Scala analysis: perz
Perz-Edwards 27 note 7-limit scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 16/15 111.731285 minor diatonic semitone 3: 15/14 119.442808 major diatonic semitone 4: 10/9 182.403712 minor whole tone 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: 5/4 386.313714 major third 10: 9/7 435.084095 septimal major third, BP third 11: 21/16 470.780907 narrow fourth 12: 4/3 498.044999 perfect fourth 13: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 14: 10/7 617.487807 Euler's tritone 15: 3/2 701.955001 perfect fifth 16: 32/21 729.219093 wide fifth 17: 14/9 764.915905 septimal minor sixth 18: 8/5 813.686286 minor sixth 19: 5/3 884.358713 major sixth, BP sixth 20: 12/7 933.129094 septimal major sixth 21: 7/4 968.825906 harmonic seventh 22: 16/9 996.089998 Pythagorean minor seventh 23: 9/5 1017.596288 just minor seventh, BP seventh 24: 28/15 1080.557192 grave major seventh 25: 15/8 1088.268715 classic major seventh 26: 40/21 1115.532807 acute major seventh 27: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/20 84.4672 minor semitone 1: 21/20 84.4672 minor semitone 2: 64/63 27.2641 septimal comma, Archytas' comma 3: 225/224 7.7115 septimal kleisma 4: 28/27 62.9609 Archytas' 1/3-tone 5: 81/80 21.5063 syntonic comma, Didymus comma 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: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 49/48 35.6968 slendro diesis, septimal 1/6-tone 12: 64/63 27.2641 septimal comma, Archytas' comma 13: 21/20 84.4672 minor semitone 14: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 15: 21/20 84.4672 minor semitone 16: 64/63 27.2641 septimal comma, Archytas' comma 17: 49/48 35.6968 slendro diesis, septimal 1/6-tone 18: 36/35 48.7704 septimal diesis, 1/4-tone 19: 25/24 70.6724 classic chromatic semitone, minor chroma 20: 36/35 48.7704 septimal diesis, 1/4-tone 21: 49/48 35.6968 slendro diesis, septimal 1/6-tone 22: 64/63 27.2641 septimal comma, Archytas' comma 23: 81/80 21.5063 syntonic comma, Didymus comma 24: 28/27 62.9609 Archytas' 1/3-tone 25: 225/224 7.7115 septimal kleisma 26: 64/63 27.2641 septimal comma, Archytas' comma 27: 21/20 84.4672 minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 225/224 7.712 cents septimal kleisma 1: 2 81/80 21.506 cents syntonic comma, Didymus comma 1: 6 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 4 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 4 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 4 21/20 84.467 cents minor semitone 2: 2 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 2: 2 36/35 48.770 cents septimal diesis, 1/4-tone 2: 4 28/27 62.961 cents Archytas' 1/3-tone 2: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 6 21/20 84.467 cents minor semitone 2: 4 16/15 111.731 cents minor diatonic semitone 2: 6 15/14 119.443 cents major diatonic semitone 2: 1 441/400 168.934 cents two (minor semitone) 3: 2 21/20 84.467 cents minor semitone 3: 2 135/128 92.179 cents major chroma, major limma 3: 2 200/189 97.937 cents 3: 6 16/15 111.731 cents minor diatonic semitone 3: 2 15/14 119.443 cents major diatonic semitone 3: 2 160/147 146.707 cents 3: 2 49/45 147.428 cents BP minor semitone 3: 4 35/32 155.140 cents septimal neutral second 3: 2 54/49 168.213 cents Zalzal's mujannab 3: 2 28/25 196.198 cents middle second 3: 1 9/8 203.910 cents major whole tone 4: 4 15/14 119.443 cents major diatonic semitone 4: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 4: 2 49/45 147.428 cents BP minor semitone 4: 8 10/9 182.404 cents minor whole tone 4: 2 28/25 196.198 cents middle second 4: 6 9/8 203.910 cents major whole tone 4: 1 256/225 223.463 cents Neapolitan diminished third 4: 2 8/7 231.174 cents septimal whole tone 