Scala analysis: xen12-hanson-06-53-just
53 tones, tonal function, Figure 6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/80 21.506290 syntonic comma, Didymus comma 2: 250/243 49.166137 maximal diesis, Porcupine comma 3: 25/24 70.672427 classic chromatic semitone, minor chroma 4: 135/128 92.178716 major chroma, major limma 5: 16/15 111.731285 minor diatonic semitone 6: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 7: 2187/2000 154.743864 Gorgo limma 8: 10/9 182.403712 minor whole tone 9: 9/8 203.910002 major whole tone 10: 256/225 223.462571 Neapolitan diminished third 11: 144/125 244.968860 classic diminished third 12: 729/625 266.475150 two (large limma, BP small semitone, Zarlino semitone) 13: 32/27 294.134997 Pythagorean minor third 14: 6/5 315.641287 minor third 15: 243/200 337.147577 acute minor third 16: 100/81 364.807424 grave major third 17: 5/4 386.313714 major third 18: 81/64 407.820003 Pythagorean major third 19: 625/486 435.479851 20: 125/96 456.986141 classic augmented third 21: 320/243 476.538710 grave fourth 22: 4/3 498.044999 perfect fourth 23: 27/20 519.551289 acute fourth 24: 1000/729 547.211136 25: 25/18 568.717426 classic augmented fourth 26: 45/32 590.223716 diatonic tritone 27: 64/45 609.776284 2nd tritone 28: 36/25 631.282574 classic diminished fifth 29: 729/500 652.788864 30: 40/27 680.448711 grave fifth 31: 3/2 701.955001 perfect fifth 32: 243/160 723.461290 acute fifth 33: 125/81 751.121138 34: 25/16 772.627428 classic augmented fifth 35: 128/81 792.179997 Pythagorean minor sixth 36: 8/5 813.686286 minor sixth 37: 81/50 835.192576 acute minor sixth 38: 400/243 862.852423 grave major sixth 39: 5/3 884.358713 major sixth, BP sixth 40: 27/16 905.865003 Pythagorean major sixth 41: 1250/729 933.524850 42: 125/72 955.031140 classic augmented sixth 43: 225/128 976.537429 augmented sixth 44: 16/9 996.089998 Pythagorean minor seventh 45: 9/5 1017.596288 just minor seventh, BP seventh 46: 729/400 1039.102577 acute minor seventh 47: 50/27 1066.762425 grave major seventh 48: 15/8 1088.268715 classic major seventh 49: 256/135 1107.821284 octave - major chroma 50: 48/25 1129.327573 classic diminished octave 51: 243/125 1150.833863 octave - maximal diesis 52: 160/81 1178.493710 octave - syntonic comma 53: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/80 21.5063 syntonic comma, Didymus comma 1: 81/80 21.5063 syntonic comma, Didymus comma 2: 20000/19683 27.6598 minimal diesis 3: 81/80 21.5063 syntonic comma, Didymus comma 4: 81/80 21.5063 syntonic comma, Didymus comma 5: 2048/2025 19.5526 diaschisma 6: 81/80 21.5063 syntonic comma, Didymus comma 7: 81/80 21.5063 syntonic comma, Didymus comma 8: 20000/19683 27.6598 minimal diesis 9: 81/80 21.5063 syntonic comma, Didymus comma 10: 2048/2025 19.5526 diaschisma 11: 81/80 21.5063 syntonic comma, Didymus comma 12: 81/80 21.5063 syntonic comma, Didymus comma 13: 20000/19683 27.6598 minimal diesis 14: 81/80 21.5063 syntonic comma, Didymus comma 15: 81/80 21.5063 syntonic comma, Didymus comma 16: 20000/19683 27.6598 minimal diesis 17: 81/80 21.5063 syntonic comma, Didymus comma 18: 81/80 21.5063 syntonic comma, Didymus comma 19: 20000/19683 27.6598 minimal diesis 20: 81/80 21.5063 syntonic comma, Didymus comma 21: 2048/2025 19.5526 diaschisma 22: 81/80 21.5063 syntonic comma, Didymus comma 23: 81/80 21.5063 syntonic comma, Didymus comma 24: 20000/19683 27.6598 minimal diesis 25: 81/80 21.5063 syntonic comma, Didymus comma 26: 81/80 21.5063 syntonic comma, Didymus comma 27: 2048/2025 19.5526 diaschisma 28: 81/80 21.5063 syntonic comma, Didymus comma 29: 81/80 21.5063 syntonic comma, Didymus comma 30: 20000/19683 27.6598 minimal diesis 31: 81/80 21.5063 syntonic comma, Didymus comma 32: 81/80 21.5063 syntonic comma, Didymus comma 33: 20000/19683 27.6598 minimal diesis 34: 81/80 21.5063 syntonic comma, Didymus comma 35: 2048/2025 19.5526 diaschisma 36: 81/80 21.5063 syntonic comma, Didymus comma 37: 81/80 21.5063 syntonic comma, Didymus comma 38: 20000/19683 27.6598 minimal diesis 39: 81/80 21.5063 syntonic comma, Didymus comma 40: 81/80 21.5063 syntonic comma, Didymus comma 41: 20000/19683 27.6598 minimal diesis 42: 81/80 21.5063 syntonic comma, Didymus comma 43: 81/80 21.5063 syntonic comma, Didymus comma 44: 2048/2025 19.5526 diaschisma 45: 81/80 21.5063 syntonic comma, Didymus comma 46: 81/80 21.5063 syntonic comma, Didymus comma 47: 20000/19683 27.6598 minimal diesis 48: 81/80 21.5063 syntonic comma, Didymus comma 49: 2048/2025 19.5526 diaschisma 50: 81/80 21.5063 syntonic comma, Didymus comma 51: 81/80 21.5063 syntonic comma, Didymus comma 52: 20000/19683 27.6598 minimal diesis 53: 81/80 21.5063 syntonic comma, Didymus comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 2048/2025 19.553 cents diaschisma 1: 34 81/80 21.506 cents syntonic comma, Didymus comma 1: 12 20000/19683 27.660 cents minimal diesis 2: 14 128/125 41.059 cents minor diesis, diesis 2: 15 6561/6400 43.013 cents Mathieu superdiesis 2: 24 250/243 49.166 cents maximal diesis, Porcupine comma 3: 17 648/625 62.565 cents major diesis 3: 4 20480/19683 68.719 cents grave minor second 3: 32 25/24 70.672 cents classic chromatic semitone, minor chroma 4: 10 6561/6250 84.071 cents ripple 4: 18 256/243 90.225 cents limma, Pythagorean minor second 4: 20 135/128 92.179 cents major chroma, major limma 4: 5 62500/59049 98.332 cents two (maximal diesis, Porcupine comma) 5: 3 531441/500000 105.578 cents wronecki 5: 32 16/15 111.731 cents minor diatonic semitone 5: 8 2187/2048 113.685 cents apotome 5: 10 3125/2916 119.839 cents quasi-equal 10-tone semitone 6: 2 32768/30375 131.284 cents 6: 32 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 6: 6 64000/59049 139.391 cents 6: 13 