Scala analysis: kleismic34trans
Kleismic[34] transversal (detempering)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128/125 41.058858 minor diesis, diesis 2: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 16/15 111.731285 minor diatonic semitone 4: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 5: 10/9 182.403712 minor whole tone 6: 9/8 203.910002 major whole tone 7: 144/125 244.968860 classic diminished third 8: 75/64 274.582429 classic augmented second 9: 6/5 315.641287 minor third 10: 100/81 364.807424 grave major third 11: 5/4 386.313714 major third 12: 32/25 427.372572 classic diminished fourth 13: 162/125 448.878862 14: 4/3 498.044999 perfect fourth 15: 27/20 519.551289 acute fourth 16: 25/18 568.717426 classic augmented fourth 17: 45/32 590.223716 diatonic tritone 18: 36/25 631.282574 classic diminished fifth 19: 40/27 680.448711 grave fifth 20: 3/2 701.955001 perfect fifth 21: 125/81 751.121138 22: 25/16 772.627428 classic augmented fifth 23: 8/5 813.686286 minor sixth 24: 81/50 835.192576 acute minor sixth 25: 5/3 884.358713 major sixth, BP sixth 26: 128/75 925.417571 diminished seventh 27: 125/72 955.031140 classic augmented sixth 28: 16/9 996.089998 Pythagorean minor seventh 29: 9/5 1017.596288 just minor seventh, BP seventh 30: 50/27 1066.762425 grave major seventh 31: 15/8 1088.268715 classic major seventh 32: 48/25 1129.327573 classic diminished octave 33: 125/64 1158.941142 classic augmented seventh, octave - minor diesis 34: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 128/125 41.0589 minor diesis, diesis 1: 128/125 41.0589 minor diesis, diesis 2: 3125/3072 29.6136 small diesis, magic comma 3: 128/125 41.0589 minor diesis, diesis 4: 81/80 21.5063 syntonic comma, Didymus comma 5: 250/243 49.1661 maximal diesis, Porcupine comma 6: 81/80 21.5063 syntonic comma, Didymus comma 7: 128/125 41.0589 minor diesis, diesis 8: 3125/3072 29.6136 small diesis, magic comma 9: 128/125 41.0589 minor diesis, diesis 10: 250/243 49.1661 maximal diesis, Porcupine comma 11: 81/80 21.5063 syntonic comma, Didymus comma 12: 128/125 41.0589 minor diesis, diesis 13: 81/80 21.5063 syntonic comma, Didymus comma 14: 250/243 49.1661 maximal diesis, Porcupine comma 15: 81/80 21.5063 syntonic comma, Didymus comma 16: 250/243 49.1661 maximal diesis, Porcupine comma 17: 81/80 21.5063 syntonic comma, Didymus comma 18: 128/125 41.0589 minor diesis, diesis 19: 250/243 49.1661 maximal diesis, Porcupine comma 20: 81/80 21.5063 syntonic comma, Didymus comma 21: 250/243 49.1661 maximal diesis, Porcupine comma 22: 81/80 21.5063 syntonic comma, Didymus comma 23: 128/125 41.0589 minor diesis, diesis 24: 81/80 21.5063 syntonic comma, Didymus comma 25: 250/243 49.1661 maximal diesis, Porcupine comma 26: 128/125 41.0589 minor diesis, diesis 27: 3125/3072 29.6136 small diesis, magic comma 28: 128/125 41.0589 minor diesis, diesis 29: 81/80 21.5063 syntonic comma, Didymus comma 30: 250/243 49.1661 maximal diesis, Porcupine comma 31: 81/80 21.5063 syntonic comma, Didymus comma 32: 128/125 41.0589 minor diesis, diesis 33: 3125/3072 29.6136 small diesis, magic comma 34: 128/125 41.0589 minor diesis, diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 11 81/80 21.506 cents syntonic comma, Didymus comma 1: 4 3125/3072 29.614 cents small diesis, magic comma 1: 11 128/125 41.059 cents minor diesis, diesis 1: 8 250/243 49.166 cents maximal diesis, Porcupine comma 2: 9 648/625 