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 Seventh Harmonic

Compiled by X. J. Scott, January 2008

Tuning	step size	recipe	Scale Pattern
15th root of 7/1	224.588 cents		0 225 225 225 449 225 674 225 898 225 1123 225 1348 225 1572 225 1797 225 2021 225 2246 225 2470 225 2695 225 2920 225 3144 225 3369   3593
16th root of 7/1	210.552 cents		0 211 211 211 421 211 632 211 842 211 1053 211 1263 211 1474 211 1684 211 1895 211 2106 211 2316 211 2527 211 2737 211 2948 211 3158 211 3369   3579
17th root of 7/1	198.166 cents		0 198 198 198 396 198 594 198 793 198 991 198 1189 198 1387 198 1585 198 1783 198 1982 198 2180 198 2378 198 2576 198 2774 198 2972 198 3171 198 3369   3567
18th root of 7/1	187.157 cents		0 187 187 187 374 187 561 187 749 187 936 187 1123 187 1310 187 1497 187 1684 187 1872 187 2059 187 2246 187 2433 187 2620 187 2807 187 2995 187 3182 187 3369   3556
19th root of 7/1	177.307 cents		0 177 177 177 355 177 532 177 709 177 887 177 1064 177 1241 177 1418 177 1596 177 1773 177 1950 177 2128 177 2305 177 2482 177 2660 177 2837 177 3014 177 3192 177 3369   3546
20th root of 7/1	168.441 cents		0 168 168 168 337 168 505 168 674 168 842 168 1011 168 1179 168 1348 168 1516 168 1684 168 1853 168 2021 168 2190 168 2358 168 2527 168 2695 168 2864 168 3032 168 3200 168 3369   3537
21st root of 7/1	160.420 cents		0 160 160 160 321 160 481 160 642 160 802 160 963 160 1123 160 1283 160 1444 160 1604 160 1765 160 1925 160 2085 160 2246 160 2406 160 2567 160 2727 160 2888 160 3048 160 3208 160 3369   3529
22nd root of 7/1	153.128 cents		0 153 153 153 306 153 459 153 613 153 766 153 919 153 1072 153 1225 153 1378 153 1531 153 1684 153 1838 153 1991 153 2144 153 2297 153 2450 153 2603 153 2756 153 2909 153 3063 153 3216 153 3369   3522
23rd root of 7/1	146.471 cents		0 146 146 146 293 146 439 146 586 146 732 146 879 146 1025 146 1172 146 1318 146 1465 146 1611 146 1758 146 1904 146 2051 146 2197 146 2344 146 2490 146 2636 146 2783 146 2929 146 3076 146 3222 146 3369   3515
24th root of 7/1	140.368 cents		0 140 140 140 281 140 421 140 561 140 702 140 842 140 983 140 1123 140 1263 140 1404 140 1544 140 1684 140 1825 140 1965 140 2106 140 2246 140 2386 140 2527 140 2667 140 2807 140 2948 140 3088 140 3228 140 3369   3509
25th root of 7/1	134.753 cents		0 135 135 135 270 135 404 135 539 135 674 135 809 135 943 135 1078 135 1213 135 1348 135 1482 135 1617 135 1752 135 1887 135 2021 135 2156 135 2291 135 2426 135 2560 135 2695 135 2830 135 2965 135 3099 135 3234 135 3369   3504
26th root of 7/1	129.570 cents		0 130 130 130 259 130 389 130 518 130 648 130 777 130 907 130 1037 130 1166 130 1296 130 1425 130 1555 130 1684 130 1814 130 1944 130 2073 130 2203 130 2332 130 2462 130 2591 130 2721 130 2851 130 2980 130 3110 130 3239 130 3369   3498
27th root of 7/1	124.771 cents		0 125 125 125 250 125 374 125 499 125 624 125 749 125 873 125 998 125 1123 125 1248 125 1372 125 1497 125 1622 125 1747 125 1872 125 1996 125 2121 125 2246 125 2371 125 2495 125 2620 125 2745 125 2870 125 2995 125 3119 125 3244 125 3369   3494
28th root of 7/1	120.315 cents		0 120 120 120 241 120 361 120 481 120 602 120 722 120 842 120 963 120 1083 120 1203 120 1323 120 1444 120 1564 120 1684 120 1805 120 1925 120 2045 120 2166 120 2286 120 2406 120 2527 120 2647 120 2767 120 2888 120 3008 120 3128 120 3249 120 3369   3489