5: 2 160/147 146.707 cents 5: 2 35/32 155.140 cents septimal neutral second 5: 2 28/25 196.198 cents middle second 5: 4 9/8 203.910 cents major whole tone 5: 8 8/7 231.174 cents septimal whole tone 5: 2 147/128 239.607 cents 5: 1 512/441 258.438 cents 5: 6 7/6 266.871 cents septimal minor third 6: 2 10/9 182.404 cents minor whole tone 6: 2 9/8 203.910 cents major whole tone 6: 2 8/7 231.174 cents septimal whole tone 6: 1 225/196 238.886 cents two (major diatonic semitone) 6: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 6: 6 7/6 266.871 cents septimal minor third 6: 2 189/160 288.377 cents 6: 4 32/27 294.135 cents Pythagorean minor third 6: 2 25/21 301.847 cents BP second, quasi-equal minor third 6: 4 6/5 315.641 cents minor third 7: 2 8/7 231.174 cents septimal whole tone 7: 2 7/6 266.871 cents septimal minor third 7: 2 75/64 274.582 cents classic augmented second 7: 2 189/160 288.377 cents 7: 2 32/27 294.135 cents Pythagorean minor third 7: 2 25/21 301.847 cents BP second, quasi-equal minor third 7: 6 6/5 315.641 cents minor third 7: 1 98/81 329.832 cents 7: 2 128/105 342.905 cents septimal neutral third 7: 2 60/49 350.617 cents smaller approximation to neutral third 7: 2 49/40 351.338 cents larger approximation to neutral third 7: 2 5/4 386.314 cents major third 8: 2 25/21 301.847 cents BP second, quasi-equal minor third 8: 4 6/5 315.641 cents minor third 8: 4 135/112 323.353 cents septimal wide minor third 8: 2 128/105 342.905 cents septimal neutral third 8: 4 49/40 351.338 cents larger approximation to neutral third 8: 1 100/81 364.807 cents grave major third 8: 4 56/45 378.602 cents septimal narrow major third 8: 2 5/4 386.314 cents major third 8: 2 80/63 413.578 cents wide major third 8: 2 9/7 435.084 cents septimal major third, BP third 9: 4 60/49 350.617 cents smaller approximation to neutral third 9: 2 315/256 359.050 cents 9: 4 56/45 378.602 cents septimal narrow major third 9: 4 5/4 386.314 cents major third 9: 4 63/50 400.108 cents quasi-equal major third 9: 2 80/63 413.578 cents wide major third 9: 1 32/25 427.373 cents classic diminished fourth 9: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 9: 2 64/49 462.348 cents 2 septatones or septatonic major third 9: 2 21/16 470.781 cents narrow fourth 10: 6 5/4 386.314 cents major third 10: 1 81/64 407.820 cents Pythagorean major third 10: 2 80/63 413.578 cents wide major third 10: 2 32/25 427.373 cents classic diminished fourth 10: 4 9/7 435.084 cents septimal major third, BP third 10: 2 98/75 463.069 cents 10: 2 21/16 470.781 cents narrow fourth 10: 8 4/3 498.045 cents perfect fourth 11: 2 80/63 413.578 cents wide major third 11: 4 9/7 435.084 cents septimal major third, BP third 11: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 11: 4 21/16 470.781 cents narrow fourth 11: 4 4/3 498.045 cents perfect fourth 11: 4 27/20 519.551 cents acute fourth 11: 2 256/189 525.309 cents 11: 2 49/36 533.742 cents Arabic lute acute fourth 11: 2 48/35 546.815 cents septimal semi-augmented fourth 11: 1 25/18 568.717 cents classic augmented fourth 12: 1 64/49 462.348 cents 2 septatones or septatonic major third 12: 2 21/16 470.781 cents narrow fourth 12: 6 4/3 498.045 cents perfect fourth 12: 4 75/56 505.757 cents marvelous fourth 12: 4 48/35 546.815 cents septimal semi-augmented fourth 12: 2 441/320 555.248 cents 12: 2 112/81 561.006 cents 12: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 12: 2 10/7 617.488 cents Euler's tritone 13: 2 4/3 498.045 cents perfect fourth 13: 2 27/20 519.551 cents acute fourth 13: 2 200/147 533.021 cents 13: 2 135/98 554.527 cents 13: 2 25/18 568.717 cents classic augmented fourth 13: 8 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 13: 2 45/32 