62.565 cents major diesis 2: 21 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 16384/15625 82.118 cents two (minor diesis, diesis) 2: 3 256/243 90.225 cents limma, Pythagorean minor second 3: 2 6561/6250 84.071 cents ripple 3: 9 135/128 92.179 cents major chroma, major limma 3: 19 16/15 111.731 cents minor diatonic semitone 3: 4 3125/2916 119.839 cents quasi-equal 10-tone semitone 4: 16 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 4: 10 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 4: 4 2048/1875 152.790 cents double diminished third 4: 4 800/729 160.897 cents grave whole tone 5: 2 2187/2000 154.744 cents Gorgo limma 5: 5 1125/1024 162.851 cents double augmented prime 5: 6 3456/3125 174.296 cents 5: 21 10/9 182.404 cents minor whole tone 6: 22 9/8 203.910 cents major whole tone 6: 8 256/225 223.463 cents Neapolitan diminished third 6: 4 2500/2187 231.570 cents 7: 1 729/640 225.416 cents acute major second 7: 2 9375/8192 233.524 cents 7: 17 144/125 244.969 cents classic diminished third 7: 14 125/108 253.076 cents semi-augmented whole tone 8: 5 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 8: 13 75/64 274.582 cents classic augmented second 8: 2 18432/15625 286.028 cents 8: 13 32/27 294.135 cents Pythagorean minor third 8: 1 15625/13122 302.242 cents 9: 27 6/5 315.641 cents minor third 9: 6 3125/2592 323.749 cents 9: 1 4096/3375 335.194 cents double diminished fourth 10: 8 243/200 337.148 cents acute minor third 10: 6 625/512 345.255 cents classic neutral third 10: 8 768/625 356.700 cents 10: 12 100/81 364.807 cents grave major third 11: 4 3888/3125 378.206 cents 11: 25 5/4 386.314 cents major third 11: 5 512/405 405.866 cents narrow diminished fourth 12: 10 81/64 407.820 cents Pythagorean major third 12: 16 32/25 427.373 cents classic diminished fourth 12: 8 625/486 435.480 cents 13: 12 162/125 448.879 cents 13: 13 125/96 456.986 cents classic augmented third 13: 2 4096/3125 468.431 cents 13: 7 320/243 476.539 cents grave fourth 14: 1 6561/5000 470.385 cents 14: 5 675/512 478.492 cents wide augmented third 14: 3 20736/15625 489.938 cents two (classic diminished third) 14: 23 4/3 498.045 cents perfect fourth 14: 2 15625/11664 506.152 cents two (semi-augmented whole tone) 15: 17 27/20 519.551 cents acute fourth 15: 4 3125/2304 527.659 cents 15: 7 512/375 539.104 cents double diminished fifth 15: 6 1000/729 547.211 cents 16: 2 5625/4096 549.165 cents double augmented third 16: 12 864/625 560.610 cents 16: 20 25/18 568.717 cents classic augmented fourth 17: 2 4374/3125 582.116 cents 17: 15 45/32 590.224 cents diatonic tritone 17: 15 64/45 609.776 cents 2nd tritone 17: 2 3125/2187 617.884 cents 18: 20 36/25 631.283 cents classic diminished fifth 18: 12 625/432 639.390 cents 18: 2 8192/5625 650.835 cents double diminished sixth 19: 6 729/500 652.789 cents 19: 7 375/256 660.896 cents double augmented fourth 19: 4 4608/3125 672.341 cents 19: 17 40/27 680.449 cents grave fifth 20: 2 23328/15625 693.848 cents 20: 23 3/2 701.955 cents perfect fifth 20: 3 15625/10368 710.062 cents 20: 5 1024/675 721.508 cents narrow diminished sixth 20: 1 10000/6561 729.615 cents two (grave major third) 21: 7 243/160 723.461 cents acute fifth 21: 2 3125/2048 731.569 cents 21: 13 192/125 743.014 cents classic diminished sixth 21: 12 125/81 751.121 cents 22: 8 972/625 764.520 cents 22: 16 25/16 772.627 cents classic augmented fifth 22: 10 128/81 792.180 cents