Scala analysis: notchedcube
Otonal tetrads sharing a note with the root tetrad, a notched chord cube
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 21/20 84.467193 minor semitone 4: 15/14 119.442808 major diatonic semitone 5: 35/32 155.139620 septimal neutral second 6: 9/8 203.910002 major whole tone 7: 8/7 231.174094 septimal whole tone 8: 7/6 266.870906 septimal minor third 9: 6/5 315.641287 minor third 10: 49/40 351.338099 larger approximation to neutral third 11: 5/4 386.313714 major third 12: 9/7 435.084095 septimal major third, BP third 13: 21/16 470.780907 narrow fourth 14: 4/3 498.044999 perfect fourth 15: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 16: 10/7 617.487807 Euler's tritone 17: 35/24 653.184619 septimal semi-diminished fifth 18: 3/2 701.955001 perfect fifth 19: 49/32 737.651813 20: 25/16 772.627428 classic augmented fifth 21: 8/5 813.686286 minor sixth 22: 5/3 884.358713 major sixth, BP sixth 23: 12/7 933.129094 septimal major sixth 24: 7/4 968.825906 harmonic seventh 25: 25/14 1003.801521 middle minor seventh 26: 9/5 1017.596288 just minor seventh, BP seventh 27: 15/8 1088.268715 classic major seventh 28: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 3: 126/125 13.7948 septimal semicomma, Starling comma 4: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 5: 49/48 35.6968 slendro diesis, septimal 1/6-tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 64/63 27.2641 septimal comma, Archytas' comma 8: 49/48 35.6968 slendro diesis, septimal 1/6-tone 9: 36/35 48.7704 septimal diesis, 1/4-tone 10: 49/48 35.6968 slendro diesis, septimal 1/6-tone 11: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 12: 36/35 48.7704 septimal diesis, 1/4-tone 13: 49/48 35.6968 slendro diesis, septimal 1/6-tone 14: 64/63 27.2641 septimal comma, Archytas' comma 15: 21/20 84.4672 minor semitone 16: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 17: 49/48 35.6968 slendro diesis, septimal 1/6-tone 18: 36/35 48.7704 septimal diesis, 1/4-tone 19: 49/48 35.6968 slendro diesis, septimal 1/6-tone 20: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 21: 128/125 41.0589 minor diesis, diesis 22: 25/24 70.6724 classic chromatic semitone, minor chroma 23: 36/35 48.7704 septimal diesis, 1/4-tone 24: 49/48 35.6968 slendro diesis, septimal 1/6-tone 25: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 26: 126/125 13.7948 septimal semicomma, Starling comma 27: 25/24 70.6724 classic chromatic semitone, minor chroma 28: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 126/125 13.795 cents septimal semicomma, Starling comma 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 6 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 8 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 128/125 41.059 cents minor diesis, diesis 1: 5 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 2: 3 36/35 48.770 cents septimal diesis, 1/4-tone 2: 2 28/27 62.961 cents Archytas' 1/3-tone 2: 6 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 2 256/245 76.034 cents septimal minor semitone 2: 1 360/343 83.746 cents 2: 8 21/20 84.467 cents minor semitone 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 15/14 119.443 cents major diatonic semitone 2: 1 49/45 147.428 cents BP minor semitone 2: 1 10/9 182.404 cents minor whole tone 3: 1 360/343 83.746 cents 3: 3 21/20 84.467 cents minor semitone 3: 5 16/15 111.731 cents minor diatonic semitone 3: 8 15/14 119.443 cents major diatonic semitone 3: 2 343/320 120.164 cents 3: 2 160/147 146.707 cents 3: 1 49/45 147.428 cents BP minor semitone 3: 2 35/32 155.140 cents septimal neutral second 3: 1 192/175 160.502 cents septimal 4/5-tone 3: 1 10/9 182.404 cents minor whole tone 3: 1 28/25 196.198 cents middle second 3: 1 245/216 218.101 cents 4: 2 15/14 119.443 cents major diatonic semitone 4: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 4: 2 160/147 146.707 cents 4: 2 49/45 147.428 cents BP minor semitone 4: 5 35/32 155.140 cents septimal neutral second 4: 2 192/175 160.502 cents septimal 4/5-tone 4: 1 54/49 168.213 cents Zalzal's mujannab 4: 3 10/9 