Scala analysis: cpak31
optimal tetrad pack scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 21/20 84.467193 minor semitone 3: 15/14 119.442808 major diatonic semitone 4: 35/32 155.139620 septimal neutral second 5: 9/8 203.910002 major whole tone 6: 8/7 231.174094 septimal whole tone 7: 7/6 266.870906 septimal minor third 8: 6/5 315.641287 minor third 9: 60/49 350.616902 smaller approximation to neutral third 10: 5/4 386.313714 major third 11: 9/7 435.084095 septimal major third, BP third 12: 21/16 470.780907 narrow fourth 13: 4/3 498.044999 perfect fourth 14: 48/35 546.815381 septimal semi-augmented fourth 15: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 16: 10/7 617.487807 Euler's tritone 17: 72/49 666.258189 Arabic lute grave fifth 18: 3/2 701.955001 perfect fifth 19: 54/35 750.725382 septimal semi-augmented fifth 20: 25/16 772.627428 classic augmented fifth 21: 8/5 813.686286 minor sixth 22: 105/64 857.094621 septimal neutral sixth 23: 5/3 884.358713 major sixth, BP sixth 24: 12/7 933.129094 septimal major sixth 25: 7/4 968.825906 harmonic seventh 26: 9/5 1017.596288 just minor seventh, BP seventh 27: 64/35 1044.860380 septimal neutral seventh 28: 15/8 1088.268715 classic major seventh 29: 48/25 1129.327573 classic diminished octave 30: 96/49 1164.303188 31: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 49/48 35.6968 slendro diesis, septimal 1/6-tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 49/48 35.6968 slendro diesis, septimal 1/6-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 64/63 27.2641 septimal comma, Archytas' comma 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 10: 49/48 35.6968 slendro diesis, septimal 1/6-tone 11: 36/35 48.7704 septimal diesis, 1/4-tone 12: 49/48 35.6968 slendro diesis, septimal 1/6-tone 13: 64/63 27.2641 septimal comma, Archytas' comma 14: 36/35 48.7704 septimal diesis, 1/4-tone 15: 49/48 35.6968 slendro diesis, septimal 1/6-tone 16: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 17: 36/35 48.7704 septimal diesis, 1/4-tone 18: 49/48 35.6968 slendro diesis, septimal 1/6-tone 19: 36/35 48.7704 septimal diesis, 1/4-tone 20: 875/864 21.9020 keema 21: 128/125 41.0589 minor diesis, diesis 22: 525/512 43.4083 Avicenna enharmonic diesis 23: 64/63 27.2641 septimal comma, Archytas' comma 24: 36/35 48.7704 septimal diesis, 1/4-tone 25: 49/48 35.6968 slendro diesis, septimal 1/6-tone 26: 36/35 48.7704 septimal diesis, 1/4-tone 27: 64/63 27.2641 septimal comma, Archytas' comma 28: 525/512 43.4083 Avicenna enharmonic diesis 29: 128/125 41.0589 minor diesis, diesis 30: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 31: 49/48 35.6968 slendro diesis, septimal 1/6-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 875/864 21.902 cents keema 1: 4 64/63 27.264 cents septimal comma, Archytas' comma 1: 4 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 9 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 128/125 41.059 cents minor diesis, diesis 1: 2 525/512 43.408 cents Avicenna enharmonic diesis 1: 9 36/35 48.770 cents septimal diesis, 1/4-tone 2: 3 28/27 62.961 cents Archytas' 1/3-tone 2: 8 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 5 256/245 76.034 cents septimal minor semitone 2: 2 360/343 83.746 cents 2: 13 21/20 84.467 cents minor semitone 3: 3 1225/1152 106.369 cents 3: 12 16/15 111.731 cents minor diatonic semitone 3: 12 15/14 119.443 cents major diatonic semitone 