Scala analysis: mundeuc45
Euclidean reduced detempered Miracle[45] with Tenney tie-breaker
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 45/44 38.905773 1/5-tone 2: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 3: 28/27 62.960904 Archytas' 1/3-tone 4: 21/20 84.467193 minor semitone 5: 15/14 119.442808 major diatonic semitone 6: 12/11 150.637059 undecimal neutral second, 3/4-tone 7: 11/10 165.004228 Ptolemy's second, 4/5-tone 8: 10/9 182.403712 minor whole tone 9: 9/8 203.910002 major whole tone 10: 8/7 231.174094 septimal whole tone 11: 7/6 266.870906 septimal minor third 12: 32/27 294.134997 Pythagorean minor third 13: 6/5 315.641287 minor third 14: 11/9 347.407941 undecimal neutral third 15: 5/4 386.313714 major third 16: 14/11 417.507964 undecimal diminished fourth or major third 17: 9/7 435.084095 septimal major third, BP third 18: 21/16 470.780907 narrow fourth 19: 4/3 498.044999 perfect fourth 20: 15/11 536.950772 undecimal augmented fourth 21: 11/8 551.317942 undecimal semi-augmented fourth 22: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 23: 10/7 617.487807 Euler's tritone 24: 16/11 648.682058 undecimal semi-diminished fifth 25: 22/15 663.049228 undecimal diminished fifth 26: 3/2 701.955001 perfect fifth 27: 32/21 729.219093 wide fifth 28: 14/9 764.915905 septimal minor sixth 29: 11/7 782.492036 undecimal augmented fifth 30: 8/5 813.686286 minor sixth 31: 18/11 852.592059 undecimal neutral sixth 32: 5/3 884.358713 major sixth, BP sixth 33: 27/16 905.865003 Pythagorean major sixth 34: 12/7 933.129094 septimal major sixth 35: 7/4 968.825906 harmonic seventh 36: 16/9 996.089998 Pythagorean minor seventh 37: 9/5 1017.596288 just minor seventh, BP seventh 38: 20/11 1034.995772 large minor seventh 39: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 40: 28/15 1080.557192 grave major seventh 41: 21/11 1119.462965 undecimal major seventh 42: 27/14 1137.039096 septimal major seventh 43: 64/33 1146.727057 33rd subharmonic 44: 55/28 1168.805750 45: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 56/55 31.1943 undecimal diesis, konbini comma 1: 45/44 38.9058 1/5-tone 2: 121/120 14.3672 undecimal seconds comma, biyatisma 3: 896/891 9.6880 undecimal semicomma, pentacircle 4: 81/80 21.5063 syntonic comma, Didymus comma 5: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 6: 56/55 31.1943 undecimal diesis, konbini comma 7: 121/120 14.3672 undecimal seconds comma, biyatisma 8: 100/99 17.3995 Ptolemy's comma 9: 81/80 21.5063 syntonic comma, Didymus comma 10: 64/63 27.2641 septimal comma, Archytas' comma 11: 49/48 35.6968 slendro diesis, septimal 1/6-tone 12: 64/63 27.2641 septimal comma, Archytas' comma 13: 81/80 21.5063 syntonic comma, Didymus comma 14: 55/54 31.7667 telepathma 15: 45/44 38.9058 1/5-tone 16: 56/55 31.1943 undecimal diesis, konbini comma 17: 99/98 17.5761 small undecimal comma 18: 49/48 35.6968 slendro diesis, septimal 1/6-tone 19: 64/63 27.2641 septimal comma, Archytas' comma 20: 45/44 38.9058 1/5-tone 21: 121/120 14.3672 undecimal seconds comma, biyatisma 22: 56/55 31.1943 undecimal diesis, konbini comma 23: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 24: 56/55 31.1943 undecimal diesis, konbini comma 25: 121/120 14.3672 undecimal seconds comma, biyatisma 26: 45/44 38.9058 1/5-tone 27: 64/63 27.2641 septimal comma, Archytas' comma 28: 49/48 35.6968 slendro diesis, septimal 1/6-tone 29: 99/98 17.5761 small undecimal comma 30: 56/55 31.1943 undecimal diesis, konbini comma 31: 45/44 38.9058 1/5-tone 32: 55/54 31.7667 telepathma 33: 81/80 21.5063 syntonic comma, Didymus comma 34: 64/63 27.2641 septimal comma, Archytas' comma 35: 49/48 35.6968 slendro diesis, septimal 1/6-tone 36: 64/63 27.2641 septimal comma, Archytas' comma 37: 81/80 21.5063 syntonic comma, Didymus comma 38: 100/99 17.3995 Ptolemy's comma 39: 121/120 14.3672 undecimal seconds comma, biyatisma 40: 56/55 31.1943 undecimal diesis, konbini comma 41: 45/44 38.9058 1/5-tone 42: 99/98 17.5761 small undecimal comma 43: 896/891 9.6880 undecimal semicomma, pentacircle 44: 1815/1792 22.0787 45: 56/55 31.1943 undecimal diesis, konbini comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 896/891 9.688 cents undecimal semicomma, pentacircle 1: 5 121/120 14.367 cents undecimal seconds comma, biyatisma 1: 2 100/99 17.399 cents Ptolemy's comma 1: 3 99/98 17.576 cents small undecimal comma 1: 5 81/80 21.506 cents syntonic comma, Didymus comma 1: 1 1815/1792 22.079 cents 1: 6 64/63 27.264 cents septimal comma, Archytas' comma 1: 7 56/55 31.194 cents undecimal diesis, konbini comma 1: 2 55/54 31.767 cents telepathma 1: 2 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: 6 45/44 38.906 cents 1/5-tone 2: 1 1232/1215 24.055 cents sensmus 2: 1 64/63 27.264 cents septimal comma, Archytas' comma 2: 1 56/55 31.194 cents undecimal diesis, konbini comma 2: 3 55/54 31.767 cents telepathma 2: 2 45/44 38.906 cents 1/5-tone 2: 4 77/75 45.561 cents 2: 6 36/35 48.770 cents septimal diesis, 1/4-tone 2: 8 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 2: 2 405/392 56.482 cents greenwoodma 2: 6 28/27 62.961 cents Archytas' 1/3-tone 2: 5 80/77 66.170 cents 2: 4 126/121 70.100 cents 2: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 3: 1 77/75 45.561 cents 3: 1 605/588 49.343 cents 3: 2 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 3: 4 28/27 62.961 cents Archytas' 1/3-tone 3: 4 80/77 66.170 cents 3: 9 22/21 80.537 cents undecimal minor semitone 3: 10 21/20 84.467 cents minor semitone 3: 4 81/77 87.676 cents 3: 2 256/243 90.225 cents limma, Pythagorean minor second 3: 3 135/128 92.179 cents major chroma, major limma 3: 1 128/121 97.364 cents undecimal semitone 3: 4 35/33 101.867 cents 4: 4 22/21 80.537 cents undecimal minor semitone 4: 3 21/20 84.467 cents minor semitone 4: 1 825/784 88.249 cents 4: 1 1568/1485 94.155 cents 4: 2 128/121 97.364 cents undecimal semitone 4: 1 200/189 97.937 cents 4: 4 35/33 101.867 cents 4: 2 297/280 102.043 cents 4: 1 1089/1024 106.546 cents two (undecimal comma, al-Farabi's 1/4-tone) 4: 10 16/15 111.731 cents minor diatonic semitone 4: 4 77/72 116.234 cents undecimal secor 4: 8 15/14 119.443 cents major diatonic semitone 4: 4 189/176 123.373 cents 5: 5 16/15 111.731 cents minor diatonic semitone 5: 1 294/275 115.661 cents 5: 4 77/72 116.234 cents undecimal secor 5: 7 15/14 119.443 cents major diatonic semitone 5: 1 189/176 123.373 cents 5: 1 242/225 126.098 cents 5: 2 320/297 129.131 cents 5: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 5: 2 121/112 133.810 cents 5: 2 243/224 140.949 cents Archytas' 2/3-tone 5: 2 88/81 143.498 cents 2nd undecimal neutral second 5: 2 160/147 146.707 cents 5: 2 49/45 147.428 cents BP minor semitone 5: 8 12/11 150.637 cents undecimal neutral second, 3/4-tone 5: 4 35/32 155.140 cents septimal neutral second 6: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 6: 1 242/225 126.098 cents 6: 2 320/297 129.131 cents 6: 2 121/112 133.810 cents 6: 1 693/640 137.740 cents 6: 2 243/224 140.949 cents Archytas' 2/3-tone 6: 2 88/81 143.498 cents 2nd undecimal neutral second 6: 1 160/147 146.707 cents 6: 2 49/45 147.428 cents BP minor semitone 6: 6 12/11 150.637 cents undecimal neutral second, 3/4-tone 6: 1 675/616 158.349 cents 6: 8 11/10 165.004 cents Ptolemy's second, 4/5-tone 6: 2 54/49 168.213 cents Zalzal's mujannab 6: 2 567/512 176.646 cents 6: 2 256/231 177.901 cents 6: 6 10/9 182.404 cents minor whole tone 6: 2 49/44 186.334 cents undecimal minor whole tone 6: 2 135/121 189.543 cents 7: 2 88/81 143.498 cents 2nd undecimal neutral second 7: 1 49/45 147.428 cents BP minor semitone 7: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 7: 1 275/252 151.209 cents 7: 4 11/10 165.004 cents Ptolemy's second, 4/5-tone 7: 2 54/49 168.213 cents Zalzal's mujannab 7: 2 495/448 172.716 cents 7: 2 448/405 174.692 cents 7: 1 672/605 181.831 cents 7: 3 10/9 182.404 cents minor whole tone 7: 1 49/44 186.334 cents undecimal minor whole tone 7: 1 135/121 189.543 cents 7: 2 352/315 192.268 cents 