29th root of 7/1	116.166 cents		0 116 116 116 232 116 348 116 465 116 581 116 697 116 813 116 929 116 1045 116 1162 116 1278 116 1394 116 1510 116 1626 116 1742 116 1859 116 1975 116 2091 116 2207 116 2323 116 2439 116 2556 116 2672 116 2788 116 2904 116 3020 116 3136 116 3253 116 3369   3485
30th root of 7/1	112.294 cents		0 112 112 112 225 112 337 112 449 112 561 112 674 112 786 112 898 112 1011 112 1123 112 1235 112 1348 112 1460 112 1572 112 1684 112 1797 112 1909 112 2021 112 2134 112 2246 112 2358 112 2470 112 2583 112 2695 112 2807 112 2920 112 3032 112 3144 112 3257 112 3369   3481
31st root of 7/1	108.672 cents		0 109 109 109 217 109 326 109 435 109 543 109 652 109 761 109 869 109 978 109 1087 109 1195 109 1304 109 1413 109 1521 109 1630 109 1739 109 1847 109 1956 109 2065 109 2173 109 2282 109 2391 109 2499 109 2608 109 2717 109 2825 109 2934 109 3043 109 3151 109 3260 109 3369   3477
32nd root of 7/1	105.276 cents		0 105 105 105 211 105 316 105 421 105 526 105 632 105 737 105 842 105 947 105 1053 105 1158 105 1263 105 1369 105 1474 105 1579 105 1684 105 1790 105 1895 105 2000 105 2106 105 2211 105 2316 105 2421 105 2527 105 2632 105 2737 105 2842 105 2948 105 3053 105 3158 105 3264 105 3369   3474
33rd root of 7/1	102.086 cents		0 102 102 102 204 102 306 102 408 102 510 102 613 102 715 102 817 102 919 102 1021 102 1123 102 1225 102 1327 102 1429 102 1531 102 1633 102 1735 102 1838 102 1940 102 2042 102 2144 102 2246 102 2348 102 2450 102 2552 102 2654 102 2756 102 2858 102 2960 102 3063 102 3165 102 3267 102 3369   3471
34th root of 7/1	99.083 cents		0 99 99 99 198 99 297 99 396 99 495 99 594 99 694 99 793 99 892 99 991 99 1090 99 1189 99 1288 99 1387 99 1486 99 1585 99 1684 99 1783 99 1883 99 1982 99 2081 99 2180 99 2279 99 2378 99 2477 99 2576 99 2675 99 2774 99 2873 99 2972 99 3072 99 3171 99 3270 99 3369   3468
35th root of 7/1	96.252 cents		0 96 96 96 193 96 289 96 385 96 481 96 578 96 674 96 770 96 866 96 963 96 1059 96 1155 96 1251 96 1348 96 1444 96 1540 96 1636 96 1733 96 1829 96 1925 96 2021 96 2118 96 2214 96 2310 96 2406 96 2503 96 2599 96 2695 96 2791 96 2888 96 2984 96 3080 96 3176 96 3273 96 3369   3465
36th root of 7/1	93.578 cents		0 94 94 94 187 94 281 94 374 94 468 94 561 94 655 94 749 94 842 94 936 94 1029 94 1123 94 1217 94 1310 94 1404 94 1497 94 1591 94 1684 94 1778 94 1872 94 1965 94 2059 94 2152 94 2246 94 2339 94 2433 94 2527 94 2620 94 2714 94 2807 94 2901 94 2995 94 3088 94 3182 94 3275 94 3369   3462
37th root of 7/1	91.049 cents		0 91 91 91 182 91 273 91 364 91 455 91 546 91 637 91 728 91 819 91 910 91 1002 91 1093 91 1184 91 1275 91 1366 91 1457 91 1548 91 1639 91 1730 91 1821 91 1912 91 2003 91 2094 91 2185 91 2276 91 2367 91 2458 91 2549 91 2640 91 2731 91 2823 91 2914 91 3005 91 3096 91 3187 91 3278 91 3369   3460
38th root of 7/1	88.653 cents		0 89 89 89 177 89 266 89 355 89 443 89 532 89 621 89 709 89 798 89 887 89 975 89 1064 89 1152 89 1241 89 1330 89 1418 89 1507 89 1596 89 1684 89 1773 89 1862 89 1950 89 2039 89 2128 89 2216 89 2305 89 2394 89 2482 89 2571 89 2660 89 2748 89 2837 89 2926 89 3014 89 3103 89 3192 89 3280 89 3369   3457
