39 40 41 0.0 : 31.8 70.7 87.7 119.4 133.2 182.4 203.9 231.2 266.9 301.8 315.6 354.5 386.3 400.1 435.1 470.8 498.0 519.6 568.7 582.5 617.5 631.3 680.4 702.0 729.2 764.9 799.9 813.7 845.5 884.4 905.9 933.1 968.8 996.1 1017.6 1066.8 1088.3 1112.3 1137.0 1165.0 1200.0 31.8 : 38.9 55.9 87.7 101.5 150.6 172.1 199.4 235.1 270.1 283.9 322.8 354.5 368.3 403.3 439.0 466.3 487.8 537.0 550.7 585.7 599.5 648.7 670.2 697.5 733.1 768.1 781.9 813.7 852.6 874.1 901.4 937.1 964.3 985.8 1035.0 1056.5 1080.6 1105.3 1133.3 1168.2 1200.0 70.7 : 17.0 48.8 62.6 111.7 133.2 160.5 196.2 231.2 245.0 283.9 315.6 329.4 364.4 400.1 427.4 448.9 498.0 511.8 546.8 560.6 609.8 631.3 658.5 694.2 729.2 743.0 774.8 813.7 835.2 862.5 898.2 925.4 946.9 996.1 1017.6 1041.7 1066.4 1094.4 1129.3 1161.1 1200.0 87.7 : 31.8 45.6 94.7 116.2 143.5 179.2 214.2 228.0 266.9 298.6 312.4 347.4 383.1 410.4 431.9 481.0 494.8 529.8 543.6 592.8 614.3 641.5 677.2 712.2 726.0 757.8 796.7 818.2 845.5 881.1 908.4 929.9 979.1 1000.6 1024.6 1049.4 1077.3 1112.3 1144.1 1183.0 1200.0 119.4 : 13.8 63.0 84.5 111.7 147.4 182.4 196.2 235.1 266.9 280.7 315.6 351.3 378.6 400.1 449.3 463.1 498.0 511.8 561.0 582.5 609.8 645.5 680.4 694.2 726.0 764.9 786.4 813.7 849.4 876.6 898.2 947.3 968.8 992.9 1017.6 1045.6 1080.6 1112.3 1151.2 1168.2 1200.0 133.2 : 49.2 70.7 97.9 133.6 168.6 182.4 221.3 253.1 266.9 301.8 337.5 364.8 386.3 435.5 449.3 484.3 498.0 547.2 568.7 596.0 631.7 666.7 680.4 712.2 751.1 772.6 799.9 835.6 862.9 884.4 933.5 955.0 979.1 1003.8 1031.8 1066.8 1098.5 1137.4 1154.4 1186.2 1200.0 182.4 : 21.5 48.8 84.5 119.4 133.2 172.1 203.9 217.7 252.7 288.4 315.6 337.1 386.3 400.1 435.1 448.9 498.0 519.6 546.8 582.5 617.5 631.3 663.0 702.0 723.5 750.7 786.4 813.7 835.2 884.4 905.9 929.9 954.6 982.6 1017.6 1049.4 1088.3 1105.3 1137.0 1150.8 1200.0 203.9 : 27.3 63.0 97.9 111.7 150.6 182.4 196.2 231.2 266.9 294.1 315.6 364.8 378.6 413.6 427.4 476.5 498.0 525.3 561.0 596.0 609.8 641.5 680.4 702.0 729.2 764.9 792.2 813.7 862.9 884.4 908.4 933.1 961.1 996.1 1027.9 1066.8 1083.8 1115.5 1129.3 1178.5 1200.0 231.2 : 35.7 70.7 84.5 123.4 155.1 168.9 203.9 239.6 266.9 288.4 337.5 351.3 386.3 400.1 449.3 470.8 498.0 533.7 568.7 582.5 614.3 653.2 674.7 702.0 737.7 764.9 786.4 835.6 857.1 881.1 905.9 933.9 968.8 1000.6 1039.5 1056.5 1088.3 1102.1 1151.2 1172.7 1200.0 266.9 : 35.0 48.8 87.7 119.4 133.2 168.2 203.9 231.2 252.7 301.8 315.6 350.6 364.4 413.6 435.1 462.3 498.0 533.0 546.8 578.6 617.5 639.0 666.3 702.0 729.2 750.7 799.9 821.4 845.5 870.2 898.2 933.1 964.9 1003.8 1020.8 1052.6 1066.4 1115.5 1137.0 1164.3 1200.0 301.8 : 13.8 52.7 84.5 98.3 133.2 168.9 196.2 217.7 266.9 280.7 315.6 329.4 378.6 400.1 427.4 463.1 498.0 511.8 543.6 582.5 604.0 631.3 667.0 694.2 715.7 764.9 786.4 810.5 835.2 863.2 898.2 929.9 968.8 985.8 1017.6 1031.4 1080.6 1102.1 1129.3 1165.0 1200.0 315.6 : 38.9 70.7 84.5 119.4 155.1 182.4 203.9 253.1 266.9 301.8 315.6 364.8 386.3 413.6 449.3 484.3 498.0 529.8 568.7 590.2 617.5 653.2 680.4 702.0 751.1 772.6 796.7 821.4 849.4 884.4 916.1 955.0 972.0 1003.8 1017.6 1066.8 1088.3 1115.5 1151.2 1186.2 1200.0 354.5 : 31.8 45.6 80.5 116.2 143.5 165.0 214.2 228.0 262.9 276.7 325.9 347.4 374.7 410.4 445.3 459.1 490.9 529.8 551.3 578.6 614.3 641.5 663.0 712.2 733.7 757.8 782.5 810.5 845.5 877.2 916.1 933.1 964.9 978.7 1027.9 1049.4 1076.6 1112.3 1147.3 1161.1 1200.0 386.3 : 13.8 48.8 84.5 111.7 133.2 182.4 196.2 231.2 245.0 294.1 315.6 342.9 378.6 413.6 427.4 459.1 498.0 519.6 546.8 582.5 609.8 631.3 680.4 702.0 726.0 750.7 778.7 813.7 845.5 884.4 901.4 933.1 946.9 