Anatomy of an Octave
Below, for the reference of tuning enthusiasts, is a table of more than a thousand pitches within an octave. The table contains all pitches that meet any one of the following six criteria:
All ratios between whole numbers 64 and lower
All ratios between 31-limit numbers up to 96 (31-limit meaning that the numbers contain no prime-number factors larger than 31)
Harmonics up to 255 (each whole number divided by the closest inferior power of 2)
All ratios between 11-limit numbers up to 128
All ratios between 5-limit numbers up to 1024
Certain historically important (or mathematically interesting) ratios such as the schisma and Pythagorean commaThe table is similar to, but much briefer than, that found in Alain Danielou's encyclopedic but long out-of-print Comparative Table of Musical Intervals.
Ratio: Cents Name (if any) 1/1 0.000 tonic 1732/1731 0.9998 superparticular cent approximation 32805/32768 1.954 schisma (3 to the 8th/2 to the 12th x 5/8) 129/128 13.473 129th harmonic 126/125 13.795 121/120 14.367 100/99 17.399 99/98 17.576 96/95 18.128 93/92 18.716 92/91 18.921 91/90 19.130 88/87 19.786 85/84 20.488 81/80 21.506 syntonic comma 78/77 22.339 77/76 22.631 76/75 22.931 531441/524288 23.460 Pythagorean comma (3 to the 12th/2 to the 19th) 74/73 23.555 superparticular Pythagorean comma approximation 70/69 24.910 69/68 25.274 66/65 26.432 65/64 26.841 65th harmonic 64/63 27.264 63/62 27.700 62/61 28.151 61/60 28.616 60/59 29.097 59/58 29.594 58/57 30.109 57/56 30.642 56/55 31.194 Ptolemy's enharmonic 55/54 31.767 54/53 32.360 53/52 32.977 52/51 33.617 51/50 34.283 50/49 34.976 49/48 35.697 48/47 36.448 95/93 36.836 47/46 37.232 93/91 37.637 46/45 38.051 inferior quarter-tone (Ptolemy) 45/44 38.906 44/43 39.800 131/128 40.108 131st harmonic 87/85 40.263 43/42 40.737 128/125 41.059 diminished second (16/15 x 24/25) 42/41 41.719 41/40 42.749 525/512 43.408 enharmonic diesis (Avicenna) 40/39 43.831 39/38 44.970 superior quarter-tone (Eratosthenes) 77/75 45.561 38/37 46.169 37/36 47.434 36/35 48.770 superior quarter-tone (Archytas) 250/243 49.166 35/34 50.184 E.T. 1/4-tone approximation 34/33 51.682 33/32 53.273 33rd harmonic 65/63 54.105 32/31 54.964 inferior quarter-tone (Didymus) 95/92 55.552 63/61 55.851 125/121 56.305 31/30 56.767 superior quarter-tone (Didymus) 61/59 57.713 91/88 58.036 30/29 58.692 59/57 59.704 88/85 60.049 29/28 60.751 57/55 61.836 28/27 62.961 inferior quarter-tone (Archytas) 55/53 64.127 27/26 65.337 80/77 66.170 133/128 66.339 133rd harmonic 53/51 66.594 26/25 67.900 1/3-tone (Avicenna) 51/49 69.259 126/121 70.100 25/24 70.672 minor 5-limit half-step 49/47 72.145 24/23 73.681 95/91 74.473 47/45 75.283 117/112 75.612 23/22 76.956 91/87 77.821 68/65 78.114 45/43 78.706 67/64 79.307 67th harmonic 22/21 80.537 hard 1/2-step (Ptolemy, Avicenna, Safiud) 65/62 81.806 43/41 82.455 64/61 83.115 85/81 