Scala analysis: breetet3
tripled Breed tetrad
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: 15/14 119.442808 major diatonic semitone 4: 35/32 155.139620 septimal neutral second 5: 9/8 203.910002 major whole tone 6: 7/6 266.870906 septimal minor third 7: 49/40 351.338099 larger approximation to neutral third 8: 5/4 386.313714 major third 9: 245/192 422.010526 10: 125/96 456.986141 classic augmented third 11: 21/16 470.780907 narrow fourth 12: 4/3 498.044999 perfect fourth 13: 10/7 617.487807 Euler's tritone 14: 35/24 653.184619 septimal semi-diminished fifth 15: 3/2 701.955001 perfect fifth 16: 49/32 737.651813 17: 25/16 772.627428 classic augmented fifth 18: 49/30 849.383098 larger approximation to neutral sixth 19: 5/3 884.358713 major sixth, BP sixth 20: 7/4 968.825906 harmonic seventh 21: 25/14 1003.801521 middle minor seventh 22: 175/96 1039.498333 23: 90/49 1052.571903 24: 15/8 1088.268715 classic major seventh 25: 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: 36/35 48.7704 septimal diesis, 1/4-tone 4: 49/48 35.6968 slendro diesis, septimal 1/6-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 21/20 84.4672 minor semitone 8: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 11: 126/125 13.7948 septimal semicomma, Starling comma 12: 64/63 27.2641 septimal comma, Archytas' comma 13: 15/14 119.4428 major diatonic semitone 14: 49/48 35.6968 slendro diesis, septimal 1/6-tone 15: 36/35 48.7704 septimal diesis, 1/4-tone 16: 49/48 35.6968 slendro diesis, septimal 1/6-tone 17: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 18: 392/375 76.7557 19: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 20: 21/20 84.4672 minor semitone 21: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 22: 49/48 35.6968 slendro diesis, septimal 1/6-tone 23: 1728/1715 13.0736 Orwell comma 24: 49/48 35.6968 slendro diesis, septimal 1/6-tone 25: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1728/1715 13.074 cents Orwell comma 1: 1 126/125 13.795 cents septimal semicomma, Starling comma 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 6 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 7 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 3 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 392/375 76.756 cents 1: 2 21/20 84.467 cents minor semitone 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 2: 1 128/125 41.059 cents minor diesis, diesis 2: 3 36/35 48.770 cents septimal diesis, 1/4-tone 2: 5 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 360/343 83.746 cents 2: 4 21/20 84.467 cents minor semitone 2: 3 16/15 111.731 cents minor diatonic semitone 2: 3 15/14 119.443 cents major diatonic semitone 2: 1 160/147 146.707 cents 2: 3 49/45 147.428 cents BP minor semitone 2: 1 35/32 155.140 cents septimal neutral second 3: 1 256/245 76.034 cents septimal minor semitone 3: 1 360/343 83.746 cents 3: 2 21/20 84.467 cents minor semitone 3: 1 625/588 105.648 cents 3: 3 15/14 119.443 cents major diatonic semitone 3: 1 343/320 120.164 cents 3: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 3: 1 160/147 146.707 cents 3: 2 49/45 147.428 cents BP minor semitone 3: 1 375/343 154.418 cents BP major semitone, minor BP chroma 3: 2 35/32 155.140 cents septimal neutral second 3: 2 192/175 160.502 cents septimal 4/5-tone 3: 3 10/9 182.404 cents minor whole tone 3: 1 2401/2160 183.125 cents 3: 2 28/25 196.198 cents middle second 3: 1 9/8 203.910 cents major whole tone 4: 1 16/15 