7: 2 28/25 196.198 cents middle second 7: 2 55/49 199.980 cents quasi-equal major second 7: 11 9/8 203.910 cents major whole tone 7: 4 112/99 213.598 cents 7: 2 25/22 221.309 cents undecimal acute whole tone 8: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 8: 1 495/448 172.716 cents 8: 2 256/231 177.901 cents 8: 4 10/9 182.404 cents minor whole tone 8: 3 28/25 196.198 cents middle second 8: 2 121/108 196.771 cents 8: 5 9/8 203.910 cents major whole tone 8: 1 640/567 209.668 cents 8: 1 112/99 213.598 cents 8: 2 25/22 221.309 cents undecimal acute whole tone 8: 2 154/135 227.965 cents 8: 10 8/7 231.174 cents septimal whole tone 8: 4 63/55 235.104 cents 8: 2 55/48 235.677 cents undecimal semi-augmented whole tone 8: 2 147/128 239.607 cents 8: 2 405/352 242.816 cents 9: 1 352/315 192.268 cents 9: 2 55/49 199.980 cents quasi-equal major second 9: 3 9/8 203.910 cents major whole tone 9: 5 112/99 213.598 cents 9: 2 363/320 218.277 cents 9: 1 25/22 221.309 cents undecimal acute whole tone 9: 2 154/135 227.965 cents 9: 3 8/7 231.174 cents septimal whole tone 9: 1 63/55 235.104 cents 9: 2 55/48 235.677 cents undecimal semi-augmented whole tone 9: 2 121/105 245.541 cents 9: 2 140/121 252.504 cents 9: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 9: 2 297/256 257.183 cents 9: 1 512/441 258.438 cents 9: 2 64/55 262.368 cents 9: 8 7/6 266.871 cents septimal minor third 9: 4 90/77 270.080 cents 10: 3 154/135 227.965 cents 10: 3 8/7 231.174 cents septimal whole tone 10: 2 63/55 235.104 cents 10: 3 55/48 235.677 cents undecimal semi-augmented whole tone 10: 1 225/196 238.886 cents two (major diatonic semitone) 10: 2 1024/891 240.862 cents 10: 1 405/352 242.816 cents 10: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 10: 1 220/189 262.941 cents 10: 5 7/6 266.871 cents septimal minor third 10: 2 90/77 270.080 cents 10: 2 88/75 276.736 cents 10: 4 33/28 284.447 cents undecimal minor third 10: 4 189/160 288.377 cents 10: 4 32/27 294.135 cents Pythagorean minor third 10: 2 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 10: 2 25/21 301.847 cents BP second, quasi-equal minor third 10: 2 105/88 305.777 cents 11: 2 280/243 245.365 cents 11: 1 121/105 245.541 cents 11: 1 231/200 249.471 cents 5/4-tone 11: 1 1408/1215 255.229 cents 11: 2 297/256 257.183 cents 11: 3 64/55 262.368 cents 11: 1 220/189 262.941 cents 11: 2 7/6 266.871 cents septimal minor third 11: 3 90/77 270.080 cents 11: 4 33/28 284.447 cents undecimal minor third 11: 2 196/165 298.065 cents 11: 1 25/21 301.847 cents BP second, quasi-equal minor third 11: 3 105/88 305.777 cents 11: 2 176/147 311.711 cents 11: 8 6/5 315.641 cents minor third 11: 2 77/64 320.144 cents Keemun minor third 11: 2 135/112 323.353 cents septimal wide minor third 11: 1 98/81 329.832 cents 11: 4 40/33 333.041 cents 12: 1 220/189 262.941 cents 12: 3 7/6 266.871 cents septimal minor third 12: 1 88/75 276.736 cents 12: 5 33/28 284.447 cents undecimal minor third 12: 4 32/27 294.135 cents Pythagorean minor third 12: 1 196/165 298.065 cents 12: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 12: 1 105/88 305.777 cents 12: 2 6/5 315.641 cents minor third 12: 2 77/64 320.144 cents Keemun minor third 12: 2 135/112 323.353 cents septimal wide minor third 12: 3 40/33 333.041 cents 12: 1 147/121 336.971 cents 12: 2 128/105 342.905 cents septimal neutral third 12: 6 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: 6 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 13: 1 33/28 284.447 cents undecimal minor third 13: 1 189/160 288.377 cents 13: 2 32/27 294.135 cents Pythagorean minor third 13: 2 25/21 301.847 cents BP second, quasi-equal minor third 13: 1 484/405 308.502 cents 13: 4 6/5 315.641 cents minor third 13: 1 605/504 316.214 cents 13: 2 77/64 320.144 cents Keemun minor third 13: 1 1792/1485 325.329 cents 13: 3 40/33 333.041 cents 13: 2 11/9 347.408 cents undecimal neutral third 13: 1 60/49 350.617 cents smaller approximation to neutral third 13: 2 49/40 351.338 cents larger approximation to neutral third 13: 3 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 13: 1 121/98 364.984 cents 13: 4 99/80 368.914 cents 13: 2 150/121 371.947 cents 13: 4 56/45 378.602 cents septimal narrow major third 13: 4 96/77 381.811 cents 13: 4 5/4 386.314 cents major third 14: 1 176/147 311.711 cents 14: 1 6/5 315.641 cents minor third 14: 2 135/112 323.353 cents septimal wide minor third 14: 2 98/81 329.832 cents 14: 1 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 14: 2 40/33 333.041 cents 14: 1 336/275 346.836 cents 14: 5 11/9 347.408 cents undecimal neutral third 14: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 14: 1 275/224 355.119 cents 14: 2 448/363 364.235 cents 14: 2 243/196 372.123 cents 14: 2 56/45 378.602 cents septimal narrow major third 14: 5 5/4 386.314 cents major third 14: 1 441/352 390.244 cents 14: 4 44/35 396.178 cents 14: 2 63/50 400.108 cents quasi-equal major third 14: 2 81/64 407.820 cents Pythagorean major third 14: 4 80/63 413.578 cents wide major third 14: 4 14/11 417.508 cents undecimal diminished fourth or major third 15: 3 11/9 347.408 cents undecimal neutral third 15: 2 60/49 350.617 cents smaller approximation to neutral third 15: 1 49/40 351.338 cents larger approximation to neutral third 15: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 15: 2 896/729 357.096 cents 15: 2 99/80 368.914 cents 15: 2 56/45 378.602 cents septimal narrow major third 15: 2 96/77 381.811 cents 15: 4 5/4 386.314 cents major third 15: 2 121/96 400.681 cents 15: 2 81/64 407.820 cents Pythagorean major third 15: 1 80/63 413.578 cents wide major third 15: 5 14/11 417.508 cents undecimal diminished fourth or major third 15: 1 32/25 427.373 cents classic diminished fourth 15: 2 77/60 431.875 cents 15: 8 9/7 435.084 cents septimal major third, BP third 15: 2 128/99 444.772 cents 15: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 16: 1 100/81 364.807 cents grave major third 16: 2 99/80 368.914 cents 16: 1 704/567 374.672 cents 16: 3 56/45 378.602 cents septimal narrow major third 16: 2 96/77 381.811 cents 16: 2 5/4 386.314 cents major third 16: 1 44/35 396.178 cents 16: 2 121/96 400.681 cents 16: 1 495/392 403.890 cents 16: 5 14/11 417.508 cents undecimal diminished fourth or major third 16: 1 225/176 425.219 cents 16: 4 77/60 431.875 cents 16: 2 9/7 435.084 cents septimal major third, BP third 16: 3 100/77 452.484 cents 16: 1 315/242 456.414 cents 16: 2 176/135 459.139 cents 16: 2 64/49 462.348 cents 2 septatones or septatonic major third 16: 4 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 17: 2 5/4 386.314 cents major third 17: 3 44/35 396.178 cents 17: 1 63/50 400.108 cents quasi-equal major third 17: 2 308/243 410.369 cents 17: 2 80/63 413.578 cents wide major third 17: 2 14/11 417.508 cents undecimal diminished fourth or major third 17: 1 77/60 431.875 cents 17: 2 9/7 435.084 cents septimal major third, BP third 17: 3 165/128 439.587 cents 17: 2 128/99 444.772 cents 17: 1 784/605 448.702 cents 17: 1 315/242 456.414 cents 17: 2 98/75 463.069 cents 17: 3 55/42 466.851 cents 17: 1 21/16 470.781 cents narrow fourth 17: 2 405/308 473.990 cents 17: 2 33/25 480.646 cents 2 pentatones 17: 2 160/121 483.678 cents 17: 2 297/224 488.357 cents 17: 8 4/3 498.045 cents perfect fourth 17: 1 162/121 505.184 cents 18: 1 81/64 407.820 cents Pythagorean major third 18: 2 80/63 413.578 cents wide major third 18: 1 242/189 427.945 cents 18: 3 77/60 431.875 cents 18: 2 9/7 435.084 cents septimal major third, BP third 18: 2 128/99 444.772 cents 18: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 18: 1 176/135 459.139 cents 18: 1 72/55 466.278 cents undecimal semi-diminished fourth 18: 1 55/42 466.851 cents 18: 4 21/16 470.781 cents narrow fourth 18: 1 405/308 473.990 cents 18: 2 160/121 483.678 cents 18: 2 297/224 488.357 cents 18: 7 4/3 498.045 cents perfect fourth 18: 1 147/110 501.975 cents 18: 2 66/49 515.621 cents 18: 4 27/20 519.551 cents acute fourth 18: 2 256/189 525.309 cents 18: 2 49/36 