182.404 cents minor whole tone 4: 1 125/112 190.115 cents classic augmented semitone 4: 1 384/343 195.477 cents 4: 3 28/25 196.198 cents middle second 4: 1 9/8 203.910 cents major whole tone 4: 1 8/7 231.174 cents septimal whole tone 4: 1 343/300 231.895 cents 4: 1 125/108 253.076 cents semi-augmented whole tone 5: 1 35/32 155.140 cents septimal neutral second 5: 1 192/175 160.502 cents septimal 4/5-tone 5: 1 54/49 168.213 cents Zalzal's mujannab 5: 3 10/9 182.404 cents minor whole tone 5: 1 125/112 190.115 cents classic augmented semitone 5: 3 28/25 196.198 cents middle second 5: 4 9/8 203.910 cents major whole tone 5: 1 245/216 218.101 cents 5: 8 8/7 231.174 cents septimal whole tone 5: 1 147/128 239.607 cents 5: 4 7/6 266.871 cents septimal minor third 6: 1 384/343 195.477 cents 6: 1 28/25 196.198 cents middle second 6: 1 9/8 203.910 cents major whole tone 6: 5 8/7 231.174 cents septimal whole tone 6: 1 343/300 231.895 cents 6: 1 147/128 239.607 cents 6: 1 144/125 244.969 cents classic diminished third 6: 2 400/343 266.150 cents 6: 7 7/6 266.871 cents septimal minor third 6: 2 75/64 274.582 cents classic augmented second 6: 1 288/245 279.944 cents 6: 1 147/125 280.666 cents 6: 2 25/21 301.847 cents BP second, quasi-equal minor third 6: 1 343/288 302.568 cents 6: 1 6/5 315.641 cents minor third 7: 2 8/7 231.174 cents septimal whole tone 7: 1 144/125 244.969 cents classic diminished third 7: 4 7/6 266.871 cents septimal minor third 7: 2 288/245 279.944 cents 7: 5 25/21 301.847 cents BP second, quasi-equal minor third 7: 1 343/288 302.568 cents 7: 9 6/5 315.641 cents minor third 7: 2 175/144 337.543 cents 7: 1 49/40 351.338 cents larger approximation to neutral third 7: 1 5/4 386.314 cents major third 8: 1 7/6 266.871 cents septimal minor third 8: 1 288/245 279.944 cents 8: 1 147/125 280.666 cents 8: 1 32/27 294.135 cents Pythagorean minor third 8: 1 25/21 301.847 cents BP second, quasi-equal minor third 8: 3 6/5 315.641 cents minor third 8: 2 175/144 337.543 cents 8: 2 128/105 342.905 cents septimal neutral third 8: 6 60/49 350.617 cents smaller approximation to neutral third 8: 5 49/40 351.338 cents larger approximation to neutral third 8: 3 5/4 386.314 cents major third 8: 1 245/192 422.011 cents 8: 1 32/25 427.373 cents classic diminished fourth 9: 3 6/5 315.641 cents minor third 9: 1 128/105 342.905 cents septimal neutral third 9: 1 60/49 350.617 cents smaller approximation to neutral third 9: 1 49/40 351.338 cents larger approximation to neutral third 9: 1 216/175 364.412 cents 9: 3 56/45 378.602 cents septimal narrow major third 9: 10 5/4 386.314 cents major third 9: 2 63/50 400.108 cents quasi-equal major third 9: 2 80/63 413.578 cents wide major third 9: 1 9/7 435.084 cents septimal major third, BP third 9: 1 125/96 456.986 cents classic augmented third 9: 1 64/49 462.348 cents 2 septatones or septatonic major third 9: 1 98/75 463.069 cents 10: 1 60/49 350.617 cents smaller approximation to neutral third 10: 1 49/40 351.338 cents larger approximation to neutral third 10: 1 216/175 364.412 cents 10: 1 56/45 378.602 cents septimal narrow major third 10: 1 5/4 386.314 cents major third 10: 1 63/50 400.108 cents quasi-equal major third 10: 1 80/63 413.578 cents wide major third 10: 2 125/98 421.289 cents 10: 3 245/192 422.011 cents 10: 4 32/25 427.373 cents classic diminished fourth 10: 4 9/7 435.084 cents septimal major third, BP third 10: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 10: 1 64/49 462.348 cents 2 septatones or septatonic major third 10: 2 21/16 470.781 cents narrow fourth 10: 3 4/3 498.045 cents perfect fourth 11: 1 5/4 386.314 cents major third 11: 1 432/343 399.387 cents 11: 1 63/50 400.108 cents quasi-equal major third 11: 1 80/63 413.578 cents wide major third 11: 1 9/7 435.084 cents septimal major third, BP third 11: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 11: 1 125/96 456.986 cents classic augmented third 11: 3 64/49 462.348 cents 2 septatones or septatonic major third 11: 3 98/75 463.069 cents 11: 5 21/16 470.781 cents narrow fourth 11: 4 4/3 498.045 cents perfect fourth 