111.731 cents minor diatonic semitone 4: 2 15/14 119.443 cents major diatonic semitone 4: 2 35/32 155.140 cents septimal neutral second 4: 2 54/49 168.213 cents Zalzal's mujannab 4: 1 10/9 182.404 cents minor whole tone 4: 2 125/112 190.115 cents classic augmented semitone 4: 1 384/343 195.477 cents 4: 5 28/25 196.198 cents middle second 4: 2 245/216 218.101 cents 4: 5 8/7 231.174 cents septimal whole tone 4: 1 343/300 231.895 cents 4: 1 147/128 239.607 cents 5: 1 160/147 146.707 cents 5: 1 2700/2401 203.189 cents 5: 3 9/8 203.910 cents major whole tone 5: 6 8/7 231.174 cents septimal whole tone 5: 2 343/300 231.895 cents 5: 1 144/125 244.969 cents classic diminished third 5: 1 125/108 253.076 cents semi-augmented whole tone 5: 1 400/343 266.150 cents 5: 7 7/6 266.871 cents septimal minor third 5: 1 75/64 274.582 cents classic augmented second 5: 1 147/125 280.666 cents 6: 1 8/7 231.174 cents septimal whole tone 6: 1 225/196 238.886 cents two (major diatonic semitone) 6: 1 400/343 266.150 cents 6: 6 7/6 266.871 cents septimal minor third 6: 3 288/245 279.944 cents 6: 1 147/125 280.666 cents 6: 4 25/21 301.847 cents BP second, quasi-equal minor third 6: 2 343/288 302.568 cents 6: 5 6/5 315.641 cents minor third 6: 1 49/40 351.338 cents larger approximation to neutral third 7: 1 32/27 294.135 cents Pythagorean minor third 7: 2 25/21 301.847 cents BP second, quasi-equal minor third 7: 1 2880/2401 314.920 cents 7: 7 6/5 315.641 cents minor third 7: 2 175/144 337.543 cents 7: 4 60/49 350.617 cents smaller approximation to neutral third 7: 5 49/40 351.338 cents larger approximation to neutral third 7: 2 56/45 378.602 cents septimal narrow major third 7: 1 5/4 386.314 cents major third 8: 1 128/105 342.905 cents septimal neutral third 8: 5 60/49 350.617 cents smaller approximation to neutral third 8: 3 49/40 351.338 cents larger approximation to neutral third 8: 1 216/175 364.412 cents 8: 8 5/4 386.314 cents major third 8: 1 784/625 392.397 cents two (middle second) 8: 2 80/63 413.578 cents wide major third 8: 1 343/270 414.299 cents 8: 1 32/25 427.373 cents classic diminished fourth 8: 1 98/75 463.069 cents 8: 1 21/16 470.781 cents narrow fourth 9: 1 56/45 378.602 cents septimal narrow major third 9: 4 5/4 386.314 cents major third 9: 1 432/343 399.387 cents 9: 2 63/50 400.108 cents quasi-equal major third 9: 2 125/98 421.289 cents 9: 2 245/192 422.011 cents 9: 3 32/25 427.373 cents classic diminished fourth 9: 2 9/7 435.084 cents septimal major third, BP third 9: 1 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: 1 98/75 463.069 cents 9: 2 4/3 498.045 cents perfect fourth 9: 1 2401/1800 498.766 cents 9: 1 75/56 505.757 cents marvelous fourth 10: 1 125/98 421.289 cents 10: 1 32/25 427.373 cents classic diminished fourth 10: 4 9/7 435.084 cents septimal major third, BP third 10: 1 125/96 456.986 cents classic augmented third 10: 1 64/49 462.348 cents 2 septatones or septatonic major third 10: 2 98/75 463.069 cents 10: 1 450/343 470.060 cents 10: 2 21/16 470.781 cents narrow fourth 10: 6 4/3 498.045 cents perfect fourth 10: 2 168/125 511.840 cents 10: 1 200/147 533.021 cents 10: 2 49/36 533.742 cents Arabic lute acute fourth 10: 1 175/128 541.453 cents 11: 1 64/49 462.348 cents 2 septatones or septatonic major third 11: 2 21/16 470.781 cents narrow fourth 11: 3 4/3 498.045 cents perfect fourth 11: 2 75/56 505.757 cents marvelous fourth 11: 1 27/20 519.551 cents acute fourth 11: 1 200/147 533.021 cents 