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 7: 5 2048/1875 152.790 cents double diminished third 7: 18 2187/2000 154.744 cents Gorgo limma 7: 21 800/729 160.897 cents grave whole tone 7: 8 1125/1024 162.851 cents double augmented prime 7: 1 390625/354294 169.005 cents 8: 8 3456/3125 174.296 cents 8: 4 177147/160000 176.250 cents 8: 36 10/9 182.404 cents minor whole tone 8: 3 18225/16384 184.357 cents two (major chroma, major limma) 8: 2 78125/69984 190.511 cents 9: 6 17496/15625 195.803 cents 9: 6 4096/3645 201.956 cents narrow diminished third 9: 33 9/8 203.910 cents major whole tone 9: 6 200000/177147 210.064 cents 9: 2 15625/13824 212.017 cents 10: 3 177147/156250 217.309 cents 10: 15 256/225 223.463 cents Neapolitan diminished third 10: 18 729/640 225.416 cents acute major second 10: 16 2500/2187 231.570 cents 10: 1 9375/8192 233.524 cents 11: 24 144/125 244.969 cents classic diminished third 11: 3 59049/51200 246.923 cents 11: 26 125/108 253.076 cents semi-augmented whole tone 12: 18 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 12: 13 2560/2187 272.629 cents grave minor third 12: 19 75/64 274.582 cents classic augmented second 12: 3 625000/531441 280.736 cents 13: 9 59049/50000 287.981 cents 13: 29 32/27 294.135 cents Pythagorean minor third 13: 9 1215/1024 296.089 cents wide augmented second 13: 6 15625/13122 302.242 cents 14: 44 6/5 315.641 cents minor third 14: 1 640000/531441 321.795 cents two (grave whole tone) 14: 8 3125/2592 323.749 cents 15: 4 4096/3375 335.194 cents double diminished fourth 15: 28 243/200 337.148 cents acute minor third 15: 16 8000/6561 343.301 cents 15: 5 625/512 345.255 cents classic neutral third 16: 8 768/625 356.700 cents 16: 12 19683/16000 358.654 cents 16: 31 100/81 364.807 cents grave major third 16: 2 10125/8192 366.761 cents double augmented second 17: 9 3888/3125 378.206 cents 17: 4 8192/6561 384.360 cents Pythagorean diminished fourth 17: 39 5/4 386.314 cents major third 17: 1 2000000/1594323 392.467 cents 18: 5 19683/15625 399.713 cents 18: 15 512/405 405.866 cents narrow diminished fourth 18: 24 81/64 407.820 cents Pythagorean major third 18: 9 25000/19683 413.974 cents 19: 1 1594323/1250000 421.219 cents 19: 26 32/25 427.373 cents classic diminished fourth 19: 9 6561/5120 429.326 cents acute major third 19: 17 625/486 435.480 cents 20: 1 65536/50625 446.925 cents two (Neapolitan diminished third) 20: 24 162/125 448.879 cents 20: 8 25600/19683 455.032 cents 20: 20 125/96 456.986 cents classic augmented third 21: 2 4096/3125 468.431 cents 21: 13 6561/5000 470.385 cents 21: 24 320/243 476.539 cents grave fourth 21: 12 675/512 478.492 cents wide augmented third 21: 2 78125/59049 484.646 cents 22: 3 20736/15625 489.938 cents two (classic diminished third) 22: 2 531441/400000 491.891 cents 22: 40 4/3 498.045 cents perfect fourth 22: 4 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 22: 4 15625/11664 506.152 cents two (semi-augmented whole tone) 23: 2 104976/78125 511.444 cents 23: 4 8192/6075 517.598 cents 23: 34 27/20 519.551 cents acute fourth 23: 9 80000/59049 525.705 cents 23: 4 3125/2304 527.659 cents 24: 1 531441/390625 532.950 cents 24: 10 512/375 539.104 cents double diminished fifth 24: 18 2187/1600 541.058 cents 24: 22 1000/729 547.211 cents 24: 2 5625/4096 549.165 cents double augmented third 25: 16 864/625 560.610 cents 25: 2 177147/128000 562.564 cents 25: 35 25/18 568.717 cents classic augmented fourth 26: 12 4374/3125 582.116 cents 26: 11 1024/729 588.270 cents Pythagorean diminished fifth 26: 24 45/32 590.224 cents diatonic tritone 26: 6 250000/177147 596.377 cents 27: 6 177147/125000 603.623 cents 27: 24 64/45 609.776 cents 2nd tritone 27: 11 729/512 611.730 cents Pythagorean tritone 27: 12 3125/2187 617.884 cents 28: 35 36/25 631.283 cents classic diminished fifth 28: 2 256000/177147 637.436 cents 28: 16 625/432 639.390 cents 29: 2 8192/5625 650.835 cents double diminished sixth 29: 22 729/500 652.789 cents 29: 18 3200/2187 658.942 cents 29: 10 375/256 660.896 cents double augmented fourth 29: 1 781250/531441 667.050 cents 30: 4 4608/3125 672.341 cents 30: 9 59049/40000 674.295 cents two (acute minor third) 30: 34 40/27 680.449 cents grave fifth 30: 4 6075/4096 682.402 cents 30: 2 78125/52488 688.556 cents 31: 4 23328/15625 693.848 cents 31: 4 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 31: 40 3/2 701.955 cents perfect fifth 31: 2 800000/531441 708.109 cents 31: 3 15625/10368 710.062 cents 32: 2 118098/78125 715.354 cents 32: 12 1024/675 721.508 cents narrow diminished sixth 32: 24 243/160 723.461 cents acute fifth 32: 13 10000/6561 729.615 cents two (grave major third) 32: 2 3125/2048 731.569 cents 33: 20 192/125 743.014 cents classic diminished sixth 33: 8 19683/12800 744.968 cents 33: 24 125/81 751.121 cents 33: 1 50625/32768 753.075 cents 34: 17 972/625 764.520 cents 34: 9 10240/6561 770.674 cents grave minor sixth 34: 26 25/16 772.627 cents classic augmented fifth 34: 1 2500000/1594323 778.781 cents 35: 9 19683/12500 786.026 cents 35: 24 128/81 792.180 cents Pythagorean minor sixth 35: 15 405/256 794.134 cents wide augmented fifth 35: 5 31250/19683 800.287 cents 36: 1 1594323/1000000 807.533 cents 36: 39 8/5 813.686 cents minor sixth 36: 4 6561/4096 815.640 cents Pythagorean augmented fifth 36: 9 3125/1944 821.794 cents 37: 2 16384/10125 833.239 cents double diminished seventh 37: 31 81/50 835.193 cents acute minor sixth 37: 12 32000/19683 841.346 cents 37: 8 625/384 843.300 cents 38: 5 1024/625 854.745 cents two (classic diminished fourth) 38: 16 6561/4000 856.699 cents 38: 28 400/243 862.852 cents grave major sixth 38: 4 3375/2048 864.806 cents double augmented fifth 39: 8 5184/3125 876.251 cents 39: 1 531441/320000 878.205 