Pythagorean minor sixth 23: 5 405/256 794.134 cents wide augmented fifth 23: 25 8/5 813.686 cents minor sixth 23: 4 3125/1944 821.794 cents 24: 12 81/50 835.193 cents acute minor sixth 24: 8 625/384 843.300 cents 24: 6 1024/625 854.745 cents two (classic diminished fourth) 24: 8 400/243 862.852 cents grave major sixth 25: 1 3375/2048 864.806 cents double augmented fifth 25: 6 5184/3125 876.251 cents 25: 27 5/3 884.359 cents major sixth, BP sixth 26: 1 26244/15625 897.758 cents 26: 13 27/16 905.865 cents Pythagorean major sixth 26: 2 15625/9216 913.972 cents two (classic augmented third) 26: 13 128/75 925.418 cents diminished seventh 26: 5 1250/729 933.525 cents 27: 14 216/125 946.924 cents semi-augmented sixth 27: 17 125/72 955.031 cents classic augmented sixth 27: 2 16384/9375 966.476 cents 27: 1 1280/729 974.584 cents grave minor seventh 28: 4 2187/1250 968.430 cents 28: 8 225/128 976.537 cents augmented sixth 28: 22 16/9 996.090 cents Pythagorean minor seventh 29: 21 9/5 1017.596 cents just minor seventh, BP seventh 29: 6 3125/1728 1025.704 cents 29: 5 2048/1125 1037.149 cents double diminished octave 29: 2 4000/2187 1045.256 cents 30: 4 729/400 1039.103 cents acute minor seventh 30: 4 1875/1024 1047.210 cents double augmented sixth 30: 10 1152/625 1058.655 cents 30: 16 50/27 1066.762 cents grave major seventh 31: 4 5832/3125 1080.161 cents 31: 19 15/8 1088.269 cents classic major seventh 31: 9 256/135 1107.821 cents octave - major chroma 31: 2 12500/6561 1115.929 cents 32: 3 243/128 1109.775 cents Pythagorean major seventh 32: 1 15625/8192 1117.882 cents 32: 21 48/25 1129.328 cents classic diminished octave 32: 9 625/324 1137.435 cents octave - major diesis 33: 8 243/125 1150.834 cents octave - maximal diesis 33: 11 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 33: 4 6144/3125 1170.386 cents octave - small diesis 33: 11 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.81818 = 42/11
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 0.0 : 41.1 70.7 111.7 133.2 182.4 203.9 245.0 274.6 315.6 364.8 386.3 427.4 448.9 498.0 519.6 568.7 590.2 631.3 680.4 702.0 751.1 772.6 813.7 835.2 884.4 925.4 955.0 996.1 1017.6 1066.8 1088.3 1129.3 1158.9 1200.0 41.1 : 29.6 70.7 92.2 141.3 162.9 203.9 233.5 274.6 323.7 345.3 386.3 407.8 457.0 478.5 527.7 549.2 590.2 639.4 660.9 710.1 731.6 772.6 794.1 843.3 884.4 914.0 955.0 976.5 1025.7 1047.2 1088.3 1117.9 1158.9 1200.0 70.7 : 41.1 62.6 111.7 133.2 174.3 203.9 245.0 294.1 315.6 356.7 378.2 427.4 448.9 498.0 519.6 560.6 609.8 631.3 680.4 702.0 743.0 764.5 813.7 854.7 884.4 925.4 946.9 996.1 1017.6 1058.7 1088.3 1129.3 1170.4 1200.0 111.7 : 21.5 70.7 92.2 133.2 162.9 203.9 253.1 274.6 315.6 337.1 386.3 407.8 457.0 478.5 519.6 568.7 590.2 639.4 660.9 702.0 723.5 772.6 813.7 843.3 884.4 905.9 955.0 976.5 1017.6 1047.2 1088.3 1129.3 1158.9 1200.0 133.2 : 49.2 70.7 111.7 141.3 182.4 231.6 253.1 294.1 315.6 364.8 386.3 435.5 457.0 498.0 547.2 568.7 617.9 639.4 680.4 702.0 751.1 792.2 821.8 862.9 884.4 933.5 955.0 996.1 1025.7 1066.8 1107.8 1137.4 1178.5 1200.0 182.4 : 21.5 62.6 92.2 133.2 182.4 203.9 245.0 266.5 315.6 337.1 386.3 407.8 448.9 498.0 519.6 568.7 590.2 631.3 652.8 702.0 743.0 772.6 813.7 835.2 884.4 905.9 946.9 976.5 1017.6 1058.7 1088.3 1129.3 1150.8 1200.0 203.9 : 41.1 70.7 111.7 160.9 182.4 223.5 245.0 294.1 315.6 364.8 386.3 427.4 476.5 498.0 547.2 568.7 609.8 631.3 680.4 721.5 751.1 792.2 813.7 862.9 884.4 