83.449 21/20 84.467 septimal semitone 62/59 85.864 41/39 86.580 61/58 87.308 81/77 87.676 20/19 88.801 256/243 90.225 Pythagorean half-step 59/56 90.346 39/37 91.139 58/55 91.946 135/128 92.179 limma ascendant 96/91 92.601 19/18 93.603 56/53 95.321 93/88 95.673 37/35 96.204 92/87 96.742 55/52 97.104 128/121 97.364 18/17 98.955 E.T. half-step approximation 2 to the 1/12th 100.000 equal-tempered half-step 89/84 100.099 ET half-step approximation 53/50 100.877 35/33 101.867 52/49 102.876 < 69/65 103.388 86/81 103.698 17/16 104.955 overtone half-step, 17th harmonic 50/47 107.121 33/31 108.237 49/46 109.377 81/76 110.307 16/15 111.731 major 5-limit half-step 63/59 113.564 47/44 114.189 31/29 115.458 77/72 116.234 46/43 116.757 61/57 117.417 137/128 117.638 137th harmonic 91/85 118.084 15/14 119.443 Cowell just half-step 59/55 121.540 44/41 122.256 29/27 123.712 43/40 125.204 57/53 125.963 14/13 128.298 69/64 130.229 69th harmonic 55/51 130.721 41/38 131.549 68/63 132.220 95/88 132.509 27/25 133.238 alternate Renaissance half-step 121/112 133.810 40/37 134.970 53/49 135.853 92/85 137.005 13/12 138.573 3/4-tone (Avicenna) 64/59 140.828 51/47 141.404 38/35 142.373 139/128 142.729 139th harmonic 63/58 143.159 88/81 143.498 25/23 144.353 87/80 145.218 62/57 145.568 37/34 146.389 135/124 147.143 49/45 147.428 61/56 148.059 85/78 148.786 12/11 150.637 undecimal "median" 1/2-step 95/87 152.295 59/54 153.307 47/43 153.989 35/32 155.140 35th harmonic 93/85 155.721 58/53 156.073 23/21 157.493 57/52 158.940 34/31 159.920 800/729 160.897 45/41 161.161 56/51 161.915 11/10 165.004 76/69 167.284 141/128 167.462 141st harmonic 54/49 168.213 43/39 169.035 75/68 169.627 32/29 170.423 85/77 171.125 53/48 171.550 21/19 173.268 < 52/47 175.021 31/28 176.210 567/512 176.646 72/65 177.069 < 41/37 177.718 51/46 178.636 61/55 179.253 71/64 179.697 71st harmonic 10/9 182.404 minor whole-tone 69/62 185.194 59/53 185.667 49/44 186.334 39/35 187.343 29/26 189.050 77/69 189.915 125/112 190.115 48/43 190.437 143/128 191.846 143rd harmonic 19/17 192.558 85/76 193.756 160/143 194.468 47/42 194.726 28/25 196.198 121/108 196.771 65/58 197.264 37/33 198.071 46/41 199.212 55/49 199.980 2 to the 1/6th 200.000 equal-tempered whole-tone 64/57 200.532 91/81 201.534 9/8 203.910 major whole-tone, 9th harmonic 62/55 207.404 53/47 207.998 44/39 208.835 35/31 210.104 96/85 210.686 61/54 211.020 87/77 211.388 26/23 212.253 95/84 213.046 112/99 213.598 43/38 214.005 60/53 214.764 77/68 215.188 145/128 215.891 145th harmonic 17/15 216.687 59/52 218.644 42/37 219.437 92/81 220.454 25/22 221.309 58/51 222.667 91/80 223.040 256/225 223.463 33/29 223.696 41/36 225.152 729/640 225.416 49/43 226.134 57/50 226.841 65/57 227.373 73/64 227.789 73rd harmonic 8/7 231.174 septimal whole-tone 87/76 234.019 63/55 235.104 55/48 235.677 47/41 236.444 39/34 237.527 225/196 238.886 31/27 239.171 147/128 