Scala analysis: partch_37
From "Exposition on Monophony" 1933, unp. see Ayers, 1/1 vol.9(2)
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: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 3: 22/21 80.537035 undecimal minor semitone 4: 16/15 111.731285 minor diatonic semitone 5: 12/11 150.637059 undecimal neutral second, 3/4-tone 6: 11/10 165.004228 Ptolemy's second, 4/5-tone 7: 10/9 182.403712 minor whole tone 8: 9/8 203.910002 major whole tone 9: 8/7 231.174094 septimal whole tone 10: 7/6 266.870906 septimal minor third 11: 6/5 315.641287 minor third 12: 11/9 347.407941 undecimal neutral third 13: 5/4 386.313714 major third 14: 14/11 417.507964 undecimal diminished fourth or major third 15: 9/7 435.084095 septimal major third, BP third 16: 4/3 498.044999 perfect fourth 17: 11/8 551.317942 undecimal semi-augmented fourth 18: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 19: 10/7 617.487807 Euler's tritone 20: 16/11 648.682058 undecimal semi-diminished fifth 21: 3/2 701.955001 perfect fifth 22: 14/9 764.915905 septimal minor sixth 23: 11/7 782.492036 undecimal augmented fifth 24: 8/5 813.686286 minor sixth 25: 18/11 852.592059 undecimal neutral sixth 26: 5/3 884.358713 major sixth, BP sixth 27: 12/7 933.129094 septimal major sixth 28: 7/4 968.825906 harmonic seventh 29: 16/9 996.089998 Pythagorean minor seventh 30: 9/5 1017.596288 just minor seventh, BP seventh 31: 20/11 1034.995772 large minor seventh 32: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 33: 15/8 1088.268715 classic major seventh 34: 21/11 1119.462965 undecimal major seventh 35: 64/33 1146.727057 33rd subharmonic 36: 96/49 1164.303188 37: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 49/48 35.6968 slendro diesis, septimal 1/6-tone 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 99/98 17.5761 small undecimal comma 3: 64/63 27.2641 septimal comma, Archytas' comma 4: 56/55 31.1943 undecimal diesis, konbini comma 5: 45/44 38.9058 1/5-tone 6: 121/120 14.3672 undecimal seconds comma, biyatisma 7: 100/99 17.3995 Ptolemy's comma 8: 81/80 21.5063 syntonic comma, Didymus comma 9: 64/63 27.2641 septimal comma, Archytas' comma 10: 49/48 35.6968 slendro diesis, septimal 1/6-tone 11: 36/35 48.7704 septimal diesis, 1/4-tone 12: 55/54 31.7667 telepathma 13: 45/44 38.9058 1/5-tone 14: 56/55 31.1943 undecimal diesis, konbini comma 15: 99/98 17.5761 small undecimal comma 16: 28/27 62.9609 Archytas' 1/3-tone 17: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 18: 56/55 31.1943 undecimal diesis, konbini comma 19: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 20: 56/55 31.1943 undecimal diesis, konbini comma 21: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 22: 28/27 62.9609 Archytas' 1/3-tone 23: 99/98 17.5761 small undecimal comma 24: 56/55 31.1943 undecimal diesis, konbini comma 25: 45/44 38.9058 1/5-tone 26: 55/54 31.7667 telepathma 27: 36/35 48.7704 septimal diesis, 1/4-tone 28: 49/48 35.6968 slendro diesis, septimal 1/6-tone 29: 64/63 27.2641 septimal comma, Archytas' comma 30: 81/80 21.5063 syntonic comma, Didymus comma 31: 100/99 17.3995 Ptolemy's comma 32: 121/120 14.3672 undecimal seconds comma, biyatisma 33: 45/44 38.9058 1/5-tone 34: 56/55 31.1943 undecimal diesis, konbini comma 35: 64/63 27.2641 septimal comma, Archytas' comma 36: 99/98 17.5761 small undecimal comma 37: 49/48 35.6968 slendro diesis, septimal 1/6-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 121/120 14.367 cents undecimal seconds comma, biyatisma 1: 2 100/99 17.399 cents Ptolemy's comma 1: 4 99/98 17.576 cents small undecimal comma 1: 2 81/80 21.506 cents syntonic comma, Didymus comma 1: 4 64/63 27.264 cents septimal comma, Archytas' comma 1: 6 56/55 31.194 cents undecimal diesis, konbini comma 1: 2 55/54 31.767 cents telepathma 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 45/44 38.906 cents 1/5-tone 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 2: 2 55/54 31.767 cents telepathma 2: 2 45/44 38.906 cents 1/5-tone 2: 2 352/343 44.840 cents supracomma 2: 4 36/35 48.770 cents septimal diesis, 1/4-tone 2: 4 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 2: 2 512/495 58.458 cents 2: 2 28/27 62.961 cents Archytas' 1/3-tone 2: 2 80/77 66.170 cents 2: 4 126/121 70.100 cents 2: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 2401/2304 71.394 cents two (slendro diesis, septimal 1/6-tone) 2: 4 22/21 80.537 cents undecimal minor semitone 2: 4 21/20 84.467 cents minor semitone 2: 2 77/72 116.234 cents undecimal secor 3: 2 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 3: 2 80/77 66.170 cents 3: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 3: 2 256/245 76.034 cents septimal minor semitone 3: 2 22/21 80.537 cents undecimal minor semitone 3: 4 21/20 84.467 cents minor semitone 3: 2 81/77 87.676 cents 3: 2 539/512 88.970 cents 3: 3 128/121 97.364 cents undecimal semitone 3: 2 35/33 101.867 cents 3: 4 16/15 111.731 cents minor diatonic semitone 3: 2 77/72 116.234 cents undecimal secor 3: 4 15/14 119.443 cents major diatonic semitone 3: 2 121/112 133.810 cents 3: 2 49/45 147.428 cents BP minor semitone 4: 2 22/21 80.537 cents undecimal minor semitone 4: 2 135/128 92.179 cents major chroma, major limma 4: 4 35/33 101.867 cents 4: 1 1089/1024 106.546 cents two (undecimal comma, al-Farabi's 1/4-tone) 4: 4 16/15 111.731 cents minor diatonic semitone 4: 2 576/539 114.940 cents 4: 2 77/72 116.234 cents undecimal secor 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 88/81 143.498 cents 2nd undecimal neutral second 4: 6 12/11 150.637 cents undecimal neutral second, 3/4-tone 4: 2 35/32 155.140 cents septimal neutral second 4: 4 11/10 165.004 cents Ptolemy's second, 4/5-tone 4: 2 10/9 182.404 cents minor whole tone 5: 2 77/72 116.234 cents undecimal secor 5: 2 15/14 119.443 cents major diatonic semitone 5: 2 189/176 123.373 cents 5: 2 320/297 129.131 cents 5: 2 264/245 129.307 cents 5: 2 121/112 133.810 cents 5: 2 49/45 147.428 cents BP minor semitone 5: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 5: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 5: 2 54/49 168.213 cents Zalzal's mujannab 5: 4 10/9 182.404 cents minor whole tone 5: 2 49/44 186.334 cents undecimal minor whole tone 5: 2 28/25 196.198 cents middle second 5: 