925.4 955.0 996.1 1037.1 1066.8 1107.8 1129.3 1178.5 1200.0 245.0 : 29.6 70.7 119.8 141.3 182.4 203.9 253.1 274.6 323.7 345.3 386.3 435.5 457.0 506.2 527.7 568.7 590.2 639.4 680.4 710.1 751.1 772.6 821.8 843.3 884.4 914.0 955.0 996.1 1025.7 1066.8 1088.3 1137.4 1158.9 1200.0 274.6 : 41.1 90.2 111.7 152.8 174.3 223.5 245.0 294.1 315.6 356.7 405.9 427.4 476.5 498.0 539.1 560.6 609.8 650.8 680.4 721.5 743.0 792.2 813.7 854.7 884.4 925.4 966.5 996.1 1037.1 1058.7 1107.8 1129.3 1170.4 1200.0 315.6 : 49.2 70.7 111.7 133.2 182.4 203.9 253.1 274.6 315.6 364.8 386.3 435.5 457.0 498.0 519.6 568.7 609.8 639.4 680.4 702.0 751.1 772.6 813.7 843.3 884.4 925.4 955.0 996.1 1017.6 1066.8 1088.3 1129.3 1158.9 1200.0 364.8 : 21.5 62.6 84.1 133.2 154.7 203.9 225.4 266.5 315.6 337.1 386.3 407.8 448.9 470.4 519.6 560.6 590.2 631.3 652.8 702.0 723.5 764.5 794.1 835.2 876.3 905.9 946.9 968.4 1017.6 1039.1 1080.2 1109.8 1150.8 1200.0 386.3 : 41.1 62.6 111.7 133.2 182.4 203.9 245.0 294.1 315.6 364.8 386.3 427.4 448.9 498.0 539.1 568.7 609.8 631.3 680.4 702.0 743.0 772.6 813.7 854.7 884.4 925.4 946.9 996.1 1017.6 1058.7 1088.3 1129.3 1178.5 1200.0 427.4 : 21.5 70.7 92.2 141.3 162.9 203.9 253.1 274.6 323.7 345.3 386.3 407.8 457.0 498.0 527.7 568.7 590.2 639.4 660.9 702.0 731.6 772.6 813.7 843.3 884.4 905.9 955.0 976.5 1017.6 1047.2 1088.3 1137.4 1158.9 1200.0 448.9 : 49.2 70.7 119.8 141.3 182.4 231.6 253.1 302.2 323.7 364.8 386.3 435.5 476.5 506.2 547.2 568.7 617.9 639.4 680.4 710.1 751.1 792.2 821.8 862.9 884.4 933.5 955.0 996.1 1025.7 1066.8 1115.9 1137.4 1178.5 1200.0 498.0 : 21.5 70.7 92.2 133.2 182.4 203.9 253.1 274.6 315.6 337.1 386.3 427.4 457.0 498.0 519.6 568.7 590.2 631.3 660.9 702.0 743.0 772.6 813.7 835.2 884.4 905.9 946.9 976.5 1017.6 1066.8 1088.3 1129.3 1150.8 1200.0 519.6 : 49.2 70.7 111.7 160.9 182.4 231.6 253.1 294.1 315.6 364.8 405.9 435.5 476.5 498.0 547.2 568.7 609.8 639.4 680.4 721.5 751.1 792.2 813.7 862.9 884.4 925.4 955.0 996.1 1045.3 1066.8 1107.8 1129.3 1178.5 1200.0 568.7 : 21.5 62.6 111.7 133.2 182.4 203.9 245.0 266.5 315.6 356.7 386.3 427.4 448.9 498.0 519.6 560.6 590.2 631.3 672.3 702.0 743.0 764.5 813.7 835.2 876.3 905.9 946.9 996.1 1017.6 1058.7 1080.2 1129.3 1150.8 1200.0 590.2 : 41.1 90.2 111.7 160.9 182.4 223.5 245.0 294.1 335.2 364.8 405.9 427.4 476.5 498.0 539.1 568.7 609.8 650.8 680.4 721.5 743.0 792.2 813.7 854.7 884.4 925.4 974.6 996.1 1037.1 1058.7 1107.8 1129.3 1178.5 1200.0 631.3 : 49.2 70.7 119.8 141.3 182.4 203.9 253.1 294.1 323.7 364.8 386.3 435.5 457.0 498.0 527.7 568.7 609.8 639.4 680.4 702.0 751.1 772.6 813.7 843.3 884.4 933.5 955.0 996.1 1017.6 1066.8 1088.3 1137.4 1158.9 1200.0 680.4 : 21.5 70.7 92.2 133.2 154.7 203.9 245.0 274.6 315.6 337.1 386.3 407.8 448.9 478.5 519.6 560.6 590.2 631.3 652.8 702.0 723.5 764.5 794.1 835.2 884.4 905.9 946.9 968.4 1017.6 1039.1 1088.3 1109.8 1150.8 1200.0 702.0 : 49.2 70.7 111.7 133.2 182.4 223.5 253.1 294.1 315.6 364.8 386.3 427.4 457.0 498.0 539.1 568.7 609.8 631.3 680.4 702.0 743.0 772.6 813.7 862.9 884.4 925.4 946.9 996.1 1017.6 1066.8 1088.3 1129.3 1178.5 1200.0 751.1 : 21.5 62.6 84.1 133.2 174.3 203.9 245.0 266.5 315.6 337.1 378.2 407.8 448.9 489.9 519.6 560.6 582.1 631.3 652.8 693.8 723.5 764.5 813.7 835.2 876.3 897.8 946.9 968.4 1017.6 1039.1 1080.2 1129.3 1150.8 1200.0 772.6 : 41.1 62.6 111.7 152.8 182.4 223.5 245.0 294.1 315.6 356.7 386.3 427.4 468.4 498.0 539.1 560.6 609.8 631.3 672.3 702.0 743.0 