239.607 54/47 240.358 169/147 241.449 23/20 241.961 61/53 243.380 2187/1900 243.545 38/33 244.240 144/125 244.969 diminished third (6/5 x 24/25) 53/46 245.230 121/105 245.541 15/13 247.741 52/45 250.304 37/32 251.344 37th harmonic 59/51 252.261 81/70 252.680 125/108 253.076 22/19 253.805 51/44 255.592 80/69 256.084 196/169 256.596 consonant interval (Avicenna) 29/25 256.950 65/56 258.015 36/31 258.874 43/37 260.174 93/80 260.677 50/43 261.110 57/49 261.816 64/55 262.368 149/128 263.002 149th harmonic 7/6 266.871 septimal minor third 90/77 270.080 76/65 270.672 62/53 271.531 55/47 272.125 48/41 272.893 41/35 273.923 75/64 274.582 augmented second (9/8 x 25/24) 34/29 275.378 95/81 276.007 61/52 276.357 88/75 276.736 27/23 277.591 47/40 279.193 20/17 281.358 53/45 283.281 33/28 284.447 46/39 285.792 151/128 286.086 151st harmonic 59/50 286.544 85/72 287.359 13/11 289.210 58/49 291.925 45/38 292.711 77/65 293.302 32/27 294.135 Pythagorean minor third 51/43 295.393 19/16 297.513 overtone minor third, 19th harmonic 63/53 299.231 44/37 299.974 2 to the 1/4th 300.000 equal-tempered minor third 69/58 300.652 25/21 301.847 81/68 302.865 56/47 303.319 31/26 304.508 68/57 305.487 105/88 305.777 37/31 306.308 43/36 307.608 92/77 308.130 49/41 308.589 153/128 308.865 153rd harmonic 55/46 309.357 61/51 309.974 91/76 311.841 6/5 315.641 5-limit minor third 77/64 320.144 77th harmonic 65/54 320.976 59/49 321.520 53/44 322.187 47/39 323.024 41/34 324.107 76/63 324.777 35/29 325.562 64/53 326.495 93/77 326.847 29/24 327.622 52/43 329.010 75/62 329.547 98/81 329.832 121/100 330.008 23/19 330.761 155/128 331.349 155th harmonic 63/52 332.208 40/33 333.041 57/47 333.961 91/75 334.771 17/14 336.130 243/200 337.148 62/51 338.125 45/37 338.880 28/23 340.552 95/78 341.344 39/32 342.483 39th harmonic 128/105 342.905 8000/6561 343.301 50/41 343.565 61/50 344.257 11/9 347.408 undecimal "median" third 93/76 349.478 60/49 350.617 49/40 351.338 38/31 352.477 157/128 353.545 157th harmonic 92/75 353.692 27/22 354.547 43/35 356.378 59/48 357.217 16/13 359.472 85/69 361.040 69/56 361.403 53/43 361.987 37/30 363.075 95/77 363.683 58/47 364.071 79/64 364.537 79th harmonic 100/81 364.807 121/98 364.984 21/17 365.825 68/55 367.324 47/38 367.994 99/80 368.914 26/21 369.747 57/46 371.194 31/25 372.408 36/29 374.333 159/128 375.460 159th harmonic 41/33 375.789 87/70 376.393 46/37 376.930 51/41 377.848 56/45 378.602 61/49 379.233 81/65 380.979 96/77 381.811 8192/6561 384.360 Pythagorean "schismatic" third 5/4 386.314 5-limit major third, 5th harmonic 69/55 392.598 64/51 393.090 59/47 393.665 54/43 394.347 49/39 395.169 44/35 396.178 161/128 397.100 161st harmonic 39/31 397.447 34/27 399.090 2 to the 1/3rd 400.000 equal-tempered major third 63/50 400.108 121/96 400.681 29/23 401.303 53/42 402.724 125/99 403.713 24/19 404.442 91/72 405.444 512/405 405.866 43/34 406.562 62/49 407.384 