533.742 cents Arabic lute acute fourth 18: 2 15/11 536.951 cents undecimal augmented fourth 19: 2 9/7 435.084 cents septimal major third, BP third 19: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 19: 2 176/135 459.139 cents 19: 2 72/55 466.278 cents undecimal semi-diminished fourth 19: 3 55/42 466.851 cents 19: 1 21/16 470.781 cents narrow fourth 19: 2 392/297 480.469 cents 19: 2 297/224 488.357 cents 19: 5 4/3 498.045 cents perfect fourth 19: 1 147/110 501.975 cents 19: 1 75/56 505.757 cents marvelous fourth 19: 1 945/704 509.687 cents 19: 2 121/90 512.412 cents 19: 2 27/20 519.551 cents acute fourth 19: 2 224/165 529.239 cents 19: 1 200/147 533.021 cents 19: 3 15/11 536.951 cents undecimal augmented fourth 19: 4 48/35 546.815 cents septimal semi-augmented fourth 19: 2 11/8 551.318 cents undecimal semi-augmented fourth 19: 2 243/176 558.457 cents 19: 2 112/81 561.006 cents 19: 1 25/18 568.717 cents classic augmented fourth 20: 1 64/49 462.348 cents 2 septatones or septatonic major third 20: 2 21/16 470.781 cents narrow fourth 20: 2 320/243 476.539 cents grave fourth 20: 2 33/25 480.646 cents 2 pentatones 20: 5 4/3 498.045 cents perfect fourth 20: 1 147/110 501.975 cents 20: 2 75/56 505.757 cents marvelous fourth 20: 1 121/90 512.412 cents 20: 1 605/448 520.124 cents 20: 2 693/512 524.054 cents 20: 3 224/165 529.239 cents 20: 3 15/11 536.951 cents undecimal augmented fourth 20: 2 308/225 543.606 cents 20: 2 11/8 551.318 cents undecimal semi-augmented fourth 20: 2 135/98 554.527 cents 20: 3 320/231 564.215 cents 20: 1 168/121 568.145 cents 20: 2 88/63 578.582 cents 20: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 20: 2 108/77 585.721 cents 20: 2 45/32 590.224 cents diatonic tritone 21: 6 4/3 498.045 cents perfect fourth 21: 2 121/90 512.412 cents 21: 1 66/49 515.621 cents 21: 1 27/20 519.551 cents acute fourth 21: 2 49/36 533.742 cents Arabic lute acute fourth 21: 4 15/11 536.951 cents undecimal augmented fourth 21: 1 308/225 543.606 cents 21: 5 11/8 551.318 cents undecimal semi-augmented fourth 21: 2 320/231 564.215 cents 21: 1 168/121 568.145 cents 21: 1 675/484 575.857 cents 21: 3 88/63 578.582 cents 21: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 21: 2 108/77 585.721 cents 21: 2 140/99 599.912 cents quasi-equal tritone 21: 2 99/70 600.088 cents 2nd quasi-equal tritone 21: 2 64/45 609.776 cents 2nd tritone 21: 1 729/512 611.730 cents Pythagorean tritone 21: 2 10/7 617.488 cents Euler's tritone 21: 2 63/44 621.418 cents 22: 2 27/20 519.551 cents acute fourth 22: 2 256/189 525.309 cents 22: 2 110/81 529.812 cents 22: 1 49/36 533.742 cents Arabic lute acute fourth 22: 3 11/8 551.318 cents undecimal semi-augmented fourth 22: 2 135/98 554.527 cents 22: 1 441/320 555.248 cents 22: 2 112/81 561.006 cents 22: 2 168/121 568.145 cents 22: 1 88/63 578.582 cents 22: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 22: 1 275/196 586.294 cents 22: 3 45/32 590.224 cents diatonic tritone 22: 2 512/363 595.409 cents 22: 2 99/70 600.088 cents 2nd quasi-equal tritone 22: 2 64/45 609.776 cents 2nd tritone 22: 2 77/54 614.279 cents 22: 3 10/7 617.488 cents Euler's tritone 22: 1 63/44 621.418 cents 22: 2 36/25 631.283 cents classic diminished fifth 22: 2 81/56 638.994 cents 22: 2 16/11 648.682 cents undecimal semi-diminished fifth 22: 2 35/24 653.185 cents septimal semi-diminished fifth 23: 2 48/35 546.815 cents septimal semi-augmented fourth 23: 2 11/8 551.318 cents undecimal semi-augmented fourth 23: 2 112/81 561.006 cents 23: 2 25/18 568.717 cents classic augmented fourth 23: 1 88/63 578.582 cents 23: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 23: 2 108/77 585.721 cents 23: 2 45/32 590.224 cents diatonic tritone 23: 2 140/99 599.912 cents quasi-equal tritone 23: 2 363/256 604.591 cents 23: 3 64/45 609.776 cents 2nd tritone 23: 1 392/275 613.706 cents 23: 3 10/7 617.488 cents Euler's tritone 23: 1 63/44 621.418 cents 23: 2 121/84 631.855 cents 23: 2 81/56 638.994 cents 23: 1 640/441 644.752 cents 23: 2 196/135 645.473 cents 23: 3 16/11 648.682 cents undecimal semi-diminished fifth 23: 1 72/49 666.258 cents Arabic lute grave fifth 23: 2 81/55 670.188 cents 23: 2 189/128 674.691 cents 23: 2 40/27 680.449 cents grave fifth 24: 2 88/63 578.582 cents 24: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 24: 1 1024/729 588.270 cents Pythagorean diminished fifth 24: 2 45/32 590.224 cents diatonic tritone 24: 2 140/99 599.912 cents quasi-equal tritone 24: 2 99/70 600.088 cents 2nd quasi-equal tritone 24: 2 77/54 614.279 cents 24: 3 10/7 617.488 cents Euler's tritone 24: 3 63/44 621.418 cents 24: 1 968/675 624.143 cents 24: 1 121/84 631.855 cents 24: 2 231/160 635.785 cents 24: 5 16/11 648.682 cents undecimal semi-diminished fifth 24: 1 225/154 656.394 cents 24: 4 22/15 663.049 cents undecimal diminished fifth 24: 2 72/49 666.258 cents Arabic lute grave fifth 24: 1 40/27 680.449 cents grave fifth 24: 1 49/33 684.379 cents 24: 2 180/121 687.588 cents 24: 6 3/2 701.955 cents perfect fifth 25: 2 64/45 609.776 cents 2nd tritone 25: 2 77/54 614.279 cents 25: 4 10/7 617.488 cents Euler's tritone 25: 2 63/44 621.418 cents 25: 1 121/84 631.855 cents 25: 3 231/160 635.785 cents 25: 2 196/135 645.473 cents 25: 2 16/11 648.682 cents undecimal semi-diminished fifth 25: 2 225/154 656.394 cents 25: 3 22/15 663.049 cents undecimal diminished fifth 25: 3 165/112 670.761 cents 25: 2 1024/693 675.946 cents 25: 1 896/605 679.876 cents 25: 1 180/121 687.588 cents 25: 2 112/75 694.243 cents marvelous fifth 25: 1 220/147 698.025 cents 25: 5 3/2 701.955 cents perfect fifth 25: 2 50/33 719.354 cents 3 pentatones 25: 2 243/160 723.461 cents acute fifth 25: 2 32/21 729.219 cents wide fifth 25: 1 49/32 737.652 cents 26: 1 36/25 631.283 cents classic diminished fifth 26: 2 81/56 638.994 cents 26: 2 352/243 641.543 cents 26: 2 16/11 648.682 cents undecimal semi-diminished fifth 26: 4 35/24 653.185 cents septimal semi-diminished fifth 26: 3 22/15 663.049 cents undecimal diminished fifth 26: 1 147/100 666.979 cents 26: 2 165/112 670.761 cents 26: 2 40/27 680.449 cents grave fifth 26: 2 180/121 687.588 cents 26: 1 1408/945 690.313 cents 26: 1 112/75 694.243 cents marvelous fifth 26: 1 220/147 698.025 cents 26: 5 3/2 701.955 cents perfect fifth 26: 2 448/297 711.643 cents 26: 2 297/196 719.531 cents 26: 1 32/21 729.219 cents wide fifth 26: 3 84/55 733.149 cents 26: 2 55/36 733.722 cents undecimal semi-augmented fifth 26: 2 135/88 740.861 cents 26: 2 54/35 750.725 cents septimal semi-augmented fifth 26: 2 14/9 764.916 cents septimal minor sixth 27: 2 22/15 663.049 cents undecimal diminished fifth 27: 2 72/49 666.258 cents Arabic lute grave fifth 27: 2 189/128 674.691 cents 27: 4 40/27 680.449 cents grave fifth 27: 2 49/33 684.379 cents 27: 1 220/147 698.025 cents 27: 7 3/2 701.955 cents perfect fifth 27: 2 448/297 711.643 cents 27: 2 121/80 716.322 cents 27: 1 616/405 726.010 cents 27: 4 32/21 729.219 cents wide fifth 27: 1 84/55 733.149 cents 27: 1 55/36 733.722 cents undecimal semi-augmented fifth 27: 1 135/88 740.861 cents 27: 2 54/35 750.725 cents septimal semi-augmented fifth 27: 2 99/64 755.228 cents 27: 2 14/9 764.916 cents septimal minor sixth 27: 3 120/77 768.125 cents 27: 1 189/121 772.055 cents 27: 2 63/40 786.422 cents narrow minor sixth 27: 1 128/81 792.180 cents Pythagorean minor sixth 28: 1 121/81 694.816 cents two (undecimal neutral third) 28: 8 3/2 701.955 cents perfect fifth 28: 2 448/297 711.643 cents 28: 2 121/80 716.322 cents 28: 2 50/33 719.354 cents 3 pentatones 28: 2 616/405 726.010 cents 28: 1 32/21 729.219 cents wide fifth 28: 3 84/55 733.149 cents 28: 2 75/49 736.931 cents BP fifth 28: 1 484/315 743.586 cents 28: 1 605/392 751.298 cents 28: 2 99/64 755.228 cents 28: 3 256/165 760.413 cents 28: 2 14/9 764.916 cents septimal minor sixth 28: 1 120/77 768.125 cents 28: 2 11/7 782.492 cents undecimal augmented fifth 28: 2 63/40 786.422 cents narrow minor sixth 28: 2 243/154 789.631 cents 28: 1 100/63 799.892 cents quasi-equal minor sixth 28: 3 