cents 39: 44 5/3 884.359 cents major sixth, BP sixth 40: 6 26244/15625 897.758 cents 40: 9 2048/1215 903.911 cents narrow diminished seventh 40: 29 27/16 905.865 cents Pythagorean major sixth 40: 9 100000/59049 912.019 cents 41: 3 531441/312500 919.264 cents 41: 19 128/75 925.418 cents diminished seventh 41: 13 2187/1280 927.371 cents acute major sixth 41: 18 1250/729 933.525 cents 42: 26 216/125 946.924 cents semi-augmented sixth 42: 3 102400/59049 953.077 cents two (grave fourth) 42: 24 125/72 955.031 cents classic augmented sixth 43: 1 16384/9375 966.476 cents 43: 16 2187/1250 968.430 cents 43: 18 1280/729 974.584 cents grave minor seventh 43: 15 225/128 976.537 cents augmented sixth 43: 3 312500/177147 982.691 cents 44: 2 27648/15625 987.983 cents 44: 6 177147/100000 989.936 cents 44: 33 16/9 996.090 cents Pythagorean minor seventh 44: 6 3645/2048 998.044 cents wide augmented sixth 44: 6 15625/8748 1004.197 cents 45: 2 139968/78125 1009.489 cents 45: 3 32768/18225 1015.643 cents 45: 36 9/5 1017.596 cents just minor seventh, BP seventh 45: 4 320000/177147 1023.750 cents 45: 8 3125/1728 1025.704 cents 46: 1 708588/390625 1030.995 cents 46: 8 2048/1125 1037.149 cents double diminished octave 46: 21 729/400 1039.103 cents acute minor seventh 46: 18 4000/2187 1045.256 cents 46: 5 1875/1024 1047.210 cents double augmented sixth 47: 13 1152/625 1058.655 cents 47: 6 59049/32000 1060.609 cents 47: 32 50/27 1066.762 cents grave major seventh 47: 2 30375/16384 1068.716 cents 48: 10 5832/3125 1080.161 cents 48: 8 4096/2187 1086.315 cents Pythagorean diminished octave 48: 32 15/8 1088.269 cents classic major seventh 48: 3 1000000/531441 1094.422 cents 49: 5 59049/31250 1101.668 cents 49: 20 256/135 1107.821 cents octave - major chroma 49: 18 243/128 1109.775 cents Pythagorean major seventh 49: 10 12500/6561 1115.929 cents 50: 32 48/25 1129.328 cents classic diminished octave 50: 4 19683/10240 1131.281 cents acute major seventh 50: 17 625/324 1137.435 cents octave - major diesis 51: 24 243/125 1150.834 cents octave - maximal diesis 51: 15 12800/6561 1156.987 cents 51: 14 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 52: 12 19683/10000 1172.340 cents octave - minimal diesis 52: 34 160/81 1178.494 cents octave - syntonic comma 52: 7 2025/1024 1180.447 cents 2 tritones Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.07692 = 53/13
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 42 43 44 45 46 47 48 49 50 51 52 53 0.0 : 21.5 49.2 70.7 92.2 111.7 133.2 154.7 182.4 203.9 223.5 245.0 266.5 294.1 315.6 337.1 364.8 386.3 407.8 435.5 457.0 476.5 498.0 519.6 547.2 568.7 590.2 609.8 631.3 652.8 680.4 702.0 723.5 751.1 772.6 792.2 813.7 835.2 862.9 884.4 905.9 933.5 955.0 976.5 996.1 1017.6 1039.1 1066.8 1088.3 1107.8 1129.3 1150.8 1178.5 1200.0 21.5 : 27.7 49.2 70.7 90.2 111.7 133.2 160.9 182.4 202.0 223.5 245.0 272.6 294.1 315.6 343.3 364.8 386.3 414.0 435.5 455.0 476.5 498.0 525.7 547.2 568.7 588.3 609.8 631.3 658.9 680.4 702.0 729.6 751.1 770.7 792.2 813.7 841.3 862.9 884.4 912.0 933.5 955.0 974.6 996.1 1017.6 1045.3 1066.8 1086.3 1107.8 1129.3 1157.0 1178.5 1200.0 49.2 : 21.5 43.0 62.6 84.1 105.6 133.2 154.7 174.3 195.8 217.3 245.0 266.5 288.0 315.6 337.1 358.7 386.3 407.8 427.4 448.9 470.4 498.0 519.6 541.1 560.6 582.1 603.6 631.3 652.8 674.3 702.0 723.5 743.0 764.5 786.0 813.7 835.2 856.7 884.4 905.9 927.4 946.9 968.4 989.9 1017.6 1039.1 1058.7 1080.2 1101.7 1129.3 1150.8 1172.3 1200.0 70.7 : 21.5 41.1 62.6 84.1 111.7 133.2 152.8 174.3 195.8 223.5 245.0 266.5 294.1 315.6 337.1 364.8 386.3 405.9 427.4 448.9 476.5 498.0 519.6 539.1 560.6 582.1 609.8 631.3 652.8 680.4 702.0 721.5 743.0 764.5 792.2 813.7 835.2 862.9 884.4 905.9 925.4 946.9 968.4 996.1 1017.6 1037.1 1058.7 1080.2 1107.8 1129.3 1150.8 1178.5 1200.0 92.2 : 19.6 41.1 62.6 90.2 111.7 131.3 152.8 174.3 202.0 223.5 245.0 272.6 294.1 315.6 343.3 364.8 384.4 405.9 427.4 455.0 476.5 498.0 517.6 539.1 560.6 588.3 609.8 631.3 658.9 680.4 700.0 721.5 743.0 770.7 792.2 813.7 841.3 862.9 884.4 903.9 925.4 946.9 974.6 996.1 1015.6 1037.1 1058.7 1086.3 1107.8 1129.3 1157.0 1178.5 1200.0 111.7 : 21.5 43.0 70.7 92.2 111.7 133.2 154.7 182.4 203.9 225.4 253.1 274.6 296.1 323.7 345.3 364.8 386.3 407.8 435.5 457.0 478.5 498.0 519.6 541.1 568.7 590.2 611.7 639.4 660.9 680.4 702.0 723.5 751.1 772.6 794.1 821.8 843.3 864.8 884.4 905.9 927.4 955.0 976.5 996.1 1017.6 1039.1 1066.8 1088.3 1109.8 1137.4 1158.9 1180.4 1200.0 133.2 : 21.5 49.2 70.7 90.2 111.7 133.2 160.9 182.4 203.9 231.6 253.1 274.6 302.2 323.7 343.3 364.8 386.3 414.0 435.5 457.0 476.5 498.0 519.6 547.2 568.7 590.2 617.9 639.4 658.9 680.4 702.0 729.6 751.1 772.6 800.3 821.8 843.3 862.9 884.4 905.9 933.5 955.0 974.6 996.1 1017.6 1045.3 1066.8 1088.3 1115.9 1137.4 1158.9 1178.5 1200.0 154.7 : 27.7 49.2 68.7 90.2 111.7 139.4 160.9 182.4 210.1 231.6 253.1 280.7 302.2 321.8 343.3 364.8 392.5 414.0 435.5 455.0 476.5 498.0 525.7 547.2 568.7 596.4 617.9 637.4 658.9 680.4 708.1 729.6 751.1 778.8 800.3 821.8 841.3 862.9 884.4 912.0 933.5 953.1 974.6 996.1 1023.7 1045.3 1066.8 1094.4 1115.9 1137.4 1157.0 1178.5 1200.0 182.4 : 21.5 41.1 62.6 84.1 111.7 133.2 154.7 182.4 203.9 225.4 253.1 274.6 294.1 315.6 337.1 364.8 386.3 407.8 427.4 448.9 470.4 498.0 519.6 541.1 568.7 590.2 609.8 631.3 652.8 680.4 702.0 723.5 751.1 772.6 794.1 813.7 835.2 856.7 884.4 905.9 925.4 946.9 968.4 996.1 1017.6 1039.1 1066.8 1088.3 1109.8 1129.3 1150.8 1172.3 1200.0 203.9 : 19.6 41.1 62.6 90.2 111.7 133.2 160.9 182.4 203.9 231.6 253.1 272.6 294.1 315.6 343.3 364.8 386.3 405.9 427.4 448.9 476.5 498.0 519.6 547.2 568.7 588.3 609.8 631.3 658.9 680.4 702.0 729.6 751.1 772.6 792.2 813.7 835.2 862.9 884.4 903.9 925.4 946.9 974.6 996.1 1017.6 1045.3 1066.8 