792.2 813.7 854.7 876.3 925.4 946.9 996.1 1017.6 1058.7 1107.8 1129.3 1178.5 1200.0 813.7 : 21.5 70.7 111.7 141.3 182.4 203.9 253.1 274.6 315.6 345.3 386.3 427.4 457.0 498.0 519.6 568.7 590.2 631.3 660.9 702.0 751.1 772.6 813.7 835.2 884.4 905.9 955.0 976.5 1017.6 1066.8 1088.3 1137.4 1158.9 1200.0 835.2 : 49.2 90.2 119.8 160.9 182.4 231.6 253.1 294.1 323.7 364.8 405.9 435.5 476.5 498.0 547.2 568.7 609.8 639.4 680.4 729.6 751.1 792.2 813.7 862.9 884.4 933.5 955.0 996.1 1045.3 1066.8 1115.9 1137.4 1178.5 1200.0 884.4 : 41.1 70.7 111.7 133.2 182.4 203.9 245.0 274.6 315.6 356.7 386.3 427.4 448.9 498.0 519.6 560.6 590.2 631.3 680.4 702.0 743.0 764.5 813.7 835.2 884.4 905.9 946.9 996.1 1017.6 1066.8 1088.3 1129.3 1150.8 1200.0 925.4 : 29.6 70.7 92.2 141.3 162.9 203.9 233.5 274.6 315.6 345.3 386.3 407.8 457.0 478.5 519.6 549.2 590.2 639.4 660.9 702.0 723.5 772.6 794.1 843.3 864.8 905.9 955.0 976.5 1025.7 1047.2 1088.3 1109.8 1158.9 1200.0 955.0 : 41.1 62.6 111.7 133.2 174.3 203.9 245.0 286.0 315.6 356.7 378.2 427.4 448.9 489.9 519.6 560.6 609.8 631.3 672.3 693.8 743.0 764.5 813.7 835.2 876.3 925.4 946.9 996.1 1017.6 1058.7 1080.2 1129.3 1170.4 1200.0 996.1 : 21.5 70.7 92.2 133.2 162.9 203.9 245.0 274.6 315.6 337.1 386.3 407.8 448.9 478.5 519.6 568.7 590.2 631.3 652.8 702.0 723.5 772.6 794.1 835.2 884.4 905.9 955.0 976.5 1017.6 1039.1 1088.3 1129.3 1158.9 1200.0 1017.6: 49.2 70.7 111.7 141.3 182.4 223.5 253.1 294.1 315.6 364.8 386.3 427.4 457.0 498.0 547.2 568.7 609.8 631.3 680.4 702.0 751.1 772.6 813.7 862.9 884.4 933.5 955.0 996.1 1017.6 1066.8 1107.8 1137.4 1178.5 1200.0 1066.8: 21.5 62.6 92.2 133.2 174.3 203.9 245.0 266.5 315.6 337.1 378.2 407.8 448.9 498.0 519.6 560.6 582.1 631.3 652.8 702.0 723.5 764.5 813.7 835.2 884.4 905.9 946.9 968.4 1017.6 1058.7 1088.3 1129.3 1150.8 1200.0 1088.3: 41.1 70.7 111.7 152.8 182.4 223.5 245.0 294.1 315.6 356.7 386.3 427.4 476.5 498.0 539.1 560.6 609.8 631.3 680.4 702.0 743.0 792.2 813.7 862.9 884.4 925.4 946.9 996.1 1037.1 1066.8 1107.8 1129.3 1178.5 1200.0 1129.3: 29.6 70.7 111.7 141.3 182.4 203.9 253.1 274.6 315.6 345.3 386.3 435.5 457.0 498.0 519.6 568.7 590.2 639.4 660.9 702.0 751.1 772.6 821.8 843.3 884.4 905.9 955.0 996.1 1025.7 1066.8 1088.3 1137.4 1158.9 1200.0 1158.9: 41.1 82.1 111.7 152.8 174.3 223.5 245.0 286.0 315.6 356.7 405.9 427.4 468.4 489.9 539.1 560.6 609.8 631.3 672.3 721.5 743.0 792.2 813.7 854.7 876.3 925.4 966.5 996.1 1037.1 1058.7 1107.8 1129.3 1170.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 49.1661 cents 20000/19683, 27.6598 cents 81/80, 21.5063 cents 2: 62.5651 .. 90.2250 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents 3: 84.0714 .. 119.8386 cents 9765625/9565938, 35.7671 cents 1594323/1600000,-6.1536 cents 4: 133.2376 .. 160.8974 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents 5: 154.7439 .. 182.4037 cents 20000/19683, 27.6598 cents 1594323/1600000,-6.1536 cents 6: 203.9100 .. 231.5698 cents 20000/19683, 27.6598 cents 81/80, 21.5063 cents 7: 225.4163 .. 253.0761 cents 20000/19683, 27.6598 cents 1594323/1600000,-6.1536 cents 8: 266.4751 .. 302.2423 cents 9765625/9565938, 35.7671 cents 78732/78125, 13.3990 cents 9: 315.6413 .. 335.1939 cents 2048/2025, 19.5526 cents 78732/78125, 13.3990 cents 10: 337.1476 .. 364.8074 cents 20000/19683, 27.6598 cents 32805/32768, 1.9537 cents 11: 378.2064 .. 405.8663 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents 12: 407.8200 .. 