996.1 1017.6 1044.9 1080.6 1115.5 1129.3 1168.2 1200.0 400.1 : 35.0 70.7 97.9 119.4 168.6 182.4 217.4 231.2 280.3 301.8 329.1 364.8 399.8 413.6 445.3 484.3 505.8 533.0 568.7 596.0 617.5 666.7 688.2 712.2 736.9 764.9 799.9 831.7 870.6 887.6 919.3 933.1 982.3 1003.8 1031.1 1066.8 1101.7 1115.5 1154.4 1186.2 1200.0 435.1 : 35.7 63.0 84.5 133.6 147.4 182.4 196.2 245.4 266.9 294.1 329.8 364.8 378.6 410.4 449.3 470.8 498.0 533.7 561.0 582.5 631.7 653.2 677.2 702.0 729.9 764.9 796.7 835.6 852.6 884.4 898.2 947.3 968.8 996.1 1031.8 1066.8 1080.6 1119.5 1151.2 1165.0 1200.0 470.8 : 27.3 48.8 97.9 111.7 146.7 160.5 209.7 231.2 258.4 294.1 329.1 342.9 374.7 413.6 435.1 462.3 498.0 525.3 546.8 596.0 617.5 641.5 666.3 694.2 729.2 761.0 799.9 816.9 848.7 862.5 911.6 933.1 960.4 996.1 1031.1 1044.9 1083.8 1115.5 1129.3 1164.3 1200.0 498.0 : 21.5 70.7 84.5 119.4 133.2 182.4 203.9 231.2 266.9 301.8 315.6 347.4 386.3 407.8 435.1 470.8 498.0 519.6 568.7 590.2 614.3 639.0 667.0 702.0 733.7 772.6 789.6 821.4 835.2 884.4 905.9 933.1 968.8 1003.8 1017.6 1056.5 1088.3 1102.1 1137.0 1172.7 1200.0 519.6 : 49.2 63.0 97.9 111.7 160.9 182.4 209.7 245.4 280.3 294.1 325.9 364.8 386.3 413.6 449.3 476.5 498.0 547.2 568.7 592.8 617.5 645.5 680.4 712.2 751.1 768.1 799.9 813.7 862.9 884.4 911.6 947.3 982.3 996.1 1035.0 1066.8 1080.6 1115.5 1151.2 1178.5 1200.0 568.7 : 13.8 48.8 62.6 111.7 133.2 160.5 196.2 231.2 245.0 276.7 315.6 337.1 364.4 400.1 427.4 448.9 498.0 519.6 543.6 568.3 596.3 631.3 663.0 702.0 719.0 750.7 764.5 813.7 835.2 862.5 898.2 933.1 946.9 985.8 1017.6 1031.4 1066.4 1102.1 1129.3 1150.8 1200.0 582.5 : 35.0 48.8 97.9 119.4 146.7 182.4 217.4 231.2 262.9 301.8 323.4 350.6 386.3 413.6 435.1 484.3 505.8 529.8 554.5 582.5 617.5 649.3 688.2 705.2 736.9 750.7 799.9 821.4 848.7 884.4 919.3 933.1 972.0 1003.8 1017.6 1052.6 1088.3 1115.5 1137.0 1186.2 1200.0 617.5 : 13.8 63.0 84.5 111.7 147.4 182.4 196.2 228.0 266.9 288.4 315.6 351.3 378.6 400.1 449.3 470.8 494.8 519.6 547.5 582.5 614.3 653.2 670.2 702.0 715.7 764.9 786.4 813.7 849.4 884.4 898.2 937.1 968.8 982.6 1017.6 1053.3 1080.6 1102.1 1151.2 1165.0 1200.0 631.3 : 49.2 70.7 97.9 133.6 168.6 182.4 214.2 253.1 274.6 301.8 337.5 364.8 386.3 435.5 457.0 481.0 505.8 533.7 568.7 600.5 639.4 656.4 688.2 702.0 751.1 772.6 799.9 835.6 870.6 884.4 923.3 955.0 968.8 1003.8 1039.5 1066.8 1088.3 1137.4 1151.2 1186.2 1200.0 680.4 : 21.5 48.8 84.5 119.4 133.2 165.0 203.9 225.4 252.7 288.4 315.6 337.1 386.3 407.8 431.9 456.6 484.6 519.6 551.3 590.2 607.2 639.0 652.8 702.0 723.5 750.7 786.4 821.4 835.2 874.1 905.9 919.7 954.6 990.3 1017.6 1039.1 1088.3 1102.1 1137.0 1150.8 1200.0 702.0 : 27.3 63.0 97.9 111.7 143.5 182.4 203.9 231.2 266.9 294.1 315.6 364.8 386.3 410.4 435.1 463.1 498.0 529.8 568.7 585.7 617.5 631.3 680.4 702.0 729.2 764.9 799.9 813.7 852.6 884.4 898.2 933.1 968.8 996.1 1017.6 1066.8 1080.6 1115.5 1129.3 1178.5 1200.0 729.2 : 35.7 70.7 84.5 116.2 155.1 176.6 203.9 239.6 266.9 288.4 337.5 359.0 383.1 407.8 435.8 470.8 502.5 541.5 558.5 590.2 604.0 653.2 674.7 702.0 737.7 772.6 786.4 825.3 857.1 870.9 905.9 941.6 968.8 990.3 1039.5 1053.3 1088.3 1102.1 1151.2 1172.7 1200.0 764.9 : 35.0 48.8 80.5 119.4 140.9 168.2 203.9 231.2 252.7 301.8 323.4 347.4 372.1 400.1 435.1 466.9 505.8 522.8 554.5 568.3 617.5 639.0 666.3 702.0 736.9 750.7 789.6 821.4 835.2 870.2 905.9 933.1 954.6 1003.8 1017.6 1052.6 1066.4 1115.5 1137.0 1164.3 1200.0 799.9 : 13.8 45.6 84.5 106.0 133.2 168.9 196.2 217.7 266.9 288.4 312.4 337.1 365.1 400.1 431.9 470.8 487.8 519.6 533.3 582.5 604.0 631.3 667.0 702.0 715.7 