11: 3 49/36 533.742 cents Arabic lute acute fourth 11: 7 48/35 546.815 cents septimal semi-augmented fourth 11: 1 343/250 547.537 cents 11: 1 135/98 554.527 cents 11: 2 25/18 568.717 cents classic augmented fourth 11: 1 2401/1728 569.439 cents 12: 1 4/3 498.045 cents perfect fourth 12: 1 200/147 533.021 cents 12: 1 135/98 554.527 cents 12: 2 25/18 568.717 cents classic augmented fourth 12: 4 480/343 581.791 cents 12: 14 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 12: 1 45/32 590.224 cents diatonic tritone 12: 1 1225/864 604.414 cents 13: 1 1728/1225 595.586 cents 13: 1 64/45 609.776 cents 2nd tritone 13: 14 10/7 617.488 cents Euler's tritone 13: 4 343/240 618.209 cents 13: 2 36/25 631.283 cents classic diminished fifth 13: 1 196/135 645.473 cents 13: 1 147/100 666.979 cents 13: 1 3/2 701.955 cents perfect fifth 14: 1 3456/2401 630.561 cents 14: 2 36/25 631.283 cents classic diminished fifth 14: 1 196/135 645.473 cents 14: 1 500/343 652.463 cents 14: 7 35/24 653.185 cents septimal semi-diminished fifth 14: 3 72/49 666.258 cents Arabic lute grave fifth 14: 1 147/100 666.979 cents 14: 1 40/27 680.449 cents grave fifth 14: 2 112/75 694.243 cents marvelous fifth 14: 3 3/2 701.955 cents perfect fifth 14: 2 32/21 729.219 cents wide fifth 14: 1 49/32 737.652 cents 15: 1 256/175 658.547 cents 15: 2 72/49 666.258 cents Arabic lute grave fifth 15: 1 147/100 666.979 cents 15: 2 125/84 688.160 cents 15: 6 3/2 701.955 cents perfect fifth 15: 2 32/21 729.219 cents wide fifth 15: 1 343/225 729.940 cents 15: 2 75/49 736.931 cents BP fifth 15: 1 49/32 737.652 cents 15: 1 192/125 743.014 cents classic diminished sixth 15: 4 14/9 764.916 cents septimal minor sixth 15: 1 25/16 772.627 cents classic augmented fifth 15: 1 196/125 778.711 cents 16: 1 112/75 694.243 cents marvelous fifth 16: 1 3600/2401 701.234 cents two (smaller approximation to neutral third) 16: 2 3/2 701.955 cents perfect fifth 16: 1 75/49 736.931 cents BP fifth 16: 2 49/32 737.652 cents 16: 1 54/35 750.725 cents septimal semi-augmented fifth 16: 2 14/9 764.916 cents septimal minor sixth 16: 3 25/16 772.627 cents classic augmented fifth 16: 2 384/245 777.989 cents 16: 2 196/125 778.711 cents 16: 2 100/63 799.892 cents quasi-equal minor sixth 16: 1 343/216 800.613 cents 16: 4 8/5 813.686 cents minor sixth 16: 1 45/28 821.398 cents septimale wide minor sixth 17: 1 32/21 729.219 cents wide fifth 17: 1 75/49 736.931 cents BP fifth 17: 1 25/16 772.627 cents classic augmented fifth 17: 1 540/343 785.701 cents 17: 2 63/40 786.422 cents narrow minor sixth 17: 1 625/392 807.603 cents 17: 8 8/5 813.686 cents minor sixth 17: 1 175/108 835.588 cents 17: 3 80/49 848.662 cents smaller approximation to neutral sixth 17: 5 49/30 849.383 cents larger approximation to neutral sixth 17: 1 105/64 857.095 cents septimal neutral sixth 18: 1 8/5 813.686 cents minor sixth 18: 2 45/28 821.398 cents septimale wide minor sixth 18: 5 80/49 848.662 cents smaller approximation to neutral sixth 18: 4 49/30 849.383 cents larger approximation to neutral sixth 18: 2 288/175 862.457 cents 18: 7 5/3 884.359 cents major sixth, BP sixth 18: 1 2401/1440 885.080 cents 18: 2 42/25 898.153 cents quasi-equal major sixth 18: 1 27/16 905.865 cents Pythagorean major sixth 19: 1 80/49 848.662 cents smaller approximation to neutral sixth 19: 5 5/3 884.359 cents major sixth, BP sixth 19: 2 576/343 897.432 cents 19: 4 42/25 898.153 cents quasi-equal major sixth 19: 1 250/147 919.334 cents 19: 