590.224 cents diatonic tritone 13: 4 64/45 609.776 cents 2nd tritone 13: 2 35/24 653.185 cents septimal semi-diminished fifth 13: 1 72/49 666.258 cents Arabic lute grave fifth 14: 1 49/36 533.742 cents Arabic lute acute fourth 14: 2 48/35 546.815 cents septimal semi-augmented fourth 14: 4 45/32 590.224 cents diatonic tritone 14: 2 64/45 609.776 cents 2nd tritone 14: 8 10/7 617.488 cents Euler's tritone 14: 2 36/25 631.283 cents classic diminished fifth 14: 2 196/135 645.473 cents 14: 2 147/100 666.979 cents 14: 2 40/27 680.449 cents grave fifth 14: 2 3/2 701.955 cents perfect fifth 15: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 15: 4 10/7 617.488 cents Euler's tritone 15: 2 81/56 638.994 cents 15: 2 640/441 644.752 cents 15: 4 35/24 653.185 cents septimal semi-diminished fifth 15: 4 112/75 694.243 cents marvelous fifth 15: 6 3/2 701.955 cents perfect fifth 15: 2 32/21 729.219 cents wide fifth 15: 1 49/32 737.652 cents 16: 1 36/25 631.283 cents classic diminished fifth 16: 2 35/24 653.185 cents septimal semi-diminished fifth 16: 2 72/49 666.258 cents Arabic lute grave fifth 16: 2 189/128 674.691 cents 16: 4 40/27 680.449 cents grave fifth 16: 4 3/2 701.955 cents perfect fifth 16: 4 32/21 729.219 cents wide fifth 16: 2 54/35 750.725 cents septimal semi-augmented fifth 16: 4 14/9 764.916 cents septimal minor sixth 16: 2 63/40 786.422 cents narrow minor sixth 17: 8 3/2 701.955 cents perfect fifth 17: 2 32/21 729.219 cents wide fifth 17: 2 75/49 736.931 cents BP fifth 17: 4 14/9 764.916 cents septimal minor sixth 17: 2 25/16 772.627 cents classic augmented fifth 17: 2 63/40 786.422 cents narrow minor sixth 17: 1 128/81 792.180 cents Pythagorean minor sixth 17: 6 8/5 813.686 cents minor sixth 18: 2 32/21 729.219 cents wide fifth 18: 2 49/32 737.652 cents 18: 2 54/35 750.725 cents septimal semi-augmented fifth 18: 1 25/16 772.627 cents classic augmented fifth 18: 2 63/40 786.422 cents narrow minor sixth 18: 4 100/63 799.892 cents quasi-equal minor sixth 18: 4 8/5 813.686 cents minor sixth 18: 4 45/28 821.398 cents septimale wide minor sixth 18: 2 512/315 840.950 cents 18: 4 49/30 849.383 cents larger approximation to neutral sixth 19: 2 14/9 764.916 cents septimal minor sixth 19: 2 63/40 786.422 cents narrow minor sixth 19: 2 8/5 813.686 cents minor sixth 19: 4 45/28 821.398 cents septimale wide minor sixth 19: 1 81/50 835.193 cents acute minor sixth 19: 4 80/49 848.662 cents smaller approximation to neutral sixth 19: 2 105/64 857.095 cents septimal neutral sixth 19: 4 224/135 876.647 cents narrow septimal major sixth 19: 4 5/3 884.359 cents major sixth, BP sixth 19: 2 42/25 898.153 cents quasi-equal major sixth 20: 2 8/5 813.686 cents minor sixth 20: 2 80/49 848.662 cents smaller approximation to neutral sixth 20: 2 49/30 849.383 cents larger approximation to neutral sixth 20: 2 105/64 857.095 cents septimal neutral sixth 20: 1 81/49 870.168 cents two (septimal major third, BP third) 20: 6 5/3 884.359 cents major sixth, BP sixth 20: 2 42/25 898.153 cents quasi-equal major sixth 20: 2 27/16 905.865 cents Pythagorean major sixth 20: 2 320/189 911.623 cents 20: 2 128/75 925.418 cents diminished seventh 20: 2 12/7 933.129 cents septimal major sixth 20: 2 7/4 968.826 cents harmonic seventh 21: 4 5/3 884.359 cents major sixth, BP sixth 21: 2 42/25 898.153 cents quasi-equal major sixth 21: 4 27/16 905.865 cents Pythagorean major sixth 21: 2 320/189 911.623 cents 21: 6 12/7 933.129 cents septimal major sixth 21: 2 140/81 947.320 cents 21: 1 392/225 961.114 cents 21: 2 7/4 968.826 cents harmonic seventh 21: 2 16/9 996.090 cents Pythagorean minor seventh 21: 2 9/5 1017.596 cents just minor seventh, BP seventh 22: 6 12/7 933.129 cents septimal major sixth 