2 55/49 199.980 cents quasi-equal major second 5: 3 9/8 203.910 cents major whole tone 5: 2 112/99 213.598 cents 6: 2 160/147 146.707 cents 6: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 6: 2 35/32 155.140 cents septimal neutral second 6: 1 484/441 161.074 cents two (undecimal minor semitone) 6: 6 11/10 165.004 cents Ptolemy's second, 4/5-tone 6: 2 10/9 182.404 cents minor whole tone 6: 2 49/44 186.334 cents undecimal minor whole tone 6: 4 9/8 203.910 cents major whole tone 6: 2 112/99 213.598 cents 6: 6 8/7 231.174 cents septimal whole tone 6: 2 63/55 235.104 cents 6: 2 55/48 235.677 cents undecimal semi-augmented whole tone 6: 2 7/6 266.871 cents septimal minor third 7: 2 54/49 168.213 cents Zalzal's mujannab 7: 2 256/231 177.901 cents 7: 2 10/9 182.404 cents minor whole tone 7: 2 49/44 186.334 cents undecimal minor whole tone 7: 2 352/315 192.268 cents 7: 2 121/108 196.771 cents 7: 2 539/480 200.701 cents 7: 4 9/8 203.910 cents major whole tone 7: 2 25/22 221.309 cents undecimal acute whole tone 7: 2 8/7 231.174 cents septimal whole tone 7: 2 63/55 235.104 cents 7: 2 64/55 262.368 cents 7: 4 7/6 266.871 cents septimal minor third 7: 2 90/77 270.080 cents 7: 4 33/28 284.447 cents undecimal minor third 7: 1 98/81 329.832 cents 8: 2 384/343 195.477 cents 8: 2 9/8 203.910 cents major whole tone 8: 2 112/99 213.598 cents 8: 2 245/216 218.101 cents 8: 2 363/320 218.277 cents 8: 1 256/225 223.463 cents Neapolitan diminished third 8: 2 8/7 231.174 cents septimal whole tone 8: 2 63/55 235.104 cents 8: 4 55/48 235.677 cents undecimal semi-augmented whole tone 8: 2 140/121 252.504 cents 8: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 8: 2 32/27 294.135 cents Pythagorean minor third 8: 2 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 8: 2 25/21 301.847 cents BP second, quasi-equal minor third 8: 4 6/5 315.641 cents minor third 8: 2 77/64 320.144 cents Keemun minor third 8: 2 11/9 347.408 cents undecimal neutral third 9: 4 8/7 231.174 cents septimal whole tone 9: 2 55/48 235.677 cents undecimal semi-augmented whole tone 9: 2 147/128 239.607 cents 9: 2 121/105 245.541 cents 9: 4 64/55 262.368 cents 9: 4 7/6 266.871 cents septimal minor third 9: 2 90/77 270.080 cents 9: 2 75/64 274.582 cents classic augmented second 9: 2 6/5 315.641 cents minor third 9: 2 40/33 333.041 cents 9: 2 11/9 347.408 cents undecimal neutral third 9: 2 60/49 350.617 cents smaller approximation to neutral third 9: 2 49/40 351.338 cents larger approximation to neutral third 9: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 9: 1 121/98 364.984 cents 9: 2 56/45 378.602 cents septimal narrow major third 10: 2 297/256 257.183 cents 10: 2 220/189 262.941 cents 10: 4 7/6 266.871 cents septimal minor third 10: 2 88/75 276.736 cents 10: 2 288/245 279.944 cents 10: 2 33/28 284.447 cents undecimal minor third 10: 2 32/27 294.135 cents Pythagorean minor third 10: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 10: 4 105/88 305.777 cents 10: 2 40/33 333.041 cents 10: 2 99/80 368.914 cents 10: 2 56/45 378.602 cents septimal narrow major third 10: 2 96/77 381.811 cents 10: 4 5/4 386.314 cents major third 10: 2 44/35 396.178 cents 10: 2 14/11 417.508 cents undecimal diminished fourth or major third 11: 4 33/28 284.447 cents undecimal minor third 11: 2 32/27 294.135 cents Pythagorean minor third 11: 2 343/288 302.568 cents 11: 2 176/147 311.711 cents 11: 4 6/5 315.641 cents minor third 11: 2 135/112 323.353 cents septimal wide minor third 11: 2 40/33 333.041 cents 11: 2 147/121 336.971 cents 11: 2 11/9 347.408 cents undecimal neutral third 11: 2 5/4 386.314 cents major third 11: 2 63/50 400.108 cents quasi-equal major third 11: 2 80/63 413.578 cents wide major third 11: 2 14/11 417.508 cents undecimal diminished fourth or major third 11: 1 32/25 427.373 cents classic diminished fourth 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 12: 2 176/147 311.711 cents 12: 2 6/5 315.641 cents minor third 12: 2 77/64 320.144 cents Keemun minor third 12: 1 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 12: 2 40/33 333.041 cents 12: 2 11/9 347.408 cents undecimal neutral third 12: 2 60/49 350.617 cents smaller approximation to neutral third 12: 2 49/40 351.338 cents larger approximation to neutral third 12: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 12: 2 448/363 364.235 cents 12: 2 5/4 386.314 cents major third 12: 2 121/96 400.681 cents 12: 2 14/11 417.508 cents undecimal diminished fourth or major third 12: 2 9/7 435.084 cents septimal major third, BP third 12: 2 128/99 444.772 cents 12: 2 72/55 466.278 cents undecimal semi-diminished fourth 12: 2 55/42 466.851 cents 12: 2 21/16 470.781 cents narrow fourth 12: 2 4/3 498.045 cents perfect fourth 13: 2 128/105 342.905 cents septimal neutral third 13: 4 11/9 347.408 cents undecimal neutral third 13: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 13: 2 99/80 368.914 cents 13: 4 96/77 381.811 cents 13: 2 539/432 383.105 cents 13: 2 5/4 386.314 cents major third 13: 2 14/11 417.508 cents undecimal diminished fourth or major third 13: 2 77/60 431.875 cents 13: 2 165/128 439.587 cents 13: 2 100/77 452.484 cents 13: 2 72/55 466.278 cents undecimal semi-diminished fourth 13: 4 4/3 498.045 cents perfect fourth 13: 1 162/121 505.184 cents 13: 2 66/49 515.621 cents 13: 2 49/36 533.742 cents Arabic lute acute fourth 14: 1 100/81 364.807 cents grave major third 14: 2 99/80 368.914 cents 14: 2 56/45 378.602 cents septimal narrow major third 14: 2 96/77 381.811 cents 14: 2 44/35 396.178 cents 14: 2 432/343 399.387 cents 14: 2 121/96 400.681 cents 14: 2 14/11 417.508 cents undecimal diminished fourth or major third 14: 2 245/192 422.011 cents 14: 2 128/99 444.772 cents 14: 2 55/42 466.851 cents 14: 4 21/16 470.781 cents narrow fourth 14: 2 160/121 483.678 cents 14: 2 27/20 519.551 cents acute fourth 14: 2 15/11 536.951 cents undecimal augmented fourth 14: 2 48/35 546.815 cents septimal semi-augmented fourth 14: 2 11/8 551.318 cents undecimal semi-augmented fourth 14: 2 112/81 561.006 cents 15: 2 5/4 386.314 cents major third 15: 2 44/35 396.178 cents 15: 2 14/11 417.508 cents undecimal diminished fourth or major third 15: 2 32/25 427.373 cents classic diminished fourth 15: 2 242/189 427.945 cents 15: 2 9/7 