11: 2 75/56 505.757 cents marvelous fourth 11: 1 168/125 511.840 cents 11: 1 200/147 533.021 cents 11: 1 49/36 533.742 cents Arabic lute acute fourth 11: 1 48/35 546.815 cents septimal semi-augmented fourth 12: 1 32/25 427.373 cents classic diminished fourth 12: 2 9/7 435.084 cents septimal major third, BP third 12: 8 4/3 498.045 cents perfect fourth 12: 2 75/56 505.757 cents marvelous fourth 12: 1 343/256 506.478 cents 12: 1 168/125 511.840 cents 12: 2 27/20 519.551 cents acute fourth 12: 2 200/147 533.021 cents 12: 2 49/36 533.742 cents Arabic lute acute fourth 12: 1 175/128 541.453 cents 12: 3 48/35 546.815 cents septimal semi-augmented fourth 12: 1 25/18 568.717 cents classic augmented fourth 12: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 13: 1 64/49 462.348 cents 2 septatones or septatonic major third 13: 1 21/16 470.781 cents narrow fourth 13: 1 168/125 511.840 cents 13: 1 200/147 533.021 cents 13: 3 49/36 533.742 cents Arabic lute acute fourth 13: 1 175/128 541.453 cents 13: 6 48/35 546.815 cents septimal semi-augmented fourth 13: 1 343/250 547.537 cents 13: 3 25/18 568.717 cents classic augmented fourth 13: 2 480/343 581.791 cents 13: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 13: 2 45/32 590.224 cents diatonic tritone 13: 2 10/7 617.488 cents Euler's tritone 13: 1 343/240 618.209 cents 14: 1 4/3 498.045 cents perfect fourth 14: 2 48/35 546.815 cents septimal semi-augmented fourth 14: 2 25/18 568.717 cents classic augmented fourth 14: 9 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 14: 9 10/7 617.488 cents Euler's tritone 14: 2 36/25 631.283 cents classic diminished fifth 14: 2 35/24 653.185 cents septimal semi-diminished fifth 14: 1 3/2 701.955 cents perfect fifth 15: 1 480/343 581.791 cents 15: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 15: 2 64/45 609.776 cents 2nd tritone 15: 3 10/7 617.488 cents Euler's tritone 15: 2 343/240 618.209 cents 15: 3 36/25 631.283 cents classic diminished fifth 15: 1 500/343 652.463 cents 15: 6 35/24 653.185 cents septimal semi-diminished fifth 15: 1 256/175 658.547 cents 15: 3 72/49 666.258 cents Arabic lute grave fifth 15: 1 147/100 666.979 cents 15: 1 125/84 688.160 cents 15: 1 32/21 729.219 cents wide fifth 15: 1 49/32 737.652 cents 16: 2 10/7 617.488 cents Euler's tritone 16: 1 36/25 631.283 cents classic diminished fifth 16: 3 35/24 653.185 cents septimal semi-diminished fifth 16: 1 256/175 658.547 cents 16: 2 72/49 666.258 cents Arabic lute grave fifth 16: 2 147/100 666.979 cents 16: 2 40/27 680.449 cents grave fifth 16: 1 125/84 688.160 cents 16: 1 512/343 693.522 cents 3 septatones or septatonic fifth 16: 2 112/75 694.243 cents marvelous fifth 16: 8 3/2 701.955 cents perfect fifth 16: 2 14/9 764.916 cents septimal minor sixth 16: 1 25/16 772.627 cents classic augmented fifth 17: 1 35/24 653.185 cents septimal semi-diminished fifth 17: 1 72/49 666.258 cents Arabic lute grave fifth 17: 1 147/100 666.979 cents 17: 1 125/84 688.160 cents 17: 2 112/75 694.243 cents marvelous fifth 17: 4 3/2 701.955 cents perfect fifth 17: 5 32/21 729.219 cents wide fifth 17: 3 75/49 736.931 cents BP fifth 17: 3 49/32 737.652 cents 17: 1 192/125 743.014 cents classic diminished sixth 17: 1 54/35 750.725 cents septimal semi-augmented fifth 17: 1 14/9 764.916 cents septimal minor sixth 17: 1 63/40 786.422 cents narrow minor sixth 17: 1 100/63 799.892 cents quasi-equal minor sixth 17: 1 343/216 800.613 cents 17: 1 8/5 813.686 cents minor sixth 18: 3 3/2 701.955 cents perfect fifth 18: 2 32/21 729.219 cents wide fifth 18: 1 49/32 737.652 cents 18: 2 54/35 750.725 cents septimal semi-augmented fifth 18: 4 14/9 764.916 cents septimal minor sixth 18: 4 25/16 772.627 cents classic augmented fifth 18: 3 384/245 777.989 cents 18: 2 196/125 778.711 cents 18: 1 63/40 786.422 cents narrow minor sixth 18: 1 100/63 799.892 cents quasi-equal minor sixth 18: 1 8/5 813.686 cents minor sixth 18: 1 45/28 821.398 cents septimale wide minor sixth 18: 1 175/108 835.588 cents 18: 1 80/49 848.662 cents smaller approximation to neutral sixth 18: 1 49/30 849.383 cents larger