22: 1 441/256 941.562 cents two (narrow fourth) 22: 2 256/147 960.393 cents 22: 8 7/4 968.826 cents harmonic seventh 22: 4 16/9 996.090 cents Pythagorean minor seventh 22: 2 25/14 1003.802 cents middle minor seventh 22: 2 64/35 1044.860 cents septimal neutral seventh 22: 2 147/80 1053.293 cents 23: 2 7/4 968.826 cents harmonic seventh 23: 1 225/128 976.537 cents augmented sixth 23: 6 16/9 996.090 cents Pythagorean minor seventh 23: 2 25/14 1003.802 cents middle minor seventh 23: 8 9/5 1017.596 cents just minor seventh, BP seventh 23: 2 90/49 1052.572 cents 23: 2 50/27 1066.762 cents grave major seventh 23: 4 28/15 1080.557 cents grave major seventh 24: 1 16/9 996.090 cents Pythagorean minor seventh 24: 2 25/14 1003.802 cents middle minor seventh 24: 2 49/27 1031.787 cents 24: 4 64/35 1044.860 cents septimal neutral seventh 24: 2 90/49 1052.572 cents 24: 2 147/80 1053.293 cents 24: 2 28/15 1080.557 cents grave major seventh 24: 6 15/8 1088.269 cents classic major seventh 24: 2 189/100 1102.063 cents 24: 2 256/135 1107.821 cents octave - major chroma 24: 2 40/21 1115.533 cents acute major seventh 25: 1 800/441 1031.066 cents 25: 6 28/15 1080.557 cents grave major seventh 25: 4 15/8 1088.269 cents classic major seventh 25: 6 40/21 1115.533 cents acute major seventh 25: 2 48/25 1129.328 cents classic diminished octave 25: 4 27/14 1137.039 cents septimal major seventh 25: 2 35/18 1151.230 cents septimal semi-diminished octave 25: 2 49/25 1165.024 cents BP eighth 26: 4 40/21 1115.533 cents acute major seventh 26: 2 48/25 1129.328 cents classic diminished octave 26: 2 27/14 1137.039 cents septimal major seventh 26: 4 35/18 1151.230 cents septimal semi-diminished octave 26: 4 96/49 1164.303 cents 26: 1 49/25 1165.024 cents BP eighth 26: 6 63/32 1172.736 cents octave - septimal comma 26: 2 160/81 1178.494 cents octave - syntonic comma 26: 2 448/225 1192.288 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 9.46154 = 123/13
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 0.0 : 84.5 111.7 119.4 182.4 203.9 231.2 266.9 315.6 386.3 435.1 470.8 498.0 582.5 617.5 702.0 729.2 764.9 813.7 884.4 933.1 968.8 996.1 1017.6 1080.6 1088.3 1115.5 1200.0 84.5 : 27.3 35.0 97.9 119.4 146.7 182.4 231.2 301.8 350.6 386.3 413.6 498.0 533.0 617.5 644.8 680.4 729.2 799.9 848.7 884.4 911.6 933.1 996.1 1003.8 1031.1 1115.5 1200.0 111.7 : 7.7 70.7 92.2 119.4 155.1 203.9 274.6 323.4 359.0 386.3 470.8 505.8 590.2 617.5 653.2 702.0 772.6 821.4 857.1 884.4 905.9 968.8 976.5 1003.8 1088.3 1172.7 1200.0 119.4 : 63.0 84.5 111.7 147.4 196.2 266.9 315.6 351.3 378.6 463.1 498.0 582.5 609.8 645.5 694.2 764.9 813.7 849.4 876.6 898.2 961.1 968.8 996.1 1080.6 1165.0 1192.3 1200.0 182.4 : 21.5 48.8 84.5 133.2 203.9 252.7 288.4 315.6 400.1 435.1 519.6 546.8 582.5 631.3 702.0 750.7 786.4 813.7 835.2 898.2 905.9 933.1 1017.6 1102.1 1129.3 1137.0 1200.0 203.9 : 27.3 63.0 111.7 182.4 231.2 266.9 294.1 378.6 413.6 498.0 525.3 561.0 609.8 680.4 729.2 764.9 792.2 813.7 876.6 884.4 911.6 996.1 1080.6 1107.8 1115.5 1178.5 1200.0 231.2 : 35.7 84.5 155.1 203.9 239.6 266.9 351.3 386.3 470.8 498.0 533.7 582.5 653.2 702.0 737.7 764.9 786.4 849.4 857.1 884.4 968.8 1053.3 1080.6 1088.3 1151.2 1172.7 1200.0 266.9 : 48.8 119.4 168.2 203.9 231.2 315.6 350.6 435.1 462.3 498.0 546.8 617.5 666.3 702.0 729.2 750.7 813.7 821.4 848.7 933.1 1017.6 1044.9 1052.6 1115.5 1137.0 1164.3 1200.0 315.6 : 70.7 119.4 155.1 182.4 266.9 301.8 386.3 413.6 449.3 498.0 568.7 617.5 653.2 680.4 702.0 764.9 772.6 799.9 884.4 968.8 996.1 1003.8 1066.8 1088.3 1115.5 1151.2 1200.0 386.3 : 48.8 84.5 111.7 196.2 231.2 315.6 342.9 378.6 427.4 498.0 546.8 582.5 609.8 631.3 694.2 702.0 729.2 813.7 898.2 925.4 933.1 996.1 1017.6 1044.9 1080.6 