754.7 786.4 800.2 835.2 870.9 898.2 919.7 968.8 982.6 1017.6 1031.4 1080.6 1102.1 1129.3 1165.0 1200.0 813.7 : 31.8 70.7 92.2 119.4 155.1 182.4 203.9 253.1 274.6 298.6 323.4 351.3 386.3 418.1 457.0 474.0 505.8 519.6 568.7 590.2 617.5 653.2 688.2 702.0 740.9 772.6 786.4 821.4 857.1 884.4 905.9 955.0 968.8 1003.8 1017.6 1066.8 1088.3 1115.5 1151.2 1186.2 1200.0 845.5 : 38.9 60.4 87.7 123.4 150.6 172.1 221.3 242.8 266.9 291.6 319.6 354.5 386.3 425.2 442.2 474.0 487.8 537.0 558.5 585.7 621.4 656.4 670.2 709.1 740.9 754.7 789.6 825.3 852.6 874.1 923.3 937.1 972.0 985.8 1035.0 1056.5 1083.8 1119.5 1154.4 1168.2 1200.0 884.4 : 21.5 48.8 84.5 111.7 133.2 182.4 203.9 228.0 252.7 280.7 315.6 347.4 386.3 403.3 435.1 448.9 498.0 519.6 546.8 582.5 617.5 631.3 670.2 702.0 715.7 750.7 786.4 813.7 835.2 884.4 898.2 933.1 946.9 996.1 1017.6 1044.9 1080.6 1115.5 1129.3 1161.1 1200.0 905.9 : 27.3 63.0 90.2 111.7 160.9 182.4 206.5 231.2 259.2 294.1 325.9 364.8 381.8 413.6 427.4 476.5 498.0 525.3 561.0 596.0 609.8 648.7 680.4 694.2 729.2 764.9 792.2 813.7 862.9 876.6 911.6 925.4 974.6 996.1 1023.4 1059.1 1094.0 1107.8 1139.6 1178.5 1200.0 933.1 : 35.7 63.0 84.5 133.6 155.1 179.2 203.9 231.9 266.9 298.6 337.5 354.5 386.3 400.1 449.3 470.8 498.0 533.7 568.7 582.5 621.4 653.2 667.0 702.0 737.7 764.9 786.4 835.6 849.4 884.4 898.2 947.3 968.8 996.1 1031.8 1066.8 1080.6 1112.3 1151.2 1172.7 1200.0 968.8 : 27.3 48.8 97.9 119.4 143.5 168.2 196.2 231.2 262.9 301.8 318.9 350.6 364.4 413.6 435.1 462.3 498.0 533.0 546.8 585.7 617.5 631.3 666.3 702.0 729.2 750.7 799.9 813.7 848.7 862.5 911.6 933.1 960.4 996.1 1031.1 1044.9 1076.6 1115.5 1137.0 1164.3 1200.0 996.1 : 21.5 70.7 92.2 116.2 140.9 168.9 203.9 235.7 274.6 291.6 323.4 337.1 386.3 407.8 435.1 470.8 505.8 519.6 558.5 590.2 604.0 639.0 674.7 702.0 723.5 772.6 786.4 821.4 835.2 884.4 905.9 933.1 968.8 1003.8 1017.6 1049.4 1088.3 1109.8 1137.0 1172.7 1200.0 1017.6: 49.2 70.7 94.7 119.4 147.4 182.4 214.2 253.1 270.1 301.8 315.6 364.8 386.3 413.6 449.3 484.3 498.0 537.0 568.7 582.5 617.5 653.2 680.4 702.0 751.1 764.9 799.9 813.7 862.9 884.4 911.6 947.3 982.3 996.1 1027.9 1066.8 1088.3 1115.5 1151.2 1178.5 1200.0 1066.8: 21.5 45.6 70.3 98.3 133.2 165.0 203.9 220.9 252.7 266.5 315.6 337.1 364.4 400.1 435.1 448.9 487.8 519.6 533.3 568.3 604.0 631.3 652.8 702.0 715.7 750.7 764.5 813.7 835.2 862.5 898.2 933.1 946.9 978.7 1017.6 1039.1 1066.4 1102.1 1129.3 1150.8 1200.0 1088.3: 24.1 48.8 76.8 111.7 143.5 182.4 199.4 231.2 245.0 294.1 315.6 342.9 378.6 413.6 427.4 466.3 498.0 511.8 546.8 582.5 609.8 631.3 680.4 694.2 729.2 743.0 792.2 813.7 841.0 876.6 911.6 925.4 957.2 996.1 1017.6 1044.9 1080.6 1107.8 1129.3 1178.5 1200.0 1112.3: 24.7 52.7 87.7 119.4 158.3 175.4 207.1 220.9 270.1 291.6 318.9 354.5 389.5 403.3 442.2 474.0 487.8 522.8 558.5 585.7 607.2 656.4 670.2 705.2 719.0 768.1 789.6 816.9 852.6 887.6 901.4 933.1 972.0 993.5 1020.8 1056.5 1083.8 1105.3 1154.4 1175.9 1200.0 1137.0: 28.0 63.0 94.7 133.6 150.6 182.4 196.2 245.4 266.9 294.1 329.8 364.8 378.6 417.5 449.3 463.1 498.0 533.7 561.0 582.5 631.7 645.5 680.4 694.2 743.4 764.9 792.2 827.9 862.9 876.6 908.4 947.3 968.8 996.1 1031.8 1059.1 1080.6 1129.7 1151.2 1175.3 1200.0 1165.0: 35.0 66.7 105.6 122.7 154.4 168.2 217.4 238.9 266.1 301.8 336.8 350.6 389.5 421.3 435.1 470.1 505.8 533.0 554.5 603.7 617.5 652.5 666.3 715.4 736.9 764.2 799.9 834.9 848.7 880.4 919.3 940.8 968.1 1003.8 1031.1 1052.6 1101.7 1123.2 1147.3 1172.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 13.7948 .. 49.1661 cents 15625/15309, 35.3714 cents 126/125, 13.7948 cents 2: 45.5614 .. 