435.084 cents septimal major third, BP third 15: 2 165/128 439.587 cents 15: 2 343/264 453.205 cents 15: 2 64/49 462.348 cents 2 septatones or septatonic major third 15: 4 4/3 498.045 cents perfect fourth 15: 2 147/110 501.975 cents 15: 2 75/56 505.757 cents marvelous fourth 15: 2 15/11 536.951 cents undecimal augmented fourth 15: 1 25/18 568.717 cents classic augmented fourth 15: 2 88/63 578.582 cents 15: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 15: 2 108/77 585.721 cents 16: 1 81/64 407.820 cents Pythagorean major third 16: 2 80/63 413.578 cents wide major third 16: 2 77/60 431.875 cents 16: 2 176/135 459.139 cents 16: 2 72/55 466.278 cents undecimal semi-diminished fourth 16: 2 55/42 466.851 cents 16: 4 21/16 470.781 cents narrow fourth 16: 2 4/3 498.045 cents perfect fourth 16: 2 66/49 515.621 cents 16: 2 224/165 529.239 cents 16: 4 15/11 536.951 cents undecimal augmented fourth 16: 2 11/8 551.318 cents undecimal semi-augmented fourth 16: 2 140/99 599.912 cents quasi-equal tritone 16: 2 99/70 600.088 cents 2nd quasi-equal tritone 16: 2 64/45 609.776 cents 2nd tritone 16: 2 10/7 617.488 cents Euler's tritone 16: 2 63/44 621.418 cents 17: 2 9/7 435.084 cents septimal major third, BP third 17: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 17: 2 33/25 480.646 cents 2 pentatones 17: 2 297/224 488.357 cents 17: 6 4/3 498.045 cents perfect fourth 17: 2 49/36 533.742 cents Arabic lute acute fourth 17: 2 48/35 546.815 cents septimal semi-augmented fourth 17: 2 11/8 551.318 cents undecimal semi-augmented fourth 17: 2 320/231 564.215 cents 17: 2 168/121 568.145 cents 17: 2 45/32 590.224 cents diatonic tritone 17: 2 77/54 614.279 cents 17: 2 10/7 617.488 cents Euler's tritone 17: 2 36/25 631.283 cents classic diminished fifth 17: 2 16/11 648.682 cents undecimal semi-diminished fifth 17: 2 35/24 653.185 cents septimal semi-diminished fifth 17: 1 72/49 666.258 cents Arabic lute grave fifth 18: 1 64/49 462.348 cents 2 septatones or septatonic major third 18: 2 21/16 470.781 cents narrow fourth 18: 2 4/3 498.045 cents perfect fourth 18: 2 121/90 512.412 cents 18: 2 66/49 515.621 cents 18: 2 224/165 529.239 cents 18: 2 15/11 536.951 cents undecimal augmented fourth 18: 2 11/8 551.318 cents undecimal semi-augmented fourth 18: 2 480/343 581.791 cents 18: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 18: 2 539/384 587.015 cents 18: 2 512/363 595.409 cents 18: 2 63/44 621.418 cents 18: 2 121/84 631.855 cents 18: 2 16/11 648.682 cents undecimal semi-diminished fifth 18: 2 35/24 653.185 cents septimal semi-diminished fifth 18: 2 81/55 670.188 cents 18: 2 40/27 680.449 cents grave fifth 18: 2 3/2 701.955 cents perfect fifth 19: 2 4/3 498.045 cents perfect fourth 19: 2 27/20 519.551 cents acute fourth 19: 2 110/81 529.812 cents 19: 2 48/35 546.815 cents septimal semi-augmented fourth 19: 2 11/8 551.318 cents undecimal semi-augmented fourth 19: 2 168/121 568.145 cents 19: 2 88/63 578.582 cents 19: 2 363/256 604.591 cents 19: 2 768/539 612.985 cents 19: 2 10/7 617.488 cents Euler's tritone 19: 2 343/240 618.209 cents 19: 2 16/11 648.682 cents undecimal semi-diminished fifth 19: 2 22/15 663.049 cents undecimal diminished fifth 19: 2 165/112 670.761 cents 19: 2 49/33 684.379 cents 19: 2 180/121 687.588 cents 19: 2 3/2 701.955 cents perfect fifth 19: 2 32/21 729.219 cents wide fifth 19: 1 49/32 737.652 cents 20: 1 49/36 533.742 cents Arabic lute acute fourth 20: 2 48/35 546.815 cents septimal semi-augmented fourth 20: 2 11/8 551.318 cents undecimal semi-augmented fourth 20: 2 25/18 568.717 cents classic augmented fourth 20: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 20: 2 108/77 585.721 cents 20: 2 64/45 609.776 cents 2nd tritone 20: 2 121/84 631.855 cents 20: 2 231/160 635.785 cents 20: 2 16/11 648.682 cents undecimal semi-diminished fifth 20: 2 35/24 653.185 cents septimal semi-diminished fifth 20: 2 72/49 666.258 cents Arabic lute grave fifth 20: 6 3/2 701.955 cents perfect fifth 20: 2 448/297 711.643 cents 20: 2 50/33 719.354 cents 3 pentatones 20: 2 54/35 750.725 cents septimal semi-augmented fifth 20: 2 14/9 764.916 cents septimal minor sixth 21: 2 88/63 578.582 cents 21: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 21: 2 45/32 590.224 cents diatonic tritone 21: 2 140/99 599.912 cents quasi-equal tritone 21: 2 99/70 600.088 cents 2nd quasi-equal tritone 21: 2 16/11 648.682 cents undecimal semi-diminished fifth 21: 4 22/15 663.049 cents undecimal diminished fifth 21: 2 165/112 670.761 cents 21: 2 49/33 684.379 cents 21: 2 3/2 701.955 cents perfect fifth 21: 4 32/21 729.219 cents wide fifth 21: 2 84/55 733.149 cents 21: 2 55/36 733.722 cents undecimal semi-augmented fifth 21: 2 135/88 740.861 cents 21: 2 120/77 768.125 cents 21: 2 63/40 786.422 cents narrow minor sixth 21: 1 128/81 792.180 cents Pythagorean minor sixth 22: 2 77/54 614.279 cents 22: 4 10/7 617.488 cents Euler's tritone 22: 2 63/44 621.418 cents 22: 1 36/25 631.283 cents classic diminished fifth 22: 2 22/15 663.049 cents undecimal diminished fifth 22: 2 112/75 694.243 cents marvelous fifth 22: 2 220/147 698.025 cents 22: 4 3/2 701.955 cents perfect fifth 22: 2 49/32 737.652 cents 22: 2 528/343 746.795 cents 22: 2 256/165 760.413 cents 22: 2 14/9 764.916 cents septimal minor sixth 22: 2 189/121 772.055 cents 22: 2 25/16 772.627 cents classic augmented fifth 22: 2 11/7 782.492 cents undecimal augmented fifth 22: 2 35/22 803.822 cents 22: 2 8/5 813.686 cents minor sixth 23: 2 81/56 638.994 cents 23: 2 16/11 648.682 cents undecimal semi-diminished fifth 23: 2 35/24 653.185 cents septimal semi-diminished fifth 23: 2 22/15 663.049 cents undecimal diminished fifth 23: 2 40/27 680.449 cents grave fifth 23: 2 121/80 716.322 cents 23: 4 32/21 729.219 cents wide fifth 23: 2 84/55 733.149 cents 23: 2 99/64 755.228 cents 23: 2 384/245 777.989 cents 23: 2 11/7 782.492 cents undecimal augmented fifth 23: 2 192/121 799.319 cents 23: 2 343/216 800.613 cents 23: 2 35/22 803.822 cents 23: 2 77/48 818.189 cents 23: 2 45/28 821.398 cents septimale wide minor sixth 23: 2 160/99 831.086 cents 23: 1 81/50 835.193 cents acute minor sixth 24: 2 72/49 666.258 cents Arabic lute grave fifth 24: 2 49/33 684.379 cents 24: 1 121/81 694.816 cents two (undecimal neutral third) 24: 4 3/2 