1088.3 1107.8 1129.3 1150.8 1178.5 1200.0 223.5 : 21.5 43.0 70.7 92.2 113.7 141.3 162.9 184.4 212.0 233.5 253.1 274.6 296.1 323.7 345.3 366.8 386.3 407.8 429.3 457.0 478.5 500.0 527.7 549.2 568.7 590.2 611.7 639.4 660.9 682.4 710.1 731.6 753.1 772.6 794.1 815.6 843.3 864.8 884.4 905.9 927.4 955.0 976.5 998.0 1025.7 1047.2 1068.7 1088.3 1109.8 1131.3 1158.9 1180.4 1200.0 245.0 : 21.5 49.2 70.7 92.2 119.8 141.3 162.9 190.5 212.0 231.6 253.1 274.6 302.2 323.7 345.3 364.8 386.3 407.8 435.5 457.0 478.5 506.2 527.7 547.2 568.7 590.2 617.9 639.4 660.9 688.6 710.1 731.6 751.1 772.6 794.1 821.8 843.3 862.9 884.4 905.9 933.5 955.0 976.5 1004.2 1025.7 1047.2 1066.8 1088.3 1109.8 1137.4 1158.9 1178.5 1200.0 266.5 : 27.7 49.2 70.7 98.3 119.8 141.3 169.0 190.5 210.1 231.6 253.1 280.7 302.2 323.7 343.3 364.8 386.3 414.0 435.5 457.0 484.6 506.2 525.7 547.2 568.7 596.4 617.9 639.4 667.0 688.6 710.1 729.6 751.1 772.6 800.3 821.8 841.3 862.9 884.4 912.0 933.5 955.0 982.7 1004.2 1025.7 1045.3 1066.8 1088.3 1115.9 1137.4 1157.0 1178.5 1200.0 294.1 : 21.5 43.0 70.7 92.2 113.7 141.3 162.9 182.4 203.9 225.4 253.1 274.6 296.1 315.6 337.1 358.7 386.3 407.8 429.3 457.0 478.5 498.0 519.6 541.1 568.7 590.2 611.7 639.4 660.9 682.4 702.0 723.5 745.0 772.6 794.1 813.7 835.2 856.7 884.4 905.9 927.4 955.0 976.5 998.0 1017.6 1039.1 1060.6 1088.3 1109.8 1129.3 1150.8 1172.3 1200.0 315.6 : 21.5 49.2 70.7 92.2 119.8 141.3 160.9 182.4 203.9 231.6 253.1 274.6 294.1 315.6 337.1 364.8 386.3 407.8 435.5 457.0 476.5 498.0 519.6 547.2 568.7 590.2 617.9 639.4 660.9 680.4 702.0 723.5 751.1 772.6 792.2 813.7 835.2 862.9 884.4 905.9 933.5 955.0 976.5 996.1 1017.6 1039.1 1066.8 1088.3 1107.8 1129.3 1150.8 1178.5 1200.0 337.1 : 27.7 49.2 70.7 98.3 119.8 139.4 160.9 182.4 210.1 231.6 253.1 272.6 294.1 315.6 343.3 364.8 386.3 414.0 435.5 455.0 476.5 498.0 525.7 547.2 568.7 596.4 617.9 639.4 658.9 680.4 702.0 729.6 751.1 770.7 792.2 813.7 841.3 862.9 884.4 912.0 933.5 955.0 974.6 996.1 1017.6 1045.3 1066.8 1086.3 1107.8 1129.3 1157.0 1178.5 1200.0 364.8 : 21.5 43.0 70.7 92.2 111.7 133.2 154.7 182.4 203.9 225.4 245.0 266.5 288.0 315.6 337.1 358.7 386.3 407.8 427.4 448.9 470.4 498.0 519.6 541.1 568.7 590.2 611.7 631.3 652.8 674.3 702.0 723.5 743.0 764.5 786.0 813.7 835.2 856.7 884.4 905.9 927.4 946.9 968.4 989.9 1017.6 1039.1 1058.7 1080.2 1101.7 1129.3 1150.8 1172.3 1200.0 386.3 : 21.5 49.2 70.7 90.2 111.7 133.2 160.9 182.4 203.9 223.5 245.0 266.5 294.1 315.6 337.1 364.8 386.3 405.9 427.4 448.9 476.5 498.0 519.6 547.2 568.7 590.2 609.8 631.3 652.8 680.4 702.0 721.5 743.0 764.5 792.2 813.7 835.2 862.9 884.4 905.9 925.4 946.9 968.4 996.1 1017.6 1037.1 1058.7 1080.2 1107.8 1129.3 1150.8 1178.5 1200.0 407.8 : 27.7 49.2 68.7 90.2 111.7 139.4 160.9 182.4 202.0 223.5 245.0 272.6 294.1 315.6 343.3 364.8 384.4 405.9 427.4 455.0 476.5 498.0 525.7 547.2 568.7 588.3 609.8 631.3 658.9 680.4 700.0 721.5 743.0 770.7 792.2 813.7 841.3 862.9 884.4 903.9 925.4 946.9 974.6 996.1 1015.6 1037.1 1058.7 1086.3 1107.8 1129.3 1157.0 1178.5 1200.0 435.5 : 21.5 41.1 62.6 84.1 111.7 133.2 154.7 174.3 195.8 217.3 245.0 266.5 288.0 315.6 337.1 356.7 378.2 399.7 427.4 448.9 470.4 498.0 519.6 541.1 560.6 582.1 603.6 631.3 652.8 672.3 693.8 715.4 743.0 764.5 786.0 813.7 835.2 856.7 876.3 897.8 919.3 946.9 968.4 988.0 1009.5 1031.0 1058.7 1080.2 1101.7 1129.3 1150.8 1172.3 1200.0 457.0 : 19.6 41.1 62.6 90.2 111.7 133.2 152.8 174.3 195.8 223.5 245.0 266.5 294.1 315.6 335.2 356.7 378.2 405.9 427.4 448.9 476.5 498.0 519.6 539.1 560.6 582.1 609.8 631.3 650.8 672.3 693.8 721.5 743.0 764.5 792.2 813.7 835.2 854.7 876.3 897.8 925.4 946.9 966.5 988.0 1009.5 1037.1 1058.7 1080.2 1107.8 1129.3 1150.8 1178.5 1200.0 476.5 : 21.5 43.0 70.7 92.2 113.7 133.2 154.7 176.3 203.9 225.4 246.9 274.6 296.1 315.6 337.1 358.7 386.3 407.8 429.3 457.0 478.5 500.0 519.6 541.1 562.6 590.2 611.7 631.3 652.8 674.3 702.0 723.5 745.0 772.6 794.1 815.6 835.2 856.7 878.2 905.9 927.4 946.9 968.4 989.9 1017.6 1039.1 1060.6 1088.3 1109.8 1131.3 1158.9 1180.4 1200.0 498.0 : 21.5 49.2 70.7 92.2 111.7 133.2 154.7 182.4 203.9 225.4 253.1 274.6 294.1 315.6 337.1 364.8 386.3 407.8 435.5 457.0 478.5 498.0 519.6 541.1 568.7 590.2 609.8 631.3 652.8 680.4 702.0 723.5 751.1 772.6 794.1 813.7 835.2 856.7 884.4 905.9 925.4 946.9 968.4 996.1 1017.6 1039.1 1066.8 1088.3 1109.8 1137.4 1158.9 1178.5 1200.0 519.6 : 27.7 49.2 70.7 90.2 111.7 133.2 160.9 182.4 203.9 231.6 253.1 272.6 294.1 315.6 343.3 364.8 386.3 414.0 435.5 457.0 476.5 498.0 519.6 547.2 568.7 588.3 609.8 631.3 658.9 680.4 702.0 729.6 751.1 772.6 792.2 813.7 835.2 862.9 884.4 903.9 925.4 946.9 974.6 996.1 1017.6 1045.3 1066.8 1088.3 1115.9 1137.4 1157.0 1178.5 1200.0 547.2 : 21.5 43.0 62.6 84.1 105.6 133.2 154.7 176.3 203.9 225.4 245.0 266.5 288.0 315.6 337.1 358.7 386.3 407.8 429.3 448.9 470.4 491.9 519.6 541.1 560.6 582.1 603.6 631.3 652.8 674.3 702.0 723.5 745.0 764.5 786.0 807.5 835.2 856.7 876.3 897.8 919.3 946.9 968.4 989.9 1017.6 1039.1 1060.6 1088.3 1109.8 1129.3 1150.8 1172.3 1200.0 568.7 : 21.5 41.1 62.6 84.1 111.7 133.2 154.7 182.4 203.9 223.5 245.0 266.5 294.1 315.6 337.1 364.8 386.3 407.8 427.4 448.9 470.4 498.0 519.6 539.1 560.6 582.1 609.8 631.3 652.8 680.4 702.0 723.5 743.0 764.5 786.0 813.7 835.2 854.7 876.3 897.8 925.4 946.9 968.4 996.1 1017.6 1039.1 1066.8 1088.3 1107.8 1129.3 1150.8 1178.5 1200.0 590.2 : 19.6 41.1 62.6 90.2 111.7 133.2 160.9 182.4 202.0 223.5 245.0 272.6 294.1 315.6 343.3 364.8 386.3 405.9 427.4 448.9 476.5 498.0 517.6 539.1 560.6 588.3 609.8 631.3 658.9 680.4 702.0 721.5 743.0 764.5 792.2 813.7 833.2 854.7 876.3 903.9 925.4 946.9 974.6 996.1 1017.6 1045.3 1066.8 1086.3 1107.8 1129.3 1157.0 1178.5 1200.0 609.8 : 21.5 43.0 70.7 92.2 113.7 141.3 162.9 182.4 