81/64 407.820 Pythagorean major third 19/15 409.244 52/41 411.465 33/26 412.745 80/63 413.578 47/37 414.163 61/48 414.930 14/11 417.508 163/128 418.474 163rd harmonic 65/51 419.931 51/40 420.597 88/69 421.089 125/98 421.289 37/29 421.767 60/47 422.762 23/18 424.364 55/43 426.114 87/68 426.577 32/25 427.373 diminished fourth 41/32 429.062 41st harmonic 50/39 430.145 59/46 430.897 77/60 431.875 9/7 435.084 septimal major third 85/66 437.996 58/45 439.353 165/128 439.587 165th harmonic 49/38 440.139 40/31 441.278 31/24 443.081 1323/1024 443.517 84/65 443.940 53/41 444.442 128/99 444.772 22/17 446.363 57/44 448.150 162/125 448.879 35/27 449.275 83/64 450.047 83rd harmonic 48/37 450.611 61/47 451.378 100/77 452.484 13/10 454.214 125/96 456.986 augmented third (5/4 x 25/24) 56/43 457.308 43/33 458.245 30/23 459.994 167/128 460.445 167th harmonic 47/36 461.597 64/49 462.348 98/75 463.069 17/13 464.428 89/68 465.925 72/55 466.278 55/42 466.851 38/29 467.936 59/45 468.948 21/16 470.781 septimal fourth 46/35 473.135 25/19 475.114 320/243 476.539 54/41 476.803 29/22 478.259 675/512 478.492 91/69 479.124 62/47 479.529 95/72 479.917 33/25 480.646 169/128 481.055 169th harmonic 37/28 482.518 41/31 484.027 45/34 485.286 49/37 486.308 53/40 487.191 57/43 487.950 61/46 488.610 65/49 489.190 69/52 489.702 85/64 491.269 85th harmonic 93/70 491.851 4/3 498.045 perfect fourth 2 to the 5/12ths 500.000 equal-tempered perfect fourth 171/128 501.423 171st harmonic 91/68 504.398 87/65 504.691 75/56 505.757 63/47 507.229 59/44 507.854 55/41 508.569 51/38 509.397 47/35 510.367 43/32 511.518 43rd harmonic 121/90 512.412 39/29 512.905 35/26 514.612 66/49 515.621 31/23 516.761 58/43 518.059 85/63 518.533 27/20 519.551 50/37 521.283 173/128 521.554 173rd harmonic 23/17 523.319 88/65 524.477 65/48 524.886 42/31 525.745 61/45 526.661 19/14 528.687 110/81 529.812 53/39 531.022 87/64 531.532 87th harmonic 34/25 532.328 49/36 533.742 64/47 534.493 15/11 536.951 512/375 539.104 56/41 539.764 41/30 540.794 175/128 541.453 175th harmonic 93/68 542.035 26/19 543.015 63/46 544.462 37/27 545.479 85/62 546.234 48/35 546.815 1000/729 547.211 59/43 547.654 11/8 551.318 undecimal tritone, 11th harmonic 95/69 553.597 62/45 554.812 51/37 555.556 91/66 556.081 40/29 556.737 69/50 557.602 29/21 558.796 76/55 559.881 47/34 560.551 112/81 561.006 177/128 561.127 177th harmonic 18/13 563.382 61/44 565.567 43/31 566.482 68/49 567.304 25/18 568.717 augmented fourth (4/3 x 25/24) 57/41 570.406 89/64 570.880 89th harmonic 32/23 571.726 39/28 573.657 46/33 575.001 53/38 575.992 60/43 576.751 88/63 578.582 95/68 578.871 179/128 580.579 179th harmonic 7/5 582.512 septimal tritone 108/77 585.721 87/62 586.497 1024/729 588.270 low Pythagorean tritone 59/42 588.391 52/37 589.184 45/32 590.224 high 5-limit tritone 38/27 591.648 69/49 592.578 31/22 593.718 55/39 595.149 24/17 597.000 65/46 598.567 