701.955 cents perfect fifth 24: 2 55/36 733.722 cents undecimal semi-augmented fifth 24: 2 77/50 747.516 cents 24: 2 256/165 760.413 cents 24: 2 120/77 768.125 cents 24: 2 11/7 782.492 cents undecimal augmented fifth 24: 2 8/5 813.686 cents minor sixth 24: 2 864/539 816.895 cents 24: 4 77/48 818.189 cents 24: 2 160/99 831.086 cents 24: 2 44/27 845.453 cents neutral sixth 24: 4 18/11 852.592 cents undecimal neutral sixth 24: 2 105/64 857.095 cents septimal neutral sixth 25: 2 3/2 701.955 cents perfect fifth 25: 2 32/21 729.219 cents wide fifth 25: 2 84/55 733.149 cents 25: 2 55/36 733.722 cents undecimal semi-augmented fifth 25: 2 99/64 755.228 cents 25: 2 14/9 764.916 cents septimal minor sixth 25: 2 11/7 782.492 cents undecimal augmented fifth 25: 2 192/121 799.319 cents 25: 2 8/5 813.686 cents minor sixth 25: 2 363/224 835.765 cents 25: 2 44/27 845.453 cents neutral sixth 25: 2 80/49 848.662 cents smaller approximation to neutral sixth 25: 2 49/30 849.383 cents larger approximation to neutral sixth 25: 2 18/11 852.592 cents undecimal neutral sixth 25: 2 33/20 866.959 cents 25: 1 200/121 869.992 cents 25: 2 128/77 879.856 cents 25: 2 5/3 884.359 cents major sixth, BP sixth 25: 2 147/88 888.289 cents 26: 2 54/35 750.725 cents septimal semi-augmented fifth 26: 4 14/9 764.916 cents septimal minor sixth 26: 1 25/16 772.627 cents classic augmented fifth 26: 2 11/7 782.492 cents undecimal augmented fifth 26: 2 63/40 786.422 cents narrow minor sixth 26: 2 100/63 799.892 cents quasi-equal minor sixth 26: 2 8/5 813.686 cents minor sixth 26: 2 18/11 852.592 cents undecimal neutral sixth 26: 2 242/147 863.029 cents 26: 2 33/20 866.959 cents 26: 2 224/135 876.647 cents narrow septimal major sixth 26: 4 5/3 884.359 cents major sixth, BP sixth 26: 2 147/88 888.289 cents 26: 2 576/343 897.432 cents 26: 2 27/16 905.865 cents Pythagorean major sixth 26: 4 56/33 915.553 cents 27: 2 11/7 782.492 cents undecimal augmented fifth 27: 2 35/22 803.822 cents 27: 4 8/5 813.686 cents minor sixth 27: 2 77/48 818.189 cents 27: 2 45/28 821.398 cents septimale wide minor sixth 27: 2 160/99 831.086 cents 27: 2 33/20 866.959 cents 27: 4 176/105 894.223 cents 27: 1 121/72 898.726 cents 27: 2 27/16 905.865 cents Pythagorean major sixth 27: 2 56/33 915.553 cents 27: 2 245/144 920.056 cents 27: 2 75/44 923.264 cents 27: 4 12/7 933.129 cents septimal major sixth 27: 2 189/110 937.059 cents 27: 2 512/297 942.817 cents 28: 2 45/28 821.398 cents septimale wide minor sixth 28: 1 196/121 835.016 cents two (undecimal diminished fourth or major third) 28: 2 44/27 845.453 cents neutral sixth 28: 2 80/49 848.662 cents smaller approximation to neutral sixth 28: 2 49/30 849.383 cents larger approximation to neutral sixth 28: 2 18/11 852.592 cents undecimal neutral sixth 28: 2 33/20 866.959 cents 28: 2 5/3 884.359 cents major sixth, BP sixth 28: 2 128/75 925.418 cents diminished seventh 28: 2 77/45 929.920 cents 28: 4 12/7 933.129 cents septimal major sixth 28: 4 55/32 937.632 cents 28: 2 210/121 954.459 cents 28: 2 256/147 960.393 cents 28: 2 96/55 964.323 cents 28: 4 7/4 968.826 cents harmonic seventh 29: 2 18/11 852.592 cents undecimal neutral sixth 29: 2 128/77 879.856 cents 29: 4 5/3 884.359 cents major sixth, BP sixth 29: 2 42/25 898.153 cents quasi-equal major sixth 29: 2 121/72 898.726 cents 29: 2 27/16 905.865 cents Pythagorean major sixth 29: 2 140/81 947.320 cents 29: 2 121/70 947.496 cents 29: 4 96/55 964.323 cents 29: 2 110/63 964.896 cents 29: 2 7/4 968.826 cents harmonic seventh 29: 1 225/128 976.537 cents augmented sixth 29: 2 640/363 981.723 cents 29: 2 432/245 981.899 cents 29: 2 99/56 986.402 cents 29: 2 16/9 996.090 cents Pythagorean minor seventh 29: 2 343/192 1004.523 cents 30: 1 81/49 870.168 cents two (septimal major third, BP third) 30: 4 56/33 915.553 cents 30: 2 77/45 929.920 cents 30: 4 12/7 933.129 cents septimal major sixth 30: 2 55/32 937.632 cents 30: 2 110/63 964.896 cents 30: 2 7/4 968.826 cents harmonic seventh 30: 2 44/25 978.691 cents undecimal grave minor seventh 30: 4 16/9 996.090 cents Pythagorean minor seventh 30: 2 960/539 999.299 cents 30: 2 216/121 1003.229 cents 30: 2 315/176 1007.732 cents 30: 2 88/49 1013.666 cents undecimal minor seventh 30: 2 9/5 1017.596 cents just minor seventh, BP seventh 30: 2 231/128 1022.099 cents 30: 2 49/27 1031.787 cents 31: 2 12/7 933.129 cents septimal major sixth 31: 2 96/55 964.323 cents 31: 2 110/63 964.896 cents 31: 6 7/4 968.826 cents harmonic seventh 31: 2 99/56 986.402 cents 31: 4 16/9 996.090 cents Pythagorean minor seventh 31: 2 88/49 1013.666 cents undecimal minor seventh 31: 2 9/5 1017.596 cents just minor seventh, BP seventh 31: 6 20/11 1034.996 cents large minor seventh 31: 1 441/242 1038.926 cents 31: 2 64/35 1044.860 cents septimal neutral seventh 31: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 31: 2 147/80 1053.293 cents 32: 2 99/56 986.402 cents 32: 3 16/9 996.090 cents Pythagorean minor seventh 32: 2 98/55 1000.020 cents quasi-equal minor seventh 32: 2 25/14 1003.802 cents middle minor seventh 32: 2 88/49 1013.666 cents undecimal minor seventh 32: 4 9/5 1017.596 cents just minor seventh, BP seventh 32: 2 49/27 1031.787 cents 32: 2 20/11 1034.996 cents large minor seventh 32: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 32: 2 90/49 1052.572 cents 32: 2 224/121 1066.190 cents 32: 2 245/132 1070.693 cents 32: 2 297/160 1070.869 cents 32: 2 352/189 1076.627 cents 32: 2 28/15 1080.557 cents grave major seventh 32: 2 144/77 1083.766 cents 33: 2 9/5 1017.596 cents just minor seventh, BP seventh 33: 4 20/11 1034.996 cents large minor seventh 33: 2 64/35 1044.860 cents septimal neutral seventh 33: 6 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 33: 2 81/44 1056.502 cents 2nd undecimal neutral seventh 33: 2 50/27 1066.762 cents grave major seventh 33: 2 28/15 1080.557 cents grave major seventh 33: 2 144/77 1083.766 cents 33: 2 539/288 1085.060 cents 33: 4 15/8 1088.269 cents classic major seventh 33: 1 2048/1089 1093.454 cents 33: 4 66/35 1098.133 cents 33: 2 256/135 1107.821 cents octave - major chroma 33: 2 21/11 1119.463 cents undecimal major seventh 34: 2 90/49 1052.572 cents 34: 2 224/121 1066.190 cents 34: 4 28/15 1080.557 cents grave major seventh 34: 2 144/77 1083.766 