435.4799 cents 20000/19683, 27.6598 cents 32805/32768, 1.9537 cents 13: 448.8789 .. 476.5387 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents 14: 470.3852 .. 506.1523 cents 9765625/9565938, 35.7671 cents 1594323/1600000,-6.1536 cents 15: 519.5513 .. 547.2111 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents 16: 549.1649 .. 568.7174 cents 2048/2025, 19.5526 cents 32805/32768, 1.9537 cents 17: 582.1164 .. 617.8836 cents 9765625/9565938, 35.7671 cents 78732/78125, 13.3990 cents 18: 631.2826 .. 650.8351 cents 2048/2025, 19.5526 cents 78732/78125, 13.3990 cents 19: 652.7889 .. 680.4487 cents 20000/19683, 27.6598 cents 32805/32768, 1.9537 cents 20: 693.8477 .. 729.6148 cents 9765625/9565938, 35.7671 cents 78732/78125, 13.3990 cents 21: 723.4613 .. 751.1211 cents 20000/19683, 27.6598 cents 1594323/1600000,-6.1536 cents 22: 764.5201 .. 792.1800 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents 23: 794.1337 .. 821.7936 cents 20000/19683, 27.6598 cents 32805/32768, 1.9537 cents 24: 835.1926 .. 862.8524 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents 25: 864.8061 .. 884.3587 cents 2048/2025, 19.5526 cents 32805/32768, 1.9537 cents 26: 897.7577 .. 933.5249 cents 9765625/9565938, 35.7671 cents 78732/78125, 13.3990 cents 27: 946.9239 .. 974.5837 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents 28: 968.4302 .. 996.0900 cents 20000/19683, 27.6598 cents 1594323/1600000,-6.1536 cents 29: 1017.5963 .. 1045.2561 cents 20000/19683, 27.6598 cents 81/80, 21.5063 cents 30: 1039.1026 .. 1066.7624 cents 20000/19683, 27.6598 cents 1594323/1600000,-6.1536 cents 31: 1080.1614 .. 1115.9286 cents 9765625/9565938, 35.7671 cents 78732/78125, 13.3990 cents 32: 1109.7750 .. 1137.4349 cents 20000/19683, 27.6598 cents 1594323/1600000,-6.1536 cents 33: 1150.8339 .. 1178.4937 cents 20000/19683, 27.6598 cents 78732/78125, 13.3990 cents
SHOW DATA
Number of notes : 34 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 35.2941 cents Largest one step interval : 250/243, 49.1661 cents Average / Smallest step : 1.641107 Largest / Average step : 1.393041 Largest / Smallest step : 2.286128 Median interval of one step : 128/125, 41.0589 cents, amount: 11 Least squares average step : 35.28239 cents, oct.: 1199.60131 cents Scale is not proper Step pattern alph. order: ABACDCABADCACDCDCADCDCACDABACDCABA Step pattern size order : CBCADACBCDACADADACDADACADCBCADACBC Scale is a Constant Structure, by a margin of 1.95372 cents Scale diversity : 1.302285 Lumma stability : 0.260110 Lumma impropriety factor : 0.041024 Number of different interval sizes : 126 = 3.81818 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.81818 = 42/11 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: 27 Most common triad is 0.0 315.641 884.359 cents, amount: 20 Number of recognisable fifths : 28, average 702.2445 cents 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 75 Formal octave complements present : 33 = 97.0588% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 5 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 125 Scale harmonicity : 0.013749 Average absolute harmonicity : 0.101589 Specific harmonicity : 0.087104 Fundamental : 1/648000, -19.3056 octaves, 0.0004 Hz. Guide tone : 1296000, 20.3056 octaves, 339066732.630 Hz. Exponens Consonantiae : 8.398080E+11, 39.61127 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 1442.0, average 42.41176 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 45.83414, average 1.34806 Sum of Tenney's harmonic distance : 91.45896, average 2.68997 Vogel's harmonic complexity : 33.67647 Wille's k value : 632812 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 14 Triangular lattice diameter : 8 Lattice compactness : 3293.09858, average 5.53462 Lattice compactness (without 2's) : 2057.41248, average 3.45784 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 0.35294 92 1 3: -4 .. 