approximation to neutral sixth 19: 1 75/49 736.931 cents BP fifth 19: 1 49/32 737.652 cents 19: 1 192/125 743.014 cents classic diminished sixth 19: 1 14/9 764.916 cents septimal minor sixth 19: 2 63/40 786.422 cents narrow minor sixth 19: 2 100/63 799.892 cents quasi-equal minor sixth 19: 10 8/5 813.686 cents minor sixth 19: 3 45/28 821.398 cents septimale wide minor sixth 19: 1 175/108 835.588 cents 19: 1 80/49 848.662 cents smaller approximation to neutral sixth 19: 1 49/30 849.383 cents larger approximation to neutral sixth 19: 1 105/64 857.095 cents septimal neutral sixth 19: 3 5/3 884.359 cents major sixth, BP sixth 20: 1 25/16 772.627 cents classic augmented fifth 20: 1 384/245 777.989 cents 20: 3 8/5 813.686 cents minor sixth 20: 5 80/49 848.662 cents smaller approximation to neutral sixth 20: 6 49/30 849.383 cents larger approximation to neutral sixth 20: 2 105/64 857.095 cents septimal neutral sixth 20: 2 288/175 862.457 cents 20: 3 5/3 884.359 cents major sixth, BP sixth 20: 1 42/25 898.153 cents quasi-equal major sixth 20: 1 27/16 905.865 cents Pythagorean major sixth 20: 1 250/147 919.334 cents 20: 1 245/144 920.056 cents 20: 1 12/7 933.129 cents septimal major sixth 21: 1 8/5 813.686 cents minor sixth 21: 1 80/49 848.662 cents smaller approximation to neutral sixth 21: 2 288/175 862.457 cents 21: 9 5/3 884.359 cents major sixth, BP sixth 21: 1 576/343 897.432 cents 21: 5 42/25 898.153 cents quasi-equal major sixth 21: 2 245/144 920.056 cents 21: 4 12/7 933.129 cents septimal major sixth 21: 1 125/72 955.031 cents classic augmented sixth 21: 2 7/4 968.826 cents harmonic seventh 22: 1 5/3 884.359 cents major sixth, BP sixth 22: 1 576/343 897.432 cents 22: 2 42/25 898.153 cents quasi-equal major sixth 22: 1 250/147 919.334 cents 22: 1 245/144 920.056 cents 22: 2 128/75 925.418 cents diminished seventh 22: 7 12/7 933.129 cents septimal major sixth 22: 2 343/200 933.850 cents 22: 1 125/72 955.031 cents classic augmented sixth 22: 1 256/147 960.393 cents 22: 1 600/343 968.105 cents 22: 5 7/4 968.826 cents harmonic seventh 22: 1 16/9 996.090 cents Pythagorean minor seventh 22: 1 25/14 1003.802 cents middle minor seventh 22: 1 343/192 1004.523 cents 23: 4 12/7 933.129 cents septimal major sixth 23: 1 256/147 960.393 cents 23: 8 7/4 968.826 cents harmonic seventh 23: 1 432/245 981.899 cents 23: 4 16/9 996.090 cents Pythagorean minor seventh 23: 3 25/14 1003.802 cents middle minor seventh 23: 1 224/125 1009.885 cents 23: 3 9/5 1017.596 cents just minor seventh, BP seventh 23: 1 49/27 1031.787 cents 23: 1 175/96 1039.498 cents 23: 1 64/35 1044.860 cents septimal neutral seventh 24: 1 216/125 946.924 cents semi-augmented sixth 24: 1 600/343 968.105 cents 24: 1 7/4 968.826 cents harmonic seventh 24: 1 16/9 996.090 cents Pythagorean minor seventh 24: 3 25/14 1003.802 cents middle minor seventh 24: 1 343/192 1004.523 cents 24: 1 224/125 1009.885 cents 24: 3 9/5 1017.596 cents just minor seventh, BP seventh 24: 1 49/27 1031.787 cents 24: 2 175/96 1039.498 cents 24: 5 64/35 1044.860 cents septimal neutral seventh 24: 2 90/49 1052.572 cents 24: 2 147/80 1053.293 cents 24: 2 50/27 1066.762 cents grave major seventh 24: 2 28/15 1080.557 cents grave major seventh 25: 1 432/245 981.899 cents 25: 1 25/14 1003.802 cents middle minor seventh 25: 1 9/5 1017.596 cents just minor seventh, BP seventh 25: 1 175/96 1039.498 cents 25: 2 64/35 1044.860 cents septimal neutral seventh 25: 1 90/49 1052.572 cents 25: 2 147/80 1053.293 cents 25: 2 640/343 1079.836 cents 25: 8 28/15 1080.557 cents grave major seventh 25: 5 15/8 1088.269 cents classic major seventh 25: 3 40/21 1115.533 cents acute major seventh 25: 1 343/180 1116.254 cents 26: 1 9/5 1017.596 cents just minor seventh, BP seventh 26: 1 90/49 1052.572 cents 26: 2 28/15 1080.557 cents grave major seventh 26: 2 15/8 1088.269 cents classic major seventh 26: 8 40/21 1115.533 cents acute major seventh 26: 1 343/180 1116.254 cents 26: 2 245/128 1123.966 cents 26: 6 48/25 1129.328 cents classic diminished octave 26: 2 27/14 1137.039 cents septimal major seventh 26: 3 35/18 1151.230 cents septimal semi-diminished octave 27: 1 15/8 1088.269 cents classic major seventh 27: 1 40/21 1115.533 cents acute major seventh 27: 2 48/25 1129.328 cents classic diminished octave 27: 5 35/18 1151.230 cents septimal semi-diminished octave 27: 1 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 27: 8 96/49 1164.303 cents 27: 6 49/25 1165.024 cents BP eighth 27: 2 63/32 1172.736 cents octave - septimal comma 27: 2 125/63 1186.205 cents Highest number of different intervals for one interval class: 16 Average number of different intervals per interval class: 12.59259 = 340/27