41/29 599.485 181/128 599.815 181st harmonic Square root of 2 600.000 equal-tempered tritone 99/70 600.088 58/41 600.515 92/65 601.433 17/12 603.000 78/55 604.851 61/43 605.367 44/31 606.282 125/88 607.623 27/19 608.352 91/64 609.354 91st harmonic 64/45 609.776 low 5-limit tritone 37/26 610.816 729/512 611.730 high Pythagorean tritone 47/33 612.234 57/40 613.154 77/54 614.279 10/7 617.488 septimal tritone 183/128 618.840 183rd harmonic 93/65 620.149 63/44 621.418 53/37 622.161 43/30 623.249 33/23 624.999 56/39 626.343 23/16 628.274 23rd harmonic 59/41 630.109 95/66 630.554 36/25 631.283 diminished fifth (3/2 x 24/25) 121/84 631.855 49/34 632.696 62/43 633.518 13/9 636.618 185/128 637.658 185th harmonic 81/56 638.994 55/38 640.119 42/29 641.204 29/20 643.263 45/31 645.188 61/42 646.104 93/64 646.991 93rd harmonic 16/11 648.682 51/35 651.771 729/500 652.789 35/24 653.185 54/37 654.521 92/63 655.538 187/128 656.273 187th harmonic 19/13 656.985 60/41 659.206 41/28 660.236 375/256 660.896 63/43 661.218 85/58 661.692 22/15 663.049 91/62 664.318 47/32 665.507 47th harmonic 72/49 666.258 25/17 667.672 53/36 669.595 81/55 670.188 28/19 671.313 59/40 672.858 31/21 674.255 189/128 674.691 96/65 675.114 65/44 675.523 34/23 676.681 37/25 678.717 40/27 680.449 dissonant "wolf" 5-limit fifth 43/29 681.941 46/31 683.239 95/64 683.827 95th harmonic 49/33 684.379 52/35 685.388 55/37 686.288 58/39 687.095 61/41 687.822 125/84 688.160 64/43 688.482 76/51 690.603 85/57 691.801 191/128 692.915 191st harmonic 112/75 694.243 121/81 694.816 2 to the 7/12ths 700.000 equal-tempered perfect fifth 3/2 701.955 perfect fifth, 3rd harmonic 193/128 710.948 193rd harmonic 95/63 711.091 68/45 714.732 62/41 715.973 121/80 716.322 59/39 716.689 56/37 717.482 53/35 718.365 50/33 719.354 97/64 719.895 97th harmonic 47/31 720.471 91/60 721.085 1024/675 721.508 44/29 721.741 85/56 722.443 41/27 723.197 243/160 723.461 38/25 724.886 35/23 726.865 195/128 728.796 195th harmonic 32/21 729.219 61/40 730.571 29/19 732.064 84/55 733.149 55/36 733.722 26/17 735.572 75/49 736.931 49/32 737.652 49th harmonic 95/62 738.791 87/55 739.901 23/15 740.006 43/28 742.692 192/125 743.014 diminished sixth (8/5 x 24/25) 63/41 743.674 20/13 745.786 197/128 746.462 197th harmonic 77/50 747.516 57/37 748.124 37/24 749.389 54/35 750.725 125/81 751.121 17/11 753.637 99/64 755.228 99th harmonic 65/42 756.060 48/31 756.919 31/20 758.722 76/49 759.861 45/29 760.674 59/38 761.659 87/56 762.706 199/128 763.950 199th harmonic 14/9 764.916 septimal minor sixth 120/77 768.125 53/34 768.549 39/25 769.855 64/41 770.938 25/16 772.627 augmented fifth 61/39 774.402 36/23 775.636 47/30 777.238 58/37 778.233 69/44 778.911 91/58 779.776 201/128 781.262 201st harmonic 11/7 782.492 undecimal minor sixth 85/54 785.404 63/40 786.422 52/33 787.255 41/26 788.535 101/64 789.854 101st harmonic 30/19 790.756 128/81 792.180 