35/22 803.822 cents 28: 2 8/5 813.686 cents minor sixth 29: 4 32/21 729.219 cents wide fifth 29: 2 84/55 733.149 cents 29: 4 55/36 733.722 cents undecimal semi-augmented fifth 29: 2 49/32 737.652 cents 29: 2 135/88 740.861 cents 29: 1 484/315 743.586 cents 29: 3 77/50 747.516 cents 29: 2 14/9 764.916 cents septimal minor sixth 29: 4 120/77 768.125 cents 29: 1 352/225 774.781 cents 29: 5 11/7 782.492 cents undecimal augmented fifth 29: 1 784/495 796.110 cents 29: 2 192/121 799.319 cents 29: 1 35/22 803.822 cents 29: 2 8/5 813.686 cents minor sixth 29: 2 77/48 818.189 cents 29: 3 45/28 821.398 cents septimale wide minor sixth 29: 1 567/352 825.328 cents 29: 2 160/99 831.086 cents 29: 1 81/50 835.193 cents acute minor sixth 30: 2 54/35 750.725 cents septimal semi-augmented fifth 30: 2 99/64 755.228 cents 30: 8 14/9 764.916 cents septimal minor sixth 30: 2 120/77 768.125 cents 30: 1 25/16 772.627 cents classic augmented fifth 30: 5 11/7 782.492 cents undecimal augmented fifth 30: 1 63/40 786.422 cents narrow minor sixth 30: 2 128/81 792.180 cents Pythagorean minor sixth 30: 2 192/121 799.319 cents 30: 4 8/5 813.686 cents minor sixth 30: 2 77/48 818.189 cents 30: 2 45/28 821.398 cents septimale wide minor sixth 30: 2 160/99 831.086 cents 30: 2 729/448 842.904 cents 30: 2 44/27 845.453 cents neutral sixth 30: 1 80/49 848.662 cents smaller approximation to neutral sixth 30: 2 49/30 849.383 cents larger approximation to neutral sixth 30: 3 18/11 852.592 cents undecimal neutral sixth 31: 4 11/7 782.492 cents undecimal augmented fifth 31: 4 63/40 786.422 cents narrow minor sixth 31: 2 128/81 792.180 cents Pythagorean minor sixth 31: 2 100/63 799.892 cents quasi-equal minor sixth 31: 4 35/22 803.822 cents 31: 1 704/441 809.756 cents 31: 5 8/5 813.686 cents minor sixth 31: 2 45/28 821.398 cents septimale wide minor sixth 31: 2 392/243 827.877 cents 31: 2 363/224 835.765 cents 31: 1 448/275 844.881 cents 31: 1 44/27 845.453 cents neutral sixth 31: 5 18/11 852.592 cents undecimal neutral sixth 31: 1 275/168 853.164 cents 31: 2 33/20 866.959 cents 31: 1 200/121 869.992 cents 31: 2 81/49 870.168 cents two (septimal major third, BP third) 31: 2 224/135 876.647 cents narrow septimal major sixth 31: 1 5/3 884.359 cents major sixth, BP sixth 31: 1 147/88 888.289 cents 32: 4 8/5 813.686 cents minor sixth 32: 4 77/48 818.189 cents 32: 4 45/28 821.398 cents septimale wide minor sixth 32: 2 121/75 828.053 cents 32: 4 160/99 831.086 cents 32: 1 196/121 835.016 cents two (undecimal diminished fourth or major third) 32: 3 44/27 845.453 cents neutral sixth 32: 2 80/49 848.662 cents smaller approximation to neutral sixth 32: 1 49/30 849.383 cents larger approximation to neutral sixth 32: 2 18/11 852.592 cents undecimal neutral sixth 32: 3 33/20 866.959 cents 32: 1 1485/896 874.671 cents 32: 2 128/77 879.856 cents 32: 1 1008/605 883.786 cents 32: 4 5/3 884.359 cents major sixth, BP sixth 32: 1 405/242 891.498 cents 32: 2 42/25 898.153 cents quasi-equal major sixth 32: 2 27/16 905.865 cents Pythagorean major sixth 32: 1 320/189 911.623 cents 32: 1 56/33 915.553 cents 33: 6 44/27 845.453 cents neutral sixth 33: 2 80/49 848.662 cents smaller approximation to neutral sixth 33: 2 49/30 849.383 cents larger approximation to neutral sixth 33: 6 18/11 852.592 cents undecimal neutral sixth 33: 2 105/64 857.095 cents septimal neutral sixth 33: 1 242/147 863.029 cents 33: 3 33/20 866.959 cents 33: 2 224/135 876.647 cents narrow septimal major sixth 33: 2 128/77 879.856 cents 33: 2 5/3 884.359 cents major sixth, BP sixth 33: 1 176/105 894.223 cents 33: 1 121/72 898.726 cents 33: 1 165/98 901.935 cents 33: 4 27/16 905.865 cents Pythagorean major sixth 33: 5 56/33 915.553 cents 33: 1 75/44 923.264 cents 33: 3 12/7 933.129 cents septimal major sixth 33: 1 189/110 937.059 cents 34: 4 33/20 866.959 cents 34: 1 81/49 870.168 cents two (septimal major third, BP third) 34: 2 224/135 876.647 cents narrow septimal major sixth 34: 2 128/77 879.856 cents 34: 8 5/3 884.359 cents major sixth, BP sixth 34: 2 147/88 888.289 cents 34: 3 176/105 894.223 cents 34: 1 42/25 898.153 cents quasi-equal major sixth 34: 2 165/98 901.935 cents 34: 4 56/33 915.553 cents 34: 3 77/45 929.920 cents 34: 2 12/7 933.129 cents septimal major sixth 34: 1 189/110 937.059 cents 34: 3 55/32 937.632 cents 34: 2 512/297 942.817 cents 34: 1 1215/704 944.771 cents 34: 1 400/231 950.529 cents 34: 1 210/121 954.459 cents 34: 2 243/140 954.635 cents 35: 2 176/105 894.223 cents 35: 2 42/25 898.153 cents quasi-equal major sixth 35: 2 121/72 898.726 cents 35: 4 27/16 905.865 cents Pythagorean major sixth 35: 4 320/189 911.623 cents 35: 4 56/33 915.553 cents 35: 2 75/44 923.264 cents 35: 2 77/45 929.920 cents 35: 5 12/7 933.129 cents septimal major sixth 35: 1 189/110 937.059 cents 35: 2 140/81 947.320 cents 35: 1 704/405 957.184 cents 35: 2 891/512 959.138 cents 35: 1 392/225 961.114 cents 35: 3 96/55 964.323 cents 35: 2 110/63 964.896 cents 35: 3 7/4 968.826 cents harmonic seventh 35: 3 135/77 972.035 cents 36: 4 77/45 929.920 cents 36: 8 12/7 933.129 cents septimal major sixth 36: 2 55/32 937.632 cents 36: 1 441/256 941.562 cents two (narrow fourth) 36: 2 512/297 942.817 cents 36: 2 140/81 947.320 cents 36: 2 121/70 947.496 cents 36: 2 210/121 954.459 cents 36: 2 96/55 964.323 cents 36: 1 110/63 964.896 cents 36: 3 7/4 968.826 cents harmonic seventh 36: 2 135/77 972.035 cents 36: 1 44/25 978.691 cents undecimal grave minor seventh 36: 2 640/363 981.723 cents 36: 5 99/56 986.402 cents 36: 3 16/9 996.090 cents Pythagorean minor seventh 36: 2 98/55 1000.020 cents quasi-equal minor seventh 36: 1 315/176 1007.732 cents 37: 2 704/405 957.184 cents 37: 2 256/147 960.393 cents 37: 2 96/55 964.323 cents 37: 4 110/63 964.896 cents 37: 10 7/4 968.826 cents harmonic seventh 37: 2 135/77 972.035 cents 37: 2 44/25 978.691 cents undecimal grave minor seventh 37: 1 99/56 986.402 cents 37: 1 567/320 990.332 cents 37: 5 16/9 996.090 cents Pythagorean minor seventh 37: 2 216/121 1003.229 cents 37: 3 25/14 1003.802 cents middle minor seventh 37: 4 9/5 1017.596 cents just minor seventh, BP seventh 37: 2 231/128 1022.099 cents 37: 1 896/495 1027.284 cents 37: 2 20/11 1034.996 cents large minor seventh 38: 2 44/25 978.691 cents undecimal grave minor seventh 38: 4 99/56 986.402 cents 38: 11 16/9 996.090 cents Pythagorean minor seventh 38: 2 98/55 1000.020 cents quasi-equal minor seventh 38: 2 25/14 1003.802 cents middle minor seventh 38: 2 315/176 1007.732 cents 38: 1 242/135 1010.457 cents 38: 1 88/49 1013.666 cents undecimal minor seventh 38: 3 9/5 1017.596 cents just minor seventh, BP seventh 38: 1 605/336 1018.169 cents 38: 2 405/224 1025.308 cents 38: 2 896/495 1027.284 cents 38: 2 49/27 1031.787 cents 38: 4 20/11 1034.996 cents large minor seventh 38: 1 504/275 1048.791 cents 38: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 38: 1 90/49 1052.572 cents 38: 2 81/44 1056.502 cents 2nd undecimal neutral seventh 39: 2 242/135 1010.457 cents 39: 2 88/49 1013.666 cents undecimal minor seventh 39: 6 9/5 1017.596 cents just minor seventh, BP seventh 39: 2 231/128 1022.099 cents 39: 2 1024/567 1023.354 cents 39: 2 49/27 1031.787 cents 39: 8 20/11 1034.996 cents large minor seventh 39: 1 1232/675 1041.651 cents 39: 6 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 39: 2 90/49 1052.572 cents 39: 1 147/80 1053.293 cents 39: 2 81/44 1056.502 cents 2nd undecimal neutral seventh 39: 2 448/243 1059.051 cents 39: 1 1280/693 1062.260 cents 39: 2 224/121 1066.190 cents 39: 2 297/160 1070.869 cents 39: 1 225/121 1073.902 cents two (undecimal augmented fourth) 39: 1 729/392 1074.078 cents 40: 4 64/35 1044.860 cents septimal neutral seventh 40: 8 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 40: 2 90/49 1052.572 cents 40: 2 147/80 1053.293 cents 40: 2 81/44 1056.502 cents 2nd undecimal neutral seventh 40: 2 448/243 1059.051 cents 40: 2 224/121 1066.190 cents 40: 2 50/27 1066.762 cents grave major seventh 40: 2 297/160 1070.869 cents 40: 1 225/121 1073.902 