3: 2 343/320 120.164 cents 3: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 4: 1 175/162 133.633 cents 4: 4 160/147 146.707 cents 4: 4 49/45 147.428 cents BP minor semitone 4: 12 35/32 155.140 cents septimal neutral second 4: 7 192/175 160.502 cents septimal 4/5-tone 4: 3 54/49 168.213 cents Zalzal's mujannab 5: 8 10/9 182.404 cents minor whole tone 5: 1 4096/3675 187.766 cents 5: 2 125/112 190.115 cents classic augmented semitone 5: 2 1715/1536 190.836 cents 5: 3 384/343 195.477 cents 5: 7 28/25 196.198 cents middle second 5: 8 9/8 203.910 cents major whole tone 6: 3 245/216 218.101 cents 6: 2 875/768 225.812 cents 6: 18 8/7 231.174 cents septimal whole tone 6: 1 343/300 231.895 cents 6: 4 147/128 239.607 cents 6: 2 144/125 244.969 cents classic diminished third 6: 1 81/70 252.680 cents Al-Hwarizmi's lute middle finger 7: 1 400/343 266.150 cents 7: 17 7/6 266.871 cents septimal minor third 7: 2 1024/875 272.233 cents 7: 5 75/64 274.582 cents classic augmented second 7: 6 288/245 279.944 cents 8: 2 32/27 294.135 cents Pythagorean minor third 8: 7 25/21 301.847 cents BP second, quasi-equal minor third 8: 2 343/288 302.568 cents 8: 1 2048/1715 307.209 cents 8: 2 1225/1024 310.279 cents two (septimal neutral second) 8: 17 6/5 315.641 cents minor third 9: 6 175/144 337.543 cents 9: 6 128/105 342.905 cents septimal neutral third 9: 7 60/49 350.617 cents smaller approximation to neutral third 9: 7 49/40 351.338 cents larger approximation to neutral third 9: 1 768/625 356.700 cents 9: 2 315/256 359.050 cents 9: 2 216/175 364.412 cents 10: 6 56/45 378.602 cents septimal narrow major third 10: 18 5/4 386.314 cents major third 10: 3 1536/1225 391.676 cents 10: 1 432/343 399.387 cents 10: 3 63/50 400.108 cents quasi-equal major third 11: 5 80/63 413.578 cents wide major third 11: 1 125/98 421.289 cents 11: 8 245/192 422.011 cents 11: 8 32/25 427.373 cents classic diminished fourth 11: 9 9/7 435.084 cents septimal major third, BP third 12: 4 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 12: 2 125/96 456.986 cents classic augmented third 12: 9 64/49 462.348 cents 2 septatones or septatonic major third 12: 3 98/75 463.069 cents 12: 11 21/16 470.781 cents narrow fourth 12: 1 1152/875 476.143 cents 12: 1 324/245 483.854 cents 13: 18 4/3 498.045 cents perfect fourth 13: 5 75/56 505.757 cents marvelous fourth 13: 2 343/256 506.478 cents 13: 1 2304/1715 511.119 cents 13: 2 168/125 511.840 cents 13: 3 27/20 519.551 cents acute fourth 14: 2 200/147 533.021 cents 14: 7 49/36 533.742 cents Arabic lute acute fourth 14: 6 175/128 541.453 cents 14: 16 48/35 546.815 cents septimal semi-augmented fourth 15: 6 25/18 568.717 cents classic augmented fourth 15: 2 1024/735 574.079 cents 15: 3 480/343 581.791 cents 15: 15 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 15: 4 45/32 590.224 cents diatonic tritone 15: 1 1728/1225 595.586 cents 16: 1 1225/864 604.414 cents 16: 4 64/45 609.776 cents 2nd tritone 16: 15 10/7 617.488 cents Euler's tritone 16: 3 343/240 618.209 cents 16: 2 735/512 625.921 cents 16: 6 36/25 631.283 cents classic diminished fifth 17: 16 35/24 653.185 cents septimal semi-diminished fifth 17: 6 256/175 658.547 cents 17: 7 72/49 666.258 cents Arabic lute grave fifth 17: 2 147/100 666.979 cents 18: 3 40/27 680.449 cents grave fifth 18: 2 125/84 688.160 cents 18: 1 1715/1152 688.881 cents 18: 2 512/343 693.522 cents 3 septatones or septatonic fifth 18: 5 