70.6724 cents 625/616, 25.1110 cents 6237/6250,-3.6047 cents 3: 62.5651 .. 105.6480 cents 390625/381024, 43.0829 cents 15552/15625,-8.1073 cents 4: 98.2620 .. 133.6333 cents 15625/15309, 35.3714 cents 388962/390625,-7.3861 cents 5: 133.2376 .. 168.6089 cents 15625/15309, 35.3714 cents 4374/4375,-0.3958 cents 6: 160.5017 .. 182.4037 cents 875/864, 21.9020 cents 15552/15625,-8.1073 cents 7: 196.1985 .. 221.3095 cents 625/616, 25.1110 cents 126/125, 13.7948 cents 8: 217.7048 .. 253.0761 cents 15625/15309, 35.3714 cents 6237/6250,-3.6047 cents 9: 244.9689 .. 280.3402 cents 15625/15309, 35.3714 cents 15552/15625,-8.1073 cents 10: 266.4751 .. 301.8465 cents 15625/15309, 35.3714 cents 1240029/1250000,-13.8651 cents 11: 312.4323 .. 337.5433 cents 625/616, 25.1110 cents 3773/3750, 10.5858 cents 12: 329.4361 .. 364.8074 cents 15625/15309, 35.3714 cents 15552/15625,-8.1073 cents 13: 364.4117 .. 399.7830 cents 15625/15309, 35.3714 cents 4374/4375,-0.3958 cents 14: 400.1085 .. 435.4799 cents 15625/15309, 35.3714 cents 250047/250000, 0.3254 cents 15: 427.3726 .. 456.9861 cents 3125/3072, 29.6136 cents 15552/15625,-8.1073 cents 16: 448.8789 .. 484.2502 cents 15625/15309, 35.3714 cents 15552/15625,-8.1073 cents 17: 484.5757 .. 505.7565 cents 3125/3087, 21.1808 cents 250047/250000, 0.3254 cents 18: 511.8398 .. 547.2111 cents 15625/15309, 35.3714 cents 3136/3125, 6.0832 cents 19: 533.3461 .. 568.7174 cents 15625/15309, 35.3714 cents 1240029/1250000,-13.8651 cents 20: 560.6101 .. 603.6930 cents 390625/381024, 43.0829 cents 15552/15625,-8.1073 cents 21: 596.3070 .. 639.3899 cents 390625/381024, 43.0829 cents 388962/390625,-7.3861 cents 22: 631.2826 .. 666.6539 cents 15625/15309, 35.3714 cents 15552/15625,-8.1073 cents 23: 652.7889 .. 688.1602 cents 15625/15309, 35.3714 cents 1240029/1250000,-13.8651 cents 24: 694.2435 .. 715.4243 cents 3125/3087, 21.1808 cents 3136/3125, 6.0832 cents 25: 715.7498 .. 751.1211 cents 15625/15309, 35.3714 cents 250047/250000, 0.3254 cents 26: 743.0139 .. 772.6274 cents 3125/3072, 29.6136 cents 15552/15625,-8.1073 cents 27: 764.5201 .. 799.8915 cents 15625/15309, 35.3714 cents 15552/15625,-8.1073 cents 28: 800.2170 .. 835.5883 cents 15625/15309, 35.3714 cents 250047/250000, 0.3254 cents 29: 835.1926 .. 870.5639 cents 15625/15309, 35.3714 cents 4374/4375,-0.3958 cents 30: 862.4567 .. 887.5677 cents 625/616, 25.1110 cents 15552/15625,-8.1073 cents 31: 898.1535 .. 933.5249 cents 15625/15309, 35.3714 cents 3773/3750, 10.5858 cents 32: 919.6598 .. 955.0311 cents 15625/15309, 35.3714 cents 1240029/1250000,-13.8651 cents 33: 946.9239 .. 982.2952 cents 15625/15309, 35.3714 cents 15552/15625,-8.1073 cents 34: 978.6905 .. 1003.8015 cents 625/616, 25.1110 cents 6237/6250,-3.6047 cents 35: 1017.5963 .. 1039.4983 cents 875/864, 21.9020 cents 126/125, 13.7948 cents 36: 1031.3911 .. 1066.7624 cents 15625/15309, 35.3714 cents 15552/15625,-8.1073 cents 37: 1066.3667 .. 1101.7380 cents 15625/15309, 35.3714 cents 4374/4375,-0.3958 cents 38: 1094.3520 .. 1137.4349 cents 390625/381024, 43.0829 cents 388962/390625,-7.3861 cents 39: 1129.3276 .. 1154.4386 cents 625/616, 25.1110 cents 15552/15625,-8.1073 cents 40: 1150.8339 .. 1186.2052 cents 15625/15309, 35.3714 cents 6237/6250,-3.6047 cents
SHOW DATA