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 0.0 : 35.7 70.7 84.5 119.4 155.1 203.9 231.2 266.9 315.6 351.3 386.3 435.1 470.8 498.0 582.5 617.5 653.2 702.0 737.7 772.6 813.7 884.4 933.1 968.8 1003.8 1017.6 1088.3 1200.0 35.7 : 35.0 48.8 83.7 119.4 168.2 195.5 231.2 279.9 315.6 350.6 399.4 435.1 462.3 546.8 581.8 617.5 666.3 702.0 736.9 778.0 848.7 897.4 933.1 968.1 981.9 1052.6 1164.3 1200.0 70.7 : 13.8 48.8 84.5 133.2 160.5 196.2 245.0 280.7 315.6 364.4 400.1 427.4 511.8 546.8 582.5 631.3 667.0 702.0 743.0 813.7 862.5 898.2 933.1 946.9 1017.6 1129.3 1165.0 1200.0 84.5 : 35.0 70.7 119.4 146.7 182.4 231.2 266.9 301.8 350.6 386.3 413.6 498.0 533.0 568.7 617.5 653.2 688.2 729.2 799.9 848.7 884.4 919.3 933.1 1003.8 1115.5 1151.2 1186.2 1200.0 119.4 : 35.7 84.5 111.7 147.4 196.2 231.9 266.9 315.6 351.3 378.6 463.1 498.0 533.7 582.5 618.2 653.2 694.2 764.9 813.7 849.4 884.4 898.2 968.8 1080.6 1116.3 1151.2 1165.0 1200.0 155.1 : 48.8 76.0 111.7 160.5 196.2 231.2 279.9 315.6 342.9 427.4 462.3 498.0 546.8 582.5 617.5 658.5 729.2 778.0 813.7 848.7 862.5 933.1 1044.9 1080.6 1115.5 1129.3 1164.3 1200.0 203.9 : 27.3 63.0 111.7 147.4 182.4 231.2 266.9 294.1 378.6 413.6 449.3 498.0 533.7 568.7 609.8 680.4 729.2 764.9 799.9 813.7 884.4 996.1 1031.8 1066.8 1080.6 1115.5 1151.2 1200.0 231.2 : 35.7 84.5 120.2 155.1 203.9 239.6 266.9 351.3 386.3 422.0 470.8 506.5 541.5 582.5 653.2 702.0 737.7 772.6 786.4 857.1 968.8 1004.5 1039.5 1053.3 1088.3 1124.0 1172.7 1200.0 266.9 : 48.8 84.5 119.4 168.2 203.9 231.2 315.6 350.6 386.3 435.1 470.8 505.8 546.8 617.5 666.3 702.0 736.9 750.7 821.4 933.1 968.8 1003.8 1017.6 1052.6 1088.3 1137.0 1164.3 1200.0 315.6 : 35.7 70.7 119.4 155.1 182.4 266.9 301.8 337.5 386.3 422.0 457.0 498.0 568.7 617.5 653.2 688.2 702.0 772.6 884.4 920.1 955.0 968.8 1003.8 1039.5 1088.3 1115.5 1151.2 1200.0 351.3 : 35.0 83.7 119.4 146.7 231.2 266.1 301.8 350.6 386.3 421.3 462.3 533.0 581.8 617.5 652.5 666.3 736.9 848.7 884.4 919.3 933.1 968.1 1003.8 1052.6 1079.8 1115.5 1164.3 1200.0 386.3 : 48.8 84.5 111.7 196.2 231.2 266.9 315.6 351.3 386.3 427.4 498.0 546.8 582.5 617.5 631.3 702.0 813.7 849.4 884.4 898.2 933.1 968.8 1017.6 1044.9 1080.6 1129.3 1165.0 1200.0 435.1 : 35.7 63.0 147.4 182.4 218.1 266.9 302.6 337.5 378.6 449.3 498.0 533.7 568.7 582.5 653.2 764.9 800.6 835.6 849.4 884.4 920.1 968.8 996.1 1031.8 1080.6 1116.3 1151.2 1200.0 470.8 : 27.3 111.7 146.7 182.4 231.2 266.9 301.8 342.9 413.6 462.3 498.0 533.0 546.8 617.5 729.2 764.9 799.9 813.7 848.7 884.4 933.1 960.4 996.1 1044.9 1080.6 1115.5 1164.3 1200.0 498.0 : 84.5 119.4 155.1 203.9 239.6 274.6 315.6 386.3 435.1 470.8 505.8 519.6 590.2 702.0 737.7 772.6 786.4 821.4 857.1 905.9 933.1 968.8 1017.6 1053.3 1088.3 1137.0 1172.7 1200.0 582.5 : 35.0 70.7 119.4 155.1 190.1 231.2 301.8 350.6 386.3 421.3 435.1 505.8 617.5 653.2 688.2 702.0 736.9 772.6 821.4 848.7 884.4 933.1 968.8 1003.8 1052.6 1088.3 1115.5 1200.0 617.5 : 35.7 84.5 120.2 155.1 196.2 266.9 315.6 351.3 386.3 400.1 470.8 582.5 618.2 653.2 667.0 702.0 737.7 786.4 813.7 849.4 898.2 933.9 968.8 1017.6 1053.3 1080.6 1165.0 1200.0 653.2 : 48.8 84.5 119.4 160.5 231.2 279.9 315.6 350.6 364.4 435.1 546.8 582.5 617.5 631.3 666.3 702.0 750.7 778.0 813.7 862.5 898.2 933.1 981.9 1017.6 1044.9 1129.3 1164.3 1200.0 702.0 : 35.7 70.7 111.7 182.4 231.2 266.9 301.8 315.6 386.3 498.0 533.7 568.7 582.5 617.5 653.2 702.0 729.2 764.9 813.7 849.4 884.4 933.1 968.8 996.1 1080.6 1115.5 1151.2 1200.0 737.7 : 35.0 76.0 146.7 195.5 231.2 266.1 279.9 350.6 