cents two (undecimal augmented fourth) 40: 1 352/189 1076.627 cents 40: 7 28/15 1080.557 cents grave major seventh 40: 4 144/77 1083.766 cents 40: 1 275/147 1084.339 cents 40: 5 15/8 1088.269 cents classic major seventh 41: 4 352/189 1076.627 cents 41: 8 28/15 1080.557 cents grave major seventh 41: 4 144/77 1083.766 cents 41: 10 15/8 1088.269 cents classic major seventh 41: 1 2048/1089 1093.454 cents 41: 2 560/297 1097.957 cents 41: 4 66/35 1098.133 cents 41: 1 189/100 1102.063 cents 41: 2 121/64 1102.636 cents two (undecimal semi-augmented fourth) 41: 1 1485/784 1105.845 cents 41: 1 1568/825 1111.751 cents 41: 3 40/21 1115.533 cents acute major seventh 41: 4 21/11 1119.463 cents undecimal major seventh 42: 4 66/35 1098.133 cents 42: 1 121/64 1102.636 cents two (undecimal semi-augmented fourth) 42: 3 256/135 1107.821 cents octave - major chroma 42: 2 243/128 1109.775 cents Pythagorean major seventh 42: 4 154/81 1112.324 cents 42: 10 40/21 1115.533 cents acute major seventh 42: 9 21/11 1119.463 cents undecimal major seventh 42: 4 77/40 1133.830 cents 42: 4 27/14 1137.039 cents septimal major seventh 42: 2 64/33 1146.727 cents 33rd subharmonic 42: 1 1176/605 1150.657 cents 42: 1 150/77 1154.439 cents 43: 2 48/25 1129.328 cents classic diminished octave 43: 4 121/63 1129.900 cents 43: 5 77/40 1133.830 cents 43: 6 27/14 1137.039 cents septimal major seventh 43: 2 784/405 1143.518 cents 43: 8 64/33 1146.727 cents 33rd subharmonic 43: 6 35/18 1151.230 cents septimal semi-diminished octave 43: 4 150/77 1154.439 cents 43: 2 88/45 1161.094 cents 43: 3 108/55 1168.233 cents 43: 1 55/28 1168.806 cents 43: 1 63/32 1172.736 cents octave - septimal comma 43: 1 1215/616 1175.945 cents 44: 6 88/45 1161.094 cents 44: 4 96/49 1164.303 cents 44: 2 49/25 1165.024 cents BP eighth 44: 2 108/55 1168.233 cents 44: 7 55/28 1168.806 cents 44: 6 63/32 1172.736 cents octave - septimal comma 44: 1 3584/1815 1177.921 cents 44: 5 160/81 1178.494 cents octave - syntonic comma 44: 3 196/99 1182.424 cents 44: 2 99/50 1182.601 cents 44: 5 240/121 1185.633 cents 44: 2 891/448 1190.312 cents Highest number of different intervals for one interval class: 23 Average number of different intervals per interval class: 18.00000 = 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 38 39 40 41 42 43 44 45 0.0 : 38.9 53.3 63.0 84.5 119.4 150.6 165.0 182.4 203.9 231.2 266.9 294.1 315.6 347.4 386.3 417.5 435.1 470.8 498.0 537.0 551.3 582.5 617.5 648.7 663.0 702.0 729.2 764.9 782.5 813.7 852.6 884.4 905.9 933.1 968.8 996.1 1017.6 1035.0 1049.4 1080.6 1119.5 1137.0 1146.7 1168.8 1200.0 38.9 : 14.4 24.1 45.6 80.5 111.7 126.1 143.5 165.0 192.3 228.0 255.2 276.7 308.5 347.4 378.6 396.2 431.9 459.1 498.0 512.4 543.6 578.6 609.8 624.1 663.0 690.3 726.0 743.6 774.8 813.7 845.5 867.0 894.2 929.9 957.2 978.7 996.1 1010.5 1041.7 1080.6 1098.1 1107.8 1129.9 1161.1 1200.0 53.3 : 9.7 31.2 66.2 97.4 111.7 129.1 150.6 177.9 213.6 240.9 262.4 294.1 333.0 364.2 381.8 417.5 444.8 483.7 498.0 529.2 564.2 595.4 609.8 648.7 675.9 711.6 729.2 760.4 799.3 831.1 852.6 879.9 915.6 942.8 964.3 981.7 996.1 1027.3 1066.2 1083.8 1093.5 1115.5 1146.7 1185.6 1200.0 63.0 : 21.5 56.5 87.7 102.0 119.4 140.9 168.2 203.9 231.2 252.7 284.4 323.4 354.5 372.1 407.8 435.1 474.0 488.4 519.6 554.5 585.7 600.1 639.0 666.3 702.0 719.5 750.7 789.6 821.4 842.9 870.2 905.9 933.1 954.6 972.0 986.4 1017.6 1056.5 1074.1 1083.8 1105.8 1137.0 1175.9 1190.3 1200.0 84.5 : 35.0 66.2 80.5 97.9 119.4 146.7 182.4 209.7 231.2 262.9 301.8 333.0 350.6 386.3 413.6 452.5 466.9 498.0 533.0 564.2 578.6 617.5 644.8 680.4 698.0 729.2 768.1 799.9 821.4 848.7 884.4 911.6 933.1 950.5 964.9 996.1 1035.0 1052.6 1062.3 1084.3 1115.5 1154.4 1168.8 1178.5 1200.0 119.4 : 31.2 45.6 63.0 84.5 111.7 147.4 174.7 196.2 228.0 266.9 298.1 315.6 351.3 378.6 417.5 431.9 463.1 498.0 529.2 543.6 582.5 609.8 645.5 663.0 694.2 733.1 764.9 786.4 813.7 849.4 876.6 898.2 915.6 929.9 961.1 1000.0 1017.6 1027.3 1049.4 1080.6 1119.5 1133.8 1143.5 1165.0 1200.0 150.6 : 14.4 31.8 53.3 80.5 116.2 143.5 165.0 196.8 235.7 266.9 284.4 320.1 347.4 386.3 400.7 431.9 466.9 498.0 512.4 551.3 578.6 614.3 631.9 663.0 702.0 733.7 755.2 782.5 818.2 845.5 867.0 884.4 898.7 929.9 968.8 986.4 996.1 1018.2 1049.4 1088.3 1102.6 1112.3 1133.8 1168.8 1200.0 165.0 : 17.4 38.9 66.2 101.9 129.1 150.6 182.4 221.3 252.5 270.1 305.8 333.0 371.9 386.3 417.5 452.5 483.7 498.0 537.0 564.2 599.9 617.5 648.7 687.6 719.4 740.9 768.1 803.8 831.1 852.6 870.0 884.4 915.6 954.5 972.0 981.7 1003.8 1035.0 1073.9 1088.3 1098.0 1119.5 1154.4 1185.6 1200.0 182.4 : 21.5 48.8 84.5 111.7 133.2 165.0 203.9 235.1 252.7 288.4 315.6 354.5 368.9 400.1 435.1 466.3 480.6 519.6 546.8 582.5 600.1 631.3 670.2 702.0 723.5 750.7 786.4 813.7 835.2 852.6 867.0 898.2 937.1 954.6 964.3 986.4 1017.6 1056.5 1070.9 1080.6 1102.1 1137.0 1168.2 1182.6 1200.0 203.9 : 27.3 63.0 90.2 111.7 143.5 182.4 213.6 231.2 266.9 294.1 333.0 347.4 378.6 413.6 444.8 459.1 498.0 525.3 561.0 578.6 609.8 648.7 680.4 702.0 729.2 764.9 792.2 813.7 831.1 845.5 876.6 915.6 933.1 942.8 964.9 996.1 1035.0 1049.4 1059.1 1080.6 1115.5 1146.7 1161.1 1178.5 1200.0 231.2 : 35.7 63.0 84.5 116.2 155.1 186.3 203.9 239.6 266.9 305.8 320.1 351.3 386.3 417.5 431.9 470.8 498.0 533.7 551.3 582.5 621.4 653.2 674.7 702.0 737.7 764.9 786.4 803.8 818.2 849.4 888.3 905.9 915.6 937.6 968.8 1007.7 1022.1 1031.8 1053.3 1088.3 1119.5 1133.8 1151.2 1172.7 1200.0 266.9 : 27.3 48.8 80.5 119.4 150.6 168.2 203.9 231.2 270.1 284.4 315.6 350.6 381.8 396.2 435.1 462.3 498.0 515.6 546.8 585.7 617.5 639.0 666.3 702.0 729.2 750.7 768.1 782.5 813.7 852.6 870.2 879.9 901.9 933.1 972.0 986.4 996.1 1017.6 1052.6 1083.8 1098.1 1115.5 1137.0 1164.3 1200.0 294.1 : 21.5 53.3 92.2 123.4 140.9 176.6 203.9 242.8 257.2 288.4 323.4 354.5 368.9 407.8 435.1 470.8 488.4 519.6 558.5 590.2 611.7 639.0 674.7 702.0 723.5 740.9 755.2 786.4 825.3 842.9 852.6 874.7 905.9 944.8 959.1 968.8 990.3 1025.3 1056.5 1070.9 1088.3 1109.8 1137.0 1172.7 1200.0 315.6 : 31.8 70.7 101.9 119.4 155.1 182.4 221.3 235.7 266.9 301.8 333.0 347.4 386.3 413.6 449.3 466.9 498.0 537.0 568.7 590.2 617.5 653.2 680.4 702.0 719.4 733.7 764.9 803.8 821.4 831.1 853.2 884.4 923.3 937.6 947.3 968.8 1003.8 1035.0 1049.4 1066.8 1088.3 1115.5 1151.2 1178.5 1200.0 347.4 : 38.9 70.1 87.7 123.4 150.6 189.5 203.9 235.1 270.1 301.3 315.6 354.5 381.8 417.5 435.1 466.3 505.2 537.0 558.5 585.7 621.4 648.7 670.2 687.6 702.0 733.1 772.1 789.6 799.3 821.4 852.6 891.5 905.9 915.6 937.1 972.0 1003.2 1017.6 1035.0 1056.5 1083.8 1119.5 1146.7 1168.2 1200.0 386.3 : 31.2 48.8 84.5 111.7 150.6 165.0 196.2 231.2 262.4 276.7 315.6 342.9 378.6 396.2 427.4 466.3 498.0 519.6 546.8 582.5 609.8 631.3 648.7 663.0 694.2 733.1 750.7 760.4 782.5 813.7 852.6 867.0 876.6 898.2 933.1 964.3 978.7 996.1 1017.6 1044.9 1080.6 1107.8 1129.3 1161.1 1200.0 417.5 : 17.6 53.3 80.5 119.4 133.8 165.0 200.0 231.2 245.5 284.4 311.7 347.4 365.0 396.2 435.1 466.9 488.4 515.6 551.3 578.6 600.1 617.5 631.9 663.0 702.0 719.5 729.2 751.3 782.5 821.4 835.8 845.5 867.0 901.9 933.1 947.5 964.9 986.4 1013.7 1049.4 1076.6 1098.1 1129.9 1168.8 1200.0 435.1 : 35.7 63.0 101.9 116.2 147.4 182.4 213.6 228.0 266.9 294.1 329.8 347.4 378.6 417.5 449.3 470.8 498.0 533.7 561.0 582.5 599.9 614.3 645.5 684.4 702.0 711.6 733.7 764.9 803.8 818.2 827.9 849.4 884.4 915.6 929.9 947.3 968.8 996.1 1031.8 1059.1 1080.6 1112.3 1151.2 1182.4 1200.0 470.8 : 27.3 66.2 80.5 111.7 146.7 177.9 192.3 231.2 258.4 294.1 311.7 342.9 381.8 413.6 435.1 462.3 498.0 525.3 546.8 564.2 578.6 609.8 648.7 666.3 675.9 698.0 729.2 768.1 782.5 792.2 813.7 848.7 879.9 894.2 911.6 933.1 960.4 996.1 1023.4 1044.9 1076.6 1115.5 1146.7 1164.3 1200.0 498.0 : 38.9 53.3 84.5 119.4 150.6 165.0 203.9 231.2 266.9 284.4 315.6 354.5 386.3 407.8 435.1 470.8 498.0 519.6 537.0 551.3 582.5 621.4 639.0 648.7 670.8 702.0 740.9 755.2 764.9 786.4 821.4 852.6 867.0 884.4 905.9 933.1 968.8 996.1 1017.6 1049.4 1088.3 1119.5 1137.0 1172.7 1200.0 537.0 : 14.4 45.6 80.5 111.7 126.1 165.0 192.3 