112/75 694.243 cents marvelous fifth 18: 18 3/2 701.955 cents perfect fifth 19: 1 245/162 716.146 cents 19: 1 875/576 723.857 cents 19: 11 32/21 729.219 cents wide fifth 19: 3 75/49 736.931 cents BP fifth 19: 9 49/32 737.652 cents 19: 2 192/125 743.014 cents classic diminished sixth 19: 4 54/35 750.725 cents septimal semi-augmented fifth 20: 9 14/9 764.916 cents septimal minor sixth 20: 8 25/16 772.627 cents classic augmented fifth 20: 8 384/245 777.989 cents 20: 1 196/125 778.711 cents 20: 5 63/40 786.422 cents narrow minor sixth 21: 3 100/63 799.892 cents quasi-equal minor sixth 21: 1 343/216 800.613 cents 21: 3 1225/768 808.324 cents 21: 18 8/5 813.686 cents minor sixth 21: 6 45/28 821.398 cents septimale wide minor sixth 22: 2 175/108 835.588 cents 22: 2 512/315 840.950 cents 22: 1 625/384 843.300 cents 22: 7 80/49 848.662 cents smaller approximation to neutral sixth 22: 7 49/30 849.383 cents larger approximation to neutral sixth 22: 6 105/64 857.095 cents septimal neutral sixth 22: 6 288/175 862.457 cents 23: 17 5/3 884.359 cents major sixth, BP sixth 23: 2 2048/1225 889.721 cents 23: 1 1715/1024 892.791 cents 23: 2 576/343 897.432 cents 23: 7 42/25 898.153 cents quasi-equal major sixth 23: 2 27/16 905.865 cents Pythagorean major sixth 24: 6 245/144 920.056 cents 24: 5 128/75 925.418 cents diminished seventh 24: 2 875/512 927.767 cents 24: 17 12/7 933.129 cents septimal major sixth 24: 1 343/200 933.850 cents 25: 1 140/81 947.320 cents 25: 2 125/72 955.031 cents classic augmented sixth 25: 4 256/147 960.393 cents 25: 1 600/343 968.105 cents 25: 18 7/4 968.826 cents harmonic seventh 25: 2 1536/875 974.188 cents 25: 3 432/245 981.899 cents 26: 8 16/9 996.090 cents Pythagorean minor seventh 26: 7 25/14 1003.802 cents middle minor seventh 26: 3 343/192 1004.523 cents 26: 2 3072/1715 1009.164 cents 26: 2 224/125 1009.885 cents 26: 1 3675/2048 1012.234 cents 26: 8 9/5 1017.596 cents just minor seventh, BP seventh 27: 3 49/27 1031.787 cents 27: 7 175/96 1039.498 cents 27: 12 64/35 1044.860 cents septimal neutral seventh 27: 4 90/49 1052.572 cents 27: 4 147/80 1053.293 cents 27: 1 324/175 1066.367 cents 28: 2 50/27 1066.762 cents grave major seventh 28: 2 640/343 1079.836 cents 28: 12 28/15 1080.557 cents grave major seventh 28: 12 15/8 1088.269 cents classic major seventh 28: 3 2304/1225 1093.631 cents two (septimal semi-augmented fourth) 29: 13 40/21 1115.533 cents acute major seventh 29: 2 343/180 1116.254 cents 29: 5 245/128 1123.966 cents 29: 8 48/25 1129.328 cents classic diminished octave 29: 3 27/14 1137.039 cents septimal major seventh 30: 9 35/18 1151.230 cents septimal semi-diminished octave 30: 2 1024/525 1156.592 cents 30: 2 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 30: 9 96/49 1164.303 cents 30: 4 49/25 1165.024 cents BP eighth 30: 4 63/32 1172.736 cents octave - septimal comma 30: 1 1728/875 1178.098 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.86667 = 88/15