3 245/144 920.056 cents 19: 6 12/7 933.129 cents septimal major sixth 19: 1 343/200 933.850 cents 19: 1 392/225 961.114 cents 19: 1 7/4 968.826 cents harmonic seventh 20: 1 250/147 919.334 cents 20: 1 128/75 925.418 cents diminished seventh 20: 7 12/7 933.129 cents septimal major sixth 20: 1 343/200 933.850 cents 20: 1 216/125 946.924 cents semi-augmented sixth 20: 1 125/72 955.031 cents classic augmented sixth 20: 2 600/343 968.105 cents 20: 6 7/4 968.826 cents harmonic seventh 20: 3 16/9 996.090 cents Pythagorean minor seventh 20: 1 2401/1350 996.811 cents 20: 1 147/80 1053.293 cents 21: 1 256/147 960.393 cents 21: 1 600/343 968.105 cents 21: 5 7/4 968.826 cents harmonic seventh 21: 2 432/245 981.899 cents 21: 5 25/14 1003.802 cents middle minor seventh 21: 1 343/192 1004.523 cents 21: 2 224/125 1009.885 cents 21: 1 9/5 1017.596 cents just minor seventh, BP seventh 21: 2 49/27 1031.787 cents 21: 2 64/35 1044.860 cents septimal neutral seventh 21: 2 28/15 1080.557 cents grave major seventh 21: 1 15/8 1088.269 cents classic major seventh 22: 1 16/9 996.090 cents Pythagorean minor seventh 22: 2 25/14 1003.802 cents middle minor seventh 22: 1 4320/2401 1016.875 cents 22: 3 9/5 1017.596 cents just minor seventh, BP seventh 22: 2 175/96 1039.498 cents 22: 2 64/35 1044.860 cents septimal neutral seventh 22: 1 686/375 1045.582 cents 22: 2 90/49 1052.572 cents 22: 1 147/80 1053.293 cents 22: 1 50/27 1066.762 cents grave major seventh 22: 1 640/343 1079.836 cents 22: 3 28/15 1080.557 cents grave major seventh 22: 1 1176/625 1094.352 cents 22: 2 40/21 1115.533 cents acute major seventh 22: 1 343/180 1116.254 cents 22: 1 245/128 1123.966 cents 23: 1 64/35 1044.860 cents septimal neutral seventh 23: 3 90/49 1052.572 cents 23: 1 147/80 1053.293 cents 23: 3 28/15 1080.557 cents grave major seventh 23: 3 15/8 1088.269 cents classic major seventh 23: 4 40/21 1115.533 cents acute major seventh 23: 1 343/180 1116.254 cents 23: 5 48/25 1129.328 cents classic diminished octave 23: 3 35/18 1151.230 cents septimal semi-diminished octave 23: 1 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 24: 1 28/15 1080.557 cents grave major seventh 24: 1 15/8 1088.269 cents classic major seventh 24: 2 40/21 1115.533 cents acute major seventh 24: 1 375/196 1123.244 cents 24: 1 27/14 1137.039 cents septimal major seventh 24: 3 35/18 1151.230 cents septimal semi-diminished octave 24: 7 96/49 1164.303 cents 24: 6 49/25 1165.024 cents BP eighth 24: 1 63/32 1172.736 cents octave - septimal comma 24: 1 125/63 1186.205 cents 24: 1 1715/864 1186.926 cents Highest number of different intervals for one interval class: 16 Average number of different intervals per interval class: 11.41667 = 137/12
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 0.0 : 35.7 70.7 119.4 155.1 203.9 266.9 351.3 386.3 422.0 457.0 470.8 498.0 617.5 653.2 702.0 737.7 772.6 849.4 884.4 968.8 1003.8 1039.5 1052.6 1088.3 1200.0 35.7 : 35.0 83.7 119.4 168.2 231.2 315.6 350.6 386.3 421.3 435.1 462.3 581.8 617.5 666.3 702.0 736.9 813.7 848.7 933.1 968.1 1003.8 1016.9 1052.6 1164.3 1200.0 70.7 : 48.8 84.5 133.2 196.2 280.7 315.6 351.3 386.3 400.1 427.4 546.8 582.5 631.3 667.0 702.0 778.7 813.7 898.2 933.1 968.8 981.9 1017.6 1129.3 1165.0 1200.0 119.4 : 35.7 84.5 147.4 231.9 266.9 302.6 337.5 351.3 378.6 498.0 533.7 582.5 618.2 653.2 729.9 764.9 849.4 884.4 920.1 933.1 968.8 1080.6 1116.3 1151.2 1200.0 155.1 : 48.8 111.7 196.2 231.2 266.9 301.8 315.6 342.9 462.3 498.0 