Tables

1. Octave (2/1)
2. Quintave (3/2)
3. Fourth (4/3)
4. Minor Sixth (8/5)
5. Major Sixth (5/3)
6. Minor Seventh (9/5)
7. Ninth (9/4)
8. Major Tenth (5/2)
9. Twelfth (3/1)
10. Double Octave (4/1)
11. Fifth Harmonic (5/1)
12. Seventh Harmonic (7/1)
13. Triple Octave (8/1)
14. 11-Subminor Tritone (11/8)
15. 11-Neutral Ninth (11/5)
16. Subminor Tenth (7/3)
17. Harmonic Seventh (7/4)
18. Just Tritone (7/5)
19. Augmented Just Tritone (10/7)
20. 11-Subminor Sixth (11/7)
21. Supermajor Sixth (12/7)

Equal Divisions of the Double Octave

Compiled by X. J. Scott, January 2008

Tuning	step size	recipe	Scale Pattern
11th root of 4/1	218.182 cents		0 218 218 218 436 218 655 218 873 218 1091 218 1309 218 1527 218 1745 218 1964 218 2182 218 2400   2618
13th root of 4/1	184.615 cents		0 185 185 185 369 185 554 185 738 185 923 185 1108 185 1292 185 1477 185 1662 185 1846 185 2031 185 2215 185 2400   2585
15th root of 4/1	160.000 cents		0 160 160 160 320 160 480 160 640 160 800 160 960 160 1120 160 1280 160 1440 160 1600 160 1760 160 1920 160 2080 160 2240 160 2400   2560
17th root of 4/1	141.176 cents		0 141 141 141 282 141 424 141 565 141 706 141 847 141 988 141 1129 141 1271 141 1412 141 1553 141 1694 141 1835 141 1976 141 2118 141 2259 141 2400   2541
19th root of 4/1	126.316 cents		0 126 126 126 253 126 379 126 505 126 632 126 758 126 884 126 1011 126 1137 126 1263 126 1389 126 1516 126 1642 126 1768 126 1895 126 2021 126 2147 126 2274 126 2400   2526
21st root of 4/1	114.286 cents		0 114 114 114 229 114 343 114 457 114 571 114 686 114 800 114 914 114 1029 114 1143 114 1257 114 1371 114 1486 114 1600 114 1714 114 1829 114 1943 114 2057 114 2171 114 2286 114 2400   2514
23rd root of 4/1	104.348 cents		0 104 104 104 209 104 313 104 417 104 522 104 626 104 730 104 835 104 939 104 1043 104 1148 104 1252 104 1357 104 1461 104 1565 104 1670 104 1774 104 1878 104 1983 104 2087 104 2191 104 2296 104 2400   2504
25th root of 4/1	96.000 cents		0 96 96 96 192 96 288 96 384 96 480 96 576 96 672 96 768 96 864 96 960 96 1056 96 1152 96 1248 96 1344 96 1440 96 1536 96 1632 96 1728 96 1824 96 1920 96 2016 96 2112 96 2208 96 2304 96 2400   2496
27th root of 4/1	88.889 cents		0 89 89 89 178 89 267 89 356 89 444 89 533 89 622 89 711 89 800 89 889 89 978 89 1067 89 1156 89 1244 89 1333 89 1422 89 1511 89 1600 89 1689 89 1778 89 1867 89 1956 89 2044 89 2133 89 2222 89 2311 89 2400   2489
29th root of 4/1	82.759 cents		0 83 83 83 166 83 248 83 331 83 414 83 497 83 579 83 662 83 745 83 828 83 910 83 993 83 1076 83 1159 83 1241 83 1324 83 1407 83 1490 83 1572 83 1655 83 1738 83 1821 83 1903 83 1986 83 2069 83 2152 83 2234 83 2317 83 2400   2483
31st root of 4/1	77.419 cents		0 77 77 77 155 77 232 77 310 77 387 77 465 77 542 77 619 77 697 77 774 77 852 77 929 77 1006 77 1084 77 1161 77 1239 77 1316 77 1394 77 1471 77 1548 77 1626 77 1703 77 1781 77 1858 77 1935 77 2013 77 2090 77 2168 77 2245 77 2323 77 2400   2477
33rd root of 4/1	72.727 cents		0 73 73 73 145 73 218 73 291 73 364 73 436 73 509 73 582 73 655 73 727 73 800 73 873 73 945 73 1018 73 1091 73 1164 73 1236 73 1309 73 1382 73 1455 73 1527 73 1600 73 1673 73 1745 73 1818 73 1891 73 1964 73 2036 73 2109 73 2182 73 2255 73 2327 73 2400   2473
35th root of 4/1	68.571 cents		0 69 69 69 137 69 206 69 274 69 343 69 411 69 480 69 549 69 617 69 686 69 754 69 823 69 891 69 960 69 1029 69 1097 69 1166 69 1234 69 1303 69 1371 69 1440 69 1509 69 1577 69 1646 69 1714 69 1783 69 1851 69 1920 69 1989 69 2057 69 2126 69 2194 69 2263 69 2331 69 2400   2469