462.3 498.0 533.0 546.8 581.8 617.5 666.3 693.5 729.2 778.0 813.7 848.7 897.4 933.1 960.4 1044.9 1079.8 1115.5 1164.3 1200.0 772.6 : 41.1 111.7 160.5 196.2 231.2 245.0 315.6 427.4 463.1 498.0 511.8 546.8 582.5 631.3 658.5 694.2 743.0 778.7 813.7 862.5 898.2 925.4 1009.9 1044.9 1080.6 1129.3 1165.0 1200.0 813.7 : 70.7 119.4 155.1 190.1 203.9 274.6 386.3 422.0 457.0 470.8 505.8 541.5 590.2 617.5 653.2 702.0 737.7 772.6 821.4 857.1 884.4 968.8 1003.8 1039.5 1088.3 1124.0 1158.9 1200.0 884.4 : 48.8 84.5 119.4 133.2 203.9 315.6 351.3 386.3 400.1 435.1 470.8 519.6 546.8 582.5 631.3 667.0 702.0 750.7 786.4 813.7 898.2 933.1 968.8 1017.6 1053.3 1088.3 1129.3 1200.0 933.1 : 35.7 70.7 84.5 155.1 266.9 302.6 337.5 351.3 386.3 422.0 470.8 498.0 533.7 582.5 618.2 653.2 702.0 737.7 764.9 849.4 884.4 920.1 968.8 1004.5 1039.5 1080.6 1151.2 1200.0 968.8 : 35.0 48.8 119.4 231.2 266.9 301.8 315.6 350.6 386.3 435.1 462.3 498.0 546.8 582.5 617.5 666.3 702.0 729.2 813.7 848.7 884.4 933.1 968.8 1003.8 1044.9 1115.5 1164.3 1200.0 1003.8: 13.8 84.5 196.2 231.9 266.9 280.7 315.6 351.3 400.1 427.4 463.1 511.8 547.5 582.5 631.3 667.0 694.2 778.7 813.7 849.4 898.2 933.9 968.8 1009.9 1080.6 1129.3 1165.0 1200.0 1017.6: 70.7 182.4 218.1 253.1 266.9 301.8 337.5 386.3 413.6 449.3 498.0 533.7 568.7 617.5 653.2 680.4 764.9 799.9 835.6 884.4 920.1 955.0 996.1 1066.8 1115.5 1151.2 1186.2 1200.0 1088.3: 111.7 147.4 182.4 196.2 231.2 266.9 315.6 342.9 378.6 427.4 463.1 498.0 546.8 582.5 609.8 694.2 729.2 764.9 813.7 849.4 884.4 925.4 996.1 1044.9 1080.6 1115.5 1129.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 13.7948 .. 111.7313 cents 200/189, 97.9365 cents 126/125, 13.7948 cents 2: 48.7704 .. 182.4037 cents 175/162, 133.6333 cents 27/28,-62.9609 cents 3: 83.7460 .. 218.1005 cents 16807/15552, 134.3545 cents 324/343,-98.6577 cents 4: 119.4428 .. 253.0761 cents 175/162, 133.6333 cents 324/343,-98.6577 cents 5: 155.1396 .. 266.8709 cents 16/15, 111.7313 cents 189/200,-97.9365 cents 6: 195.4773 .. 315.6413 cents 343/320, 120.1640 cents 2304/2401,-71.3936 cents 7: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 20/21,-84.4672 cents 8: 266.8709 .. 427.3726 cents 192/175, 160.5017 cents 14/15,-119.4428 cents 9: 315.6413 .. 463.0694 cents 49/45, 147.4281 cents 15/16,-111.7313 cents 10: 350.6169 .. 498.0450 cents 49/45, 147.4281 cents 2250/2401,-112.4525 cents 11: 386.3137 .. 546.8154 cents 192/175, 160.5017 cents 15/16,-111.7313 cents 12: 427.3726 .. 582.5122 cents 35/32, 155.1396 cents 14/15,-119.4428 cents 13: 462.3482 .. 618.2090 cents 16807/15360, 155.8608 cents 320/343,-120.1640 cents 14: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 320/343,-120.1640 cents 15: 581.7910 .. 737.6518 cents 16807/15360, 155.8608 cents 320/343,-120.1640 cents 16: 617.4878 .. 772.6274 cents 35/32, 155.1396 cents 320/343,-120.1640 cents 17: 653.1846 .. 813.6863 cents 192/175, 160.5017 cents 14/15,-119.4428 cents 18: 701.9550 .. 849.3831 cents 49/45, 147.4281 cents 15/16,-111.7313 cents 19: 736.9306 .. 884.3587 cents 49/45, 147.4281 cents 2250/2401,-112.4525 cents 20: 772.6274 .. 933.1291 cents 192/175, 160.5017 cents 15/16,-111.7313 cents 21: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 14/15,-119.4428 cents 22: 884.3587 .. 1004.5227 cents 343/320, 120.1640 cents 20/21,-84.4672 cents 23: 933.1291 .. 1044.8604 cents 16/15, 111.7313 cents 2304/2401,-71.3936 cents 24: 946.9239 .. 1080.5572 cents 175/162, 133.6333 cents 189/200,-97.9365 cents 25: 981.8995 .. 1116.2540 cents 16807/15552, 134.3545 cents 324/343,-98.6577 cents 26: 1017.5963 .. 1151.2296 cents 175/162, 133.6333 cents 324/343,-98.6577 cents 27: 1088.2687 .. 1186.2052 cents 200/189, 97.9365 cents 27/28,-62.9609 cents
SHOW DATA