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 0.0 : 48.8 84.5 119.4 155.1 203.9 231.2 266.9 315.6 350.6 386.3 435.1 470.8 498.0 546.8 582.5 617.5 666.3 702.0 750.7 772.6 813.7 857.1 884.4 933.1 968.8 1017.6 1044.9 1088.3 1129.3 1164.3 1200.0 48.8 : 35.7 70.7 106.4 155.1 182.4 218.1 266.9 301.8 337.5 386.3 422.0 449.3 498.0 533.7 568.7 617.5 653.2 702.0 723.9 764.9 808.3 835.6 884.4 920.1 968.8 996.1 1039.5 1080.6 1115.5 1151.2 1200.0 84.5 : 35.0 70.7 119.4 146.7 182.4 231.2 266.1 301.8 350.6 386.3 413.6 462.3 498.0 533.0 581.8 617.5 666.3 688.2 729.2 772.6 799.9 848.7 884.4 933.1 960.4 1003.8 1044.9 1079.8 1115.5 1164.3 1200.0 119.4 : 35.7 84.5 111.7 147.4 196.2 231.2 266.9 315.6 351.3 378.6 427.4 463.1 498.0 546.8 582.5 631.3 653.2 694.2 737.7 764.9 813.7 849.4 898.2 925.4 968.8 1009.9 1044.9 1080.6 1129.3 1165.0 1200.0 155.1 : 48.8 76.0 111.7 160.5 195.5 231.2 279.9 315.6 342.9 391.7 427.4 462.3 511.1 546.8 595.6 617.5 658.5 702.0 729.2 778.0 813.7 862.5 889.7 933.1 974.2 1009.2 1044.9 1093.6 1129.3 1164.3 1200.0 203.9 : 27.3 63.0 111.7 146.7 182.4 231.2 266.9 294.1 342.9 378.6 413.6 462.3 498.0 546.8 568.7 609.8 653.2 680.4 729.2 764.9 813.7 841.0 884.4 925.4 960.4 996.1 1044.9 1080.6 1115.5 1151.2 1200.0 231.2 : 35.7 84.5 119.4 155.1 203.9 239.6 266.9 315.6 351.3 386.3 435.1 470.8 519.6 541.5 582.5 625.9 653.2 702.0 737.7 786.4 813.7 857.1 898.2 933.1 968.8 1017.6 1053.3 1088.3 1124.0 1172.7 1200.0 266.9 : 48.8 83.7 119.4 168.2 203.9 231.2 279.9 315.6 350.6 399.4 435.1 483.9 505.8 546.8 590.2 617.5 666.3 702.0 750.7 778.0 821.4 862.5 897.4 933.1 981.9 1017.6 1052.6 1088.3 1137.0 1164.3 1200.0 315.6 : 35.0 70.7 119.4 155.1 182.4 231.2 266.9 301.8 350.6 386.3 435.1 457.0 498.0 541.5 568.7 617.5 653.2 702.0 729.2 772.6 813.7 848.7 884.4 933.1 968.8 1003.8 1039.5 1088.3 1115.5 1151.2 1200.0 350.6 : 35.7 84.5 120.2 147.4 196.2 231.9 266.9 315.6 351.3 400.1 422.0 463.1 506.5 533.7 582.5 618.2 667.0 694.2 737.7 778.7 813.7 849.4 898.2 933.9 968.8 1004.5 1053.3 1080.6 1116.3 1165.0 1200.0 386.3 : 48.8 84.5 111.7 160.5 196.2 231.2 279.9 315.6 364.4 386.3 427.4 470.8 498.0 546.8 582.5 631.3 658.5 702.0 743.0 778.0 813.7 862.5 898.2 933.1 968.8 1017.6 1044.9 1080.6 1129.3 1164.3 1200.0 435.1 : 35.7 63.0 111.7 147.4 182.4 231.2 266.9 315.6 337.5 378.6 422.0 449.3 498.0 533.7 582.5 609.8 653.2 694.2 729.2 764.9 813.7 849.4 884.4 920.1 968.8 996.1 1031.8 1080.6 1115.5 1151.2 1200.0 470.8 : 27.3 76.0 111.7 146.7 195.5 231.2 279.9 301.8 342.9 386.3 413.6 462.3 498.0 546.8 574.1 617.5 658.5 693.5 729.2 778.0 813.7 848.7 884.4 933.1 960.4 996.1 1044.9 1079.8 1115.5 1164.3 1200.0 498.0 : 48.8 84.5 119.4 168.2 203.9 252.7 274.6 315.6 359.0 386.3 435.1 470.8 519.6 546.8 590.2 631.3 666.3 702.0 750.7 786.4 821.4 857.1 905.9 933.1 968.8 1017.6 1052.6 1088.3 1137.0 1172.7 1200.0 546.8 : 35.7 70.7 119.4 155.1 203.9 225.8 266.9 310.3 337.5 386.3 422.0 470.8 498.0 541.5 582.5 617.5 653.2 702.0 737.7 772.6 808.3 857.1 884.4 920.1 968.8 1003.8 1039.5 1088.3 1124.0 1151.2 1200.0 582.5 : 35.0 83.7 119.4 168.2 190.1 231.2 274.6 301.8 350.6 386.3 435.1 462.3 505.8 546.8 581.8 617.5 666.3 702.0 736.9 772.6 821.4 848.7 884.4 933.1 968.1 1003.8 1052.6 1088.3 1115.5 1164.3 1200.0 617.5 : 48.8 84.5 133.2 155.1 196.2 239.6 266.9 315.6 351.3 400.1 427.4 470.8 511.8 546.8 582.5 631.3 667.0 702.0 737.7 786.4 813.7 849.4 898.2 933.1 968.8 1017.6 1053.3 1080.6 1129.3 1165.0 1200.0 666.3 : 35.7 84.5 106.4 147.4 190.8 218.1 266.9 302.6 351.3 378.6 422.0 463.1 498.0 533.7 582.5 618.2 653.2 688.9 737.7 764.9 800.6 849.4 884.4 920.1 968.8 1004.5 1031.8 1080.6 1116.3 1151.2 1200.0 702.0 : 48.8 70.7 111.7 155.1 182.4 231.2 266.9 315.6 342.9 386.3 427.4 462.3 498.0 546.8 582.5 617.5 653.2 702.0 729.2 764.9 813.7 848.7 884.4 933.1 968.8 996.1 1044.9 1080.6 1115.5 1164.3 1200.0 750.7 : 21.9 63.0 106.4 133.6 182.4 218.1 266.9 294.1 337.5 378.6 413.6 449.3 498.0 533.7 568.7 