546.8 582.5 617.5 694.2 729.2 813.7 848.7 884.4 897.4 933.1 1044.9 1080.6 1115.5 1164.3 1200.0 203.9 : 63.0 147.4 182.4 218.1 253.1 266.9 294.1 413.6 449.3 498.0 533.7 568.7 645.5 680.4 764.9 799.9 835.6 848.7 884.4 996.1 1031.8 1066.8 1115.5 1151.2 1200.0 266.9 : 84.5 119.4 155.1 190.1 203.9 231.2 350.6 386.3 435.1 470.8 505.8 582.5 617.5 702.0 736.9 772.6 785.7 821.4 933.1 968.8 1003.8 1052.6 1088.3 1137.0 1200.0 351.3 : 35.0 70.7 105.6 119.4 146.7 266.1 301.8 350.6 386.3 421.3 498.0 533.0 617.5 652.5 688.2 701.2 736.9 848.7 884.4 919.3 968.1 1003.8 1052.6 1115.5 1200.0 386.3 : 35.7 70.7 84.5 111.7 231.2 266.9 315.6 351.3 386.3 463.1 498.0 582.5 617.5 653.2 666.3 702.0 813.7 849.4 884.4 933.1 968.8 1017.6 1080.6 1165.0 1200.0 422.0 : 35.0 48.8 76.0 195.5 231.2 279.9 315.6 350.6 427.4 462.3 546.8 581.8 617.5 630.6 666.3 778.0 813.7 848.7 897.4 933.1 981.9 1044.9 1129.3 1164.3 1200.0 457.0 : 13.8 41.1 160.5 196.2 245.0 280.7 315.6 392.4 427.4 511.8 546.8 582.5 595.6 631.3 743.0 778.7 813.7 862.5 898.2 946.9 1009.9 1094.4 1129.3 1165.0 1200.0 470.8 : 27.3 146.7 182.4 231.2 266.9 301.8 378.6 413.6 498.0 533.0 568.7 581.8 617.5 729.2 764.9 799.9 848.7 884.4 933.1 996.1 1080.6 1115.5 1151.2 1186.2 1200.0 498.0 : 119.4 155.1 203.9 239.6 274.6 351.3 386.3 470.8 505.8 541.5 554.5 590.2 702.0 737.7 772.6 821.4 857.1 905.9 968.8 1053.3 1088.3 1124.0 1158.9 1172.7 1200.0 617.5 : 35.7 84.5 120.2 155.1 231.9 266.9 351.3 386.3 422.0 435.1 470.8 582.5 618.2 653.2 702.0 737.7 786.4 849.4 933.9 968.8 1004.5 1039.5 1053.3 1080.6 1200.0 653.2 : 48.8 84.5 119.4 196.2 231.2 315.6 350.6 386.3 399.4 435.1 546.8 582.5 617.5 666.3 702.0 750.7 813.7 898.2 933.1 968.8 1003.8 1017.6 1044.9 1164.3 1200.0 702.0 : 35.7 70.7 147.4 182.4 266.9 301.8 337.5 350.6 386.3 498.0 533.7 568.7 617.5 653.2 702.0 764.9 849.4 884.4 920.1 955.0 968.8 996.1 1115.5 1151.2 1200.0 737.7 : 35.0 111.7 146.7 231.2 266.1 301.8 314.9 350.6 462.3 498.0 533.0 581.8 617.5 666.3 729.2 813.7 848.7 884.4 919.3 933.1 960.4 1079.8 1115.5 1164.3 1200.0 772.6 : 76.8 111.7 196.2 231.2 266.9 279.9 315.6 427.4 463.1 498.0 546.8 582.5 631.3 694.2 778.7 813.7 849.4 884.4 898.2 925.4 1044.9 1080.6 1129.3 1165.0 1200.0 849.4 : 35.0 119.4 154.4 190.1 203.2 238.9 350.6 386.3 421.3 470.1 505.8 554.5 617.5 702.0 736.9 772.6 807.6 821.4 848.7 968.1 1003.8 1052.6 1088.3 1123.2 1200.0 884.4 : 84.5 119.4 155.1 168.2 203.9 315.6 351.3 386.3 435.1 470.8 519.6 582.5 667.0 702.0 737.7 772.6 786.4 813.7 933.1 968.8 1017.6 1053.3 1088.3 1165.0 1200.0 968.8 : 35.0 70.7 83.7 119.4 231.2 266.9 301.8 350.6 386.3 435.1 498.0 582.5 617.5 653.2 688.2 702.0 729.2 848.7 884.4 933.1 968.8 1003.8 1080.6 1115.5 1200.0 1003.8: 35.7 48.8 84.5 196.2 231.9 266.9 315.6 351.3 400.1 463.1 547.5 582.5 618.2 653.2 667.0 694.2 813.7 849.4 898.2 933.9 968.8 1045.6 1080.6 1165.0 1200.0 1039.5: 13.1 48.8 160.5 196.2 231.2 279.9 315.6 364.4 427.4 511.8 546.8 582.5 617.5 631.3 658.5 778.0 813.7 862.5 898.2 933.1 1009.9 1044.9 1129.3 1164.3 1200.0 1052.6: 35.7 147.4 183.1 218.1 266.9 302.6 351.3 414.3 498.8 533.7 569.4 604.4 618.2 645.5 764.9 800.6 849.4 885.1 920.1 996.8 1031.8 1116.3 1151.2 1186.9 1200.0 1088.3: 111.7 147.4 182.4 231.2 266.9 315.6 378.6 463.1 498.0 533.7 568.7 582.5 609.8 729.2 764.9 813.7 849.4 884.4 961.1 996.1 1080.6 1115.5 1151.2 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 13.0736 .. 119.4428 cents 1225/1152, 106.3692 cents 1728/1715, 13.0736 cents 2: 41.0589 .. 