cents 34: 4 15/8 1088.269 cents classic major seventh 34: 2 66/35 1098.133 cents 34: 3 121/64 1102.636 cents two (undecimal semi-augmented fourth) 34: 2 1024/539 1111.030 cents 34: 2 154/81 1112.324 cents 34: 4 40/21 1115.533 cents acute major seventh 34: 2 21/11 1119.463 cents undecimal major seventh 34: 2 245/128 1123.966 cents 34: 2 48/25 1129.328 cents classic diminished octave 34: 2 77/40 1133.830 cents 34: 2 64/33 1146.727 cents 33rd subharmonic 35: 2 144/77 1083.766 cents 35: 4 40/21 1115.533 cents acute major seventh 35: 4 21/11 1119.463 cents undecimal major seventh 35: 1 4608/2401 1128.606 cents 35: 2 48/25 1129.328 cents classic diminished octave 35: 4 121/63 1129.900 cents 35: 2 77/40 1133.830 cents 35: 2 27/14 1137.039 cents septimal major seventh 35: 2 495/256 1141.542 cents 35: 4 64/33 1146.727 cents 33rd subharmonic 35: 4 35/18 1151.230 cents septimal semi-diminished octave 35: 2 343/176 1155.160 cents 35: 2 88/45 1161.094 cents 35: 2 108/55 1168.233 cents 36: 2 27/14 1137.039 cents septimal major seventh 36: 2 64/33 1146.727 cents 33rd subharmonic 36: 2 35/18 1151.230 cents septimal semi-diminished octave 36: 4 88/45 1161.094 cents 36: 4 96/49 1164.303 cents 36: 1 49/25 1165.024 cents BP eighth 36: 2 108/55 1168.233 cents 36: 6 55/28 1168.806 cents 36: 4 63/32 1172.736 cents octave - septimal comma 36: 2 160/81 1178.494 cents octave - syntonic comma 36: 4 196/99 1182.424 cents 36: 2 99/50 1182.601 cents 36: 2 240/121 1185.633 cents Highest number of different intervals for one interval class: 19 Average number of different intervals per interval class: 16.05556 = 289/18
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 0.0 : 35.7 53.3 80.5 111.7 150.6 165.0 182.4 203.9 231.2 266.9 315.6 347.4 386.3 417.5 435.1 498.0 551.3 582.5 617.5 648.7 702.0 764.9 782.5 813.7 852.6 884.4 933.1 968.8 996.1 1017.6 1035.0 1049.4 1088.3 1119.5 1146.7 1164.3 1200.0 35.7 : 17.6 44.8 76.0 114.9 129.3 146.7 168.2 195.5 231.2 279.9 311.7 350.6 381.8 399.4 462.3 515.6 546.8 581.8 613.0 666.3 729.2 746.8 778.0 816.9 848.7 897.4 933.1 960.4 981.9 999.3 1013.7 1052.6 1083.8 1111.0 1128.6 1164.3 1200.0 53.3 : 27.3 58.5 97.4 111.7 129.1 150.6 177.9 213.6 262.4 294.1 333.0 364.2 381.8 444.8 498.0 529.2 564.2 595.4 648.7 711.6 729.2 760.4 799.3 831.1 879.9 915.6 942.8 964.3 981.7 996.1 1035.0 1066.2 1093.5 1111.0 1146.7 1182.4 1200.0 80.5 : 31.2 70.1 84.5 101.9 123.4 150.6 186.3 235.1 266.9 305.8 337.0 354.5 417.5 470.8 502.0 537.0 568.1 621.4 684.4 702.0 733.1 772.1 803.8 852.6 888.3 915.6 937.1 954.5 968.8 1007.7 1038.9 1066.2 1083.8 1119.5 1155.2 1172.7 1200.0 111.7 : 38.9 53.3 70.7 92.2 119.4 155.1 203.9 235.7 274.6 305.8 323.4 386.3 439.6 470.8 505.8 537.0 590.2 653.2 670.8 702.0 740.9 772.6 821.4 857.1 884.4 905.9 923.3 937.6 976.5 1007.7 1035.0 1052.6 1088.3 1124.0 1141.5 1168.8 1200.0 150.6 : 14.4 31.8 53.3 80.5 116.2 165.0 196.8 235.7 266.9 284.4 347.4 400.7 431.9 466.9 498.0 551.3 614.3 631.9 663.0 702.0 733.7 782.5 818.2 845.5 867.0 884.4 898.7 937.6 968.8 996.1 1013.7 1049.4 1085.1 1102.6 1129.9 1161.1 1200.0 165.0 : 17.4 38.9 66.2 101.9 150.6 182.4 221.3 252.5 270.1 333.0 386.3 417.5 452.5 483.7 537.0 599.9 617.5 648.7 687.6 719.4 768.1 803.8 831.1 852.6 870.0 884.4 923.3 954.5 981.7 999.3 1035.0 1070.7 1088.3 1115.5 1146.7 1185.6 1200.0 182.4 : 21.5 48.8 84.5 133.2 165.0 203.9 235.1 252.7 315.6 368.9 400.1 435.1 466.3 519.6 582.5 600.1 631.3 670.2 702.0 750.7 786.4 813.7 835.2 852.6 867.0 905.9 937.1 964.3 981.9 1017.6 1053.3 1070.9 1098.1 1129.3 1168.2 1182.6 1200.0 203.9 : 27.3 63.0 111.7 143.5 182.4 213.6 231.2 294.1 347.4 378.6 413.6 444.8 498.0 561.0 578.6 609.8 648.7 680.4 729.2 764.9 792.2 813.7 831.1 845.5 884.4 915.6 942.8 960.4 996.1 1031.8 1049.4 1076.6 1107.8 1146.7 1161.1 1178.5 1200.0 231.2 : 35.7 84.5 116.2 155.1 186.3 203.9 266.9 320.1 351.3 386.3 417.5 470.8 533.7 551.3 582.5 621.4 653.2 702.0 737.7 764.9 786.4 803.8 818.2 857.1 888.3 915.6 933.1 968.8 1004.5 1022.1 1049.4 1080.6 1119.5 1133.8 1151.2 1172.7 1200.0 266.9 : 48.8 80.5 119.4 150.6 168.2 231.2 284.4 315.6 350.6 381.8 435.1 498.0 515.6 546.8 585.7 617.5 666.3 702.0 729.2 750.7 768.1 782.5 821.4 852.6 879.9 897.4 933.1 968.8 986.4 1013.7 1044.9 1083.8 1098.1 1115.5 1137.0 1164.3 1200.0 315.6 : 31.8 70.7 101.9 119.4 182.4 235.7 266.9 301.8 333.0 386.3 449.3 466.9 498.0 537.0 568.7 617.5 653.2 680.4 702.0 719.4 733.7 772.6 803.8 831.1 848.7 884.4 920.1 937.6 964.9 996.1 1035.0 1049.4 1066.8 1088.3 1115.5 1151.2 1200.0 347.4 : 38.9 70.1 87.7 150.6 203.9 235.1 270.1 301.3 354.5 417.5 435.1 466.3 505.2 537.0 585.7 621.4 648.7 670.2 687.6 702.0 740.9 772.1 799.3 816.9 852.6 888.3 905.9 933.1 964.3 1003.2 1017.6 1035.0 1056.5 1083.8 1119.5 1168.2 1200.0 386.3 : 31.2 48.8 111.7 165.0 196.2 231.2 262.4 315.6 378.6 396.2 427.4 466.3 498.0 546.8 582.5 609.8 631.3 648.7 663.0 702.0 733.1 760.4 778.0 813.7 849.4 867.0 894.2 925.4 964.3 978.7 996.1 1017.6 1044.9 1080.6 1129.3 1161.1 1200.0 417.5 : 17.6 80.5 133.8 165.0 200.0 231.2 284.4 347.4 365.0 396.2 435.1 466.9 515.6 551.3 578.6 600.1 617.5 631.9 670.8 702.0 729.2 746.8 782.5 818.2 835.8 863.0 894.2 933.1 947.5 964.9 986.4 1013.7 1049.4 1098.1 1129.9 1168.8 1200.0 435.1 : 63.0 116.2 147.4 182.4 213.6 266.9 329.8 347.4 378.6 417.5 449.3 498.0 533.7 561.0 582.5 599.9 614.3 653.2 684.4 711.6 729.2 764.9 800.6 818.2 845.5 876.6 915.6 929.9 947.3 968.8 996.1 1031.8 1080.6 1112.3 1151.2 1182.4 1200.0 498.0 : 53.3 84.5 119.4 150.6 203.9 266.9 284.4 315.6 354.5 386.3 435.1 470.8 498.0 519.6 537.0 551.3 590.2 621.4 648.7 666.3 702.0 737.7 755.2 782.5 813.7 852.6 867.0 884.4 905.9 933.1 968.8 1017.6 1049.4 1088.3 1119.5 1137.0 1200.0 551.3 : 31.2 66.2 97.4 150.6 213.6 231.2 262.4 301.3 333.0 381.8 417.5 444.8 466.3 483.7 498.0 537.0 568.1 595.4 613.0 648.7 684.4 702.0 729.2 760.4 799.3 813.7 831.1 852.6 879.9 915.6 964.3 996.1 1035.0 1066.2 1083.8 1146.7 1200.0 582.5 : 35.0 66.2 119.4 182.4 200.0 231.2 270.1 301.8 350.6 386.3 413.6 435.1 452.5 466.9 505.8 537.0 564.2 581.8 617.5 653.2 670.8 698.0 729.2 768.1 782.5 799.9 821.4 848.7 884.4 933.1 964.9 1003.8 1035.0 1052.6 1115.5 1168.8 1200.0 617.5 : 31.2 84.5 147.4 165.0 196.2 235.1 266.9 315.6 351.3 378.6 400.1 417.5 431.9 470.8 502.0 529.2 546.8 582.5 618.2 635.8 663.0 694.2 