4 0.05882 56 4 5: -3 .. 3 0.02941 53 29 Average exponent except 2's : 3 / 34 = 0.08824 Average absolute exponent except 2's: 109 / 34 = 3.20588 Scale is JI-epimorphic with val: <34 54 79| = patent
FIT/MODE
34: 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: 6.5567 c. M: 11.8662 c. 48: 2 1 1 1 2 1 2 1 2 2 0 2 1 2 1 2 1 1 2 1 2 1 2 0 2 2 1 2 1 2 1 1 1 2 N D3 I SD: 7.0580 c. M:-11.7313 c. 49: 2 1 2 0 2 1 2 1 2 2 1 1 1 2 1 2 1 2 2 1 2 1 1 1 2 2 1 2 1 2 0 2 1 2 N SD: 7.1664 c. M: 11.0460 c. 51: 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 0 3 1 2 1 1 2 1 2 1 2 N SD: 6.7277 c. M: 11.8662 c. 53: 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 P M ME SD: 2.4814 c. M:-4.2242 c. 99: 3 3 3 2 4 2 3 3 3 4 2 3 2 4 2 4 2 3 4 2 4 2 3 2 4 3 3 3 2 4 2 3 3 3 P SD: 2.2774 c. M:-4.6952 c. 114: 4 3 4 2 4 2 4 3 4 5 2 4 2 4 2 5 2 4 5 2 4 2 4 2 5 4 3 4 2 4 2 4 3 4 N SD: 3.0310 c. M: 4.2064 c. 116: 4 3 4 2 5 2 4 3 4 4 2 4 2 5 2 5 2 4 5 2 5 2 4 2 4 4 3 4 2 5 2 4 3 4 N SD: 2.9295 c. M: 5.0484 c. 117: 4 3 4 2 5 2 4 3 4 5 2 4 2 5 2 4 3 4 4 2 5 2 4 2 5 4 3 4 2 5 2 4 3 4 N SD: 2.8142 c. M:-4.6481 c. 118: 4 3 4 2 5 2 4 3 4 5 2 4 2 5 2 5 2 4 5 2 5 2 4 2 5 4 3 4 2 5 2 4 3 4 N SD: 0.7067 c. M:-1.4212 c. 171: 6 4 6 3 7 3 6 4 6 7 3 6 3 7 3 7 3 6 7 3 7 3 6 3 7 6 4 6 3 7 3 6 4 6 N SD: 0.4979 c. M: 1.0464 c. 289: 10 7 10 5 12 5 10 7 10 12 5 10 5 12 5 12 5 10 12 5 12 5 10 5 12 10 7 10 5 12 5 10 7 10 N SD: 0.3647 c. M: 0.6043 c. 441: 15 11 15 8 18 8 15 11 15 18 8 15 8 18 8 18 8 15 18 8 18 8 15 8 18 15 11 15 8 18 8 15 11 15 N SD: 0.1439 c. M:-0.2525 c. 612: 21 15 21 11 25 11 21 15 21 25 11 21 11 25 11 25 11 21 25 11 25 11 21 11 25 21 15 21 11 25 11 21 15 21 N SD: 0.0795 c. M:-0.1407 c. 730: 25 18 25 13 30 13 25 18 25 30 13 25 13 30 13 30 13 25 30 13 30 13 25 13 30 25 18 25 13 30 13 25 18 25 N SD: 0.0655 c. M:-0.1241 c. 1171: 40 29 40 21 48 21 40 29 40 48 21 40 21 48 21 48 21 40 48 21 48 21 40 21 48 40 29 40 21 48 21 40 29 40 N SD: 0.0332 c. M: 0.0683 c. 1783: 61 44 61 32 73 32 61 44 61 73 32 61 32 73 32 73 32 61 73 32 73 32 61 32 73 61 44 61 32 73 32 61 44 61 N SD: 0.0150 c. M: 0.0290 c. 2513: 86 62 86 45 103 45 86 62 86 103 45 86 45 103 45 103 45 86 103 45 103 45 86 45 103 86 62 86 45 103 45 86 62 86 N SD: 0.0086 c. M: 0.0155 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: 3.4487 cents 5 .. 10 match: 5 H SD: 1.5423 cents 6 .. 12 match: 6 H SD: 3.1720 cents 7 .. 14 match: 7 H SD: 3.5607 cents 8 .. 16 match: 8 H SD: 2.8545 cents 9 .. 18 match: 9 H SD: 2.6150 cents 10 .. 20 match: 10 H SD: 2.7663 cents 11 .. 22 match: 11 H SD: 4.0724 cents 12 .. 24 match: 12 H SD: 2.7410 cents 13 .. 26 match: 13 H SD: 2.7239 cents 14 .. 28 match: 14 H SD: 3.1063 cents 15 .. 30 match: 15 H SD: 2.2982 cents 16 .. 32 match: 16 H SD: 2.8668 cents 17 .. 34 match: 17 H SD: 2.7565 cents 18 .. 36 match: 18 H SD: 2.2204 cents 19 .. 38 match: 19 H SD: 3.4312 cents 20 .. 40 match: 20 H SD: 2.0430 cents 21 .. 42 match: 21 H SD: 2.4534 cents 22 .. 