155.1396 cents 4375/4096, 114.0808 cents 1792/1875,-78.3839 cents 3: 76.0345 .. 203.9100 cents 2205/2048, 127.8755 cents 8192/8575,-79.1051 cents 4: 111.7313 .. 239.6068 cents 2205/2048, 127.8755 cents 128/135,-92.1787 cents 5: 146.7069 .. 280.6657 cents 21609/20000, 133.9588 cents 20480/21609,-92.8999 cents 6: 231.1741 .. 351.3381 cents 343/320, 120.1640 cents 1000/1029,-49.4916 cents 7: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 1280/1323,-57.2031 cents 8: 342.9054 .. 470.7809 cents 2205/2048, 127.8755 cents 512/525,-43.4083 cents 9: 378.6022 .. 505.7565 cents 3375/3136, 127.1543 cents 128/135,-92.1787 cents 10: 421.2893 .. 541.4533 cents 343/320, 120.1640 cents 20/21,-84.4672 cents 11: 462.3482 .. 569.4386 cents 117649/110592, 107.0904 cents 8192/8575,-79.1051 cents 12: 498.0450 .. 604.4142 cents 1225/1152, 106.3692 cents 2304/2401,-71.3936 cents 13: 595.5858 .. 701.9550 cents 1225/1152, 106.3692 cents 1492992/1500625,-8.8285 cents 14: 630.5614 .. 737.6518 cents 117649/110592, 107.0904 cents 2304/2401,-71.3936 cents 15: 658.5467 .. 778.7107 cents 343/320, 120.1640 cents 8192/8575,-79.1051 cents 16: 694.2435 .. 821.3978 cents 3375/3136, 127.1543 cents 20/21,-84.4672 cents 17: 729.2191 .. 857.0946 cents 2205/2048, 127.8755 cents 128/135,-92.1787 cents 18: 813.6863 .. 905.8650 cents 135/128, 92.1787 cents 512/525,-43.4083 cents 19: 848.6619 .. 968.8259 cents 343/320, 120.1640 cents 1280/1323,-57.2031 cents 20: 919.3343 .. 1053.2931 cents 21609/20000, 133.9588 cents 1000/1029,-49.4916 cents 21: 960.3932 .. 1088.2687 cents 2205/2048, 127.8755 cents 20480/21609,-92.8999 cents 22: 996.0900 .. 1123.9655 cents 2205/2048, 127.8755 cents 128/135,-92.1787 cents 23: 1044.8604 .. 1158.9411 cents 4375/4096, 114.0808 cents 8192/8575,-79.1051 cents 24: 1080.5572 .. 1186.9264 cents 1225/1152, 106.3692 cents 1792/1875,-78.3839 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 1728/1715, 13.0736 cents, class 1 Average step (divided formal octave): 48.0000 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 3.671530 Largest / Average step : 2.488392 Largest / Smallest step : 9.136205 Median interval of one step : 49/48, 35.6968 cents, amount: 7 Most common interval of one step : 49/48, 35.6968 cents, amount: 7 Least squares average step : 46.55794 cents, oct.: 1163.94860 cents Scale is not proper Step pattern alph. order: ABCACDEBABFGHACABIBEBAJAK Step pattern size order : EDFEFGIDEDBCKEFEDHDIDEAEJ Scale is not a Constant Structure Scale diversity : 1.447796 Lumma stability : 0.021789 Lumma impropriety factor : 0.865541 Number of different interval sizes : 174 = 7.25000 / class Number of one step interval sizes : 11 Highest interval variety : 16 Mean interval variety : 11.41667 = 137/12 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 14 Most common triad is 0.0 582.512 617.488 cents, amount: 6 Number of recognisable fifths : 18, average 699.0969 cents Number of appreciable fifths : 16, average 700.4640 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 7 Formal octave complements present : 3 = 12.0000% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 2401 (O: 2401 U: 2401) Highest odd numerator or denominator: 245 Scale harmonicity : 0.012086 Average absolute harmonicity : 0.110106 Specific harmonicity : 0.085901 Fundamental : 1/47040, -15.5216 octaves, 0.0056 Hz. Guide tone : 220500, 17.7504 octaves, 57688437.149 Hz. Exponens Consonantiae : 1.037232E+10, 33.27202 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 924.0, average 36.96000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 31.97817, average 1.27913 Sum of Tenney's harmonic distance : 61.88159, average 2.47526 Vogel's harmonic complexity : 32.16000 Wille's k value : 30012 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 11 Triangular lattice diameter : 5 Lattice compactness : 1188.11263, average 3.65573 Lattice compactness (without 2's) : 728.00020, average 2.24000 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -2.28000 67 1 3: -1 .. 