203.9 225.4 253.1 274.6 296.1 323.7 345.3 366.8 386.3 407.8 429.3 457.0 478.5 498.0 519.6 541.1 568.7 590.2 611.7 639.4 660.9 682.4 702.0 723.5 745.0 772.6 794.1 813.7 835.2 856.7 884.4 905.9 927.4 955.0 976.5 998.0 1025.7 1047.2 1066.8 1088.3 1109.8 1137.4 1158.9 1180.4 1200.0 631.3 : 21.5 49.2 70.7 92.2 119.8 141.3 160.9 182.4 203.9 231.6 253.1 274.6 302.2 323.7 345.3 364.8 386.3 407.8 435.5 457.0 476.5 498.0 519.6 547.2 568.7 590.2 617.9 639.4 660.9 680.4 702.0 723.5 751.1 772.6 792.2 813.7 835.2 862.9 884.4 905.9 933.5 955.0 976.5 1004.2 1025.7 1045.3 1066.8 1088.3 1115.9 1137.4 1158.9 1178.5 1200.0 652.8 : 27.7 49.2 70.7 98.3 119.8 139.4 160.9 182.4 210.1 231.6 253.1 280.7 302.2 323.7 343.3 364.8 386.3 414.0 435.5 455.0 476.5 498.0 525.7 547.2 568.7 596.4 617.9 639.4 658.9 680.4 702.0 729.6 751.1 770.7 792.2 813.7 841.3 862.9 884.4 912.0 933.5 955.0 982.7 1004.2 1023.7 1045.3 1066.8 1094.4 1115.9 1137.4 1157.0 1178.5 1200.0 680.4 : 21.5 43.0 70.7 92.2 111.7 133.2 154.7 182.4 203.9 225.4 253.1 274.6 296.1 315.6 337.1 358.7 386.3 407.8 427.4 448.9 470.4 498.0 519.6 541.1 568.7 590.2 611.7 631.3 652.8 674.3 702.0 723.5 743.0 764.5 786.0 813.7 835.2 856.7 884.4 905.9 927.4 955.0 976.5 996.1 1017.6 1039.1 1066.8 1088.3 1109.8 1129.3 1150.8 1172.3 1200.0 702.0 : 21.5 49.2 70.7 90.2 111.7 133.2 160.9 182.4 203.9 231.6 253.1 274.6 294.1 315.6 337.1 364.8 386.3 405.9 427.4 448.9 476.5 498.0 519.6 547.2 568.7 590.2 609.8 631.3 652.8 680.4 702.0 721.5 743.0 764.5 792.2 813.7 835.2 862.9 884.4 905.9 933.5 955.0 974.6 996.1 1017.6 1045.3 1066.8 1088.3 1107.8 1129.3 1150.8 1178.5 1200.0 723.5 : 27.7 49.2 68.7 90.2 111.7 139.4 160.9 182.4 210.1 231.6 253.1 272.6 294.1 315.6 343.3 364.8 384.4 405.9 427.4 455.0 476.5 498.0 525.7 547.2 568.7 588.3 609.8 631.3 658.9 680.4 700.0 721.5 743.0 770.7 792.2 813.7 841.3 862.9 884.4 912.0 933.5 953.1 974.6 996.1 1023.7 1045.3 1066.8 1086.3 1107.8 1129.3 1157.0 1178.5 1200.0 751.1 : 21.5 41.1 62.6 84.1 111.7 133.2 154.7 182.4 203.9 225.4 245.0 266.5 288.0 315.6 337.1 356.7 378.2 399.7 427.4 448.9 470.4 498.0 519.6 541.1 560.6 582.1 603.6 631.3 652.8 672.3 693.8 715.4 743.0 764.5 786.0 813.7 835.2 856.7 884.4 905.9 925.4 946.9 968.4 996.1 1017.6 1039.1 1058.7 1080.2 1101.7 1129.3 1150.8 1172.3 1200.0 772.6 : 19.6 41.1 62.6 90.2 111.7 133.2 160.9 182.4 203.9 223.5 245.0 266.5 294.1 315.6 335.2 356.7 378.2 405.9 427.4 448.9 476.5 498.0 519.6 539.1 560.6 582.1 609.8 631.3 650.8 672.3 693.8 721.5 743.0 764.5 792.2 813.7 835.2 862.9 884.4 903.9 925.4 946.9 974.6 996.1 1017.6 1037.1 1058.7 1080.2 1107.8 1129.3 1150.8 1178.5 1200.0 792.2 : 21.5 43.0 70.7 92.2 113.7 141.3 162.9 184.4 203.9 225.4 246.9 274.6 296.1 315.6 337.1 358.7 386.3 407.8 429.3 457.0 478.5 500.0 519.6 541.1 562.6 590.2 611.7 631.3 652.8 674.3 702.0 723.5 745.0 772.6 794.1 815.6 843.3 864.8 884.4 905.9 927.4 955.0 976.5 998.0 1017.6 1039.1 1060.6 1088.3 1109.8 1131.3 1158.9 1180.4 1200.0 813.7 : 21.5 49.2 70.7 92.2 119.8 141.3 162.9 182.4 203.9 225.4 253.1 274.6 294.1 315.6 337.1 364.8 386.3 407.8 435.5 457.0 478.5 498.0 519.6 541.1 568.7 590.2 609.8 631.3 652.8 680.4 702.0 723.5 751.1 772.6 794.1 821.8 843.3 862.9 884.4 905.9 933.5 955.0 976.5 996.1 1017.6 1039.1 1066.8 1088.3 1109.8 1137.4 1158.9 1178.5 1200.0 835.2 : 27.7 49.2 70.7 98.3 119.8 141.3 160.9 182.4 203.9 231.6 253.1 272.6 294.1 315.6 343.3 364.8 386.3 414.0 435.5 457.0 476.5 498.0 519.6 547.2 568.7 588.3 609.8 631.3 658.9 680.4 702.0 729.6 751.1 772.6 800.3 821.8 841.3 862.9 884.4 912.0 933.5 955.0 974.6 996.1 1017.6 1045.3 1066.8 1088.3 1115.9 1137.4 1157.0 1178.5 1200.0 862.9 : 21.5 43.0 70.7 92.2 113.7 133.2 154.7 176.3 203.9 225.4 245.0 266.5 288.0 315.6 337.1 358.7 386.3 407.8 429.3 448.9 470.4 491.9 519.6 541.1 560.6 582.1 603.6 631.3 652.8 674.3 702.0 723.5 745.0 772.6 794.1 813.7 835.2 856.7 884.4 905.9 927.4 946.9 968.4 989.9 1017.6 1039.1 1060.6 1088.3 1109.8 1129.3 1150.8 1172.3 1200.0 884.4 : 21.5 49.2 70.7 92.2 111.7 133.2 154.7 182.4 203.9 223.5 245.0 266.5 294.1 315.6 337.1 364.8 386.3 407.8 427.4 448.9 470.4 498.0 519.6 539.1 560.6 582.1 609.8 631.3 652.8 680.4 702.0 723.5 751.1 772.6 792.2 813.7 835.2 862.9 884.4 905.9 925.4 946.9 968.4 996.1 1017.6 1039.1 1066.8 1088.3 1107.8 1129.3 1150.8 1178.5 1200.0 905.9 : 27.7 49.2 70.7 90.2 111.7 133.2 160.9 182.4 202.0 223.5 245.0 272.6 294.1 315.6 343.3 364.8 386.3 405.9 427.4 448.9 476.5 498.0 517.6 539.1 560.6 588.3 609.8 631.3 658.9 680.4 702.0 729.6 751.1 770.7 792.2 813.7 841.3 862.9 884.4 903.9 925.4 946.9 974.6 996.1 1017.6 1045.3 1066.8 1086.3 1107.8 1129.3 1157.0 1178.5 1200.0 933.5 : 21.5 43.0 62.6 84.1 105.6 133.2 154.7 174.3 195.8 217.3 245.0 266.5 288.0 315.6 337.1 358.7 378.2 399.7 421.2 448.9 470.4 489.9 511.4 533.0 560.6 582.1 603.6 631.3 652.8 674.3 702.0 723.5 743.0 764.5 786.0 813.7 835.2 856.7 876.3 897.8 919.3 946.9 968.4 989.9 1017.6 1039.1 1058.7 1080.2 1101.7 1129.3 1150.8 1172.3 1200.0 955.0 : 21.5 41.1 62.6 84.1 111.7 133.2 152.8 174.3 195.8 223.5 245.0 266.5 294.1 315.6 337.1 356.7 378.2 399.7 427.4 448.9 468.4 489.9 511.4 539.1 560.6 582.1 609.8 631.3 652.8 680.4 702.0 721.5 743.0 764.5 792.2 813.7 835.2 854.7 876.3 897.8 925.4 946.9 968.4 996.1 1017.6 1037.1 1058.7 1080.2 1107.8 1129.3 1150.8 1178.5 1200.0 976.5 : 19.6 41.1 62.6 90.2 111.7 131.3 152.8 174.3 202.0 223.5 245.0 272.6 294.1 315.6 335.2 356.7 378.2 405.9 427.4 446.9 468.4 489.9 517.6 539.1 560.6 588.3 609.8 631.3 658.9 680.4 700.0 721.5 743.0 770.7 792.2 813.7 833.2 854.7 876.3 903.9 925.4 946.9 974.6 996.1 1015.6 1037.1 1058.7 1086.3 1107.8 1129.3 1157.0 1178.5 1200.0 996.1 : 21.5 43.0 70.7 92.2 111.7 133.2 154.7 182.4 203.9 225.4 253.1 274.6 296.1 315.6 337.1 358.7 386.3 407.8 427.4 448.9 470.4 498.0 519.6 541.1 