Pythagorean minor sixth 49/31 792.616 405/256 794.134 19/12 795.558 203/128 798.403 203rd harmonic 46/29 798.697 100/63 799.892 2 to the 2/3rds 800.000 equal-tempered minor sixth 27/17 800.910 62/39 802.553 35/22 803.822 78/49 804.831 43/27 805.653 51/32 806.910 51st harmonic 59/37 807.828 91/57 809.886 8/5 813.686 5-limit minor sixth 205/128 815.376 205th harmonic 6561/4096 815.640 Pythagorean "schismatic" sixth 93/58 817.413 77/48 818.189 61/38 819.372 53/33 820.232 45/28 821.398 37/23 823.070 103/64 823.801 103rd harmonic 29/18 825.667 50/31 827.592 121/75 828.053 92/57 828.806 21/13 830.253 207/128 832.184 207th harmonic 55/34 832.676 34/21 834.175 81/50 835.193 47/29 835.929 60/37 836.925 125/77 838.797 13/8 840.528 overtone sixth, 13th harmonic 57/35 844.328 44/27 845.453 31/19 847.523 80/49 848.662 209/128 848.831 209th harmonic 49/30 849.383 85/52 850.741 18/11 852.592 undecimal "median" sixth 95/58 854.250 59/36 855.262 41/25 856.435 105/64 857.095 105th harmonic 64/39 857.517 23/14 859.448 51/31 861.875 400/243 862.852 28/17 863.870 211/128 865.319 211th harmonic 61/37 865.541 33/20 866.959 38/23 869.239 81/49 870.168 43/26 870.990 91/55 871.722 48/29 872.378 53/32 873.505 53rd harmonic 58/35 874.438 63/38 875.223 128/77 879.856 213/128 881.652 213th harmonic 5/3 884.359 5-limit major sixth 107/64 889.760 107th harmonic tr> 92/55 890.643 87/52 891.005 62/37 893.692 57/34 894.513 52/31 895.492 47/28 896.681 215/128 897.314 215th harmonic 42/25 898.153 121/72 898.726 2 to the 3/4ths 900.000 equal-tempered major sixth 37/22 900.026 32/19 902.487 91/54 903.489 59/35 904.032 27/16 905.865 Pythagorean major sixth 76/45 907.289 49/29 908.075 22/13 910.790 61/36 912.975 217/128 913.861 217th harmonic 39/23 914.208 95/56 915.001 56/33 915.553 17/10 918.642 63/37 921.392 109/64 921.821 109th harmonic 46/27 922.409 75/44 923.264 29/17 924.622 128/75 925.418 diminished seventh (16/9 x 24/25) 41/24 927.107 53/31 928.469 65/38 929.328 219/128 929.744 219th harmonic 77/45 929.920 12/7 933.129 septimal major sixth 55/32 937.632 55th harmonic 43/25 938.890 31/18 941.126 441/256 941.562 50/29 943.050 69/40 943.916 221/128 945.483 221st harmonic 19/11 946.195 216/125 946.924 121/70 947.496 64/37 948.656 45/26 949.696 26/15 952.259 111/64 953.299 111th harmonic 85/49 953.617 59/34 954.216 125/72 955.031 augmented sixth (5/3 x 25/24) 33/19 955.760 40/23 958.039 87/50 958.905 47/27 959.642 54/31 960.829 223/128 961.080 223rd harmonic 61/35 961.745 68/39 962.473 96/55 964.323 110/63 964.896 7/4 968.826 septimal minor seventh, 7th harmonic 58/33 976.304 225/128 976.537 225th harmonic 51/29 977.333 95/54 977.962 44/25 978.691 37/21 980.563 30/17 983.313 113/64 984.215 113th harmonic 53/30 985.236 99/56 986.402 23/13 987.747 85/48 989.314 62/35 989.896 39/22 991.165 227/128 991.858 227th harmonic 55/31 992.596 87/49 993.880 16/9 996.090 Pythagorean