733.1 747.5 764.9 786.4 813.7 849.4 898.2 929.9 968.8 1000.0 1017.6 1080.6 1133.8 1165.0 1200.0 648.7 : 53.3 116.2 133.8 165.0 203.9 235.7 284.4 320.1 347.4 368.9 386.3 400.7 439.6 470.8 498.0 515.6 551.3 587.0 604.6 631.9 663.0 702.0 716.3 733.7 755.2 782.5 818.2 867.0 898.7 937.6 968.8 986.4 1049.4 1102.6 1133.8 1168.8 1200.0 702.0 : 63.0 80.5 111.7 150.6 182.4 231.2 266.9 294.1 315.6 333.0 347.4 386.3 417.5 444.8 462.3 498.0 533.7 551.3 578.6 609.8 648.7 663.0 680.4 702.0 729.2 764.9 813.7 845.5 884.4 915.6 933.1 996.1 1049.4 1080.6 1115.5 1146.7 1200.0 764.9 : 17.6 48.8 87.7 119.4 168.2 203.9 231.2 252.7 270.1 284.4 323.4 354.5 381.8 399.4 435.1 470.8 488.4 515.6 546.8 585.7 600.1 617.5 639.0 666.3 702.0 750.7 782.5 821.4 852.6 870.2 933.1 986.4 1017.6 1052.6 1083.8 1137.0 1200.0 782.5 : 31.2 70.1 101.9 150.6 186.3 213.6 235.1 252.5 266.9 305.8 337.0 364.2 381.8 417.5 453.2 470.8 498.0 529.2 568.1 582.5 599.9 621.4 648.7 684.4 733.1 764.9 803.8 835.0 852.6 915.6 968.8 1000.0 1035.0 1066.2 1119.5 1182.4 1200.0 813.7 : 38.9 70.7 119.4 155.1 182.4 203.9 221.3 235.7 274.6 305.8 333.0 350.6 386.3 422.0 439.6 466.9 498.0 537.0 551.3 568.7 590.2 617.5 653.2 702.0 733.7 772.6 803.8 821.4 884.4 937.6 968.8 1003.8 1035.0 1088.3 1151.2 1168.8 1200.0 852.6 : 31.8 80.5 116.2 143.5 165.0 182.4 196.8 235.7 266.9 294.1 311.7 347.4 383.1 400.7 427.9 459.1 498.0 512.4 529.8 551.3 578.6 614.3 663.0 694.8 733.7 764.9 782.5 845.5 898.7 929.9 964.9 996.1 1049.4 1112.3 1129.9 1161.1 1200.0 884.4 : 48.8 84.5 111.7 133.2 150.6 165.0 203.9 235.1 262.4 279.9 315.6 351.3 368.9 396.2 427.4 466.3 480.6 498.0 519.6 546.8 582.5 631.3 663.0 702.0 733.1 750.7 813.7 867.0 898.2 933.1 964.3 1017.6 1080.6 1098.1 1129.3 1168.2 1200.0 933.1 : 35.7 63.0 84.5 101.9 116.2 155.1 186.3 213.6 231.2 266.9 302.6 320.1 347.4 378.6 417.5 431.9 449.3 470.8 498.0 533.7 582.5 614.3 653.2 684.4 702.0 764.9 818.2 849.4 884.4 915.6 968.8 1031.8 1049.4 1080.6 1119.5 1151.2 1200.0 968.8 : 27.3 48.8 66.2 80.5 119.4 150.6 177.9 195.5 231.2 266.9 284.4 311.7 342.9 381.8 396.2 413.6 435.1 462.3 498.0 546.8 578.6 617.5 648.7 666.3 729.2 782.5 813.7 848.7 879.9 933.1 996.1 1013.7 1044.9 1083.8 1115.5 1164.3 1200.0 996.1 : 21.5 38.9 53.3 92.2 123.4 150.6 168.2 203.9 239.6 257.2 284.4 315.6 354.5 368.9 386.3 407.8 435.1 470.8 519.6 551.3 590.2 621.4 639.0 702.0 755.2 786.4 821.4 852.6 905.9 968.8 986.4 1017.6 1056.5 1088.3 1137.0 1172.7 1200.0 1017.6: 17.4 31.8 70.7 101.9 129.1 146.7 182.4 218.1 235.7 262.9 294.1 333.0 347.4 364.8 386.3 413.6 449.3 498.0 529.8 568.7 599.9 617.5 680.4 733.7 764.9 799.9 831.1 884.4 947.3 964.9 996.1 1035.0 1066.8 1115.5 1151.2 1178.5 1200.0 1035.0: 14.4 53.3 84.5 111.7 129.3 165.0 200.7 218.3 245.5 276.7 315.6 330.0 347.4 368.9 396.2 431.9 480.6 512.4 551.3 582.5 600.1 663.0 716.3 747.5 782.5 813.7 867.0 929.9 947.5 978.7 1017.6 1049.4 1098.1 1133.8 1161.1 1182.6 1200.0 1049.4: 38.9 70.1 97.4 114.9 150.6 186.3 203.9 231.2 262.4 301.3 315.6 333.0 354.5 381.8 417.5 466.3 498.0 537.0 568.1 585.7 648.7 702.0 733.1 768.1 799.3 852.6 915.6 933.1 964.3 1003.2 1035.0 1083.8 1119.5 1146.7 1168.2 1185.6 1200.0 1088.3: 31.2 58.5 76.0 111.7 147.4 165.0 192.3 223.5 262.4 276.7 294.1 315.6 342.9 378.6 427.4 459.1 498.0 529.2 546.8 609.8 663.0 694.2 729.2 760.4 813.7 876.6 894.2 925.4 964.3 996.1 1044.9 1080.6 1107.8 1129.3 1146.7 1161.1 1200.0 1119.5: 27.3 44.8 80.5 116.2 133.8 161.1 192.3 231.2 245.5 262.9 284.4 311.7 347.4 396.2 427.9 466.9 498.0 515.6 578.6 631.9 663.0 698.0 729.2 782.5 845.5 863.0 894.2 933.1 964.9 1013.7 1049.4 1076.6 1098.1 1115.5 1129.9 1168.8 1200.0 1146.7: 17.6 53.3 89.0 106.5 133.8 165.0 203.9 218.3 235.7 257.2 284.4 320.1 368.9 400.7 439.6 470.8 488.4 551.3 604.6 635.8 670.8 702.0 755.2 818.2 835.8 867.0 905.9 937.6 986.4 1022.1 1049.4 1070.9 1088.3 1102.6 1141.5 1172.7 1200.0 1164.3: 35.7 71.4 89.0 116.2 147.4 186.3 200.7 218.1 239.6 266.9 302.6 351.3 383.1 422.0 453.2 470.8 533.7 587.0 618.2 653.2 684.4 737.7 800.6 818.2 849.4 888.3 920.1 968.8 1004.5 1031.8 1053.3 1070.7 1085.1 1124.0 1155.2 1182.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.3672 .. 62.9609 cents 1120/1089, 48.5937 cents 121/120, 14.3672 cents 2: 31.7667 .. 116.2338 cents 21/20, 84.4672 cents 55/56,-31.1943 cents 3: 53.2729 .. 147.4281 cents 1568/1485, 94.1552 cents 27/28,-62.9609 cents 4: 80.5370 .. 182.4037 cents 35/33, 101.8667 cents 330/343,-66.8911 cents 5: 116.2338 .. 213.5980 cents 128/121, 97.3641 cents 77/80,-66.1699 cents 6: 146.7069 .. 266.8709 cents 343/320, 120.1640 cents 330/343,-66.8911 cents 7: 168.2132 .. 329.8318 cents 2401/2187, 161.6186 cents 324/343,-98.6577 cents 8: 195.4773 .. 347.4079 cents 3773/3456, 151.9307 cents 15552/16807,-134.3545 cents 9: 231.1741 .. 378.6022 cents 49/45, 147.4281 cents 72/77,-116.2338 cents 10: 257.1829 .. 417.5080 cents 3584/3267, 160.3250 cents 13365/14336,-121.4192 cents 11: 284.4470 .. 449.2746 cents 980/891, 164.8276 cents 363/392,-133.0609 cents 12: 311.7111 .. 498.0450 cents 49/44, 186.3339 cents 1584/1715,-137.5635 cents 13: 342.9054 .. 533.7418 cents 1715/1536, 190.8364 cents 32/35,-155.1396 cents 14: 364.8074 .. 561.0059 cents 28/25, 196.1985 cents 400/441,-168.9344 cents 15: 386.3137 .. 585.7212 cents 432/385, 199.4074 cents 405/448,-174.6922 cents 16: 407.8200 .. 621.4180 cents 112/99, 213.5980 cents 231/256,-177.9012 cents 17: 435.0841 .. 666.2582 cents 8/7, 231.1741 cents 44/49,-186.3339 cents 18: 462.3482 .. 701.9550 cents 147/128, 239.6068 cents 8/9,-203.9100 cents 19: 498.0450 .. 737.6518 cents 147/128, 239.6068 cents 8/9,-203.9100 cents 20: 533.7418 .. 764.9159 cents 8/7, 231.1741 cents 8/9,-203.9100 cents 21: 578.5820 .. 792.1800 cents 112/99, 213.5980 cents 44/49,-186.3339 cents 22: 614.2788 .. 813.6863 cents 432/385, 199.4074 cents 231/256,-177.9012 cents 23: 638.9941 .. 835.1926 cents 28/25, 196.1985 cents 405/448,-174.6922 cents 24: 666.2582 .. 857.0946 cents 1715/1536, 190.8364 cents 400/441,-168.9344 cents 25: 701.9550 .. 888.2889 cents 49/44, 186.3339 cents 32/35,-155.1396 cents 26: 750.7254 .. 915.5530 cents 980/891, 164.8276 cents 1584/1715,-137.5635 cents 27: 782.4920 .. 942.8171 cents 3584/3267, 160.3250 cents 363/392,-133.0609 cents 28: 821.3978 .. 968.8259 cents 49/45, 147.4281 cents 13365/14336,-121.4192 cents 29: 852.5921 .. 1004.5227 cents 3773/3456, 151.9307 cents 72/77,-116.2338 cents 30: 870.1682 .. 1031.7868 cents 2401/2187, 161.6186 cents 15552/16807,-134.3545 cents 31: 933.1291 .. 1053.2931 cents 343/320, 120.1640 cents 324/343,-98.6577 cents 32: 986.4020 .. 1083.7662 cents 128/121, 97.3641 cents 330/343,-66.8911 cents 33: 1017.5963 .. 1119.4630 cents 35/33, 101.8667 cents 77/80,-66.1699 cents 34: 1052.5719 .. 1146.7271 cents 1568/1485, 94.1552 cents 330/343,-66.8911 cents 35: 1083.7662 .. 1168.2333 cents 21/20, 84.4672 cents 27/28,-62.9609 cents 36: 1137.0391 .. 1185.6328 cents 1120/1089, 48.5937 cents 55/56,-31.1943 cents