2 -0.08000 18 3 5: -1 .. 3 0.72000 22 6 7: -2 .. 2 0.44000 21 15 Average exponent except 2's : 27 / 25 = 1.08000 Average absolute exponent except 2's: 61 / 25 = 2.44000
FIT/MODE
25: 0 1 1 1 1 1 2 1 0 1 0 1 2 1 1 1 1 1 1 2 0 1 0 1 3 N SD: 27.4327 c. M: 44.5719 c. 27: 0 1 1 1 1 1 2 1 1 1 0 1 2 1 1 1 1 1 1 2 1 1 0 1 3 N SD: 29.9752 c. M: 49.3831 c. 28: 0 1 1 1 1 2 2 0 1 1 0 1 3 1 1 1 0 2 1 2 1 1 0 1 3 N SD: 27.0326 c. M: 44.0560 c. 29: 1 1 1 1 1 1 2 1 1 1 0 1 3 1 1 1 1 1 1 2 1 1 0 1 3 N SD: 11.8954 c. M: 21.7969 c. 30: 1 1 1 1 1 1 3 0 1 1 1 0 3 1 1 1 1 2 1 2 1 1 0 1 3 N SD: 13.6772 c. M: 26.8709 c. 31: 1 1 1 1 1 2 2 1 1 1 0 1 3 1 1 1 1 2 1 2 1 1 0 1 3 N SD: 4.7019 c. M: 10.3616 c. 57: 2 1 3 1 3 3 4 1 2 2 0 2 5 2 2 2 2 3 2 4 2 1 1 2 5 N SD: 5.9539 c. M: 7.9194 c. 60: 2 2 2 2 2 3 5 1 2 2 1 1 6 2 2 2 2 3 2 4 2 2 1 1 6 N SD: 5.8255 c. M: 9.3831 c. 62: 2 2 2 2 3 3 4 2 2 2 0 2 6 2 2 2 2 4 2 4 2 2 0 2 6 N SD: 4.5878 c. M:-8.9932 c. 68: 2 2 3 2 3 3 5 2 2 2 1 1 7 2 3 2 2 4 2 5 2 2 1 2 6 N SD: 3.4190 c. M:-7.8547 c. 72: 2 2 3 2 3 4 5 2 2 2 1 2 7 2 3 2 2 5 2 5 2 2 1 2 7 N SD: 3.6781 c. M: 6.9861 c. 79: 2 3 3 2 3 5 5 2 3 2 1 2 8 2 3 3 2 5 2 6 2 2 1 3 7 N SD: 4.1481 c. M:-6.6520 c. 84: 3 2 3 3 3 5 6 2 3 2 1 2 8 3 3 3 2 6 2 6 2 3 1 2 8 N SD: 3.8994 c. M:-7.7598 c. 89: 3 2 4 3 3 5 6 3 2 3 1 2 9 2 4 3 2 6 3 6 2 3 1 3 8 N SD: 3.4601 c. M:-6.6581 c. 90: 3 2 4 3 3 5 6 3 3 2 1 2 9 3 4 2 3 6 2 7 2 3 1 3 8 N SD: 3.6023 c. M:-5.0646 c. 92: 3 2 4 3 4 4 7 3 2 3 1 2 9 3 4 3 2 6 3 6 3 3 1 2 9 N SD: 3.5594 c. M: 6.0013 c. 96: 3 3 4 2 4 5 7 3 3 3 1 2 9 3 4 3 3 6 3 7 2 3 1 3 9 N SD: 3.4429 c. M:-6.1741 c. 99: 3 3 4 3 4 5 7 3 3 3 1 2 10 3 4 3 3 6 3 7 3 3 1 3 9 N SD: 1.8608 c. M:-3.6199 c. 130: 4 4 5 4 5 7 9 4 4 4 1 3 13 4 5 4 4 8 4 9 4 4 1 4 12 N SD: 1.8255 c. M:-4.5523 c. 140: 4 4 6 4 6 7 10 4 4 4 2 3 14 4 6 4 4 9 4 10 4 4 2 4 13 N SD: 1.3135 c. M: 2.7004 c. 171: 5 5 7 5 7 9 12 5 5 5 2 4 17 5 7 5 5 11 5 12 5 5 2 5 16 N SD: 0.5190 c. M: 0.9579 c. 270: 8 8 11 8 11 14 19 8 8 8 3 6 27 8 11 8 8 17 8 19 8 8 3 8 25 N SD: 0.4303 c. M:-0.7916 c. 441: 13 13 18 13 18 23 31 13 13 13 5 10 44 13 18 13 13 28 13 31 13 13 5 13 41 N SD: 0.2127 c. M:-0.4893 c. 612: 18 18 25 18 25 32 43 18 18 18 7 14 61 18 25 18 18 39 18 43 18 18 7 18 57 N SD: 0.2303 c. M: 0.4419 c. 913: 27 27 37 27 37 48 64 27 27 27 10 21 91 27 37 27 27 58 27 64 27 27 10 27 85 N SD: 0.2189 c. M: 0.4071 c. 935: 28 27 38 28 38 49 66 27 28 27 11 21 93 28 38 28 27 60 27 66 27 28 10 28 87 N SD: 0.1607 c. M:-0.3197 c. 1106: 33 32 45 33 45 58 78 32 33 32 13 25 110 33 45 33 32 71 32 78 32 33 12 33 103 N SD: 0.1091 c. M: 0.2049 c. 1277: 38 37 52 38 52 67 90 37 38 37 15 29 127 38 52 38 37 82 37 90 37 38 14 38 119 N SD: 0.1169 c. M: 0.2908 c. 1376: 41 40 56 41 56 72 97 40 41 40 16 31 137 41 56 41 40 88 40 97 40 41 15 41 128 N SD: 0.0757 c. M:-0.1598 c. 1547: 46 45 63 46 63 81 109 45 46 45 18 35 154 46 63 46 45 99 45 109 45 46 17 46 144 N SD: 0.0501 c. M: 0.1018 c. 1578: 47 46 64 47 64 83 111 46 47 46 18 36 157 47 64 47 46 101 46 111 46 47 17 47 147 N SD: 0.0478 c. M: 0.1077 c. 2019: 60 59 82 60 82 106 142 59 60 59 23 46 201 60 82 60 59 129 59 142 59 60 22 60 188 N SD: 0.0399 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: 12.5891 cents 6 .. 