568.7 590.2 611.7 639.4 660.9 680.4 702.0 723.5 751.1 772.6 794.1 813.7 835.2 856.7 884.4 905.9 927.4 955.0 976.5 996.1 1017.6 1039.1 1066.8 1088.3 1109.8 1137.4 1158.9 1180.4 1200.0 1017.6: 21.5 49.2 70.7 90.2 111.7 133.2 160.9 182.4 203.9 231.6 253.1 274.6 294.1 315.6 337.1 364.8 386.3 405.9 427.4 448.9 476.5 498.0 519.6 547.2 568.7 590.2 617.9 639.4 658.9 680.4 702.0 729.6 751.1 772.6 792.2 813.7 835.2 862.9 884.4 905.9 933.5 955.0 974.6 996.1 1017.6 1045.3 1066.8 1088.3 1115.9 1137.4 1158.9 1178.5 1200.0 1039.1: 27.7 49.2 68.7 90.2 111.7 139.4 160.9 182.4 210.1 231.6 253.1 272.6 294.1 315.6 343.3 364.8 384.4 405.9 427.4 455.0 476.5 498.0 525.7 547.2 568.7 596.4 617.9 637.4 658.9 680.4 708.1 729.6 751.1 770.7 792.2 813.7 841.3 862.9 884.4 912.0 933.5 953.1 974.6 996.1 1023.7 1045.3 1066.8 1094.4 1115.9 1137.4 1157.0 1178.5 1200.0 1066.8: 21.5 41.1 62.6 84.1 111.7 133.2 154.7 182.4 203.9 225.4 245.0 266.5 288.0 315.6 337.1 356.7 378.2 399.7 427.4 448.9 470.4 498.0 519.6 541.1 568.7 590.2 609.8 631.3 652.8 680.4 702.0 723.5 743.0 764.5 786.0 813.7 835.2 856.7 884.4 905.9 925.4 946.9 968.4 996.1 1017.6 1039.1 1066.8 1088.3 1109.8 1129.3 1150.8 1172.3 1200.0 1088.3: 19.6 41.1 62.6 90.2 111.7 133.2 160.9 182.4 203.9 223.5 245.0 266.5 294.1 315.6 335.2 356.7 378.2 405.9 427.4 448.9 476.5 498.0 519.6 547.2 568.7 588.3 609.8 631.3 658.9 680.4 702.0 721.5 743.0 764.5 792.2 813.7 835.2 862.9 884.4 903.9 925.4 946.9 974.6 996.1 1017.6 1045.3 1066.8 1088.3 1107.8 1129.3 1150.8 1178.5 1200.0 1107.8: 21.5 43.0 70.7 92.2 113.7 141.3 162.9 184.4 203.9 225.4 246.9 274.6 296.1 315.6 337.1 358.7 386.3 407.8 429.3 457.0 478.5 500.0 527.7 549.2 568.7 590.2 611.7 639.4 660.9 682.4 702.0 723.5 745.0 772.6 794.1 815.6 843.3 864.8 884.4 905.9 927.4 955.0 976.5 998.0 1025.7 1047.2 1068.7 1088.3 1109.8 1131.3 1158.9 1180.4 1200.0 1129.3: 21.5 49.2 70.7 92.2 119.8 141.3 162.9 182.4 203.9 225.4 253.1 274.6 294.1 315.6 337.1 364.8 386.3 407.8 435.5 457.0 478.5 506.2 527.7 547.2 568.7 590.2 617.9 639.4 660.9 680.4 702.0 723.5 751.1 772.6 794.1 821.8 843.3 862.9 884.4 905.9 933.5 955.0 976.5 1004.2 1025.7 1047.2 1066.8 1088.3 1109.8 1137.4 1158.9 1178.5 1200.0 1150.8: 27.7 49.2 70.7 98.3 119.8 141.3 160.9 182.4 203.9 231.6 253.1 272.6 294.1 315.6 343.3 364.8 386.3 414.0 435.5 457.0 484.6 506.2 525.7 547.2 568.7 596.4 617.9 639.4 658.9 680.4 702.0 729.6 751.1 772.6 800.3 821.8 841.3 862.9 884.4 912.0 933.5 955.0 982.7 1004.2 1025.7 1045.3 1066.8 1088.3 1115.9 1137.4 1157.0 1178.5 1200.0 1178.5: 21.5 43.0 70.7 92.2 113.7 133.2 154.7 176.3 203.9 225.4 245.0 266.5 288.0 315.6 337.1 358.7 386.3 407.8 429.3 457.0 478.5 498.0 519.6 541.1 568.7 590.2 611.7 631.3 652.8 674.3 702.0 723.5 745.0 772.6 794.1 813.7 835.2 856.7 884.4 905.9 927.4 955.0 976.5 998.0 1017.6 1039.1 1060.6 1088.3 1109.8 1129.3 1150.8 1172.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 19.5526 .. 27.6598 cents 15625/15552, 8.1073 cents 2048/2025, 19.5526 cents 2: 41.0589 .. 49.1661 cents 15625/15552, 8.1073 cents 78732/78125, 13.3990 cents 3: 62.5651 .. 70.6724 cents 15625/15552, 8.1073 cents 78732/78125, 13.3990 cents 4: 84.0714 .. 98.3323 cents 390625000/387420489, 14.2608 cents 78732/78125, 13.3990 cents 5: 105.5777 .. 119.8386 cents 390625000/387420489, 14.2608 cents 7.24545 cents 6: 131.2839 .. 141.3449 cents 2109375/2097152, 10.0610 cents 393216/390625, 11.4453 cents 7: 152.7901 .. 169.0047 cents 244140625/241864704, 16.2146 cents 393216/390625, 11.4453 cents 8: 174.2964 .. 190.5110 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 9: 195.8027 .. 212.0173 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 10: 217.3090 .. 233.5236 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 11: 244.9689 .. 253.0761 cents 15625/15552, 8.1073 cents 393216/390625, 11.4453 cents 12: 266.4751 .. 280.7360 cents 390625000/387420489, 14.2608 cents 78732/78125, 13.3990 cents 13: 287.9814 .. 302.2423 cents 390625000/387420489, 14.2608 cents 7.24545 cents 14: 315.6413 .. 323.7486 cents 15625/15552, 8.1073 cents 78732/78125, 13.3990 cents 15: 335.1939 .. 345.2549 cents 2109375/2097152, 10.0610 cents 393216/390625, 11.4453 cents 16: 356.7001 .. 366.7611 cents 2109375/2097152, 10.0610 cents 393216/390625, 11.4453 cents 17: 378.2064 .. 392.4673 cents 390625000/387420489, 14.2608 cents 393216/390625, 11.4453 cents 18: 399.7127 .. 413.9736 cents 390625000/387420489, 14.2608 cents 7.24545 cents 19: 421.2190 .. 435.4799 cents 390625000/387420489, 14.2608 cents 7.24545 cents 20: 446.9251 .. 456.9861 cents 2109375/2097152, 10.0610 cents 393216/390625, 11.4453 cents 21: 468.4314 .. 484.6460 cents 244140625/241864704, 16.2146 cents 393216/390625, 11.4453 cents 22: 489.9377 .. 506.1523 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 23: 511.4440 .. 527.6586 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 24: 532.9503 .. 549.1649 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 25: 560.6101 .. 568.7174 cents 15625/15552, 8.1073 cents 393216/390625, 11.4453 cents 26: 582.1164 .. 596.3773 cents 390625000/387420489, 14.2608 cents 78732/78125, 13.3990 cents 27: 603.6227 .. 617.8836 cents 390625000/387420489, 14.2608 cents 7.24545 cents 28: 631.2826 .. 639.3899 cents 15625/15552, 8.1073 cents 78732/78125, 13.3990 cents 29: 650.8351 .. 667.0497 cents 244140625/241864704, 16.2146 cents 393216/390625, 11.4453 cents 30: 672.3414 .. 688.5560 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 31: 693.8477 .. 710.0623 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 32: 715.3540 .. 731.5686 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 33: 743.0139 .. 753.0749 cents 2109375/2097152, 10.0610 cents 393216/390625, 11.4453 cents 34: 764.5201 .. 