Number of notes : 41 -- Interval properties -- Smallest interval : 126/125, 13.7948 cents, class 1 Average step (divided formal octave): 29.2683 cents Largest one step interval : 250/243, 49.1661 cents Average / Smallest step : 2.121695 Largest / Average step : 1.679843 Largest / Smallest step : 3.564115 Median interval of one step : 686/675, 27.9853 cents, amount: 1 Least squares average step : 29.27814 cents, oct.: 1200.40383 cents Scale is not proper Step pattern alph. order: ABCADEFGHIDBADIHGFEDIDEFGHIDABFGHGFEFJKLI Step pattern size order : HKBHALCFJIAKHAIJFCLAIALCFJIAHKCFJFCLCDEGI Scale is a Constant Structure, by a margin of 0.32544 cents Scale diversity : 1.493177 Lumma stability : 0.074849 Lumma impropriety factor : 0.172602 Number of different interval sizes : 402 = 10.05000 / class Number of one step interval sizes : 12 Highest interval variety : 13 Mean interval variety : 10.05000 = 201/20 Median interval variety : 7.5 Lowest interval variety : 7 Smallest interval difference : 250047/250000, 0.3254 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 24 Most common triad is 0.0 498.045 701.955 cents, amount: 15 Number of recognisable fifths : 52, average 703.2559 cents Number of appreciable fifths : 40, average 702.1144 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 5 7 9 Length of longest harmonic part : 2 at degree 8 Length of longest subharmonic part : 2 at degree 14 Formal octave complements present : 33 = 80.4878% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.008120 Average absolute harmonicity : 0.094815 Specific harmonicity : 0.073930 Fundamental : 1/2494800, -21.2505 octaves, 0.0001 Hz. Guide tone : 34927200, 25.0578 octaves, 9137848444.381 Hz. Exponens Consonantiae : 8.713638E+13, 46.30834 octaves Euler's gradus suavitatis : 80 Sum of Mann's harmonic distance : 948.5, average 23.13415 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 47.43167, average 1.15687 Sum of Tenney's harmonic distance : 94.76700, average 2.31139 Vogel's harmonic complexity : 45.02439 Wille's k value : 2104987 Wilson's harmonic complexity : 87 Rectangular lattice diameter : 17 Triangular lattice diameter : 8 Lattice compactness : 3580.13134, average 4.15811 Lattice compactness (without 2's) : 2643.86675, average 3.07069 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.09756 66 1 3: -4 .. 4 0.07317 67 5 5: -2 .. 2 0.12195 31 14 7: -1 .. 2 -0.02439 19 16 11: -1 .. 1 0.02439 5 5 Average exponent except 2's : 8 / 41 = 0.19512 Average absolute exponent except 2's: 122 / 41 = 2.97561 Scale is JI-epimorphic with val: <41 65 95 115 142| = patent
FIT/MODE
41: 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 1 1 1 1 SP B ME I SD: 6.3353 c. M: 13.1039 c. 44: 1 2 0 1 1 2 0 1 2 1 1 1 1 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 1 1 1 1 2 1 0 2 1 1 1 1 1 N D3 SD: 7.5071 c. M:-13.0009 c. 46: 1 2 0 2 0 2 1 1 1 2 0 2 1 0 2 1 1 1 2 0 2 0 2 1 1 1 2 0 1 2 1 1 1 1 1 2 1 1 1 1 1 N D3 SD: 6.6024 c. M:-11.1970 c. 53: 1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 1 2 1 1 2 1 1 2 1 1 1 1 2 N D3 SD: 4.5992 c. M: 10.3074 c. 60: 2 2 0 2 1 2 1 2 1 2 1 2 1 1 2 2 1 1 2 1 2 1 2 1 1 2 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 N SD: 5.7703 c. M:-9.3276 c. 61: 2 2 0 2 1 2 1 2 2 1 1 2 2 0 2 2 1 1 3 1 1 1 3 1 1 2 2 0 2 2 1 1 2 2 1 2 1 2 1 1 2 N SD: 5.7147 c. M:-8.9876 c. 63: 2 2 1 1 1 3 1 1 2 2 1 2 1 1 2 2 1 1 3 1 1 1 3 1 1 2 2 1 1 2 2 1 2 1 1 3 1 1 2 1 2 N SD: 5.2652 c. M:-8.4207 c. 64: 2 2 1 1 1 3 1 1 2 2 1 2 2 0 2 2 2 1 2 1 2 1 2 1 2 2 2 0 2 2 1 2 2 1 1 3 1 1 2 1 2 N SD: 4.8825 c. M:-8.2050 c. 68: 2 2 1 2 1 2 2 1 2 2 1 2 2 1 2 2 1 1 3 1 2 1 3 1 1 2 2 1 2 2 1 2 2 1 2 2 2 1 1 2 2 N SD: 4.7011 c. M: 7.9389 c. 71: 2 2 1 2 1 3 1 2 2 2 1 2 2 1 2 2 1 2 3 0 3 0 3 2 1 2 2 1 2 2 2 1 2 2 1 3 1 2 1 2 2 N SD: 4.4540 c. M:-7.9042 c. 72: 2 2 1 2 1 3 1 2 2 2 1 2 2 1 2 2 2 1 3 1 2 1 3 1 2 2 