604.4 653.2 680.4 716.1 764.9 799.9 835.6 884.4 920.1 947.3 996.1 1031.8 1066.8 1115.5 1151.2 1200.0 772.6 : 41.1 84.5 111.7 160.5 196.2 245.0 272.2 315.6 356.7 391.7 427.4 476.1 511.8 546.8 582.5 631.3 658.5 694.2 743.0 778.0 813.7 862.5 898.2 925.4 974.2 1009.9 1044.9 1093.6 1129.3 1178.1 1200.0 813.7 : 43.4 70.7 119.4 155.1 203.9 231.2 274.6 315.6 350.6 386.3 435.1 470.8 505.8 541.5 590.2 617.5 653.2 702.0 736.9 772.6 821.4 857.1 884.4 933.1 968.8 1003.8 1052.6 1088.3 1137.0 1158.9 1200.0 857.1 : 27.3 76.0 111.7 160.5 187.8 231.2 272.2 307.2 342.9 391.7 427.4 462.3 498.0 546.8 574.1 609.8 658.5 693.5 729.2 778.0 813.7 841.0 889.7 925.4 960.4 1009.2 1044.9 1093.6 1115.5 1156.6 1200.0 884.4 : 48.8 84.5 133.2 160.5 203.9 245.0 279.9 315.6 364.4 400.1 435.1 470.8 519.6 546.8 582.5 631.3 666.3 702.0 750.7 786.4 813.7 862.5 898.2 933.1 981.9 1017.6 1066.4 1088.3 1129.3 1172.7 1200.0 933.1 : 35.7 84.5 111.7 155.1 196.2 231.2 266.9 315.6 351.3 386.3 422.0 470.8 498.0 533.7 582.5 617.5 653.2 702.0 737.7 764.9 813.7 849.4 884.4 933.1 968.8 1017.6 1039.5 1080.6 1124.0 1151.2 1200.0 968.8 : 48.8 76.0 119.4 160.5 195.5 231.2 279.9 315.6 350.6 386.3 435.1 462.3 498.0 546.8 581.8 617.5 666.3 702.0 729.2 778.0 813.7 848.7 897.4 933.1 981.9 1003.8 1044.9 1088.3 1115.5 1164.3 1200.0 1017.6: 27.3 70.7 111.7 146.7 182.4 231.2 266.9 301.8 337.5 386.3 413.6 449.3 498.0 533.0 568.7 617.5 653.2 680.4 729.2 764.9 799.9 848.7 884.4 933.1 955.0 996.1 1039.5 1066.8 1115.5 1151.2 1200.0 1044.9: 43.4 84.5 119.4 155.1 203.9 239.6 274.6 310.3 359.0 386.3 422.0 470.8 505.8 541.5 590.2 625.9 653.2 702.0 737.7 772.6 821.4 857.1 905.9 927.8 968.8 1012.2 1039.5 1088.3 1124.0 1172.7 1200.0 1088.3: 41.1 76.0 111.7 160.5 196.2 231.2 266.9 315.6 342.9 378.6 427.4 462.3 498.0 546.8 582.5 609.8 658.5 694.2 729.2 778.0 813.7 862.5 884.4 925.4 968.8 996.1 1044.9 1080.6 1129.3 1156.6 1200.0 1129.3: 35.0 70.7 119.4 155.1 190.1 225.8 274.6 301.8 337.5 386.3 421.3 457.0 505.8 541.5 568.7 617.5 653.2 688.2 736.9 772.6 821.4 843.3 884.4 927.8 955.0 1003.8 1039.5 1088.3 1115.5 1158.9 1200.0 1164.3: 35.7 84.5 120.2 155.1 190.8 239.6 266.9 302.6 351.3 386.3 422.0 470.8 506.5 533.7 582.5 618.2 653.2 702.0 737.7 786.4 808.3 849.4 892.8 920.1 968.8 1004.5 1053.3 1080.6 1124.0 1165.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.9020 .. 48.7704 cents 31104/30625, 26.8683 cents 875/864, 21.9020 cents 2: 62.9609 .. 84.4672 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 3: 106.3692 .. 133.2376 cents 31104/30625, 26.8683 cents 875/864, 21.9020 cents 4: 133.6333 .. 168.2132 cents 8748/8575, 34.5799 cents 4375/4374, 0.3958 cents 5: 182.4037 .. 203.9100 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 6: 218.1005 .. 252.6804 cents 8748/8575, 34.5799 cents 245/243, 14.1905 cents 7: 266.1497 .. 279.9445 cents 126/125, 13.7948 cents 4000/3969, 13.4693 cents 8: 294.1350 .. 315.6413 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 9: 337.5433 .. 364.4117 cents 31104/30625, 26.8683 cents 875/864, 21.9020 cents 10: 378.6022 .. 400.1085 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 11: 413.5778 .. 435.0841 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 12: 449.2746 .. 483.8545 cents 8748/8575, 34.5799 cents 245/243, 14.1905 cents 13: 498.0450 .. 519.5513 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 14: 533.0206 .. 546.8154 cents 126/125, 13.7948 cents 4000/3969, 13.4693 cents 15: 568.7174 .. 