Number of notes : 28 -- Interval properties -- Smallest interval : 126/125, 13.7948 cents, class 1 Average step (divided formal octave): 42.8571 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 3.106768 Largest / Average step : 2.607063 Largest / Smallest step : 8.099542 Median interval of one step : 49/48, 35.6968 cents, amount: 8 Most common interval of one step : 49/48, 35.6968 cents, amount: 8 Least squares average step : 39.30459 cents, oct.: 1100.52847 cents Scale is not proper Step pattern alph. order: ABCBADEADABDAEFBADABGHDABCHI Step pattern size order : DCACDFBDFDCFDBHCDFDCEGFDCAGI Scale is not a Constant Structure Scale diversity : 1.365558 Lumma stability : 0.022991 Lumma impropriety factor : 0.918716 Number of different interval sizes : 146 = 5.40741 / class Number of one step interval sizes : 9 Highest interval variety : 16 Mean interval variety : 12.59259 = 340/27 Median interval variety : 13 Lowest interval variety : 8 Smallest interval difference : 2401/2400, 0.7212 cents Number of recognisable fifths : 24, average 698.5940 cents Number of appreciable fifths : 21, average 700.0846 cents Scale contains a complete diamond : 3 5 7 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 13 = 46.4286% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 7 Odd number limit : 343 (O: 343 U: 343) Highest odd numerator or denominator: 49 Scale harmonicity : 0.015138 Average absolute harmonicity : 0.114145 Specific harmonicity : 0.094060 Fundamental : 1/3360, -11.7142 octaves, 0.0779 Hz. Guide tone : 88200, 16.4285 octaves, 23075374.860 Hz. Exponens Consonantiae : 2.963520E+08, 28.14274 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 421.0, average 15.03571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 29.03260, average 1.03688 Sum of Tenney's harmonic distance : 56.46440, average 2.01659 Vogel's harmonic complexity : 22.53571 Wille's k value : 2572 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 9 Triangular lattice diameter : 3 Lattice compactness : 1468.35302, average 3.61663 Lattice compactness (without 2's) : 849.05650, average 2.09127 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -1.21429 60 1 3: -1 .. 2 0.25000 19 3 5: -1 .. 2 0.25000 19 8 7: -1 .. 2 0.25000 19 16 Average exponent except 2's : 21 / 28 = 0.75000 Average absolute exponent except 2's: 57 / 28 = 2.03571
FIT/MODE
28: 1 1 0 1 1 1 0 1 1 1 1 1 1 1 2 0 1 1 1 1 1 2 1 1 0 1 1 3 N SD: 12.1901 c. M: 18.0872 c. 31: 1 1 0 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 2 1 1 1 0 2 3 N SD: 5.0257 c. M: 11.1447 c. 53: 2 1 1 1 2 2 1 2 2 2 1 2 2 1 4 1 2 2 2 1 2 3 2 2 1 1 3 5 N SD: 4.9966 c. M:-10.9261 c. 54: 2 1 1 1 2 2 1 2 2 2 1 3 1 1 4 2 1 3 1 2 2 3 2 2 1 1 3 5 N SD: 6.0850 c. M:-9.3603 c. 57: 2 1 1 2 1 3 1 2 2 2 1 3 1 2 4 1 2 2 2 2 2 3 2 2 2 0 4 5 N SD: 5.9167 c. M: 7.7712 c. 58: 2 1 1 2 2 2 1 2 2 2 2 2 2 1 4 2 2 2 2 1 2 4 2 2 2 0 4 5 N SD: 5.4964 c. M:-10.3776 c. 62: 2 2 0 2 2 3 1 2 2 2 2 2 2 2 4 2 2 2 2 2 2 4 2 2 2 1 3 6 N SD: 4.7205 c. M: 9.2776 c. 68: 2 2 1 2 2 3 1 2 3 2 2 3 2 1 5 2 2 3 2 2 2 4 3 2 2 1 4 6 N SD: 3.4913 c. M:-7.8547 c. 72: 2 2 1 2 2 3 2 2 3 2 2 3 2 2 5 2 2 3 2 2 3 4 3 2 2 1 4 7 N SD: 2.9055 c. M: 5.9608 c. 95: 3 3 1 2 3 4 2 3 4 3 3 3 3 2 7 3 3 4 2 3 3 6 4 3 2 2 5 9 N SD: 3.8243 c. M: 5.9068 c. 99: 3 3 1 3 3 4 2 3 4 3 3 4 3 2 7 3 3 4 3 3 3 6 4 3 3 1 6 9 N SD: 1.4798 c. M:-3.1301 c. 130: 4 4 1 4 4 5 3 4 5 4 4 5 4 3 9 4 4 5 4 4 4 8 5 4 4 1 8 12 N SD: 1.4413 c. M:-3.1737 c. 140: 4 4 2 4 4 6 3 4 6 4 4 6 4 3 10 4 4 6 4 4 5 8 6 4 4 2 8 13 N SD: 1.1705 c. M:-2.4037 c. 171: 5 5 2 5 5 7 4 5 7 5 5 7 5 4 12 5 5 7 5 5 6 10 7 5 5 2 10 16 N SD: 0.4069 c. M: 0.8097 c. 270: 8 8 3 8 8 11 6 8 11 8 8 11 8 6 19 8 8 11 8 8 9 16 11 8 8 3 16 25 N SD: 0.3484 c. M:-0.7059 c. 441: 13 13 5 13 13 18 10 13 18 13 13 18 13 10 31 13 13 18 13 13 15 26 18 13 13 5 26 41 N SD: 0.1744 c. M: 0.3227 c. 935: 28 27 11 27 28 38 21 28 38 28 27 38 28 21 66 27 28 38 28 27 32 55 38 28 27 11 55 87 N SD: 0.1509 c. M:-0.3197 c. 1106: 33 32 13 32 33 45 25 33 45 33 32 45 33 25 78 32 33 45 33 32 38 65 45 33 32 13 65 103 N SD: 0.0998 c. M:-0.1990 c. 1277: 38 37 15 37 38 52 29 38 52 38 37 52 38 29 90 37 38 52 38 37 44 75 52 38 37 15 75 119 N SD: 0.0932 c. M: 0.1993 c. 1376: 41 40 16 40 41 56 31 41 56 41 40 56 41 31 97 40 41 56 41 40 47 81 56 41 40 16 81 128 N SD: 0.0813 c. M:-0.1598 c. 1407: 42 41 16 41 42 57 32 42 57 42 41 57 42 32 99 41 42 57 42 41 48 83 57 42 41 16 83 131 N SD: 0.0698 c. M:-0.1241 c. 1547: 46 45 18 45 46 63 35 46 63 46 45 63 46 35 109 45 46 63 46 45 53 91 63 46 45 18 91 144 N SD: 0.0530 c. M:-0.1154 c. 1578: 47 46 18 46 47 64 36 47 64 47 46 64 47 36 111 46 47 64 47 46 54 93 64 47 46 18 93 147 N SD: 0.0496 c. M: 0.1077 c. 1848: 55 54 21 54 55 75 42 55 75 55 54 75 55 42 130 54 55 75 55 54 63 109 75 55 54 21 109 172 N SD: 0.0484 c. M:-0.1068 c. 2019: 60 59 23 59 60 82 46 60 82 60 59 82 60 46 142 59 60 82 60 59 69 119 82 60 59 23 119 188 N SD: 0.0396 c. M: 0.0751 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: 5.2944 cents 7 .. 