778.7810 cents 390625000/387420489, 14.2608 cents 393216/390625, 11.4453 cents 35: 786.0264 .. 800.2873 cents 390625000/387420489, 14.2608 cents 7.24545 cents 36: 807.5327 .. 821.7936 cents 390625000/387420489, 14.2608 cents 7.24545 cents 37: 833.2389 .. 843.2999 cents 2109375/2097152, 10.0610 cents 393216/390625, 11.4453 cents 38: 854.7451 .. 864.8061 cents 2109375/2097152, 10.0610 cents 393216/390625, 11.4453 cents 39: 876.2514 .. 884.3587 cents 15625/15552, 8.1073 cents 393216/390625, 11.4453 cents 40: 897.7577 .. 912.0186 cents 390625000/387420489, 14.2608 cents 78732/78125, 13.3990 cents 41: 919.2640 .. 933.5249 cents 390625000/387420489, 14.2608 cents 7.24545 cents 42: 946.9239 .. 955.0311 cents 15625/15552, 8.1073 cents 78732/78125, 13.3990 cents 43: 966.4764 .. 982.6910 cents 244140625/241864704, 16.2146 cents 393216/390625, 11.4453 cents 44: 987.9827 .. 1004.1973 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 45: 1009.4890 .. 1025.7036 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 46: 1030.9953 .. 1047.2099 cents 244140625/241864704, 16.2146 cents 1224440064/1220703125, 5.2917 cents 47: 1058.6551 .. 1068.7161 cents 2109375/2097152, 10.0610 cents 393216/390625, 11.4453 cents 48: 1080.1614 .. 1094.4223 cents 390625000/387420489, 14.2608 cents 393216/390625, 11.4453 cents 49: 1101.6677 .. 1115.9286 cents 390625000/387420489, 14.2608 cents 7.24545 cents 50: 1129.3276 .. 1137.4349 cents 15625/15552, 8.1073 cents 78732/78125, 13.3990 cents 51: 1150.8339 .. 1158.9411 cents 15625/15552, 8.1073 cents 78732/78125, 13.3990 cents 52: 1172.3402 .. 1180.4474 cents 15625/15552, 8.1073 cents 78732/78125, 13.3990 cents
SHOW DATA
Number of notes : 53 -- Interval properties -- Smallest interval : 2048/2025, 19.5526 cents, class 1 Average step (divided formal octave): 22.6415 cents Largest one step interval : 20000/19683, 27.6598 cents Average / Smallest step : 1.157981 Largest / Average step : 1.221643 Largest / Smallest step : 1.414640 Median interval of one step : 81/80, 21.5063 cents, amount: 34 Most common interval of one step : 81/80, 21.5063 cents, amount: 34 Least squares average step : 22.64960 cents, oct.: 1200.42875 cents Scale is strictly proper Step pattern alph. order: ABAACAABACAABAABAABACAABAACAABAABACAABAABAACAABACAABA Step pattern size order : MLMMSMMLMSMMLMMLMMLMSMMLMMSMMLMMLMSMMLMMLMMSMMLMSMMLM Scale is a Constant Structure, by a margin of 5.29173 cents Scale diversity : 1.263182 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.445515 Number of different interval sizes : 212 = 4.07692 / class Number of one step interval sizes : 3 Highest interval variety : 5 Mean interval variety : 4.07692 = 53/13 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 44 Most common triad is 0.0 315.641 884.359 cents, amount: 35 Number of recognisable fifths : 57, average 701.8916 cents Number of appreciable fifths : 53, average 701.8868 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 3 5 9 15 25 27 45 81 135 243 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 47 = 88.6792% -- Rational properties -- Prime limit : 5 Odd number limit : 1594323 (O: 1594323 U: 1594323) Highest odd numerator or denominator: 2187 Scale harmonicity : 0.009914 Average absolute harmonicity : 0.079557 Specific harmonicity : 0.069117 Fundamental : 1/58320000, -25.7975 octaves, 0.0000 Hz. Guide tone : 349920000, 28.3824 octaves, 91548017810.126 Hz. Exponens Consonantiae : 2.040733E+16, 54.17994 octaves Euler's gradus suavitatis : 74 Sum of Mann's harmonic distance : 10031.5, average 189.27358 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 92.37017, average 1.74283 Sum of Tenney's harmonic distance : 184.29147, average 3.47720 Vogel's harmonic complexity : 45.94340 Wille's k value : 51257812 Wilson's harmonic complexity : 79 Rectangular lattice diameter : 21 Triangular lattice diameter : 13 Lattice compactness : 10065.80391, average 7.03410 Lattice compactness (without 2's) : 6980.46189, average 4.87803 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 8 0.11321 166 1 3: -6 .. 7 0.05660 157 8 5: -4 .. 4 0.13208 85 44 Average exponent except 2's : 10 / 53 = 0.18868 Average absolute exponent except 2's: 242 / 53 = 4.56604 Scale is JI-epimorphic with val: <53 84 123| = patent
FIT/MODE
53: 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 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 2.5872 c. M: 5.2912 c. 99: 2 2 2 2 1 2 2 2 2 1 2 2 2 2 2 2 2 2 2 2 1 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 2 1 2 2 2 2 1 2 2 2 2 P D3 SD: 2.5861 c. M:-5.2808 c. 112: 2 3 2 2 1 2 2 3 2 2 2 2 2 2 2 3 2 2 3 2 1 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2 2 2 2 2 3 2 1 2 2 3 2 N SD: 3.3043 c. M: 5.2656 c. 114: 2 3 2 2 2 2 2 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 2 2 2 2 3 2 P D3 I SD: 2.8599 c. M: 4.3546 c. 116: 2 3 2 2 2 2 2 3 2 2 2 2 2 3 2 2 2 2 3 2 2 2 2 3 2 2 2 2 2 3 2 2 3 2 2 2 2 2 2 3 2 2 2 2 2 2 3 2 2 2 2 3 2 P D3 SD: 2.8352 c. M: 5.0484 c. 118: 2 3 2 2 2 2 2 3 2 2 2 2 3 2 2 3 2 2 3 2 2 2 2 3 2 2 2 2 2 3 2 2 3 2 2 2 2 3 2 2 3 2 2 2 2 2 3 2 2 2 2 3 2 P D3 SD: 1.1018 c. M: 2.2015 c. 171: 3 4 3 3 3 3 3 4 3 3 3 3 4 3 3 4 3 3 4 3 3 3 3 4 3 3 3 3 3 4 3 3 4 3 3 3 3 4 3 3 4 3 3 3 3 3 4 3 3 3 3 4 3 SP D3 SD: 0.5086 c. M:-1.0988 c. 388: 7 9 7 7 6 7 7 9 7 6 7 7 9 7 7 9 7 7 9 7 6 7 7 9 7 7 6 7 7 9 7 7 9 7 6 7 7 9 7 7 9 7 7 6 7 7 9 7 6 7 7 9 7 SP SD: 0.3818 c. M: 0.7822 c. 441: 8 10 8 8 7 8 8 10 8 7 8 8 10 8 8 10 8 8 10 8 7 8 8 10 8 8 7 8 8 10 8 8 10 8 7 8 8 10 8 8 10 8 8 7 8 8 10 8 7 8 8 10 8 SP SD: 0.2134 c. M:-0.3582 c. 559: 10 13 10 10 9 10 10 13 10 9 10 10 13 10 10 13 10 10 13 10 9 10 10 13 10 10 9 10 10 13 10 10 13 10 9 10 10 13 10 10 13 10 10 9 10 10 13 10 9 10 10 13 10 SP SD: 0.1479 c. M:-0.2983 c. 612: 11 14 11 11 10 