2 1 2 2 1 2 2 2 1 3 1 2 1 2 2 N D3 I SD: 2.7917 c. M: 5.8650 c. 99: 3 3 1 3 1 4 2 2 3 3 1 3 3 1 3 3 2 2 4 1 3 1 4 2 2 3 3 1 3 3 2 2 3 2 2 4 2 2 2 2 3 N SD: 1.7644 c. M:-4.5970 c. 114: 3 4 1 3 2 4 2 3 3 4 1 4 3 1 3 4 2 2 5 1 4 1 5 2 2 4 3 1 3 4 2 3 3 3 2 4 2 3 2 3 3 N SD: 2.9408 c. M: 4.0582 c. 118: 3 4 2 3 1 5 2 3 3 4 1 4 3 1 4 3 3 2 5 1 4 1 5 2 3 3 4 1 3 4 2 3 3 3 2 5 2 2 3 3 3 N SD: 2.0892 c. M:-4.4671 c. 138: 4 4 2 4 1 6 2 4 4 4 1 5 3 2 4 4 3 3 5 2 4 2 5 3 3 4 4 2 3 5 2 3 4 4 2 6 2 3 3 3 4 N SD: 2.2937 c. M:-3.9100 c. 140: 4 4 2 4 2 5 3 3 4 4 2 4 4 2 4 4 3 3 5 2 4 2 5 3 3 4 4 2 4 4 3 3 4 3 3 5 3 3 3 3 4 P SD: 2.1015 c. M: 3.9053 c. 146: 4 5 2 4 1 6 3 3 4 5 1 5 4 2 4 4 4 2 6 2 4 2 6 2 4 4 4 2 4 5 2 4 4 3 3 6 2 3 3 4 4 N SD: 2.2418 c. M: 3.8572 c. 150: 4 5 2 4 2 6 3 3 4 5 1 5 4 2 4 5 3 3 6 2 4 2 6 3 3 5 4 2 4 5 2 4 4 4 2 6 3 3 3 4 4 N SD: 2.0785 c. M:-4.0900 c. 151: 4 5 2 4 2 6 3 3 5 4 2 5 4 1 5 4 4 2 7 1 5 1 7 2 4 4 5 1 4 5 3 3 5 3 3 6 3 3 3 4 4 N SD: 2.2212 c. M:-3.4680 c. 152: 4 5 2 4 2 6 3 3 5 4 2 5 4 2 4 5 3 3 6 2 4 2 6 3 3 5 4 2 4 5 3 3 5 3 3 6 3 3 3 4 4 N SD: 1.4727 c. M:-3.3967 c. 159: 4 5 3 4 2 6 3 4 4 5 2 5 4 2 5 4 4 3 6 2 5 2 6 3 4 4 5 2 4 5 3 4 4 4 3 6 3 3 4 3 5 N SD: 1.9212 c. M:-2.8899 c. 171: 5 5 2 5 2 7 3 4 5 5 2 6 4 2 5 5 4 3 7 2 5 2 7 3 4 5 5 2 4 6 3 4 5 4 3 7 3 4 3 4 5 N SD: 1.2162 c. M: 3.4656 c. 183: 5 6 2 5 2 8 3 4 6 5 2 6 5 2 5 6 4 3 8 2 5 2 8 3 4 6 5 2 5 6 3 4 6 4 3 8 3 4 3 5 5 N SD: 1.4464 c. M: 2.6129 c. 204: 5 7 3 5 3 8 4 4 6 6 3 6 6 2 6 6 5 3 9 2 6 2 9 3 5 6 6 2 6 6 4 5 6 4 4 8 4 4 4 5 6 N SD: 1.4858 c. M: 2.3549 c. 217: 6 7 3 6 2 9 4 5 6 7 2 7 6 2 7 6 5 4 9 2 7 2 9 4 5 6 7 2 6 7 4 5 6 5 4 9 4 4 5 5 6 N SD: 1.2038 c. M:-2.3009 c. 224: 6 7 3 6 3 9 4 5 7 6 3 7 6 3 6 7 5 4 9 3 6 3 9 4 5 7 6 3 6 7 4 5 7 5 4 9 4 5 4 5 7 N SD: 1.0603 c. M: 2.5244 c. 237: 6 8 3 7 2 10 4 6 7 7 2 8 6 3 7 7 5 5 9 3 7 3 9 5 5 7 7 3 6 8 4 5 7 6 4 10 4 5 5 5 7 N SD: 1.3126 c. M:-2.2014 c. 243: 6 8 4 6 3 10 4 6 7 7 3 8 6 3 7 7 6 4 10 3 7 3 10 4 6 7 7 3 6 8 4 6 7 6 4 10 4 5 5 6 7 N SD: 1.0183 c. M: 2.1613 c. 261: 7 8 4 7 3 11 4 6 8 8 3 8 7 3 8 7 6 5 11 3 7 3 11 5 6 7 8 3 7 8 5 6 8 6 4 11 5 5 5 6 8 N SD: 1.1741 c. M: 1.8154 c. 270: 7 9 4 7 3 11 5 6 8 8 3 9 7 3 8 8 6 5 11 3 8 3 11 5 6 8 8 3 7 9 5 6 8 6 5 11 5 5 6 6 8 N SD: 0.5043 c. M: 1.2127 c. 342: 9 11 5 9 4 14 6 8 10 10 4 11 9 4 10 10 8 6 14 4 10 4 14 6 8 10 10 4 9 11 6 8 10 8 6 14 6 7 7 8 10 N SD: 0.2826 c. M: 0.6055 c. 612: 16 20 9 16 7 25 11 14 18 18 7 20 16 7 18 18 14 11 25 7 18 7 25 11 14 18 18 7 16 20 11 14 18 14 11 25 11 12 13 14 18 N SD: 0.2025 c. M:-0.5591 c. 711: 19 23 10 19 8 29 13 16 21 21 8 23 19 8 21 21 16 13 29 8 21 8 29 13 16 21 21 8 19 23 13 16 21 16 13 29 13 14 15 16 21 N SD: 0.2335 c. M:-0.5136 c. 764: 20 25 11 20 9 31 14 17 23 22 9 25 20 9 22 23 17 14 31 9 22 9 31 14 17 23 22 9 20 25 14 17 23 17 14 31 14 15 16 18 22 N SD: 0.2638 c. M:-0.4268 c. 783: 21 25 11 21 9 32 14 18 23 23 9 25 21 9 23 23 18 14 32 9 23 9 32 14 18 23 23 9 21 25 14 18 23 18 14 32 14 16 16 18 23 N SD: 0.2024 c. M:-0.5241 c. 935: 25 30 13 25 11 38 17 21 28 27 11 30 25 11 27 28 21 17 38 11 27 11 38 17 21 28 27 11 25 30 17 21 28 21 17 38 17 19 19 22 27 N SD: 0.2039 c. M: 0.4034 c. 954: 25 31 14 25 11 39 17 22 28 28 11 31 25 11 28 28 22 17 39 11 28 11 39 17 22 28 28 11 25 31 17 22 28 22 17 39 17 19 20 22 28 N SD: 0.1842 c. M:-0.3742 c. 1053: 28 34 15 28 12 43 19 24 31 31 12 34 28 12 31 31 24 19 43 12 31 12 43 19 24 31 31 12 28 34 19 24 31 24 19 43 19 21 22 24 31 N SD: 0.1398 c. M: 0.3520 c. 1106: 29 36 16 29 13 45 20 25 33 32 13 36 29 13 32 33 25 20 45 13 32 13 45 20 25 