1129.3 1200.0 435.1 : 35.7 63.0 147.4 182.4 266.9 294.1 329.8 378.6 449.3 498.0 533.7 561.0 582.5 645.5 653.2 680.4 764.9 849.4 876.6 884.4 947.3 968.8 996.1 1031.8 1080.6 1151.2 1200.0 470.8 : 27.3 111.7 146.7 231.2 258.4 294.1 342.9 413.6 462.3 498.0 525.3 546.8 609.8 617.5 644.8 729.2 813.7 841.0 848.7 911.6 933.1 960.4 996.1 1044.9 1115.5 1164.3 1200.0 498.0 : 84.5 119.4 203.9 231.2 266.9 315.6 386.3 435.1 470.8 498.0 519.6 582.5 590.2 617.5 702.0 786.4 813.7 821.4 884.4 905.9 933.1 968.8 1017.6 1088.3 1137.0 1172.7 1200.0 582.5 : 35.0 119.4 146.7 182.4 231.2 301.8 350.6 386.3 413.6 435.1 498.0 505.8 533.0 617.5 702.0 729.2 736.9 799.9 821.4 848.7 884.4 933.1 1003.8 1052.6 1088.3 1115.5 1200.0 617.5 : 84.5 111.7 147.4 196.2 266.9 315.6 351.3 378.6 400.1 463.1 470.8 498.0 582.5 667.0 694.2 702.0 764.9 786.4 813.7 849.4 898.2 968.8 1017.6 1053.3 1080.6 1165.0 1200.0 702.0 : 27.3 63.0 111.7 182.4 231.2 266.9 294.1 315.6 378.6 386.3 413.6 498.0 582.5 609.8 617.5 680.4 702.0 729.2 764.9 813.7 884.4 933.1 968.8 996.1 1080.6 1115.5 1200.0 729.2 : 35.7 84.5 155.1 203.9 239.6 266.9 288.4 351.3 359.0 386.3 470.8 555.2 582.5 590.2 653.2 674.7 702.0 737.7 786.4 857.1 905.9 941.6 968.8 1053.3 1088.3 1172.7 1200.0 764.9 : 48.8 119.4 168.2 203.9 231.2 252.7 315.6 323.4 350.6 435.1 519.6 546.8 554.5 617.5 639.0 666.3 702.0 750.7 821.4 870.2 905.9 933.1 1017.6 1052.6 1137.0 1164.3 1200.0 813.7 : 70.7 119.4 155.1 182.4 203.9 266.9 274.6 301.8 386.3 470.8 498.0 505.8 568.7 590.2 617.5 653.2 702.0 772.6 821.4 857.1 884.4 968.8 1003.8 1088.3 1115.5 1151.2 1200.0 884.4 : 48.8 84.5 111.7 133.2 196.2 203.9 231.2 315.6 400.1 427.4 435.1 498.0 519.6 546.8 582.5 631.3 702.0 750.7 786.4 813.7 898.2 933.1 1017.6 1044.9 1080.6 1129.3 1200.0 933.1 : 35.7 63.0 84.5 147.4 155.1 182.4 266.9 351.3 378.6 386.3 449.3 470.8 498.0 533.7 582.5 653.2 702.0 737.7 764.9 849.4 884.4 968.8 996.1 1031.8 1080.6 1151.2 1200.0 968.8 : 27.3 48.8 111.7 119.4 146.7 231.2 315.6 342.9 350.6 413.6 435.1 462.3 498.0 546.8 617.5 666.3 702.0 729.2 813.7 848.7 933.1 960.4 996.1 1044.9 1115.5 1164.3 1200.0 996.1 : 21.5 84.5 92.2 119.4 203.9 288.4 315.6 323.4 386.3 407.8 435.1 470.8 519.6 590.2 639.0 674.7 702.0 786.4 821.4 905.9 933.1 968.8 1017.6 1088.3 1137.0 1172.7 1200.0 1017.6: 63.0 70.7 97.9 182.4 266.9 294.1 301.8 364.8 386.3 413.6 449.3 498.0 568.7 617.5 653.2 680.4 764.9 799.9 884.4 911.6 947.3 996.1 1066.8 1115.5 1151.2 1178.5 1200.0 1080.6: 7.7 35.0 119.4 203.9 231.2 238.9 301.8 323.4 350.6 386.3 435.1 505.8 554.5 590.2 617.5 702.0 736.9 821.4 848.7 884.4 933.1 1003.8 1052.6 1088.3 1115.5 1137.0 1200.0 1088.3: 27.3 111.7 196.2 223.5 231.2 294.1 315.6 342.9 378.6 427.4 498.0 546.8 582.5 609.8 694.2 729.2 813.7 841.0 876.6 925.4 996.1 1044.9 1080.6 1107.8 1129.3 1192.3 1200.0 1115.5: 84.5 168.9 196.2 203.9 266.9 288.4 315.6 351.3 400.1 470.8 519.6 555.2 582.5 667.0 702.0 786.4 813.7 849.4 898.2 968.8 1017.6 1053.3 1080.6 1102.1 1165.0 1172.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 7.7115 .. 84.4672 cents 392/375, 76.7557 cents 225/224, 7.7115 cents 2: 34.9756 .. 168.9344 cents 21609/20000, 133.9588 cents 1000/1029,-49.4916 cents 3: 84.4672 .. 203.9100 cents 15/14, 119.4428 cents 20/21,-84.4672 cents 4: 119.4428 .. 231.1741 cents 16/15, 111.7313 cents 20/21,-84.4672 cents 5: 146.7069 .. 266.8709 cents 343/320, 120.1640 cents 20/21,-84.4672 cents 6: 182.4037 .. 315.6413 cents 27/25, 133.2376 cents 20/21,-84.4672 cents 7: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 20/21,-84.4672 cents 8: 301.8465 .. 435.0841 cents 27/25, 133.2376 cents 20/21,-84.4672 cents 9: 350.6169 .. 470.7809 cents 343/320, 120.1640 cents 20/21,-84.4672 cents 10: 386.3137 .. 