37th root of 4/1	64.865 cents		0 65 65 65 130 65 195 65 259 65 324 65 389 65 454 65 519 65 584 65 649 65 714 65 778 65 843 65 908 65 973 65 1038 65 1103 65 1168 65 1232 65 1297 65 1362 65 1427 65 1492 65 1557 65 1622 65 1686 65 1751 65 1816 65 1881 65 1946 65 2011 65 2076 65 2141 65 2205 65 2270 65 2335 65 2400   2465
39th root of 4/1	61.538 cents		0 62 62 62 123 62 185 62 246 62 308 62 369 62 431 62 492 62 554 62 615 62 677 62 738 62 800 62 862 62 923 62 985 62 1046 62 1108 62 1169 62 1231 62 1292 62 1354 62 1415 62 1477 62 1538 62 1600 62 1662 62 1723 62 1785 62 1846 62 1908 62 1969 62 2031 62 2092 62 2154 62 2215 62 2277 62 2338 62 2400   2462
41st root of 4/1	58.537 cents		0 59 59 59 117 59 176 59 234 59 293 59 351 59 410 59 468 59 527 59 585 59 644 59 702 59 761 59 820 59 878 59 937 59 995 59 1054 59 1112 59 1171 59 1229 59 1288 59 1346 59 1405 59 1463 59 1522 59 1580 59 1639 59 1698 59 1756 59 1815 59 1873 59 1932 59 1990 59 2049 59 2107 59 2166 59 2224 59 2283 59 2341 59 2400   2459
43rd root of 4/1	55.814 cents		0 56 56 56 112 56 167 56 223 56 279 56 335 56 391 56 447 56 502 56 558 56 614 56 670 56 726 56 781 56 837 56 893 56 949 56 1005 56 1060 56 1116 56 1172 56 1228 56 1284 56 1340 56 1395 56 1451 56 1507 56 1563 56 1619 56 1674 56 1730 56 1786 56 1842 56 1898 56 1953 56 2009 56 2065 56 2121 56 2177 56 2233 56 2288 56 2344 56 2400   2456
45th root of 4/1	53.333 cents		0 53 53 53 107 53 160 53 213 53 267 53 320 53 373 53 427 53 480 53 533 53 587 53 640 53 693 53 747 53 800 53 853 53 907 53 960 53 1013 53 1067 53 1120 53 1173 53 1227 53 1280 53 1333 53 1387 53 1440 53 1493 53 1547 53 1600 53 1653 53 1707 53 1760 53 1813 53 1867 53 1920 53 1973 53 2027 53 2080 53 2133 53 2187 53 2240 53 2293 53 2347 53 2400   2453
47th root of 4/1	51.064 cents		0 51 51 51 102 51 153 51 204 51 255 51 306 51 357 51 409 51 460 51 511 51 562 51 613 51 664 51 715 51 766 51 817 51 868 51 919 51 970 51 1021 51 1072 51 1123 51 1174 51 1226 51 1277 51 1328 51 1379 51 1430 51 1481 51 1532 51 1583 51 1634 51 1685 51 1736 51 1787 51 1838 51 1889 51 1940 51 1991 51 2043 51 2094 51 2145 51 2196 51 2247 51 2298 51 2349 51 2400   2451
49th root of 4/1	48.980 cents		0 49 49 49 98 49 147 49 196 49 245 49 294 49 343 49 392 49 441 49 490 49 539 49 588 49 637 49 686 49 735 49 784 49 833 49 882 49 931 49 980 49 1029 49 1078 49 1127 49 1176 49 1224 49 1273 49 1322 49 1371 49 1420 49 1469 49 1518 49 1567 49 1616 49 1665 49 1714 49 1763 49 1812 49 1861 49 1910 49 1959 49 2008 49 2057 49 2106 49 2155 49 2204 49 2253 49 2302 49 2351 49 2400   2449
51st root of 4/1	47.059 cents		0 47 47 47 94 47 141 47 188 47 235 47 282 47 329 47 376 47 424 47 471 47 518 47 565 47 612 47 659 47 706 47 753 47 800 47 847 47 894 47 941 47 988 47 1035 47 1082 47 1129 47 1176 47 1224 47 1271 47 1318 47 1365 47 1412 47 1459 47 1506 47 1553 47 1600 47 1647 47 1694 47 1741 47 1788 47 1835 47 1882 47 1929 47 1976 47 2024 47 2071 47 2118 47 2165 47 2212 47 2259 47 2306 47 2353 47 2400   2447
53rd root of 4/1	45.283 cents		0 45 45 45 91 45 136 45 181 45 226 45 272 45 317 45 362 45 408 45 453 45 498 45 543 45 589 45 634 45 679 45 725 45 770 45 815 45 860 45 906 45 951 45 996 45 1042 45 1087 45 1132 45 1177 45 1223 45 1268 45 1313 45 1358 45 1404 45 1449 45 1494 45 1540 45 1585 45 1630 45 1675 45 1721 45 1766 45 1811 45 1857 45 1902 45 1947 45 1992 45 2038 45 2083 45 2128 45 2174 45 2219 45 2264 45 2309 45 2355 45 2400   2445