33 32 13 29 36 20 25 33 25 20 45 20 22 23 26 32 N SD: 0.1503 c. M: 0.3019 c. 1236: 33 40 17 33 14 51 22 28 37 36 14 40 33 14 36 37 28 22 51 14 36 14 51 22 28 37 36 14 33 40 22 28 37 28 22 51 22 25 25 29 36 N SD: 0.1419 c. M:-0.2975 c. 1277: 34 41 18 34 15 52 23 29 38 37 15 41 34 15 37 38 29 23 52 15 37 15 52 23 29 38 37 15 34 41 23 29 38 29 23 52 23 26 26 30 37 N SD: 0.1427 c. M: 0.2838 c. 1395: 37 45 20 37 16 57 25 32 41 41 16 45 37 16 41 41 32 25 57 16 41 16 57 25 32 41 41 16 37 45 25 32 41 32 25 57 25 28 29 32 41 N SD: 0.1331 c. M: 0.2932 c. 1407: 37 46 20 37 16 58 25 32 42 41 16 46 37 16 41 42 32 25 58 16 41 16 58 25 32 42 41 16 37 46 25 32 42 32 25 58 25 28 29 33 41 N SD: 0.1174 c. M:-0.2504 c. 1506: 40 49 21 40 17 62 27 34 45 44 17 49 40 17 44 45 34 27 62 17 44 17 62 27 34 45 44 17 40 49 27 34 45 34 27 62 27 30 31 35 44 N SD: 0.1074 c. M:-0.2439 c. 1547: 41 50 22 41 18 63 28 35 46 45 18 50 41 18 45 46 35 28 63 18 45 18 63 28 35 46 45 18 41 50 28 35 46 35 28 63 28 31 32 36 45 N SD: 0.0934 c. M: 0.1819 c. 1848: 49 60 26 49 21 76 33 42 55 54 21 60 49 21 54 55 42 33 76 21 54 21 76 33 42 55 54 21 49 60 33 42 55 42 33 76 33 37 38 43 54 N SD: 0.0607 c. M: 0.1207 c. 2190: 58 71 31 58 25 90 39 50 65 64 25 71 58 25 64 65 50 39 90 25 64 25 90 39 50 65 64 25 58 71 39 50 65 50 39 90 39 44 45 51 64 N SD: 0.0606 c. M: 0.1116 c. 2342: 62 76 33 62 27 96 42 53 70 68 27 76 62 27 68 70 53 42 96 27 68 27 96 42 53 70 68 27 62 76 42 53 70 53 42 96 42 47 48 55 68 N SD: 0.0538 c. M:-0.1336 c. 2684: 71 87 38 71 31 110 48 61 80 78 31 87 71 31 78 80 61 48 110 31 78 31 110 48 61 80 78 31 71 87 48 61 80 61 48 110 48 54 55 63 78 N SD: 0.0393 c. M:-0.1023 c. 2954: 78 96 42 78 34 121 53 67 88 86 34 96 78 34 86 88 67 53 121 34 86 34 121 53 67 88 86 34 78 96 53 67 88 67 53 121 53 59 61 69 86 N SD: 0.0333 c. M:-0.0907 c. 3296: 87 107 47 87 38 135 59 75 98 96 38 107 87 38 96 98 75 59 135 38 96 38 135 59 75 98 96 38 87 107 59 75 98 75 59 135 59 66 68 77 96 N SD: 0.0320 c. M: 0.0919 c. 3395: 90 110 48 90 39 139 61 77 101 99 39 110 90 39 99 101 77 61 139 39 99 39 139 61 77 101 99 39 90 110 61 77 101 77 61 139 61 68 70 79 99 N SD: 0.0241 c. M:-0.0555 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0000 cents 3 .. 6 match: 3 H SD: 0.0000 cents 4 .. 8 match: 4 H SD: 0.0000 cents 5 .. 10 match: 5 H SD: 0.0000 cents 6 .. 12 match: 6 H SD: 2.8999 cents 7 .. 14 match: 7 H SD: 2.5839 cents 8 .. 16 match: 8 H SD: 2.2604 cents 9 .. 18 match: 9 H SD: 1.5972 cents 10 .. 20 match: 10 H SD: 2.7234 cents 11 .. 22 match: 11 H SD: 4.1394 cents 12 .. 24 match: 12 H SD: 2.1647 cents 13 .. 26 match: 13 H SD: 3.0718 cents 14 .. 28 match: 14 H SD: 2.2646 cents 15 .. 30 match: 15 H SD: 2.1883 cents 16 .. 32 match: 16 H SD: 1.8024 cents 17 .. 34 match: 17 H SD: 2.8678 cents 18 .. 36 match: 18 H SD: 1.8064 cents 19 .. 38 match: 19 H SD: 2.2723 cents 20 .. 40 match: 20 H SD: 1.8937 cents 21 .. 42 match: 21 H SD: 1.9855 cents 22 .. 44 match: 22 H SD: 2.3175 cents 23 .. 46 match: 22 SD: 1.7581 cents 24 .. 48 match: 24 H SD: 1.8787 cents 25 .. 50 match: 25 H SD: 1.4085 cents 26 .. 52 match: 25 SD: 1.8196 cents 27 .. 54 match: 26 S SD: 1.3191 cents 28 .. 56 match: 27 S SD: 1.8195 cents 29 .. 58 match: 28 S SD: 1.6375 cents 30 .. 60 match: 28 SD: 1.8263 cents 31 .. 62 match: 31 H SD: 1.6915 cents 32 .. 64 match: 32 H SD: 1.6502 cents 33 .. 66 match: 32 SD: 1.9579 cents 34 .. 68 match: 31 SD: 1.7434 cents 35 .. 70 match: 31 SD: 1.3260 cents 36 .. 72 match: 34 SD: 1.3286 cents 37 .. 74 match: 31 SD: 1.7120 cents 38 .. 76 match: 34 SD: 1.4188 cents 39 .. 