498.0450 cents 16/15, 111.7313 cents 20/21,-84.4672 cents 11: 413.5778 .. 568.7174 cents 35/32, 155.1396 cents 20/21,-84.4672 cents 12: 462.3482 .. 617.4878 cents 35/32, 155.1396 cents 1152/1225,-106.3692 cents 13: 498.0450 .. 666.2582 cents 54/49, 168.2132 cents 14/15,-119.4428 cents 14: 533.7418 .. 701.9550 cents 54/49, 168.2132 cents 2401/2592,-132.5164 cents 15: 582.5122 .. 737.6518 cents 35/32, 155.1396 cents 14/15,-119.4428 cents 16: 631.2826 .. 786.4222 cents 35/32, 155.1396 cents 1152/1225,-106.3692 cents 17: 701.9550 .. 813.6863 cents 16/15, 111.7313 cents 20/21,-84.4672 cents 18: 729.2191 .. 849.3831 cents 343/320, 120.1640 cents 20/21,-84.4672 cents 19: 764.9159 .. 898.1535 cents 27/25, 133.2376 cents 20/21,-84.4672 cents 20: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 20/21,-84.4672 cents 21: 884.3587 .. 1017.5963 cents 27/25, 133.2376 cents 20/21,-84.4672 cents 22: 933.1291 .. 1053.2931 cents 343/320, 120.1640 cents 20/21,-84.4672 cents 23: 968.8259 .. 1080.5572 cents 16/15, 111.7313 cents 20/21,-84.4672 cents 24: 996.0900 .. 1115.5328 cents 15/14, 119.4428 cents 20/21,-84.4672 cents 25: 1031.0656 .. 1165.0244 cents 21609/20000, 133.9588 cents 20/21,-84.4672 cents 26: 1115.5328 .. 1192.2885 cents 392/375, 76.7557 cents 1000/1029,-49.4916 cents
SHOW DATA
Number of notes : 27 -- Interval properties -- Smallest interval : 225/224, 7.7115 cents, class 1 Average step (divided formal octave): 44.4444 cents Largest one step interval : 21/20, 84.4672 cents Average / Smallest step : 5.763381 Largest / Average step : 1.900512 Largest / Smallest step : 10.953374 Median interval of one step : 49/48, 35.6968 cents, amount: 4 Most common interval of one step : 64/63, 27.2641 cents, amount: 6 Least squares average step : 44.57664 cents, oct.: 1203.56926 cents Scale is not proper Step pattern alph. order: ABCDEBFGHGFBAIABFGHGFBEDCBA Step pattern size order : ICAGBCEFHFECIDICEFHFECBGACI Scale is not a Constant Structure Scale diversity : 1.399738 Lumma stability : 0.012853 Lumma impropriety factor : 0.941707 Number of different interval sizes : 130 = 5.00000 / class Number of one step interval sizes : 9 Highest interval variety : 12 Mean interval variety : 9.46154 = 123/13 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 20 Most common triad is 0.0 498.045 701.955 cents, amount: 13 Number of recognisable fifths : 24, average 700.6697 cents Scale is a complete diamond : 1 3 5 7 9 15 21 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 27 = 100.0000% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 13-14 -- Rational properties -- Prime limit : 7 Odd number limit : 441 (O: 441 U: 441) Highest odd numerator or denominator: 21 Scale harmonicity : 0.018854 Average absolute harmonicity : 0.122611 Specific harmonicity : 0.107816 Fundamental : 1/5040, -12.2992 octaves, 0.0519 Hz. Guide tone : 10080, 13.2992 octaves, 2637185.698 Hz. Exponens Consonantiae : 5.080320E+07, 25.59842 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 287.5, average 10.64815 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 24.53941, average 0.90887 Sum of Tenney's harmonic distance : 49.67567, average 1.83984 Vogel's harmonic complexity : 22.51852 Wille's k value : 3307 Wilson's harmonic complexity : 36 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 1355.32843, average 3.58552 Lattice compactness (without 2's) : 779.27997, average 2.06159 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.51852 52 1 3: -2 .. 2 0.00000 26 4 5: -1 .. 1 0.00000 14 8 7: -1 .. 1 0.00000 14 14 Average exponent except 2's : 0 / 27 = 0.00000 Average absolute exponent except 2's: 54 / 27 = 2.00000
FIT/MODE