SHOW DATA
Number of notes : 37 -- Interval properties -- Smallest interval : 121/120, 14.3672 cents, class 1 Average step (divided formal octave): 32.4324 cents Largest one step interval : 28/27, 62.9609 cents Average / Smallest step : 2.257399 Largest / Average step : 1.941295 Largest / Smallest step : 4.382276 Median interval of one step : 56/55, 31.1943 cents, amount: 6 Most common interval of one step : 56/55, 31.1943 cents, amount: 6 Least squares average step : 32.94604 cents, oct.: 1219.00360 cents Scale is not proper Step pattern alph. order: ABCDEFGHCAIJEDBKLDMDLKBDEJIACHGFEDCBA Step pattern size order : ICEFJABDEIKGJFCMLFHFLMCFJGKIEDBAJFECI Scale is not a Constant Structure Scale diversity : 1.480696 Lumma stability : 0.023945 Lumma impropriety factor : 0.947056 Number of different interval sizes : 304 = 8.44444 / class Number of one step interval sizes : 13 Highest interval variety : 19 Mean interval variety : 16.05556 = 289/18 Median interval variety : 13 Lowest interval variety : 13 Smallest interval difference : 9801/9800, 0.1766 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 22 Most common triad is 0.0 498.045 701.955 cents, amount: 13 Number of recognisable fifths : 35, average 702.6336 cents Number of appreciable fifths : 29, average 701.5741 cents Scale contains a complete diamond : 1 3 5 7 9 11 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 : 37 = 100.0000% Scale is differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 18-19 -- Rational properties -- Prime limit : 11 Odd number limit : 2401 (O: 2401 U: 2401) Highest odd numerator or denominator: 49 Scale harmonicity : 0.008931 Average absolute harmonicity : 0.098121 Specific harmonicity : 0.072562 Fundamental : 1/776160, -19.5660 octaves, 0.0003 Hz. Guide tone : 1552320, 20.5660 octaves, 406126597.528 Hz. Exponens Consonantiae : 1.204849E+12, 40.13199 octaves Euler's gradus suavitatis : 72 Sum of Mann's harmonic distance : 510.0, average 13.78378 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 36.37413, average 0.98308 Sum of Tenney's harmonic distance : 73.12972, average 1.97648 Vogel's harmonic complexity : 41.51351 Wille's k value : 400207 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 12 Triangular lattice diameter : 4 Lattice compactness : 2628.76895, average 3.73936 Lattice compactness (without 2's) : 1490.50602, average 2.12021 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.51351 71 1 3: -2 .. 2 0.00000 32 4 5: -1 .. 1 0.00000 12 8 7: -2 .. 2 0.00000 16 10 11: -1 .. 1 0.00000 14 14 Average exponent except 2's : 0 / 37 = 0.00000 Average absolute exponent except 2's: 74 / 37 = 2.00000
FIT/MODE
37: 1 1 0 1 2 0 1 0 1 1 2 1 1 1 0 2 2 1 1 1 2 2 0 1 1 1 2 1 1 0 1 0 2 1 0 1 1 N I SD: 9.1588 c. M:-15.6722 c. 38: 1 1 1 1 1 0 1 0 1 1 2 1 1 1 1 2 1 1 2 1 1 2 1 1 1 1 2 1 1 0 1 0 1 1 1 1 1 N I SD: 9.8868 c. M: 14.5845 c. 39: 1 1 1 1 1 0 1 1 1 1 1 1 2 1 0 2 2 1 1 1 2 2 0 1 2 1 1 1 1 1 1 0 1 1 1 1 1 N I SD: 9.0805 c. M:-14.9798 c. 41: 1 1 1 1 1 1 0 1 1 1 2 1 1 1 1 2 2 1 1 1 2 2 1 1 1 1 2 1 1 1 0 1 1 1 1 1 1 N I SD: 5.4243 c. M: 10.6055 c. 46: 1 1 1 1 2 0 1 1 1 1 2 1 2 1 1 2 2 1 2 1 2 2 1 1 2 1 2 1 1 1 1 0 2 1 1 1 1 N I SD: 5.6680 c. M:-9.6099 c. 54: 2 0 2 1 2 0 1 1 1 2 2 2 1 2 1 2 3 1 2 1 3 2 1 2 1 2 2 2 1 1 1 0 2 1 2 0 2 N I SD: 6.7734 c. M: 9.4487 c. 55: 2 0 2 1 2 1 0 1 2 1 2 2 2 1 1 3 2 2 1 2 2 3 1 1 2 2 2 1 2 1 0 1 2 1 2 0 2 N I SD: 6.4758 c. M: 10.1867 c. 58: 2 1 1 1 2 1 1 1 1 2 2 2 2 1 1 3 3 1 2 1 3 3 1 1 2 2 2 2 1 1 1 1 2 1 1 1 2 N I SD: 4.8246 c. M: 8.7960 c. 63: 2 1 1 2 2 1 1 1 1 2 3 1 2 2 1 3 3 2 1 2 3 3 1 2 2 1 3 2 1 1 1 1 2 2 1 1 2 N I SD: 4.6149 c. M: 8.1682 c. 66: 2 1 1 2 2 1 1 1 2 2 2 2 2 2 1 3 3 2 2 2 3 3 1 2 2 2 2 2 2 1 1 1 2 2 1 1 2 N I SD: 4.2262 c. M: 7.8098 c. 72: 2 1 2 2 2 1 1 1 2 2 3 2 2 2 1 4 3 2 2 2 3 4 1 2 2 2 3 2 2 1 1 1 2 2 2 1 2 N I SD: 2.3152 c. M: 4.9354 c. 94: 3 1 2 3 3 1 1 2 2 3 4 2 3 3 1 5 4 3 2 3 4 5 1 3 3 2 4 3 2 2 1 1 3 3 2 1 3 N I SD: 2.7096 c. M:-4.7218 c. 111: 3 2 2 3 4 1 2 2 2 4 4 3 4 3 1 6 5 3 3 3 5 6 1 3 4 3 4 4 2 2 2 1 4 3 2 2 3 N I SD: 2.6567 c. M: 4.8614 c. 114: 3 2 3 3 3 2 1 2 3 3 5 3 4 3 1 6 5 3 4 3 5 6 1 3 4 3 5 3 3 2 1 2 3 3 3 2 3 N I SD: 3.1622 c. M:-4.1179 c. 117: 3 2 3 3 4 1 2 2 3 3 5 3 4 3 1 7 5 3 3 3 5 7 1 3 4 3 5 3 3 2 2 1 4 3 3 2 3 N I SD: 2.8404 c. M:-4.9276 c. 118: 4 1 3 3 4 1 2 2 3 3 5 3 4 3 2 6 5 3 4 3 5 6 2 3 4 3 5 3 3 2 2 1 4 3 3 1 4 N I SD: 2.0186 c. M:-4.9812 c. 130: 4 2 3 3 4 2 2 2 3 4 5 4 4 3 2 7 6 3 4 3 6 7 2 3 4 4 5 4 3 2 2 2 4 3 3 2 4 N I SD: 1.7969 c. M: 3.3613 c. 152: 5 2 3 4 5 2 2 3 3 5 6 4 5 4 2 8 7 4 4 4 7 8 2 4 5 4 6 5 3 3 2 2 5 4 3 2 5 N I SD: 1.4717 c. M:-3.7769 c. 158: 5 2 4 4 5 2 2 3 3 5 7 4 5 4 2 9 7 4 4 4 7 9 2 4 5 4 7 5 3 3 2 2 5 4 4 2 5 N I SD: 2.1396 c. M:-3.3461 c. 159: 5 2 4 4 5 2 2 3 4 4 7 4 5 4 3 8 7 4 5 4 7 8 3 4 5 4 7 4 4 3 2 2 5 4 4 2 5 N I SD: 1.6342 c. M:-2.7882 c. 176: 5 3 4 4 6 2 3 3 4 5 7 5 6 4 3 9 8 4 6 4 8 9 3 4 6 5 7 5 4 3 3 2 6 4 4 3 5 N I SD: 1.5282 c. M:-2.9667 c. 180: 5 3 4 5 6 2 2 4 4 5 7 5 6 5 2 10 8 4 6 4 8 10 2 5 6 5 7 5 4 4 2 2 6 5 4 3 5 N I SD: 1.8892 c. M:-2.7567 c. 181: 5 3 4 5 6 2 2 4 4 5 8 4 6 5 3 9 8 5 5 5 8 9 3 5 6 4 8 5 4 3 3 2 6 5 4 3 5 N SD: 1.7293 c. M: 3.3982 c. 183: 5 3 4 5 6 2 3 3 4 6 7 5 6 5 2 10 8 5 5 5 8 10 2 5 6 5 7 6 4 3 3 2 6 5 4 3 5 N I SD: 1.3750 c. M:-2.9099 c. 190: 6 2 5 5 6 2 3 3 5 5 8 5 6 5 3 10 8 5 6 5 8 10 3 5 6 5 8 5 5 3 3 2 6 5 5 2 6 N I SD: 1.4940 c. M: 2.7466 c. 193: 6 3 4 5 6 3 2 4 4 6 8 5 6 5 3 10 9 5 5 5 9 10 3 5 6 5 8 6 4 4 2 3 6 5 4 3 6 N I SD: 1.4765 c. M: 2.8714 c. 196: 6 3 4 5 7 2 3 3 5 6 8 5 6 5 3 10 9 5 6 5 9 10 3 5 6 5 8 6 5 3 3 2 7 5 4 3 6 N I SD: 1.5499 