228.0 245.5 276.7 315.6 347.4 368.9 396.2 431.9 459.1 480.6 498.0 512.4 543.6 582.5 600.1 609.8 631.9 663.0 702.0 716.3 726.0 747.5 782.5 813.7 828.1 845.5 867.0 894.2 929.9 957.2 978.7 1010.5 1049.4 1080.6 1098.1 1133.8 1161.1 1200.0 551.3 : 31.2 66.2 97.4 111.7 150.6 177.9 213.6 231.2 262.4 301.3 333.0 354.5 381.8 417.5 444.8 466.3 483.7 498.0 529.2 568.1 585.7 595.4 617.5 648.7 687.6 702.0 711.6 733.1 768.1 799.3 813.7 831.1 852.6 879.9 915.6 942.8 964.3 996.1 1035.0 1066.2 1083.8 1119.5 1146.7 1185.6 1200.0 582.5 : 35.0 66.2 80.5 119.4 146.7 182.4 200.0 231.2 270.1 301.8 323.4 350.6 386.3 413.6 435.1 452.5 466.9 498.0 537.0 554.5 564.2 586.3 617.5 656.4 670.8 680.4 702.0 736.9 768.1 782.5 799.9 821.4 848.7 884.4 911.6 933.1 964.9 1003.8 1035.0 1052.6 1088.3 1115.5 1154.4 1168.8 1200.0 617.5 : 31.2 45.6 84.5 111.7 147.4 165.0 196.2 235.1 266.9 288.4 315.6 351.3 378.6 400.1 417.5 431.9 463.1 502.0 519.6 529.2 551.3 582.5 621.4 635.8 645.5 667.0 702.0 733.1 747.5 764.9 786.4 813.7 849.4 876.6 898.2 929.9 968.8 1000.0 1017.6 1053.3 1080.6 1119.5 1133.8 1165.0 1200.0 648.7 : 14.4 53.3 80.5 116.2 133.8 165.0 203.9 235.7 257.2 284.4 320.1 347.4 368.9 386.3 400.7 431.9 470.8 488.4 498.0 520.1 551.3 590.2 604.6 614.3 635.8 670.8 702.0 716.3 733.7 755.2 782.5 818.2 845.5 867.0 898.7 937.6 968.8 986.4 1022.1 1049.4 1088.3 1102.6 1133.8 1168.8 1200.0 663.0 : 38.9 66.2 101.9 119.4 150.6 189.5 221.3 242.8 270.1 305.8 333.0 354.5 371.9 386.3 417.5 456.4 474.0 483.7 505.8 537.0 575.9 590.2 599.9 621.4 656.4 687.6 702.0 719.4 740.9 768.1 803.8 831.1 852.6 884.4 923.3 954.5 972.0 1007.7 1035.0 1073.9 1088.3 1119.5 1154.4 1185.6 1200.0 702.0 : 27.3 63.0 80.5 111.7 150.6 182.4 203.9 231.2 266.9 294.1 315.6 333.0 347.4 378.6 417.5 435.1 444.8 466.9 498.0 537.0 551.3 561.0 582.5 617.5 648.7 663.0 680.4 702.0 729.2 764.9 792.2 813.7 845.5 884.4 915.6 933.1 968.8 996.1 1035.0 1049.4 1080.6 1115.5 1146.7 1161.1 1200.0 729.2 : 35.7 53.3 84.5 123.4 155.1 176.6 203.9 239.6 266.9 288.4 305.8 320.1 351.3 390.2 407.8 417.5 439.6 470.8 509.7 524.1 533.7 555.2 590.2 621.4 635.8 653.2 674.7 702.0 737.7 764.9 786.4 818.2 857.1 888.3 905.9 941.6 968.8 1007.7 1022.1 1053.3 1088.3 1119.5 1133.8 1172.7 1200.0 764.9 : 17.6 48.8 87.7 119.4 140.9 168.2 203.9 231.2 252.7 270.1 284.4 315.6 354.5 372.1 381.8 403.9 435.1 474.0 488.4 498.0 519.6 554.5 585.7 600.1 617.5 639.0 666.3 702.0 729.2 750.7 782.5 821.4 852.6 870.2 905.9 933.1 972.0 986.4 1017.6 1052.6 1083.8 1098.1 1137.0 1164.3 1200.0 782.5 : 31.2 70.1 101.9 123.4 150.6 186.3 213.6 235.1 252.5 266.9 298.1 337.0 354.5 364.2 386.3 417.5 456.4 470.8 480.5 502.0 537.0 568.1 582.5 599.9 621.4 648.7 684.4 711.6 733.1 764.9 803.8 835.0 852.6 888.3 915.6 954.5 968.8 1000.0 1035.0 1066.2 1080.6 1119.5 1146.7 1182.4 1200.0 813.7 : 38.9 70.7 92.2 119.4 155.1 182.4 203.9 221.3 235.7 266.9 305.8 323.4 333.0 355.1 386.3 425.2 439.6 449.3 470.8 505.8 537.0 551.3 568.7 590.2 617.5 653.2 680.4 702.0 733.7 772.6 803.8 821.4 857.1 884.4 923.3 937.6 968.8 1003.8 1035.0 1049.4 1088.3 1115.5 1151.2 1168.8 1200.0 852.6 : 31.8 53.3 80.5 116.2 143.5 165.0 182.4 196.8 228.0 266.9 284.4 294.1 316.2 347.4 386.3 400.7 410.4 431.9 466.9 498.0 512.4 529.8 551.3 578.6 614.3 641.5 663.0 694.8 733.7 764.9 782.5 818.2 845.5 884.4 898.7 929.9 964.9 996.1 1010.5 1049.4 1076.6 1112.3 1129.9 1161.1 1200.0 884.4 : 21.5 48.8 84.5 111.7 133.2 150.6 165.0 196.2 235.1 252.7 262.4 284.4 315.6 354.5 368.9 378.6 400.1 435.1 466.3 480.6 498.0 519.6 546.8 582.5 609.8 631.3 663.0 702.0 733.1 750.7 786.4 813.7 852.6 867.0 898.2 933.1 964.3 978.7 1017.6 1044.9 1080.6 1098.1 1129.3 1168.2 1200.0 905.9 : 27.3 63.0 90.2 111.7 129.1 143.5 174.7 213.6 231.2 240.9 262.9 294.1 333.0 347.4 357.1 378.6 413.6 444.8 459.1 476.5 498.0 525.3 561.0 588.3 609.8 641.5 680.4 711.6 729.2 764.9 792.2 831.1 845.5 876.6 911.6 942.8 957.2 996.1 1023.4 1059.1 1076.6 1107.8 1146.7 1178.5 1200.0 933.1 : 35.7 63.0 84.5 101.9 116.2 147.4 186.3 203.9 213.6 235.7 266.9 305.8 320.1 329.8 351.3 386.3 417.5 431.9 449.3 470.8 498.0 533.7 561.0 582.5 614.3 653.2 684.4 702.0 737.7 764.9 803.8 818.2 849.4 884.4 915.6 929.9 968.8 996.1 1031.8 1049.4 1080.6 1119.5 1151.2 1172.7 1200.0 968.8 : 27.3 48.8 66.2 80.5 111.7 150.6 168.2 177.9 200.0 231.2 270.1 284.4 294.1 315.6 350.6 381.8 396.2 413.6 435.1 462.3 498.0 525.3 546.8 578.6 617.5 648.7 666.3 702.0 729.2 768.1 782.5 813.7 848.7 879.9 894.2 933.1 960.4 996.1 1013.7 1044.9 1083.8 1115.5 1137.0 1164.3 1200.0 996.1 : 21.5 38.9 53.3 84.5 123.4 140.9 150.6 172.7 203.9 242.8 257.2 266.9 288.4 323.4 354.5 368.9 386.3 407.8 435.1 470.8 498.0 519.6 551.3 590.2 621.4 639.0 674.7 702.0 740.9 755.2 786.4 821.4 852.6 867.0 905.9 933.1 968.8 986.4 1017.6 1056.5 1088.3 1109.8 1137.0 1172.7 1200.0 1017.6: 17.4 31.8 63.0 101.9 119.4 129.1 151.2 182.4 221.3 235.7 245.4 266.9 301.8 333.0 347.4 364.8 386.3 413.6 449.3 476.5 498.0 529.8 568.7 599.9 617.5 653.2 680.4 719.4 733.7 764.9 799.9 831.1 845.5 884.4 911.6 947.3 964.9 996.1 1035.0 1066.8 1088.3 1115.5 1151.2 1178.5 1200.0 1035.0: 14.4 45.6 84.5 102.0 111.7 133.8 165.0 203.9 218.3 228.0 249.5 284.4 315.6 330.0 347.4 368.9 396.2 431.9 459.1 480.6 512.4 551.3 582.5 600.1 635.8 663.0 702.0 716.3 747.5 782.5 813.7 828.1 867.0 894.2 929.9 947.5 978.7 1017.6 1049.4 1070.9 1098.1 1133.8 1161.1 1182.6 1200.0 1049.4: 31.2 70.1 87.7 97.4 119.4 150.6 189.5 203.9 213.6 235.1 270.1 301.3 315.6 333.0 354.5 381.8 417.5 444.8 466.3 498.0 537.0 568.1 585.7 621.4 648.7 687.6 702.0 733.1 768.1 799.3 813.7 852.6 879.9 915.6 933.1 964.3 1003.2 1035.0 1056.5 1083.8 1119.5 1146.7 1168.2 1185.6 1200.0 1080.6: 38.9 56.5 66.2 88.2 119.4 158.3 172.7 182.4 203.9 238.9 270.1 284.4 301.8 323.4 350.6 386.3 413.6 435.1 466.9 505.8 537.0 554.5 590.2 617.5 656.4 670.8 702.0 736.9 768.1 782.5 821.4 848.7 884.4 901.9 933.1 972.0 1003.8 1025.3 1052.6 1088.3 1115.5 1137.0 1154.4 1168.8 1200.0 1119.5: 17.6 27.3 49.3 80.5 119.4 133.8 143.5 165.0 200.0 231.2 245.5 262.9 284.4 311.7 347.4 374.7 396.2 427.9 466.9 498.0 515.6 551.3 578.6 617.5 631.9 663.0 698.0 729.2 743.6 782.5 809.8 845.5 863.0 894.2 933.1 964.9 986.4 1013.7 1049.4 1076.6 1098.1 1115.5 1129.9 1161.1 1200.0 1137.0: 9.7 31.8 63.0 101.9 116.2 125.9 147.4 182.4 213.6 228.0 245.4 266.9 294.1 329.8 357.1 378.6 410.4 449.3 480.5 498.0 533.7 561.0 599.9 614.3 645.5 680.4 711.6 726.0 764.9 792.2 827.9 845.5 876.6 915.6 947.3 968.8 996.1 1031.8 1059.1 1080.6 1098.0 1112.3 1143.5 1182.4 1200.0 1146.7: 22.1 53.3 92.2 106.5 116.2 137.7 172.7 203.9 218.3 235.7 257.2 284.4 320.1 347.4 368.9 400.7 439.6 470.8 488.4 524.1 551.3 590.2 604.6 635.8 670.8 702.0 716.3 755.2 782.5 818.2 835.8 867.0 905.9 937.6 959.1 986.4 1022.1 1049.4 1070.9 1088.3 1102.6 1133.8 1172.7 1190.3 1200.0 1168.8: 31.2 70.1 84.5 94.2 115.7 150.6 181.8 196.2 213.6 235.1 262.4 298.1 325.3 346.8 378.6 417.5 448.7 466.3 502.0 529.2 568.1 582.5 613.7 648.7 679.9 694.2 733.1 760.4 796.1 813.7 844.9 883.8 915.6 937.1 964.3 1000.0 1027.3 1048.8 1066.2 1080.6 1111.8 1150.7 1168.2 1177.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 9.6880 .. 38.9058 cents 3645/3584, 29.2178 cents 896/891, 9.6880 cents 2: 24.0551 .. 70.6724 cents 10125/9856, 46.6173 cents 54208/54675,-14.8506 cents 3: 45.5614 .. 101.8667 cents 125/121, 56.3053 cents 616/625,-25.1110 cents 4: 80.5370 .. 123.3730 cents 3969/3872, 42.8359 cents 242/245,-21.3296 cents 5: 111.7313 .. 155.1396 cents 525/512, 43.4083 cents 2816/2835,-11.6417 cents 6: 125.9218 .. 189.5428 cents 98415/94864, 63.6210 cents 3584/3645,-29.2178 cents 7: 143.4979 .. 221.3095 cents 2025/1936, 77.8115 cents 10648/10935,-46.0449 cents 8: 165.0042 .. 242.8158 cents 2025/1936, 77.8115 cents 121/125,-56.3053 cents 9: 192.2683 .. 270.0799 cents 2025/1936, 77.8115 cents 123904/127575,-50.5475 cents 10: 227.9651 .. 305.7767 cents 2025/1936, 77.8115 cents 5929/6075,-42.1147 cents 11: 245.3646 .. 333.0408 cents 81/77, 87.6762 cents 704/729,-60.4121 cents 12: 262.9407 .. 354.5471 cents 5103/4840, 91.6063 cents 121/126,-70.1000 cents 13: 284.4470 .. 