27: 2 0 1 1 1 0 1 1 2 1 1 0 2 1 2 0 1 1 2 1 1 0 1 1 0 1 2 N SD: 11.7795 c. M: 22.8424 c. 28: 2 1 0 1 1 0 1 1 2 1 1 1 2 0 2 1 1 1 2 1 1 0 1 1 0 1 2 N I SD: 11.6551 c. M:-17.4878 c. 30: 2 1 0 2 0 1 1 1 2 1 1 0 3 0 3 0 1 1 2 1 1 1 0 2 0 1 2 N I SD: 10.9231 c. M:-18.0450 c. 31: 2 1 0 2 0 1 1 1 2 1 1 1 2 1 2 1 1 1 2 1 1 1 0 2 0 1 2 N I SD: 6.2144 c. M: 11.1447 c. 41: 3 1 0 2 1 1 1 2 2 2 1 1 3 1 3 1 1 2 2 2 1 1 1 2 0 1 3 N I SD: 4.0094 c. M: 6.7940 c. 53: 4 1 0 3 1 1 2 2 3 2 2 1 4 1 4 1 2 2 3 2 2 1 1 3 0 1 4 N I SD: 3.9779 c. M:-6.2353 c. 72: 5 2 0 4 1 2 2 3 4 3 2 2 5 2 5 2 2 3 4 3 2 2 1 4 0 2 5 N I SD: 2.5623 c. M: 4.9354 c. 94: 7 2 0 5 2 2 3 4 5 4 3 2 7 2 7 2 3 4 5 4 3 2 2 5 0 2 7 N I SD: 2.9936 c. M:-4.8945 c. 99: 7 2 1 5 2 2 3 4 6 4 3 2 7 3 7 2 3 4 6 4 3 2 2 5 1 2 7 N I SD: 1.3816 c. M:-2.6404 c. 130: 9 3 1 7 2 3 4 5 8 5 4 3 9 4 9 3 4 5 8 5 4 3 2 7 1 3 9 N I SD: 1.1343 c. M: 2.2117 c. 171: 12 4 1 9 3 4 5 7 10 7 5 4 12 5 12 4 5 7 10 7 5 4 3 9 1 4 12 N I SD: 0.3117 c. M: 0.6055 c. 441: 31 10 3 23 8 10 13 18 26 18 13 10 31 13 31 10 13 18 26 18 13 10 8 23 3 10 31 N I SD: 0.1620 c. M: 0.2901 c. 612: 43 14 4 32 11 14 18 25 36 25 18 14 43 18 43 14 18 25 36 25 18 14 11 32 4 14 43 N I SD: 0.1350 c. M: 0.2100 c. 935: 66 21 6 49 17 21 28 38 55 38 28 21 66 27 66 21 28 38 55 38 28 21 17 49 6 21 66 N I SD: 0.1343 c. M:-0.2387 c. 1065: 75 24 7 56 19 24 32 43 63 43 32 24 75 31 75 24 32 43 63 43 32 24 19 56 7 24 75 N I SD: 0.1316 c. M:-0.2050 c. 1106: 78 25 7 58 20 25 33 45 65 45 33 25 78 32 78 25 33 45 65 45 33 25 20 58 7 25 78 N I SD: 0.0871 c. M:-0.1621 c. 1236: 87 28 8 65 22 28 37 50 73 50 37 28 87 36 87 28 37 50 73 50 37 28 22 65 8 28 87 N I SD: 0.0838 c. M: 0.1326 c. 1277: 90 29 8 67 23 29 38 52 75 52 38 29 90 37 90 29 38 52 75 52 38 29 23 67 8 29 90 N I SD: 0.0721 c. M:-0.1060 c. 1407: 99 32 9 74 25 32 42 57 83 57 42 32 99 41 99 32 42 57 83 57 42 32 25 74 9 32 99 N I SD: 0.0615 c. M: 0.1161 c. 1677: 118 38 11 88 30 38 50 68 99 68 50 38 118 49 118 38 50 68 99 68 50 38 30 88 11 38 118 N I SD: 0.0567 c. M:-0.1034 c. 1718: 121 39 11 90 31 39 51 70 101 70 51 39 121 50 121 39 51 70 101 70 51 39 31 90 11 39 121 N I SD: 0.0494 c. M: 0.0987 c. 1848: 130 42 12 97 33 42 55 75 109 75 55 42 130 54 130 42 55 75 109 75 55 42 33 97 12 42 130 N I SD: 0.0370 c. M: 0.0638 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: 5.1990 cents 7 .. 14 match: 7 H SD: 2.8116 cents 8 .. 16 match: 8 H SD: 5.1441 cents 9 .. 18 match: 9 H SD: 4.3579 cents 10 .. 20 match: 10 H SD: 2.8388 cents 11 .. 22 match: 11 H SD: 6.9787 cents 12 .. 24 match: 12 H SD: 3.7211 cents 13 .. 26 match: 13 H SD: 5.3281 cents 14 .. 28 match: 14 H SD: 3.8389 cents 15 .. 30 match: 14 SD: 2.9832 cents 16 .. 32 match: 15 S SD: 3.5590 cents 17 .. 34 match: 15 S SD: 3.8194 cents 18 .. 36 match: 16 S SD: 2.8875 cents 19 .. 38 match: 15 SD: 3.4500 cents 20 .. 40 match: 19 S SD: 2.6998 cents 21 .. 42 match: 19 S SD: 2.7305 cents 22 .. 44 match: 17 SD: 3.2790 cents 23 .. 46 match: 20 SD: 2.9168 cents 24 .. 48 match: 19 SD: 2.2083 cents 25 .. 50 match: 20 SD: 2.0848 cents 26 .. 52 match: 20 SD: 2.9960 cents 27 .. 54 match: 21 SD: 2.4634 cents 28 .. 56 match: 22 SD: 2.2741 cents 29 .. 58 match: 21 SD: 2.4365 cents 30 .. 60 match: 21 SD: 2.0834 cents 31 .. 62 match: 21 SD: 2.1494 cents 32 .. 64 match: 22 SD: 1.7490 cents 33 .. 66 match: 21 SD: 2.3244 cents 34 .. 68 match: 22 SD: 2.3030 cents 35 .. 70 match: 24 SD: 1.7424 cents 36 .. 72 match: 25 SD: 1.6551 cents 37 .. 74 match: 22 SD: 2.1173 cents 38 .. 76 match: 23 SD: 1.8873 cents 39 .. 78 match: 24 SD: 1.8288 cents 40 .. 80 match: 24 SD: 1.4481 cents 41 .. 82 match: 23 SD: 1.5563 cents 42 .. 84 match: 25 SD: 1.3288 cents 43 .. 86 match: 25 SD: 1.6718 cents 44 .. 88 match: 25 SD: 1.4810 cents 45 .. 90 match: 24 SD: 1.3246 cents 46 .. 92 match: 25 SD: 1.6350 cents 47 .. 