595.5858 cents 31104/30625, 26.8683 cents 875/864, 21.9020 cents 16: 604.4142 .. 631.2826 cents 31104/30625, 26.8683 cents 1500625/1492992, 8.8285 cents 17: 653.1846 .. 666.9794 cents 126/125, 13.7948 cents 875/864, 21.9020 cents 18: 680.4487 .. 701.9550 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 19: 716.1455 .. 750.7254 cents 8748/8575, 34.5799 cents 245/243, 14.1905 cents 20: 764.9159 .. 786.4222 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 21: 799.8915 .. 821.3978 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 22: 835.5883 .. 862.4567 cents 31104/30625, 26.8683 cents 245/243, 14.1905 cents 23: 884.3587 .. 905.8650 cents 81/80, 21.5063 cents 875/864, 21.9020 cents 24: 920.0555 .. 933.8503 cents 126/125, 13.7948 cents 245/243, 14.1905 cents 25: 947.3196 .. 981.8995 cents 8748/8575, 34.5799 cents 4000/3969, 13.4693 cents 26: 996.0900 .. 1017.5963 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 27: 1031.7868 .. 1066.3667 cents 8748/8575, 34.5799 cents 245/243, 14.1905 cents 28: 1066.7624 .. 1093.6308 cents 31104/30625, 26.8683 cents 4375/4374, 0.3958 cents 29: 1115.5328 .. 1137.0391 cents 81/80, 21.5063 cents 875/864, 21.9020 cents 30: 1151.2296 .. 1178.0980 cents 31104/30625, 26.8683 cents 245/243, 14.1905 cents
SHOW DATA
Number of notes : 31 -- Interval properties -- Smallest interval : 875/864, 21.9020 cents, class 1 Average step (divided formal octave): 38.7097 cents Largest one step interval : 36/35, 48.7704 cents Average / Smallest step : 1.767400 Largest / Average step : 1.259902 Largest / Smallest step : 2.226750 Median interval of one step : 49/48, 35.6968 cents, amount: 9 Least squares average step : 38.86282 cents, oct.: 1204.74744 cents Scale is strictly proper Step pattern alph. order: ABCBADBACBABDABCABAEFGDABADGFCB Step pattern size order : GDCDGBDGCDGDBGDCGDGAEFBGDGBFECD Scale is a Constant Structure, by a margin of 0.39576 cents Scale diversity : 1.374522 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.386933 Number of different interval sizes : 176 = 5.86667 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 5.86667 = 88/15 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 4375/4374, 0.3958 cents Number of recognisable fifths : 29, average 699.1310 cents Number of appreciable fifths : 25, average 699.7381 cents Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 5 7 Length of longest harmonic part : 2 at degree 1 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 15 = 48.3871% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 3675 (O: 3675 U: 3675) Highest odd numerator or denominator: 105 Scale harmonicity : 0.012638 Average absolute harmonicity : 0.106657 Specific harmonicity : 0.090095 Fundamental : 1/235200, -17.8435 octaves, 0.0011 Hz. Guide tone : 302400, 18.2061 octaves, 79115570.947 Hz. Exponens Consonantiae : 7.112448E+10, 36.04963 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 693.5, average 22.37097 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 34.28806, average 1.10607 Sum of Tenney's harmonic distance : 68.90614, average 2.22278 Vogel's harmonic complexity : 33.35484 Wille's k value : 192937 Wilson's harmonic complexity : 53 Rectangular lattice diameter : 11 Triangular lattice diameter : 5 Lattice compactness : 2086.47105, average 4.20659 Lattice compactness (without 2's) : 1055.47020, average 2.12796 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 6 0.19355 74 1 3: -1 .. 3 0.70968 28 3 5: -2 .. 2 -0.03226 21 8 7: -2 .. 1 -0.25806 22 19 Average exponent except 2's : 13 / 31 = 0.41935 Average absolute exponent except 2's: 71 / 31 = 2.29032 Scale is JI-epimorphic with val: <31 49 72 87| = patent