11 11 14 11 10 11 11 14 11 11 14 11 11 14 11 10 11 11 14 11 11 10 11 11 14 11 11 14 11 10 11 11 14 11 11 14 11 11 10 11 11 14 11 10 11 11 14 11 SP SD: 0.0925 c. M:-0.1915 c. 1171: 21 27 21 21 19 21 21 27 21 19 21 21 27 21 21 27 21 21 27 21 19 21 21 27 21 21 19 21 21 27 21 21 27 21 19 21 21 27 21 21 27 21 21 19 21 21 27 21 19 21 21 27 21 SP SD: 0.0305 c. M: 0.0638 c. 1783: 32 41 32 32 29 32 32 41 32 29 32 32 41 32 32 41 32 32 41 32 29 32 32 41 32 32 29 32 32 41 32 32 41 32 29 32 32 41 32 32 41 32 32 29 32 32 41 32 29 32 32 41 32 SP SD: 0.0258 c. M:-0.0514 c. 2513: 45 58 45 45 41 45 45 58 45 41 45 45 58 45 45 58 45 45 58 45 41 45 45 58 45 45 41 45 45 58 45 45 58 45 41 45 45 58 45 45 58 45 45 41 45 45 58 45 41 45 45 58 45 SP SD: 0.0147 c. M: 0.0284 c. 3125: 56 72 56 56 51 56 56 72 56 51 56 56 72 56 56 72 56 56 72 56 51 56 56 72 56 56 51 56 56 72 56 56 72 56 51 56 56 72 56 56 72 56 56 51 56 56 72 56 51 56 56 72 56 SP SD: 0.0134 c. M: 0.0261 c. 3684: 66 85 66 66 60 66 66 85 66 60 66 66 85 66 66 85 66 66 85 66 60 66 66 85 66 66 60 66 66 85 66 66 85 66 60 66 66 85 66 66 85 66 66 60 66 66 85 66 60 66 66 85 66 SP SD: 0.0124 c. M:-0.0256 c. 4296: 77 99 77 77 70 77 77 99 77 70 77 77 99 77 77 99 77 77 99 77 70 77 77 99 77 77 70 77 77 99 77 77 99 77 70 77 77 99 77 77 99 77 77 70 77 77 99 77 70 77 77 99 77 SP SD: 0.0026 c. M:-0.0053 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: 1.9279 cents 5 .. 10 match: 5 H SD: 1.5423 cents 6 .. 12 match: 6 H SD: 1.7113 cents 7 .. 14 match: 7 H SD: 2.2016 cents 8 .. 16 match: 8 H SD: 1.2796 cents 9 .. 18 match: 9 H SD: 1.7182 cents 10 .. 20 match: 10 H SD: 1.8630 cents 11 .. 22 match: 11 H SD: 2.1532 cents 12 .. 24 match: 12 H SD: 1.3430 cents 13 .. 26 match: 13 H SD: 1.4285 cents 14 .. 28 match: 14 H SD: 1.6162 cents 15 .. 30 match: 15 H SD: 1.4819 cents 16 .. 32 match: 16 H SD: 1.1331 cents 17 .. 34 match: 17 H SD: 1.9077 cents 18 .. 36 match: 18 H SD: 1.3820 cents 19 .. 38 match: 19 H SD: 1.4584 cents 20 .. 40 match: 20 H SD: 1.2961 cents 21 .. 42 match: 21 H SD: 1.3568 cents 22 .. 44 match: 22 H SD: 1.4936 cents 23 .. 46 match: 23 H SD: 1.2999 cents 24 .. 48 match: 24 H SD: 1.1213 cents 25 .. 50 match: 25 H SD: 1.2611 cents 26 .. 52 match: 26 H SD: 1.1932 cents 27 .. 54 match: 27 H SD: 1.2161 cents 28 .. 56 match: 28 H SD: 1.2563 cents 29 .. 58 match: 29 H SD: 1.4443 cents 30 .. 60 match: 30 H SD: 1.2426 cents 31 .. 62 match: 31 H SD: 1.1865 cents 32 .. 64 match: 32 H SD: 1.0934 cents 33 .. 66 match: 33 H SD: 1.0599 cents 34 .. 68 match: 34 H SD: 1.1869 cents 35 .. 70 match: 35 H SD: 1.0011 cents 36 .. 72 match: 36 H SD: 1.0714 cents 37 .. 74 match: 36 SD: 0.9771 cents 38 .. 76 match: 38 H SD: 1.0187 cents 39 .. 78 match: 39 H SD: 0.9492 cents 40 .. 80 match: 40 H SD: 1.0640 cents 41 .. 82 match: 41 H SD: 1.0417 cents 42 .. 84 match: 42 H SD: 0.9553 cents 43 .. 86 match: 42 S SD: 1.0736 cents 44 .. 88 match: 42 SD: 1.0912 cents 45 .. 90 match: 44 SD: 0.9154 cents 46 .. 92 match: 45 SD: 0.8834 cents 47 .. 94 match: 44 SD: 1.0855 cents 48 .. 96 match: 46 SD: 0.8196 cents 49 .. 98 match: 44 SD: 1.0013 cents 50 .. 100 match: 47 SD: 0.8513 cents 51 .. 102 match: 46 SD: 1.0050 cents 52 .. 104 match: 48 SD: 0.8193 cents 53 .. 106 match: 47 SD: 0.9361 cents 54 .. 108 match: 49 SD: 0.7907 cents 55 .. 110 match: 49 SD: 0.8838 cents 56 .. 112 match: 49 SD: 0.8413 cents 57 .. 114 match: 49 SD: 0.7960 cents 58 .. 116 match: 47 SD: 1.0076 cents 59 .. 118 match: 51 SD: 0.7996 cents 60 .. 120 match: 51 SD: 0.6960 cents 61 .. 122 match: 51 SD: 0.8249 cents 62 .. 124 match: 50 SD: 0.8259 cents 63 .. 126 match: 51 SD: 0.7921 cents 64 .. 128 match: 52 SD: 0.6440 cents 65 .. 130 match: 52 SD: 0.7255 cents 66 .. 132 match: 52 SD: 0.6714 cents 67 .. 134 match: 52 SD: 0.7577 cents 68 .. 136 match: 51 SD: 0.7847 cents 69 .. 138 match: 51 SD: 0.7345 cents 70 .. 140 match: 53 SD: 0.7135 cents 71 .. 142 match: 53 SD: 0.6458 cents 72 .. 144 match: 53 SD: 0.5899 cents 73 .. 146 match: 53 SD: 0.5693 cents 76 .. 152 match: 52 SD: 0.6086 cents 79 .. 158 match: 53 SD: 0.5829 cents 86 .. 172 match: 53 SD: 0.5793 cents 87 .. 174 match: 53 SD: 0.5409 cents 88 .. 176 match: 53 SD: 0.5374 cents 90 .. 180 match: 53 SD: 0.5154 cents 94 .. 188 match: 53 SD: 0.5098 cents 95 .. 190 match: 53 SD: 0.5025 cents 96 .. 192 match: 53 SD: 0.4996 cents 98 .. 196 match: 53 SD: 0.4767 cents 102 .. 204 match: 53 SD: 0.4507 cents 108 .. 216 match: 53 SD: 0.4353 cents 114 .. 228 match: 53 SD: 0.4342 cents 116 .. 232 match: 53 SD: 0.3953 cents 125 .. 250 match: 53 SD: 0.3770 cents 126 .. 252 match: 53 SD: 0.3713 cents 129 .. 258 match: 53 SD: 0.3592 cents 135 .. 270 match: 53 SD: 0.3479 cents 136 .. 272 match: 53 SD: 0.3336 cents 140 .. 280 match: 53 SD: 0.3214 cents 144 .. 288 match: 53 SD: 0.3184 cents 145 .. 290 match: 53 SD: 0.3056 cents 150 .. 300 match: 53 SD: 0.2914 cents 162 .. 324 match: 53 SD: 0.2441 cents 195 .. 390 match: 53 SD: 0.2424 cents 199 .. 398 match: 53 SD: 0.2378 cents 209 .. 418 match: 53 SD: 0.2372 cents 210 .. 420 match: 53 SD: 0.2151 cents 216 .. 432 match: 53 SD: 0.2032 cents 224 .. 448 match: 53 SD: 0.2025 cents 234 .. 468 match: 53 SD: 0.1783 cents 255 .. 510 match: 53 SD: 0.1747 cents 270 .. 540 match: 53 SD: 0.1661 cents 288 .. 576 match: 53 SD: 0.1449 cents 311 .. 622 match: 53 SD: 0.1394 cents 312 .. 624 match: 53 SD: 0.1321 cents 350 .. 700 match: 53 SD: 0.1234 cents 376 .. 752 match: 53 SD: 0.1219 cents 384 .. 768 match: 53 SD: 0.1006 cents 414 .. 828 match: 53 SD: 0.0991 cents 455 .. 910 match: 53 SD: 0.0964 cents 474 .. 948 match: 53 SD: 0.0931 cents 480 .. 960 match: 53 SD: 0.0782 cents 552 .. 1104 match: 53 SD: 0.0776 cents 576 .. 1152 match: 53 SD: 0.0759 cents 600 .. 1200 match: 53 SD: 0.0682 cents