386.3137 cents 35/33, 101.8667 cents 121/126,-70.1000 cents 14: 311.7111 .. 417.5080 cents 1029/968, 105.7968 cents 704/735,-74.6026 cents 15: 347.4079 .. 449.2746 cents 35/33, 101.8667 cents 121/126,-70.1000 cents 16: 364.8074 .. 470.7809 cents 1701/1600, 105.9735 cents 20/21,-84.4672 cents 17: 386.3137 .. 505.1841 cents 648/605, 118.8704 cents 20/21,-84.4672 cents 18: 407.8200 .. 536.9508 cents 320/297, 129.1308 cents 121/128,-97.3641 cents 19: 435.0841 .. 568.7174 cents 175/162, 133.6333 cents 33/35,-101.8667 cents 20: 462.3482 .. 590.2237 cents 2205/2048, 127.8755 cents 1152/1225,-106.3692 cents 21: 498.0450 .. 621.4180 cents 189/176, 123.3730 cents 128/135,-92.1787 cents 22: 519.5513 .. 653.1846 cents 175/162, 133.6333 cents 33/35,-101.8667 cents 23: 546.8154 .. 680.4487 cents 175/162, 133.6333 cents 1152/1225,-106.3692 cents 24: 578.5820 .. 701.9550 cents 189/176, 123.3730 cents 33/35,-101.8667 cents 25: 609.7763 .. 737.6518 cents 2205/2048, 127.8755 cents 128/135,-92.1787 cents 26: 631.2826 .. 764.9159 cents 175/162, 133.6333 cents 1152/1225,-106.3692 cents 27: 663.0492 .. 792.1800 cents 320/297, 129.1308 cents 33/35,-101.8667 cents 28: 694.8159 .. 813.6863 cents 648/605, 118.8704 cents 121/128,-97.3641 cents 29: 729.2191 .. 835.1926 cents 1701/1600, 105.9735 cents 20/21,-84.4672 cents 30: 750.7254 .. 852.5921 cents 35/33, 101.8667 cents 20/21,-84.4672 cents 31: 782.4920 .. 888.2889 cents 1029/968, 105.7968 cents 121/126,-70.1000 cents 32: 813.6863 .. 915.5530 cents 35/33, 101.8667 cents 704/735,-74.6026 cents 33: 845.4529 .. 937.0593 cents 5103/4840, 91.6063 cents 121/126,-70.1000 cents 34: 866.9592 .. 954.6354 cents 81/77, 87.6762 cents 121/126,-70.1000 cents 35: 894.2233 .. 972.0349 cents 2025/1936, 77.8115 cents 704/729,-60.4121 cents 36: 929.9201 .. 1007.7317 cents 2025/1936, 77.8115 cents 5929/6075,-42.1147 cents 37: 957.1842 .. 1034.9958 cents 2025/1936, 77.8115 cents 123904/127575,-50.5475 cents 38: 978.6905 .. 1056.5021 cents 2025/1936, 77.8115 cents 121/125,-56.3053 cents 39: 1010.4572 .. 1074.0782 cents 98415/94864, 63.6210 cents 10648/10935,-46.0449 cents 40: 1044.8604 .. 1088.2687 cents 525/512, 43.4083 cents 3584/3645,-29.2178 cents 41: 1076.6270 .. 1119.4630 cents 3969/3872, 42.8359 cents 2816/2835,-11.6417 cents 42: 1098.1333 .. 1154.4386 cents 125/121, 56.3053 cents 242/245,-21.3296 cents 43: 1129.3276 .. 1175.9449 cents 10125/9856, 46.6173 cents 616/625,-25.1110 cents 44: 1161.0942 .. 1190.3120 cents 3645/3584, 29.2178 cents 54208/54675,-14.8506 cents
SHOW DATA
Number of notes : 45 -- Interval properties -- Smallest interval : 896/891, 9.6880 cents, class 1 Average step (divided formal octave): 26.6667 cents Largest one step interval : 45/44, 38.9058 cents Average / Smallest step : 2.752557 Largest / Average step : 1.458966 Largest / Smallest step : 4.015889 Median interval of one step : 64/63, 27.2641 cents, amount: 6 Most common interval of one step : 56/55, 31.1943 cents, amount: 7 Least squares average step : 26.93902 cents, oct.: 1212.25582 cents Scale is not proper Step pattern alph. order: ABCDEFBGDHIHDJAFKIHABFEFBAHIKFAJDHIHDGBFAKCLF Step pattern size order : LBAEJHBCEGKGEILHDKGLBHJHBLGKDHLIEGKGECBHLDAFH Scale is not a Constant Structure Scale diversity : 1.483818 Lumma stability : 0.016147 Lumma impropriety factor : 0.911685 Number of different interval sizes : 392 = 8.90909 / class Number of one step interval sizes : 12 Highest interval variety : 23 Mean interval variety : 18.00000 = 18 Median interval variety : 12 Lowest interval variety : 12 Smallest interval difference : 9801/9800, 0.1766 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 31 Most common triad is 0.0 498.045 701.955 cents, amount: 19 Number of recognisable fifths : 60, average 703.5351 cents Number of appreciable fifths : 45, average 702.0533 cents Scale contains a complete diamond : 1 3 7 9 21 27 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 41 = 91.1111% Scale is differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 1815 (O: 1815 U: 1815) Highest odd numerator or denominator: 55 Scale harmonicity : 0.010338 Average absolute harmonicity : 0.089273 Specific harmonicity : 0.070631 Fundamental : 1/332640, -18.3436 octaves, 0.0008 Hz. Guide tone : 665280, 19.3436 octaves, 174054256.083 Hz. Exponens Consonantiae : 2.212987E+11, 37.68720 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 658.5, average 14.63333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 47.10939, average 1.04688 Sum of Tenney's harmonic distance : 94.13240, average 2.09183 Vogel's harmonic complexity : 37.62222 Wille's k value : 171517 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 12 Triangular lattice diameter : 6 Lattice compactness : 3990.81566, average 3.85586 Lattice compactness (without 2's) : 2412.35369, average 2.33078 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.33333 85 1 3: -3 .. 3 0.08889 48 6 5: -1 .. 1 0.02222 17 6 7: -1 .. 1 0.02222 19 15 11: -1 .. 1 -0.02222 17 17 Average exponent except 2's : 5 / 45 = 0.11111 Average absolute exponent except 2's: 101 / 45 = 2.24444
FIT/MODE
45: 1 1 0 1 1 2 0 1 1 1 1 1 1 1 1 2 0 2 1 1 1 1 1 1 1 1 1 2 0 1 2 1 1 1 1 1 1 1 0 2 1 1 0 1 1 N SD: 7.5031 c. M: 13.6863 c. 46: 1 1 0 1 2 1 0 1 1 1 1 1 1 1 2 1 1 1 1 2 0 1 2 1 0 2 1 1 1 1 2 1 1 1 1 1 1 1 0 1 2 1 0 1 1 N I SD: 6.5585 c. M: 12.8188 c. 49: 2 0 1 0 2 1 1 0 1 1 2 1 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 2 1 1 0 1 1 2 0 1 1 1 N SD: 6.7416 c. M: 11.9474 c. 52: 2 0 1 1 1 2 0 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 1 1 2 0 1 1 1 N SD: 6.4074 c. M:-12.1755 c. 53: 2 0 1 1 1 2 0 1 1 1 2 1 1 1 2 1 1 2 1 2 0 2 1 2 0 2 1 2 1 1 2 1 1 1 2 1 1 1 0 2 1 1 1 1 1 N SD: 5.7996 c. M: 10.0290 c. 58: 2 1 0 1 2 1 1 1 1 1 2 1 1 2 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1 1 2 2 1 1 2 1 1 1 1 1 2 1 0 1 2 N I SD: 4.4886 c. M: 10.1851 c. 60: 2 1 0 1 2 2 0 1 1 2 1 2 1 1 2 2 1 2 1 2 1 1 2 1 1 2 1 2 1 2 2 1 1 2 1 2 1 1 0 2 2 1 0 1 2 N I SD: 5.6608 c. M:-9.3629 c. 61: 2 1 0 1 2 2 0 1 1 2 2 1 1 2 2 1 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 2 1 1 2 2 1 1 0 2 2 1 0 1 2 N I SD: 5.3256 c. M:-8.5389 c. 63: 2 1 0 1 2 2 1 1 1 1 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 1 2 1 1 1 1 2 2 1 0 1 2 N I SD: 5.1828 c. M: 8.4207 c. 66: 2 1 0 2 2 1 1 1 1 2 2 1 1 2 2 2 1 2 1 3 0 2 2 2 0 3 1 2 1 2 2 2 1 1 2 2 1 1 1 1 3 1 0 1 2 N SD: 4.9373 c. M:-8.5038 c. 68: 2 1 1 1 2 2 0 1 2 1 2 2 1 2 2 2 1 2 1 2 1 2 2 2 1 2 1 2 1 2 2 2 1 2 2 1 2 1 0 2 2 1 1 1 2 N I SD: 5.1874 c. M:-8.1865 c. 69: 2 1 1 1 2 2 0 1 2 1 2 2 1 2 2 2 1 2 2 2 1 1 2 2 1 2 2 2 1 2 2 2 1 2 2 1 1 1 1 2 2 1 1 1 2 N SD: 4.8589 c. M: 8.9088 c. 71: 2 1 1 1 2 2 1 1 1 2 2 1 2 2 2 2 1 2 1 3 1 1 3 1 1 3 1 2 1 2 2 2 2 1 2 2 1 1 1 2 2 1 1 1 2 N I SD: 4.7036 c. M:-7.9042 c. 72: 2 1 1 1 2 2 1 1 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 2 2 2 1 1 1 2 2 1 1 1 2 N I SD: 2.7456 c. M:-5.8650 c. 90: 3 1 1 1 3 2 1 2 1 2 3 2 2 2 3 2 2 2 2 3 1 3 2 3 1 3 2 2 2 2 3 2 2 2 3 2 1 2 1 2 3 1 1 2 2 N SD: 3.5444 c. M: 5.0042 c. 94: 3 1 1 2 2 3 1 1 2 2 3 2 2 2 3 3 1 3 2 3 1 3 2 3 1 3 2 3 1 3 3 2 2 2 3 2 2 1 1 3 3 1 1 2 2 N SD: 2.7018 c. M:-5.6623 c. 111: 4 1 1 2 3 3 1 2 2 2 4 2 2 3 4 3 1 4 2 4 1 3 3 3 1 4 2 4 1 3 4 3 2 2 4 2 2 2 1 3 4 1 1 2 3 N SD: 2.6073 c. M:-4.8948 c. 114: 4 1 1 2 3 3 2 1 2 3 3 3 2 3 4 3 1 4 2 4 1 3 4 3 1 4 2 4 1 3 4 3 2 3 3 3 2 1 2 3 3 2 1 2 3 N SD: 2.7667 c. M: 3.9495 c. 117: 4 1 1 2 4 3 1 2 2 3 3 3 2 3 4 3 1 4 3 3 2 3 3 3 2 3 3 4 1 3 4 3 2 3 3 3 2 2 1 3 4 2 1 2 3 N SD: 2.7336 c. M:-4.7233 c. 118: 4 1 1 2 4 3 1 2 2 3 3 3 2 3 4 3 2 3 3 4 1 3 4 3 1 4 3 3 2 3 4 3 2 3 3 3 2 2 1 3 4 2 1 2 3 N SD: 1.8973 c. M: 3.1113 c. 130: 4 2 1 2 4 3 2 2 2 3 4 3 2 4 4 3 2 4 3 4 2 3 4 3 2 4 3 4 2 3 4 4 2 3 4 3 2 2 2 3 4 2 1 3 3 N SD: 1.7664 c. M:-3.5019 c. 152: 5 2 1 3 4 4 2 2 3 3 5 3 3 4 5 4 2 5 3 5 2 4 4 4 2 5 3 5 2 4 5 4 3 3 5 3 3 2 2 4 5 2 1 3 4 N SD: 1.3298 c. M:-2.9033 c. 159: 5 2 1 3 5 4 2 2 3 4 4 4 3 4 5 4 3 4 4 5 2 4 5 4 2 5 4 4 3 4 5 4 3 4 4 4 3 2 2 4 5 