78 match: 34 SD: 1.3820 cents 40 .. 80 match: 35 SD: 1.2756 cents 41 .. 82 match: 33 SD: 1.1789 cents 42 .. 84 match: 34 SD: 1.0832 cents 43 .. 86 match: 36 SD: 1.3098 cents 44 .. 88 match: 35 SD: 1.3065 cents 45 .. 90 match: 37 SD: 1.1772 cents 46 .. 92 match: 36 SD: 1.1954 cents 47 .. 94 match: 36 SD: 1.2225 cents 48 .. 96 match: 37 SD: 0.8852 cents 49 .. 98 match: 39 SD: 1.0697 cents 50 .. 100 match: 37 SD: 1.1128 cents 51 .. 102 match: 35 SD: 1.1512 cents 52 .. 104 match: 37 SD: 0.9724 cents 53 .. 106 match: 38 SD: 1.0987 cents 54 .. 108 match: 38 SD: 0.7968 cents 55 .. 110 match: 38 SD: 0.9739 cents 56 .. 112 match: 38 SD: 0.9145 cents 57 .. 114 match: 40 SD: 0.9341 cents 58 .. 116 match: 39 SD: 1.0014 cents 59 .. 118 match: 38 SD: 1.0115 cents 60 .. 120 match: 39 SD: 0.8739 cents 61 .. 122 match: 38 SD: 0.8958 cents 62 .. 124 match: 37 SD: 0.8963 cents 63 .. 126 match: 37 SD: 0.7877 cents 64 .. 128 match: 38 SD: 0.8694 cents 65 .. 130 match: 39 SD: 0.8145 cents 66 .. 132 match: 36 SD: 0.8431 cents 67 .. 134 match: 36 SD: 0.8552 cents 68 .. 136 match: 40 SD: 0.8840 cents 69 .. 138 match: 39 SD: 0.8854 cents 70 .. 140 match: 40 SD: 0.6882 cents 71 .. 142 match: 38 SD: 0.7373 cents 72 .. 144 match: 40 SD: 0.6773 cents 74 .. 148 match: 40 SD: 0.7275 cents 76 .. 152 match: 39 SD: 0.8341 cents 77 .. 154 match: 39 SD: 0.7122 cents 78 .. 156 match: 39 SD: 0.7319 cents 79 .. 158 match: 40 SD: 0.7397 cents 80 .. 160 match: 40 SD: 0.5996 cents 81 .. 162 match: 39 SD: 0.7448 cents 82 .. 164 match: 39 SD: 0.7742 cents 83 .. 166 match: 41 SD: 0.7289 cents 84 .. 168 match: 40 SD: 0.6268 cents 85 .. 170 match: 40 SD: 0.7014 cents 86 .. 172 match: 39 SD: 0.7436 cents 87 .. 174 match: 40 SD: 0.7056 cents 88 .. 176 match: 41 SD: 0.6443 cents 89 .. 178 match: 41 SD: 0.6167 cents 90 .. 180 match: 40 SD: 0.5895 cents 91 .. 182 match: 40 SD: 0.6449 cents 92 .. 184 match: 39 SD: 0.6118 cents 93 .. 186 match: 40 SD: 0.6301 cents 94 .. 188 match: 40 SD: 0.6375 cents 95 .. 190 match: 41 SD: 0.5260 cents 96 .. 192 match: 41 SD: 0.4993 cents 98 .. 196 match: 40 SD: 0.5310 cents 100 .. 200 match: 41 SD: 0.4510 cents 105 .. 210 match: 40 SD: 0.5017 cents 106 .. 212 match: 40 SD: 0.5872 cents 108 .. 216 match: 41 SD: 0.5395 cents 109 .. 218 match: 41 SD: 0.5212 cents 110 .. 220 match: 41 SD: 0.5198 cents 111 .. 222 match: 41 SD: 0.4699 cents 112 .. 224 match: 41 SD: 0.4393 cents 115 .. 230 match: 41 SD: 0.4326 cents 120 .. 240 match: 41 SD: 0.4196 cents 126 .. 252 match: 41 SD: 0.3941 cents 140 .. 280 match: 41 SD: 0.3795 cents 150 .. 300 match: 41 SD: 0.3406 cents 151 .. 302 match: 41 SD: 0.3376 cents 154 .. 308 match: 41 SD: 0.3189 cents 162 .. 324 match: 41 SD: 0.3142 cents 168 .. 336 match: 41 SD: 0.2698 cents 195 .. 390 match: 41 SD: 0.2690 cents 198 .. 396 match: 41 SD: 0.2661 cents 200 .. 400 match: 41 SD: 0.2602 cents 208 .. 416 match: 41 SD: 0.2433 cents 210 .. 420 match: 41 SD: 0.2271 cents 216 .. 432 match: 41 SD: 0.2075 cents 224 .. 448 match: 41 SD: 0.2051 cents 252 .. 504 match: 41 SD: 0.1868 cents 265 .. 530 match: 41 SD: 0.1849 cents 280 .. 560 match: 41 SD: 0.1838 cents 288 .. 576 match: 41 SD: 0.1590 cents 324 .. 648 match: 41 SD: 0.1581 cents 330 .. 660 match: 41 SD: 0.1553 cents 335 .. 670 match: 41 SD: 0.1473 cents 336 .. 672 match: 41 SD: 0.1345 cents 378 .. 756 match: 41 SD: 0.1080 cents 432 .. 864 match: 41 SD: 0.1023 cents 480 .. 960 match: 41 SD: 0.0889 cents 504 .. 1008 match: 41 SD: 0.0855 cents 560 .. 1120 match: 41 SD: 0.0807 cents 576 .. 1152 match: 41 SD: 0.0751 cents 600 .. 1200 match: 41 SD: 0.0722 cents