c. M: 2.7261 c. 198: 6 3 4 5 7 2 3 4 4 6 8 5 7 5 3 10 9 5 6 5 9 10 3 5 7 5 8 6 4 4 3 2 7 5 4 3 6 N I SD: 1.2899 c. M:-2.6404 c. 204: 6 3 5 5 7 2 3 4 4 6 9 5 7 5 3 11 9 5 6 5 9 11 3 5 7 5 9 6 4 4 3 2 7 5 5 3 6 N I SD: 1.3762 c. M:-2.3041 c. 224: 7 3 5 6 7 3 3 4 5 7 9 6 7 6 3 12 10 6 6 6 10 12 3 6 7 6 9 7 5 4 3 3 7 6 5 3 7 N I SD: 0.8133 c. M:-1.8032 c. 270: 8 4 6 7 9 3 4 5 6 8 11 7 9 7 4 14 12 7 8 7 12 14 4 7 9 7 11 8 6 5 4 3 9 7 6 4 8 N I SD: 0.3872 c. M: 0.7413 c. 342: 10 5 8 9 11 4 5 6 8 10 14 9 11 9 5 18 15 9 10 9 15 18 5 9 11 9 14 10 8 6 5 4 11 9 8 5 10 N I SD: 0.3231 c. M: 0.6414 c. 494: 15 7 11 13 16 6 7 9 11 15 20 13 16 13 7 26 22 13 14 13 22 26 7 13 16 13 20 15 11 9 7 6 16 13 11 7 15 N I SD: 0.2881 c. M:-0.7404 c. 566: 17 8 13 15 18 7 8 10 13 17 23 15 18 15 8 30 25 15 16 15 25 30 8 15 18 15 23 17 13 10 8 7 18 15 13 8 17 N I SD: 0.3184 c. M:-0.6362 c. 612: 18 9 14 16 20 7 9 11 14 18 25 16 20 16 9 32 27 16 18 16 27 32 9 16 20 16 25 18 14 11 9 7 20 16 14 9 18 N I SD: 0.2222 c. M:-0.4027 c. 742: 22 11 17 19 24 9 11 13 17 22 30 20 24 19 11 39 33 19 22 19 33 39 11 19 24 20 30 22 17 13 11 9 24 19 17 11 22 N I SD: 0.2020 c. M: 0.3456 c. 836: 25 12 19 22 27 10 12 15 19 25 34 22 27 22 12 44 37 22 24 22 37 44 12 22 27 22 34 25 19 15 12 10 27 22 19 12 25 N I SD: 0.1460 c. M:-0.2629 c. 1106: 33 16 25 29 36 13 16 20 25 33 45 29 36 29 16 58 49 29 32 29 49 58 16 29 36 29 45 33 25 20 16 13 36 29 25 16 33 N I SD: 0.1252 c. M: 0.2477 c. 1236: 37 18 28 32 40 15 18 22 28 37 50 33 40 32 18 65 55 32 36 32 55 65 18 32 40 33 50 37 28 22 18 15 40 32 28 18 37 N I SD: 0.1106 c. M:-0.2255 c. 1506: 45 22 34 39 49 18 22 27 34 45 61 40 49 39 22 79 67 39 44 39 67 79 22 39 49 40 61 45 34 27 22 18 49 39 34 22 45 N I SD: 0.0879 c. M:-0.1775 c. 1578: 47 23 36 41 51 19 23 28 36 47 64 42 51 41 23 83 70 41 46 41 70 83 23 41 51 42 64 47 36 28 23 19 51 41 36 23 47 N I SD: 0.0628 c. M: 0.1206 c. 1848: 55 27 42 48 60 22 27 33 42 55 75 49 60 48 27 97 82 48 54 48 82 97 27 48 60 49 75 55 42 33 27 22 60 48 42 27 55 N I SD: 0.0342 c. M: 0.0692 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0000 cents 3 .. 6 match: 3 H SD: 0.0000 cents 4 .. 8 match: 4 H SD: 0.0000 cents 5 .. 10 match: 5 H SD: 0.0000 cents 6 .. 12 match: 6 H SD: 0.0000 cents 7 .. 14 match: 7 H SD: 2.3667 cents 8 .. 16 match: 8 H SD: 1.5080 cents 9 .. 18 match: 9 H SD: 1.9525 cents 10 .. 20 match: 10 H SD: 2.5380 cents 11 .. 22 match: 11 H SD: 2.8796 cents 12 .. 24 match: 12 H SD: 1.9951 cents 13 .. 26 match: 13 H SD: 4.4084 cents 14 .. 28 match: 14 H SD: 2.4470 cents 15 .. 30 match: 15 H SD: 2.5138 cents 16 .. 32 match: 16 H SD: 2.7486 cents 17 .. 34 match: 17 H SD: 3.5359 cents 18 .. 36 match: 18 H SD: 1.7074 cents 19 .. 38 match: 19 H SD: 3.2399 cents 20 .. 40 match: 20 H SD: 2.1355 cents 21 .. 42 match: 21 H SD: 2.5361 cents 22 .. 44 match: 22 H SD: 2.1204 cents 23 .. 46 match: 22 SD: 2.5943 cents 24 .. 48 match: 24 H SD: 1.5513 cents 25 .. 50 match: 24 S SD: 2.1934 cents 26 .. 52 match: 24 SD: 2.3594 cents 27 .. 54 match: 26 SD: 2.0318 cents 28 .. 56 match: 25 SD: 1.6507 cents 29 .. 58 match: 26 SD: 2.0045 cents 30 .. 60 match: 28 SD: 1.5033 cents 31 .. 62 match: 29 SD: 1.6058 cents 32 .. 64 match: 29 SD: 1.5202 cents 33 .. 66 match: 30 SD: 1.6769 cents 34 .. 68 match: 28 SD: 1.8720 cents 35 .. 70 match: 31 SD: 1.3513 cents 36 .. 72 match: 30 S SD: 1.4221 cents 37 .. 74 match: 30 SD: 1.6869 cents 38 .. 76 match: 29 SD: 1.7063 cents 39 .. 78 match: 31 SD: 1.6839 cents 40 .. 80 match: 31 SD: 1.1540 cents 41 .. 82 match: 31 SD: 1.3751 cents 42 .. 84 match: 32 SD: 1.1870 cents 43 .. 86 match: 33 SD: 1.3854 cents 44 .. 88 match: 34 SD: 1.1901 cents 45 .. 90 match: 34 SD: 1.0969 cents 46 .. 92 match: 32 SD: 1.2642 cents 47 .. 94 match: 33 SD: 1.2319 cents 48 .. 96 match: 34 SD: 1.0322 cents 49 .. 98 match: 35 SD: 1.0816 cents 50 .. 100 match: 33 SD: 1.1437 cents 51 .. 102 match: 34 SD: 1.2739 cents 52 .. 104 match: 33 SD: 1.2639 cents 53 .. 106 match: 36 SD: 1.2176 cents 54 .. 108 match: 35 SD: 1.0529 cents 55 .. 110 match: 35 SD: 0.9331 cents 56 .. 112 match: 36 SD: 0.9271 cents 57 .. 114 match: 35 SD: 1.0911 cents 58 .. 116 match: 36 SD: 1.0306 cents 59 .. 118 match: 36 SD: 0.9610 cents 60 .. 120 match: 37 SD: 0.9294 cents 61 .. 122 match: 35 SD: 0.9600 cents 62 .. 124 match: 36 SD: 0.9560 cents 63 .. 126 match: 36 SD: 0.8122 cents 64 .. 128 match: 36 SD: 0.8403 cents 65 .. 130 match: 36 SD: 0.8630 cents 66 .. 132 match: 36 SD: 0.8397 cents 67 .. 134 match: 36 SD: 0.9122 cents 68 .. 136 match: 36 SD: 0.9596 cents 69 .. 138 match: 37 SD: 0.9477 cents 70 .. 140 match: 37 SD: 0.8243 cents 72 .. 144 match: 35 SD: 0.6769 cents 73 .. 146 match: 35 SD: 0.8413 cents 74 .. 148 match: 35 SD: 0.8992 cents 75 .. 150 match: 35 SD: 0.8493 cents 76 .. 152 match: 35 SD: 0.8599 cents 77 .. 154 match: 36 SD: 0.6912 cents 78 .. 156 match: 36 SD: 0.7694 cents 79 .. 158 match: 36 SD: 0.7637 cents 80 .. 160 match: 37 SD: 0.6716 cents 83 .. 166 match: 36 SD: 0.7933 cents 84 .. 168 match: 36 SD: 0.6959 cents 85 .. 170 match: 36 SD: 0.6852 cents 88 .. 176 match: 37 SD: 0.5640 cents 90 .. 180 match: 37 SD: 0.5299 cents 94 .. 188 match: 36 SD: 0.6858 cents 95 .. 190 match: 37 SD: 0.6260 cents 96 .. 192 match: 37 SD: 0.5695 cents 99 .. 198 match: 37 SD: 0.5314 cents 108 .. 216 match: 37 SD: 0.5206 cents 119 .. 238 match: 37 SD: 0.4783 cents 120 .. 240 match: 37 SD: 0.4106 cents 140 .. 280 match: 37 SD: 0.4041 cents 143 .. 286 match: 37 SD: 0.4016 cents 144 .. 288 match: 37 SD: 0.3527 cents 150 .. 300 match: 37 SD: 0.3444 cents 161 .. 322 match: 37 SD: 0.3368 cents 162 .. 324 match: 37 SD: 0.3363 cents 168 .. 336 match: 37 SD: 0.2859 cents 189 .. 378 match: 37 SD: 0.2762 cents 192 .. 384 match: 37 SD: 0.2632 cents 198 .. 396 match: 37 SD: 0.2453 cents 210 .. 420 match: 37 SD: 0.2422 cents 224 .. 448 match: 37 SD: 0.2295 cents 231 .. 462 match: 37 SD: 0.2242 cents 240 .. 480 match: 37 SD: 0.2139 cents 252 .. 504 match: 37 SD: 0.1850 cents 280 .. 560 match: 37 SD: 0.1714 cents 288 .. 576 match: 37 SD: 0.1544 cents 330 .. 660 match: 37 SD: 0.1475 cents 360 .. 720 match: 37 SD: 0.1173 cents 420 .. 840 match: 37 SD: 0.1123 cents 440 .. 880 match: 37 SD: 0.0969 cents 480 .. 960 match: 37 SD: 0.0877 cents 539 .. 1078 match: 37 SD: 0.0869 cents