3 1 3 4 N SD: 1.6335 c. M:-2.8564 c. 183: 6 2 2 3 5 5 2 3 3 4 6 4 3 5 6 5 2 6 4 6 2 5 5 5 2 6 4 6 2 5 6 5 3 4 6 4 3 3 2 5 6 2 2 3 5 N SD: 1.3082 c. M:-2.6129 c. 204: 7 2 2 3 6 6 2 3 4 4 6 5 4 5 7 5 3 6 5 6 3 5 6 5 3 6 5 6 3 5 7 5 4 5 6 4 4 3 2 6 6 3 2 4 5 N SD: 1.4709 c. M:-2.3041 c. 212: 7 2 2 4 6 6 2 3 4 5 6 5 4 5 7 6 3 6 5 7 2 6 6 6 2 7 5 6 3 6 7 5 4 5 6 5 4 3 2 6 7 3 2 3 6 N SD: 1.2934 c. M: 2.7680 c. 224: 7 3 2 4 6 6 3 3 4 5 7 5 4 6 7 6 3 7 5 7 3 6 6 6 3 7 5 7 3 6 7 6 4 5 7 5 4 3 3 6 7 3 2 4 6 N SD: 0.8710 c. M: 1.5857 c. 270: 9 3 2 5 8 7 3 4 5 6 8 6 5 7 9 7 4 8 6 9 3 7 8 7 3 9 6 8 4 7 9 7 5 6 8 6 5 4 3 7 9 4 2 5 7 N SD: 0.4770 c. M:-1.0942 c. 342: 11 4 3 6 10 9 4 5 6 8 10 8 6 9 11 9 5 10 8 11 4 9 10 9 4 11 8 10 5 9 11 9 6 8 10 8 6 5 4 9 11 5 3 6 9 N SD: 0.3127 c. M: 0.6414 c. 494: 16 6 4 9 14 13 6 7 9 11 15 11 9 13 16 13 7 15 11 16 6 13 14 13 6 16 11 15 7 13 16 13 9 11 15 11 9 7 6 13 16 7 4 9 13 N SD: 0.2696 c. M:-0.5530 c. 612: 20 7 5 11 18 16 7 9 11 14 18 14 11 16 20 16 9 18 14 20 7 16 18 16 7 20 14 18 9 16 20 16 11 14 18 14 11 9 7 16 20 9 5 11 16 N SD: 0.2128 c. M: 0.3491 c. 742: 24 9 6 13 22 19 9 11 13 17 22 17 13 20 24 19 11 22 17 24 9 19 22 19 9 24 17 22 11 19 24 20 13 17 22 17 13 11 9 19 24 11 6 14 19 N SD: 0.2092 c. M:-0.4665 c. 836: 27 10 7 15 24 22 10 12 15 19 25 19 15 22 27 22 12 25 19 27 10 22 24 22 10 27 19 25 12 22 27 22 15 19 25 19 15 12 10 22 27 12 7 15 22 N SD: 0.1582 c. M: 0.3847 c. 1084: 35 13 9 19 32 28 13 16 19 25 32 25 19 29 35 28 16 32 25 35 13 28 32 28 13 35 25 32 16 28 35 29 19 25 32 25 19 16 13 28 35 16 9 20 28 N SD: 0.1758 c. M: 0.3344 c. 1106: 36 13 9 20 32 29 13 16 20 25 33 25 20 29 36 29 16 33 25 36 13 29 32 29 13 36 25 33 16 29 36 29 20 25 33 25 20 16 13 29 36 16 9 20 29 N SD: 0.1255 c. M: 0.2705 c. 1236: 40 15 10 22 36 32 15 18 22 28 37 28 22 33 40 32 18 37 28 40 15 32 36 32 15 40 28 37 18 32 40 33 22 28 37 28 22 18 15 32 40 18 10 23 32 N SD: 0.0975 c. M: 0.1649 c. 1506: 49 18 12 27 44 39 18 22 27 34 45 34 27 40 49 39 22 45 34 49 18 39 44 39 18 49 34 45 22 39 49 40 27 34 45 34 27 22 18 39 49 22 12 28 39 N SD: 0.0811 c. M: 0.1405 c. 1578: 51 19 13 28 46 41 19 23 28 36 47 36 28 42 51 41 23 47 36 51 19 41 46 41 19 51 36 47 23 41 51 42 28 36 47 36 28 23 19 41 51 23 13 29 41 N SD: 0.0778 c. M:-0.1616 c. 1848: 60 22 15 33 54 48 22 27 33 42 55 42 33 49 60 48 27 55 42 60 22 48 54 48 22 60 42 55 27 48 60 49 33 42 55 42 33 27 22 48 60 27 15 34 48 N SD: 0.0359 c. M: 0.0692 c. 3737: 121 45 30 67 109 97 45 54 67 85 111 85 67 99 121 97 55 111 85 121 45 97 109 97 45 121 85 111 55 97 121 99 67 85 111 85 67 54 45 97 121 55 30 69 97 N SD: 0.0311 c. M: 0.0624 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: 1.2651 cents 8 .. 16 match: 8 H SD: 1.7898 cents 9 .. 18 match: 9 H SD: 2.4464 cents 10 .. 20 match: 10 H SD: 2.2494 cents 11 .. 22 match: 11 H SD: 1.6318 cents 12 .. 24 match: 12 H SD: 1.9951 cents 13 .. 26 match: 13 H SD: 3.0127 cents 14 .. 28 match: 14 H SD: 1.3931 cents 15 .. 30 match: 15 H SD: 1.7639 cents 16 .. 32 match: 16 H SD: 1.5741 cents 17 .. 34 match: 17 H SD: 2.7367 cents 18 .. 36 match: 18 H SD: 1.7858 cents 19 .. 38 match: 19 H SD: 2.0662 cents 20 .. 40 match: 20 H SD: 1.9554 cents 21 .. 42 match: 21 H SD: 1.7352 cents 22 .. 44 match: 22 H SD: 1.3980 cents 23 .. 46 match: 23 H SD: 2.0053 cents 24 .. 48 match: 24 H SD: 1.5783 cents 25 .. 50 match: 25 H SD: 1.6458 cents 26 .. 52 match: 26 H SD: 2.0560 cents 27 .. 54 match: 26 S SD: 1.5246 cents 28 .. 56 match: 28 H SD: 1.2852 cents 29 .. 58 match: 29 H SD: 1.7361 cents 30 .. 60 match: 29 SD: 1.2890 cents 31 .. 62 match: 30 SD: 1.5122 cents 32 .. 64 match: 32 H SD: 1.2453 cents 33 .. 66 match: 32 S SD: 1.4492 cents 34 .. 68 match: 31 SD: 1.7792 cents 35 .. 70 match: 33 SD: 1.1391 cents 36 .. 72 match: 35 SD: 1.1854 cents 37 .. 74 match: 32 SD: 1.5274 cents 38 .. 76 match: 35 SD: 1.3365 cents 39 .. 78 match: 36 SD: 1.3295 cents 40 .. 80 match: 36 SD: 1.0843 cents 41 .. 82 match: 35 SD: 1.2012 cents 42 .. 84 match: 37 SD: 1.0440 cents 43 .. 86 match: 37 SD: 1.3102 cents 44 .. 88 match: 40 SD: 1.0845 cents 45 .. 90 match: 39 SD: 1.0118 cents 46 .. 92 match: 35 SD: 1.2827 cents 47 .. 94 match: 38 SD: 1.1790 cents 48 .. 96 match: 39 SD: 1.0329 cents 49 .. 98 match: 39 SD: 0.9905 cents 50 .. 100 match: 40 SD: 1.1167 cents 51 .. 102 match: 40 SD: 1.1020 cents 52 .. 104 match: 39 SD: 1.0412 cents 53 .. 106 match: 43 SD: 1.0038 cents 54 .. 108 match: 40 SD: 0.8089 cents 55 .. 110 match: 42 SD: 0.7545 cents 56 .. 112 match: 43 SD: 0.8889 cents 57 .. 114 match: 40 SD: 0.9634 cents 58 .. 116 match: 42 SD: 0.8965 cents 59 .. 118 match: 42 SD: 0.9229 cents 60 .. 120 match: 43 SD: 0.8416 cents 61 .. 122 match: 40 SD: 0.8898 cents 62 .. 124 match: 41 SD: 0.9881 cents 63 .. 126 match: 41 SD: 0.8484 cents 64 .. 128 match: 43 SD: 0.8270 cents 65 .. 130 match: 41 SD: 0.8271 cents 66 .. 132 match: 42 SD: 0.7580 cents 67 .. 134 match: 42 SD: 0.7820 cents 68 .. 136 match: 42 SD: 0.8303 cents 69 .. 138 match: 43 SD: 0.8263 cents 70 .. 140 match: 44 SD: 0.7535 cents 71 .. 142 match: 44 SD: 0.7710 cents 72 .. 144 match: 43 SD: 0.7004 cents 73 .. 146 match: 42 SD: 0.7663 cents 74 .. 148 match: 43 SD: 0.7816 cents 75 .. 150 match: 42 SD: 0.7586 cents 76 .. 152 match: 41 SD: 0.7615 cents 77 .. 154 match: 43 SD: 0.6116 cents 78 .. 156 match: 44 SD: 0.7224 cents 79 .. 158 match: 44 SD: 0.6837 cents 80 .. 160 match: 44 SD: 0.5104 cents 81 .. 162 match: 44 SD: 0.6152 cents 82 .. 164 match: 44 SD: 0.6418 cents 83 .. 166 match: 43 SD: 0.6276 cents 84 .. 168 match: 43 SD: 0.5716 cents 85 .. 170 match: 43 SD: 0.6006 cents 86 .. 172 match: 44 SD: 0.6175 cents 87 .. 174 match: 44 SD: 0.6429 cents 88 .. 176 match: 44 SD: 0.5605 cents 89 .. 178 match: 44 SD: 0.6333 cents 90 .. 180 match: 44 SD: 0.5346 cents 91 .. 182 match: 43 SD: 0.6010 cents 92 .. 184 match: 44 SD: 0.6336 cents 93 .. 186 match: 44 SD: 0.6320 cents 94 .. 188 match: 43 SD: 0.6189 cents 95 .. 190 match: 45 SD: 0.5893 cents 96 .. 192 match: 45 SD: 0.4879 cents 99 .. 198 match: 45 SD: 0.4523 cents 110 .. 220 match: 44 SD: 0.4899 cents 111 .. 222 match: 44 SD: 0.5247 cents 112 .. 224 match: 44 SD: 0.4185 cents 113 .. 226 match: 44 SD: 0.4701 cents 114 .. 228 match: 44 SD: 0.4927 cents 115 .. 230 match: 44 SD: 0.4805 cents 116 .. 232 match: 44 SD: 0.5117 cents 117 .. 234 match: 44 SD: 0.5050 cents 118 .. 236 match: 44 SD: 0.4591 cents 119 .. 238 match: 44 SD: 0.4383 cents 120 .. 240 match: 44 SD: 0.3936 cents 121 .. 242 match: 44 SD: 0.4187 cents 126 .. 252 match: 45 SD: 0.3822 cents 135 .. 270 match: 45 SD: 0.3545 cents 140 .. 280 match: 45 SD: 0.3281 cents 144 .. 288 match: 44 SD: 0.3175 cents 145 .. 290 match: 44 SD: 0.3731 cents 146 .. 292 match: 44 SD: 0.4220 cents 147 .. 294 match: 44 SD: 0.4044 cents 148 .. 296 match: 44 SD: 0.4235 cents 149 .. 298 match: 45 SD: 0.4217 cents 150 .. 300 match: 45 SD: 0.3716 cents 151 .. 302 match: 45 SD: 0.3711 cents 152 .. 304 match: 45 SD: 0.3635 cents 154 .. 308 match: 45 SD: 0.3374 cents 157 .. 314 match: 45 SD: 0.3301 cents 160 .. 320 match: 45 SD: 0.3113 cents 162 .. 324 match: 45 SD: 0.3046 cents 168 .. 336 match: 45 SD: 0.2674 cents 180 .. 360 match: 45 SD: 0.2575 cents 198 .. 396 match: 45 SD: 0.2352 cents 210 .. 420 match: 45 SD: 0.2301 cents 216 .. 432 match: 45 SD: 0.2224 cents 217 .. 434 match: 45 SD: 0.2210 cents 220 .. 440 match: 45 SD: 0.2031 cents 240 .. 480 match: 45 SD: 0.1978 cents 252 .. 504 match: 45 SD: 0.1840 cents 264 .. 528 match: 45 SD: 0.1684 cents 280 .. 560 match: 45 SD: 0.1643 cents 297 .. 594 match: 45 SD: 0.1586 cents 319 .. 638 match: 45 SD: 0.1424 cents 320 .. 640 match: 45 SD: 0.1394 cents 350 .. 700 match: 45 SD: 0.1371 cents 352 .. 704 match: 45 SD: 0.1202 cents 360 .. 720 match: 45 SD: 0.1151 cents 420 .. 840 match: 45 SD: 0.1082 cents 432 .. 864 match: 45 SD: 0.1041 cents 448 .. 896 match: 45 SD: 0.0991 cents 480 .. 960 match: 45 SD: 0.0840 cents 540 .. 1080 match: 45 SD: 0.0804 cents 560 .. 1120 match: 45 SD: 0.0784 cents 576 .. 1152 match: 45 SD: 0.0766 cents