94 match: 25 SD: 1.5932 cents 48 .. 96 match: 25 SD: 1.2830 cents 50 .. 100 match: 25 SD: 1.4532 cents 51 .. 102 match: 25 SD: 1.5483 cents 52 .. 104 match: 25 SD: 1.3568 cents 53 .. 106 match: 25 SD: 1.4274 cents 54 .. 108 match: 25 SD: 1.2029 cents 55 .. 110 match: 25 SD: 1.0625 cents 56 .. 112 match: 25 SD: 1.0603 cents 57 .. 114 match: 26 SD: 1.2097 cents 58 .. 116 match: 26 SD: 1.3083 cents 59 .. 118 match: 25 SD: 1.1863 cents 60 .. 120 match: 26 SD: 0.9768 cents 61 .. 122 match: 25 SD: 1.1166 cents 62 .. 124 match: 25 SD: 1.2163 cents 63 .. 126 match: 26 SD: 0.9996 cents 68 .. 136 match: 26 SD: 1.1599 cents 69 .. 138 match: 25 SD: 1.1756 cents 70 .. 140 match: 25 SD: 0.9446 cents 71 .. 142 match: 25 SD: 0.9872 cents 72 .. 144 match: 26 SD: 0.8457 cents 73 .. 146 match: 26 SD: 0.9153 cents 74 .. 148 match: 26 SD: 0.9468 cents 75 .. 150 match: 26 SD: 0.9445 cents 76 .. 152 match: 26 SD: 0.9254 cents 77 .. 154 match: 26 SD: 0.9227 cents 78 .. 156 match: 26 SD: 0.9361 cents 79 .. 158 match: 27 SD: 0.9143 cents 80 .. 160 match: 27 SD: 0.6883 cents 83 .. 166 match: 26 SD: 0.8261 cents 84 .. 168 match: 26 SD: 0.6665 cents 85 .. 170 match: 25 SD: 0.8454 cents 86 .. 172 match: 25 SD: 0.8915 cents 87 .. 174 match: 26 SD: 0.8568 cents 88 .. 176 match: 26 SD: 0.7780 cents 89 .. 178 match: 26 SD: 0.8152 cents 90 .. 180 match: 26 SD: 0.6553 cents 93 .. 186 match: 26 SD: 0.8526 cents 94 .. 188 match: 27 SD: 0.8203 cents 95 .. 190 match: 27 SD: 0.6754 cents 96 .. 192 match: 27 SD: 0.6154 cents 98 .. 196 match: 26 SD: 0.6679 cents 99 .. 198 match: 26 SD: 0.6564 cents 100 .. 200 match: 26 SD: 0.6711 cents 101 .. 202 match: 25 SD: 0.7302 cents 102 .. 204 match: 26 SD: 0.6773 cents 103 .. 206 match: 26 SD: 0.6549 cents 104 .. 208 match: 26 SD: 0.6482 cents 105 .. 210 match: 27 SD: 0.5583 cents 113 .. 226 match: 26 SD: 0.6120 cents 114 .. 228 match: 26 SD: 0.6242 cents 115 .. 230 match: 26 SD: 0.5522 cents 116 .. 232 match: 26 SD: 0.6197 cents 117 .. 234 match: 26 SD: 0.6237 cents 118 .. 236 match: 26 SD: 0.5819 cents 119 .. 238 match: 27 SD: 0.5195 cents 120 .. 240 match: 27 SD: 0.4527 cents 128 .. 256 match: 26 SD: 0.4962 cents 129 .. 258 match: 26 SD: 0.5933 cents 130 .. 260 match: 26 SD: 0.5909 cents 131 .. 262 match: 26 SD: 0.6214 cents 132 .. 264 match: 26 SD: 0.5385 cents 134 .. 268 match: 27 SD: 0.5366 cents 135 .. 270 match: 27 SD: 0.4368 cents 140 .. 280 match: 27 SD: 0.4298 cents 143 .. 286 match: 26 SD: 0.4603 cents 144 .. 288 match: 26 SD: 0.3595 cents 145 .. 290 match: 26 SD: 0.4400 cents 146 .. 292 match: 26 SD: 0.5310 cents 147 .. 294 match: 27 SD: 0.4945 cents 150 .. 300 match: 27 SD: 0.4457 cents 151 .. 302 match: 27 SD: 0.4451 cents 153 .. 306 match: 27 SD: 0.4246 cents 158 .. 316 match: 26 SD: 0.4732 cents 159 .. 318 match: 26 SD: 0.4578 cents 160 .. 320 match: 26 SD: 0.3316 cents 168 .. 336 match: 27 SD: 0.3280 cents 173 .. 346 match: 26 SD: 0.4465 cents 174 .. 348 match: 26 SD: 0.4228 cents 175 .. 350 match: 27 SD: 0.3726 cents 179 .. 358 match: 27 SD: 0.3609 cents 180 .. 360 match: 27 SD: 0.2780 cents 188 .. 376 match: 26 SD: 0.4164 cents 189 .. 378 match: 27 SD: 0.3786 cents 192 .. 384 match: 27 SD: 0.3283 cents 195 .. 390 match: 27 SD: 0.3259 cents 196 .. 392 match: 27 SD: 0.3111 cents 198 .. 396 match: 27 SD: 0.3087 cents 200 .. 400 match: 27 SD: 0.2977 cents 210 .. 420 match: 27 SD: 0.2709 cents 224 .. 448 match: 27 SD: 0.2217 cents 240 .. 480 match: 27 SD: 0.1842 cents 280 .. 560 match: 27 SD: 0.1838 cents 336 .. 672 match: 27 SD: 0.1407 cents 360 .. 720 match: 27 SD: 0.1281 cents 420 .. 840 match: 27 SD: 0.1053 cents 480 .. 960 match: 27 SD: 0.0985 cents 504 .. 1008 match: 27 SD: 0.0915 cents 560 .. 1120 match: 27 SD: 0.0810 cents