FIT/MODE
31: 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: 6.0176 c. M: 15.2415 c. 38: 2 1 1 1 1 1 1 2 1 1 2 1 1 1 1 2 1 1 2 0 2 1 1 2 1 1 1 1 2 1 1 N D3 S SD: 9.1677 c. M: 14.7327 c. 39: 2 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 2 1 1 1 1 2 1 1 2 1 1 1 2 1 1 N D3 SD: 8.9121 c. M:-15.7895 c. 41: 2 1 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 2 0 2 1 1 2 1 2 1 1 2 1 1 N D3 SD: 6.2295 c. M:-12.1358 c. 48: 2 1 2 1 2 1 2 2 1 1 2 2 1 2 1 2 2 1 2 1 2 1 1 2 2 2 1 2 1 2 1 N D3 SD: 7.0453 c. M:-11.7313 c. 53: 2 2 1 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 P M ME S SD: 4.7266 c. M: 10.9943 c. 54: 2 2 1 2 2 1 2 2 2 1 3 1 1 3 1 2 2 2 2 1 2 2 1 2 2 2 1 2 2 1 2 N D3 SD: 6.0755 c. M:-9.5720 c. 56: 2 2 2 1 3 1 1 3 1 2 2 2 1 3 1 2 2 2 2 1 2 2 1 3 1 2 2 2 2 1 2 N D3 SD: 5.9606 c. M: 10.4534 c. 60: 2 2 2 2 2 2 1 3 2 1 3 2 1 2 2 2 2 2 3 1 2 2 1 3 1 3 1 2 2 2 2 N SD: 6.1151 c. M:-9.3831 c. 62: 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 1 2 2 2 2 2 2 2 2 2 2 2 P T3 SD: 5.4095 c. M: 11.1447 c. 66: 3 2 2 2 2 2 2 2 2 2 3 2 1 3 2 2 3 2 2 1 3 2 2 2 2 3 1 3 2 2 2 P SD: 5.2370 c. M: 8.9911 c. 68: 3 2 2 2 3 1 2 3 2 2 3 2 1 3 2 2 3 2 3 1 2 3 1 3 2 3 1 3 2 2 2 N SD: 4.0186 c. M:-8.0981 c. 71: 3 2 2 2 3 2 2 3 2 2 3 2 1 3 2 3 2 3 2 2 2 3 1 3 2 3 2 2 3 2 2 P SD: 4.8360 c. M:-7.9042 c. 72: 3 2 2 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 3 1 3 2 2 3 2 3 2 2 3 2 2 P D3 SD: 3.0098 c. M: 7.0946 c. 85: 3 3 2 3 3 2 3 3 3 2 4 2 2 4 2 3 3 3 3 2 3 3 2 3 3 3 2 3 3 2 3 P D3 SD: 3.9625 c. M: 6.6561 c. 87: 4 2 3 2 4 2 2 4 2 3 4 2 2 4 2 3 3 3 3 2 3 3 2 4 2 4 2 3 3 2 3 P SD: 3.5904 c. M:-6.4020 c. 92: 4 2 3 3 4 2 2 4 3 3 3 3 2 4 3 2 4 3 4 1 3 4 2 4 2 4 2 3 4 2 3 N SD: 3.8178 c. M: 6.2063 c. 94: 4 3 2 3 4 2 3 4 2 3 4 3 2 4 3 2 4 3 4 1 4 3 2 4 3 4 2 3 3 3 3 N SD: 3.2338 c. M: 6.6700 c. 99: 4 3 3 3 4 2 3 4 3 3 4 3 2 4 3 3 4 3 4 2 3 4 2 4 3 4 2 4 3 3 3 P SD: 1.5355 c. M:-3.5114 c. 130: 5 4 4 4 5 3 4 5 4 4 5 4 3 5 4 4 5 4 5 3 4 5 3 5 4 5 3 5 4 4 4 SP SD: 1.5603 c. M: 3.1737 c. 140: 6 4 4 4 6 3 4 6 4 4 6 4 3 6 4 4 6 4 6 2 5 5 3 6 4 6 3 5 5 4 4 N SD: 1.4333 c. M:-3.5603 c. 147: 6 4 5 4 6 3 5 6 4 4 6 5 3 6 4 5 6 4 6 3 5 5 3 6 5 6 3 5 5 5 4 N SD: 2.2163 c. M:-3.1296 c. 149: 6 4 5 4 6 4 4 6 4 5 6 4 4 6 4 5 6 4 6 3 5 5 4 6 4 6 4 5 5 5 4 SP SD: 2.1700 c. M: 4.3082 c. 152: 6 5 4 5 6 3 5 6 4 5 6 5 3 6 5 4 6 5 6 3 5 6 3 6 5 6 3 6 5 4 5 P SD: 1.8949 c. M: 3.7769 c. 171: 7 5 5 5 7 4 5 7 5 5 7 5 4 7 5 5 7 5 7 3 6 6 4 7 5 7 4 6 6 5 5 P SD: 0.4229 c. M: 0.9543 c. 270: 11 8 8 8 11 6 8 11 8 8 11 8 6 11 8 8 11 8 11 5 9 10 6 11 8 11 6 10 9 8 8 P SD: 0.3651 c. M:-0.7059 c. 441: 18 13 13 13 18 10 13 18 13 13 18 13 10 18 13 13 18 13 18 8 15 16 10 18 13 18 10 16 15 13 13 P SD: 0.1867 c. M:-0.4085 c. 836: 34 25 24 25 34 19 25 34 24 25 34 25 19 34 25 24 34 25 34 15 29 30 19 34 25 34 19 30 29 24 25 P SD: 0.1866 c. M: 0.3786 c. 913: 37 27 27 27 37 21 27 37 27 27 37 27 21 37 27 27 37 27 37 17 31 33 21 37 27 37 21 33 31 27 27 SP SD: 0.1814 c. M: 0.3489 c. 935: 38 28 27 28 38 21 28 38 27 28 38 28 21 38 28 27 38 28 38 17 32 34 21 38 28 38 21 34 32 27 28 P SD: 0.1363 c. M: 0.2426 c. 1106: 45 33 32 33 45 25 33 45 32 33 45 33 25 45 33 32 