14 match: 7 H SD: 2.7545 cents 8 .. 16 match: 8 H SD: 5.1441 cents 9 .. 18 match: 9 H SD: 3.5739 cents 10 .. 20 match: 10 H SD: 3.3279 cents 11 .. 22 match: 11 H SD: 6.4752 cents 12 .. 24 match: 12 H SD: 4.7653 cents 13 .. 26 match: 12 S SD: 4.2961 cents 14 .. 28 match: 13 S SD: 3.5772 cents 15 .. 30 match: 14 S SD: 2.4592 cents 16 .. 32 match: 15 S SD: 3.6237 cents 17 .. 34 match: 16 S SD: 3.6257 cents 18 .. 36 match: 16 S SD: 2.5239 cents 19 .. 38 match: 15 SD: 3.4688 cents 20 .. 40 match: 18 S SD: 2.6533 cents 21 .. 42 match: 19 S SD: 2.6713 cents 22 .. 44 match: 18 SD: 2.7885 cents 23 .. 46 match: 20 SD: 2.6425 cents 24 .. 48 match: 19 SD: 1.8441 cents 25 .. 50 match: 19 SD: 1.9756 cents 26 .. 52 match: 22 SD: 2.6770 cents 27 .. 54 match: 21 SD: 2.5021 cents 28 .. 56 match: 22 SD: 2.0081 cents 29 .. 58 match: 21 SD: 2.4856 cents 30 .. 60 match: 23 SD: 2.0148 cents 31 .. 62 match: 23 SD: 2.1708 cents 32 .. 64 match: 25 SD: 1.8122 cents 33 .. 66 match: 24 SD: 2.4025 cents 34 .. 68 match: 24 SD: 2.3408 cents 35 .. 70 match: 25 SD: 1.7257 cents 36 .. 72 match: 25 SD: 1.7952 cents 37 .. 74 match: 24 SD: 2.0406 cents 38 .. 76 match: 25 SD: 2.0620 cents 39 .. 78 match: 26 SD: 1.7255 cents 40 .. 80 match: 26 SD: 1.4561 cents 41 .. 82 match: 27 SD: 1.4291 cents 42 .. 84 match: 27 SD: 1.3699 cents 43 .. 86 match: 26 SD: 1.6037 cents 44 .. 88 match: 25 SD: 1.4847 cents 45 .. 90 match: 26 SD: 1.3429 cents 46 .. 92 match: 27 SD: 1.5880 cents 47 .. 94 match: 27 SD: 1.5917 cents 48 .. 96 match: 26 SD: 1.2825 cents 49 .. 98 match: 26 SD: 1.4153 cents 52 .. 104 match: 27 SD: 1.3013 cents 53 .. 106 match: 27 SD: 1.3308 cents 54 .. 108 match: 28 SD: 1.2134 cents 55 .. 110 match: 28 SD: 1.0334 cents 58 .. 116 match: 27 SD: 1.3488 cents 59 .. 118 match: 28 SD: 1.3126 cents 60 .. 120 match: 27 SD: 1.1062 cents 61 .. 122 match: 27 SD: 1.1946 cents 62 .. 124 match: 27 SD: 1.2023 cents 63 .. 126 match: 26 SD: 1.1391 cents 64 .. 128 match: 27 SD: 1.0213 cents 65 .. 130 match: 27 SD: 1.0788 cents 66 .. 132 match: 27 SD: 1.0311 cents 67 .. 134 match: 27 SD: 1.1056 cents 68 .. 136 match: 27 SD: 1.1247 cents 69 .. 138 match: 27 SD: 1.1988 cents 70 .. 140 match: 28 SD: 0.9723 cents 72 .. 144 match: 28 SD: 0.9611 cents 75 .. 150 match: 28 SD: 0.9515 cents 77 .. 154 match: 28 SD: 0.9306 cents 79 .. 158 match: 28 SD: 0.9202 cents 80 .. 160 match: 28 SD: 0.7872 cents 84 .. 168 match: 27 SD: 0.6854 cents 85 .. 170 match: 27 SD: 0.7163 cents 86 .. 172 match: 27 SD: 0.8811 cents 87 .. 174 match: 27 SD: 0.8018 cents 88 .. 176 match: 27 SD: 0.7949 cents 89 .. 178 match: 27 SD: 0.7653 cents 94 .. 188 match: 28 SD: 0.7147 cents 95 .. 190 match: 28 SD: 0.6755 cents 96 .. 192 match: 28 SD: 0.5187 cents 108 .. 216 match: 27 SD: 0.6664 cents 109 .. 218 match: 27 SD: 0.6961 cents 111 .. 222 match: 28 SD: 0.6695 cents 112 .. 224 match: 28 SD: 0.5863 cents 115 .. 230 match: 28 SD: 0.5664 cents 120 .. 240 match: 28 SD: 0.4977 cents 126 .. 252 match: 28 SD: 0.4899 cents 137 .. 274 match: 28 SD: 0.4535 cents 140 .. 280 match: 28 SD: 0.3946 cents 160 .. 320 match: 28 SD: 0.3486 cents 183 .. 366 match: 28 SD: 0.3452 cents 185 .. 370 match: 28 SD: 0.3368 cents 192 .. 384 match: 28 SD: 0.2588 cents 224 .. 448 match: 28 SD: 0.2426 cents 240 .. 480 match: 28 SD: 0.2055 cents 280 .. 560 match: 28 SD: 0.1836 cents 320 .. 640 match: 28 SD: 0.1692 cents 336 .. 672 match: 28 SD: 0.1475 cents 384 .. 768 match: 28 SD: 0.1343 cents 448 .. 896 match: 28 SD: 0.1245 cents 476 .. 952 match: 28 SD: 0.1240 cents 480 .. 960 match: 28 SD: 0.0678 cents