44 match: 22 H SD: 2.6259 cents 23 .. 46 match: 22 SD: 2.2096 cents 24 .. 48 match: 24 H SD: 1.9372 cents 25 .. 50 match: 25 H SD: 2.0545 cents 26 .. 52 match: 25 SD: 1.8786 cents 27 .. 54 match: 26 S SD: 1.8213 cents 28 .. 56 match: 26 SD: 2.1242 cents 29 .. 58 match: 26 S SD: 2.2093 cents 30 .. 60 match: 28 S SD: 1.8968 cents 31 .. 62 match: 28 S SD: 2.0329 cents 32 .. 64 match: 28 SD: 1.9290 cents 33 .. 66 match: 28 SD: 1.9970 cents 34 .. 68 match: 31 SD: 1.6165 cents 35 .. 70 match: 29 SD: 1.5834 cents 36 .. 72 match: 30 SD: 1.7413 cents 37 .. 74 match: 30 SD: 1.6983 cents 38 .. 76 match: 28 SD: 1.8019 cents 39 .. 78 match: 33 SD: 1.3626 cents 40 .. 80 match: 32 SD: 1.3199 cents 41 .. 82 match: 29 SD: 1.3595 cents 42 .. 84 match: 31 SD: 1.4129 cents 43 .. 86 match: 30 SD: 1.4509 cents 44 .. 88 match: 33 SD: 1.4133 cents 45 .. 90 match: 31 SD: 1.2151 cents 46 .. 92 match: 34 SD: 1.1188 cents 47 .. 94 match: 32 SD: 1.1566 cents 48 .. 96 match: 34 SD: 1.0552 cents 50 .. 100 match: 33 SD: 1.1612 cents 51 .. 102 match: 33 SD: 1.1808 cents 52 .. 104 match: 33 SD: 1.1689 cents 53 .. 106 match: 33 SD: 1.2602 cents 54 .. 108 match: 33 SD: 1.0068 cents 55 .. 110 match: 33 SD: 1.1532 cents 56 .. 112 match: 33 SD: 1.2081 cents 57 .. 114 match: 34 SD: 1.0867 cents 59 .. 118 match: 32 SD: 1.1162 cents 60 .. 120 match: 34 SD: 1.0024 cents 64 .. 128 match: 34 SD: 0.7758 cents 68 .. 136 match: 33 SD: 0.9540 cents 71 .. 142 match: 34 SD: 0.7742 cents 72 .. 144 match: 34 SD: 0.6775 cents 87 .. 174 match: 34 SD: 0.6550 cents 88 .. 176 match: 34 SD: 0.6336 cents 89 .. 178 match: 34 SD: 0.6054 cents 98 .. 196 match: 34 SD: 0.5940 cents 100 .. 200 match: 34 SD: 0.5671 cents 105 .. 210 match: 34 SD: 0.5616 cents 111 .. 222 match: 34 SD: 0.5125 cents 114 .. 228 match: 34 SD: 0.5100 cents 116 .. 232 match: 34 SD: 0.5029 cents 118 .. 236 match: 34 SD: 0.4847 cents 120 .. 240 match: 34 SD: 0.4499 cents 125 .. 250 match: 34 SD: 0.4480 cents 126 .. 252 match: 34 SD: 0.4402 cents 129 .. 258 match: 34 SD: 0.4393 cents 135 .. 270 match: 34 SD: 0.4069 cents 136 .. 272 match: 34 SD: 0.3918 cents 150 .. 300 match: 34 SD: 0.3705 cents 152 .. 304 match: 34 SD: 0.3677 cents 160 .. 320 match: 34 SD: 0.3500 cents 162 .. 324 match: 34 SD: 0.3210 cents 175 .. 350 match: 34 SD: 0.3061 cents 192 .. 384 match: 34 SD: 0.2851 cents 197 .. 394 match: 34 SD: 0.2733 cents 200 .. 400 match: 34 SD: 0.2646 cents 210 .. 420 match: 34 SD: 0.2454 cents 216 .. 432 match: 34 SD: 0.2277 cents 239 .. 478 match: 34 SD: 0.2143 cents 264 .. 528 match: 34 SD: 0.2092 cents 280 .. 560 match: 34 SD: 0.2022 cents 285 .. 570 match: 34 SD: 0.1860 cents 289 .. 578 match: 34 SD: 0.1859 cents 297 .. 594 match: 34 SD: 0.1756 cents 315 .. 630 match: 34 SD: 0.1688 cents 336 .. 672 match: 34 SD: 0.1636 cents 337 .. 674 match: 34 SD: 0.1621 cents 345 .. 690 match: 34 SD: 0.1607 cents 360 .. 720 match: 34 SD: 0.1386 cents 375 .. 750 match: 34 SD: 0.1364 cents 409 .. 818 match: 34 SD: 0.1319 cents 414 .. 828 match: 34 SD: 0.1233 cents 432 .. 864 match: 34 SD: 0.1193 cents 440 .. 880 match: 34 SD: 0.1188 cents 450 .. 900 match: 34 SD: 0.1150 cents 460 .. 920 match: 34 SD: 0.1092 cents 500 .. 1000 match: 34 SD: 0.1037 cents 512 .. 1024 match: 34 SD: 0.0997 cents 540 .. 1080 match: 34 SD: 0.0983 cents 552 .. 1104 match: 34 SD: 0.0983 cents 575 .. 1150 match: 34 SD: 0.0933 cents 576 .. 1152 match: 34 SD: 0.0843 cents 600 .. 1200 match: 34 SD: 0.0711 cents