12 match: 6 H SD: 0.5348 cents 7 .. 14 match: 7 H SD: 7.2285 cents 8 .. 16 match: 8 H SD: 6.7505 cents 9 .. 18 match: 9 H SD: 3.5739 cents 10 .. 20 match: 10 H SD: 7.5949 cents 11 .. 22 match: 11 H SD: 5.6370 cents 12 .. 24 match: 12 H SD: 4.1402 cents 13 .. 26 match: 11 SD: 4.0982 cents 14 .. 28 match: 12 SD: 4.2144 cents 15 .. 30 match: 13 SD: 4.5575 cents 16 .. 32 match: 14 SD: 3.1172 cents 17 .. 34 match: 15 S SD: 4.0111 cents 18 .. 36 match: 15 S SD: 3.0831 cents 19 .. 38 match: 17 SD: 3.3385 cents 20 .. 40 match: 15 SD: 3.5554 cents 21 .. 42 match: 17 SD: 3.6894 cents 22 .. 44 match: 17 SD: 2.8427 cents 23 .. 46 match: 18 SD: 2.5655 cents 24 .. 48 match: 20 S SD: 2.2504 cents 25 .. 50 match: 17 SD: 2.3490 cents 26 .. 52 match: 20 SD: 2.6023 cents 27 .. 54 match: 19 SD: 2.7083 cents 28 .. 56 match: 21 SD: 2.5339 cents 29 .. 58 match: 20 SD: 2.6004 cents 30 .. 60 match: 21 SD: 1.8495 cents 31 .. 62 match: 20 SD: 2.3786 cents 32 .. 64 match: 23 SD: 1.7866 cents 33 .. 66 match: 23 SD: 2.2299 cents 34 .. 68 match: 21 SD: 2.5497 cents 35 .. 70 match: 21 SD: 2.2024 cents 36 .. 72 match: 22 SD: 2.1576 cents 37 .. 74 match: 23 SD: 2.1552 cents 38 .. 76 match: 24 SD: 2.2679 cents 39 .. 78 match: 24 SD: 1.8070 cents 40 .. 80 match: 23 SD: 1.5512 cents 41 .. 82 match: 24 SD: 1.5784 cents 42 .. 84 match: 23 SD: 1.6254 cents 43 .. 86 match: 24 SD: 1.5159 cents 44 .. 88 match: 25 SD: 1.4217 cents 45 .. 90 match: 24 SD: 1.6374 cents 46 .. 92 match: 23 SD: 1.5929 cents 47 .. 94 match: 24 SD: 1.5372 cents 48 .. 96 match: 23 SD: 1.3329 cents 49 .. 98 match: 24 SD: 1.5534 cents 50 .. 100 match: 25 SD: 1.4890 cents 51 .. 102 match: 25 SD: 1.4342 cents 52 .. 104 match: 24 SD: 1.3666 cents 53 .. 106 match: 24 SD: 1.3499 cents 54 .. 108 match: 25 SD: 1.1236 cents 55 .. 110 match: 24 SD: 1.1339 cents 58 .. 116 match: 24 SD: 1.3729 cents 59 .. 118 match: 23 SD: 1.4376 cents 60 .. 120 match: 25 SD: 1.3270 cents 61 .. 122 match: 25 SD: 1.2680 cents 62 .. 124 match: 24 SD: 1.2810 cents 63 .. 126 match: 25 SD: 1.2445 cents 64 .. 128 match: 25 SD: 1.1530 cents 65 .. 130 match: 24 SD: 1.1695 cents 66 .. 132 match: 25 SD: 0.9800 cents 68 .. 136 match: 24 SD: 1.0754 cents 72 .. 144 match: 25 SD: 0.8699 cents 75 .. 150 match: 24 SD: 1.0474 cents 76 .. 152 match: 25 SD: 0.9954 cents 78 .. 156 match: 24 SD: 1.1007 cents 79 .. 158 match: 25 SD: 0.8753 cents 80 .. 160 match: 25 SD: 0.8430 cents 84 .. 168 match: 25 SD: 0.8093 cents 87 .. 174 match: 25 SD: 0.7784 cents 89 .. 178 match: 25 SD: 0.7638 cents 93 .. 186 match: 25 SD: 0.7610 cents 94 .. 188 match: 25 SD: 0.7381 cents 96 .. 192 match: 25 SD: 0.4512 cents 151 .. 302 match: 25 SD: 0.4276 cents 152 .. 304 match: 25 SD: 0.4195 cents 160 .. 320 match: 25 SD: 0.4068 cents 168 .. 336 match: 25 SD: 0.3796 cents 182 .. 364 match: 25 SD: 0.3788 cents 183 .. 366 match: 25 SD: 0.3750 cents 185 .. 370 match: 25 SD: 0.3449 cents 191 .. 382 match: 25 SD: 0.3423 cents 192 .. 384 match: 25 SD: 0.1766 cents 288 .. 576 match: 25 SD: 0.1727 cents 352 .. 704 match: 25 SD: 0.1693 cents 377 .. 754 match: 25 SD: 0.1665 cents 384 .. 768 match: 25 SD: 0.1176 cents 480 .. 960 match: 25 SD: 0.0804 cents 576 .. 1152 match: 25 SD: 0.0548 cents