45 33 45 20 38 40 25 45 33 45 25 40 38 32 33 P SD: 0.0863 c. M: 0.1648 c. 1376: 56 41 40 41 56 31 41 56 40 41 56 41 31 56 41 40 56 41 56 25 47 50 31 56 41 56 31 50 47 40 41 P SD: 0.0839 c. M:-0.1728 c. 1547: 63 46 45 46 63 35 46 63 45 46 63 46 35 63 46 45 63 46 63 28 53 56 35 63 46 63 35 56 53 45 46 P SD: 0.0596 c. M:-0.1473 c. 1578: 64 47 46 47 64 36 47 64 46 47 64 47 36 64 47 46 64 47 64 29 54 57 36 64 47 64 36 57 54 46 47 SP SD: 0.0618 c. M: 0.1550 c. 1848: 75 55 54 55 75 42 55 75 54 55 75 55 42 75 55 54 75 55 75 34 63 67 42 75 55 75 42 67 63 54 55 SP SD: 0.0484 c. M: 0.1068 c. 2019: 82 60 59 60 82 46 60 82 59 60 82 60 46 82 60 59 82 60 82 37 69 73 46 82 60 82 46 73 69 59 60 SP SD: 0.0357 c. M: 0.0690 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: 0.7504 cents 7 .. 14 match: 7 H SD: 2.7545 cents 8 .. 16 match: 8 H SD: 2.1460 cents 9 .. 18 match: 9 H SD: 4.3376 cents 10 .. 20 match: 10 H SD: 3.0171 cents 11 .. 22 match: 11 H SD: 3.6687 cents 12 .. 24 match: 12 H SD: 2.4185 cents 13 .. 26 match: 13 H SD: 3.6651 cents 14 .. 28 match: 14 H SD: 2.4386 cents 15 .. 30 match: 15 H SD: 2.4506 cents 16 .. 32 match: 16 H SD: 2.6534 cents 17 .. 34 match: 17 H SD: 3.0659 cents 18 .. 36 match: 18 H SD: 2.6709 cents 19 .. 38 match: 19 H SD: 2.9726 cents 20 .. 40 match: 20 H SD: 2.5750 cents 21 .. 42 match: 21 H SD: 2.3305 cents 22 .. 44 match: 22 H SD: 2.4682 cents 23 .. 46 match: 23 H SD: 2.4355 cents 24 .. 48 match: 24 H SD: 1.7721 cents 25 .. 50 match: 25 H SD: 2.0084 cents 26 .. 52 match: 25 SD: 2.5462 cents 27 .. 54 match: 25 SD: 2.3731 cents 28 .. 56 match: 27 SD: 1.9071 cents 29 .. 58 match: 25 SD: 2.2286 cents 30 .. 60 match: 28 SD: 1.7353 cents 31 .. 62 match: 26 SD: 1.9572 cents 32 .. 64 match: 28 SD: 1.6788 cents 33 .. 66 match: 29 SD: 2.0832 cents 34 .. 68 match: 29 SD: 2.0109 cents 35 .. 70 match: 30 SD: 1.5060 cents 36 .. 72 match: 28 SD: 1.5467 cents 37 .. 74 match: 28 SD: 1.8457 cents 38 .. 76 match: 29 SD: 1.8528 cents 39 .. 78 match: 31 SD: 1.5852 cents 40 .. 80 match: 30 SD: 1.2850 cents 44 .. 88 match: 30 SD: 1.4129 cents 45 .. 90 match: 30 SD: 1.3083 cents 47 .. 94 match: 30 SD: 1.5692 cents 48 .. 96 match: 31 SD: 1.2862 cents 52 .. 104 match: 30 SD: 1.3318 cents 53 .. 106 match: 31 SD: 1.2686 cents 54 .. 108 match: 31 SD: 1.1932 cents 55 .. 110 match: 31 SD: 1.0676 cents 60 .. 120 match: 31 SD: 1.0332 cents 63 .. 126 match: 31 SD: 1.0077 cents 64 .. 128 match: 31 SD: 0.8570 cents 70 .. 140 match: 31 SD: 0.8230 cents 72 .. 144 match: 31 SD: 0.7907 cents 80 .. 160 match: 31 SD: 0.7205 cents 84 .. 168 match: 31 SD: 0.6754 cents 95 .. 190 match: 31 SD: 0.6369 cents 96 .. 192 match: 31 SD: 0.5625 cents 105 .. 210 match: 31 SD: 0.5150 cents 112 .. 224 match: 31 SD: 0.5122 cents 120 .. 240 match: 31 SD: 0.4838 cents 126 .. 252 match: 31 SD: 0.4605 cents 137 .. 274 match: 31 SD: 0.4275 cents 138 .. 276 match: 31 SD: 0.4136 cents 140 .. 280 match: 31 SD: 0.3468 cents 168 .. 336 match: 31 SD: 0.3268 cents 175 .. 350 match: 31 SD: 0.3081 cents 192 .. 384 match: 31 SD: 0.2863 cents 200 .. 400 match: 31 SD: 0.2796 cents 210 .. 420 match: 31 SD: 0.2582 cents 215 .. 430 match: 31 SD: 0.2516 cents 224 .. 448 match: 31 SD: 0.2307 cents 240 .. 480 match: 31 SD: 0.1881 cents 280 .. 560 match: 31 SD: 0.1699 cents 320 .. 640 match: 31 SD: 0.1352 cents 384 .. 768 match: 31 SD: 0.1332 cents 420 .. 840 match: 31 SD: 0.0997 cents 560 .. 1120 match: 31 SD: 0.0702 cents