small min. seventh 57/32 999.468 57th harmonic 2 to the 5/6ths 1000.000 equal-tempered minor seventh 98/55 1000.020 41/23 1000.788 91/51 1002.443 25/14 1003.802 59/33 1005.899 229/128 1007.045 229th harmonic 34/19 1007.442 43/24 1009.563 52/29 1010.950 61/34 1011.929 88/49 1013.666 115/64 1014.588 115th harmonic 9/5 1017.596 5-limit large minor seventh 92/51 1021.364 231/128 1022.099 231st harmonic 65/36 1022.931 56/31 1023.790 47/26 1024.979 38/21 1026.732 29/16 1029.577 29th harmonic 49/27 1031.787 69/38 1032.716 20/11 1034.996 91/50 1036.726 233/128 1037.023 233rd harmonic 51/28 1038.085 729/400 1039.103 31/17 1040.080 42/23 1042.507 95/52 1043.299 53/29 1043.927 117/64 1044.438 117th harmonic 64/35 1044.860 4000/2187 1045.256 11/6 1049.363 undecimal "median" seventh 235/128 1051.820 235th harmonic 90/49 1052.572 57/31 1054.432 46/25 1055.647 81/44 1056.502 35/19 1057.627 59/32 1059.172 59th harmonic 24/13 1061.427 85/46 1062.995 61/33 1063.612 37/20 1065.030 237/128 1066.492 237th harmonic 50/27 1066.762 63/34 1067.780 13/7 1071.702 119/64 1073.781 119th harmonic 54/29 1076.288 95/51 1076.916 41/22 1077.744 28/15 1080.557 239/128 1081.040 239th harmonic 43/23 1083.243 58/31 1084.542 15/8 1088.269 5-limit major seventh, 15th harmonic 92/49 1090.623 62/33 1091.763 47/25 1092.879 32/17 1095.045 241/128 1095.467 241st harmonic 49/26 1097.124 66/35 1098.133 2 to the 11/12ths 1100.000 equal-tempered major seventh 17/9 1101.045 121/64 1102.636 121st harmonic 87/46 1103.258 53/28 1104.679 125/66 1105.668 36/19 1106.397 91/48 1107.399 256/135 1107.821 55/29 1108.054 243/128 1109.775 Pythagorean major seventh, 243rd harmonic 19/10 1111.199 59/31 1114.136 40/21 1115.533 61/32 1116.885 61st harmonic 21/11 1119.463 65/34 1121.886 44/23 1123.044 245/128 1123.966 245th harmonic 23/12 1126.319 48/25 1129.328 121/63 1129.900 123/64 1131.017 123rd harmonic 25/13 1132.100 77/40 1133.830 52/27 1134.663 27/14 1137.039 septimal major seventh 247/128 1138.041 247th harmonic 56/29 1139.249 85/44 1139.951 29/15 1141.308 60/31 1143.233 31/16 1145.036 31st harmonic 95/49 1146.175 64/33 1146.727 33/17 1148.318 68/35 1149.816 243/125 1150.834 35/18 1151.230 249/128 1152.002 249th harmonic 37/19 1153.831 76/39 1155.030 39/20 1156.169 41/21 1158.281 125/64 1158.941 augmented seventh (15/8 x 25/24) 43/22 1160.200 88/45 1161.094 45/23 1161.949 47/24 1163.552 96/49 1164.303 49/25 1165.024 251/128 1165.852 251st harmonic 51/26 1166.383 53/27 1167.640 108/55 1168.233 55/28 1168.806 57/29 1169.891 59/30 1170.903 61/31 1171.849 63/32 1172.736 63rd harmonic 65/33 1173.568 69/35 1175.090 160/81 1178.494 253/128 1179.592 253rd harmonic 87/44 1180.214 91/46 1181.079 95/48 1181.872 99/50 1182.601 125/63 1186.205 127/64 1186.422 127th harmonic 255/128 1193.224 255th harmonic 2/1 1200.000 octave
Copyright, Kyle Gann, 1998
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