39th root of 7/1	86.380 cents		0 86 86 86 173 86 259 86 346 86 432 86 518 86 605 86 691 86 777 86 864 86 950 86 1037 86 1123 86 1209 86 1296 86 1382 86 1468 86 1555 86 1641 86 1728 86 1814 86 1900 86 1987 86 2073 86 2160 86 2246 86 2332 86 2419 86 2505 86 2591 86 2678 86 2764 86 2851 86 2937 86 3023 86 3110 86 3196 86 3282 86 3369   3455
40th root of 7/1	84.221 cents		0 84 84 84 168 84 253 84 337 84 421 84 505 84 590 84 674 84 758 84 842 84 926 84 1011 84 1095 84 1179 84 1263 84 1348 84 1432 84 1516 84 1600 84 1684 84 1769 84 1853 84 1937 84 2021 84 2106 84 2190 84 2274 84 2358 84 2442 84 2527 84 2611 84 2695 84 2779 84 2864 84 2948 84 3032 84 3116 84 3200 84 3285 84 3369   3453
41st root of 7/1	82.166 cents		0 82 82 82 164 82 246 82 329 82 411 82 493 82 575 82 657 82 739 82 822 82 904 82 986 82 1068 82 1150 82 1232 82 1315 82 1397 82 1479 82 1561 82 1643 82 1725 82 1808 82 1890 82 1972 82 2054 82 2136 82 2218 82 2301 82 2383 82 2465 82 2547 82 2629 82 2711 82 2794 82 2876 82 2958 82 3040 82 3122 82 3204 82 3287 82 3369   3451
42nd root of 7/1	80.210 cents		0 80 80 80 160 80 241 80 321 80 401 80 481 80 561 80 642 80 722 80 802 80 882 80 963 80 1043 80 1123 80 1203 80 1283 80 1364 80 1444 80 1524 80 1604 80 1684 80 1765 80 1845 80 1925 80 2005 80 2085 80 2166 80 2246 80 2326 80 2406 80 2487 80 2567 80 2647 80 2727 80 2807 80 2888 80 2968 80 3048 80 3128 80 3208 80 3289 80 3369   3449
43rd root of 7/1	78.345 cents		0 78 78 78 157 78 235 78 313 78 392 78 470 78 548 78 627 78 705 78 783 78 862 78 940 78 1018 78 1097 78 1175 78 1254 78 1332 78 1410 78 1489 78 1567 78 1645 78 1724 78 1802 78 1880 78 1959 78 2037 78 2115 78 2194 78 2272 78 2350 78 2429 78 2507 78 2585 78 2664 78 2742 78 2820 78 2899 78 2977 78 3055 78 3134 78 3212 78 3290 78 3369   3447
44th root of 7/1	76.564 cents		0 77 77 77 153 77 230 77 306 77 383 77 459 77 536 77 613 77 689 77 766 77 842 77 919 77 995 77 1072 77 1148 77 1225 77 1302 77 1378 77 1455 77 1531 77 1608 77 1684 77 1761 77 1838 77 1914 77 1991 77 2067 77 2144 77 2220 77 2297 77 2373 77 2450 77 2527 77 2603 77 2680 77 2756 77 2833 77 2909 77 2986 77 3063 77 3139 77 3216 77 3292 77 3369   3445
45th root of 7/1	74.863 cents		0 75 75 75 150 75 225 75 299 75 374 75 449 75 524 75 599 75 674 75 749 75 823 75 898 75 973 75 1048 75 1123 75 1198 75 1273 75 1348 75 1422 75 1497 75 1572 75 1647 75 1722 75 1797 75 1872 75 1946 75 2021 75 2096 75 2171 75 2246 75 2321 75 2396 75 2470 75 2545 75 2620 75 2695 75 2770 75 2845 75 2920 75 2995 75 3069 75 3144 75 3219 75 3294 75 3369   3444
46th root of 7/1	73.235 cents		0 73 73 73 146 73 220 73 293 73 366 73 439 73 513 73 586 73 659 73 732 73 806 73 879 73 952 73 1025 73 1099 73 1172 73 1245 73 1318 73 1391 73 1465 73 1538 73 1611 73 1684 73 1758 73 1831 73 1904 73 1977 73 2051 73 2124 73 2197 73 2270 73 2344 73 2417 73 2490 73 2563 73 2636 73 2710 73 2783 73 2856 73 2929 73 3003 73 3076 73 3149 73 3222 73 3296 73 3369   3442
47th root of 7/1	71.677 cents		0 72 72 72 143 72 215 72 287 72 358 72 430 72 502 72 573 72 645 72 717 72 788 72 860 72 932 72 1003 72 1075 72 1147 72 1219 72 1290 72 1362 72 1434 72 1505 72 1577 72 1649 72 1720 72 1792 72 1864 72 1935 72 2007 72 2079 72 2150 72 2222 72 2294 72 2365 72 2437 72 2509 72 2580 72 2652 72 2724 72 2795 72 2867 72 2939 72 3010 72 3082 72 3154 72 3225 72 3297 72 3369   3441
48th root of 7/1	70.184 cents		0 70 70 70 140 70 211 70 281 70 351 70 421 70 491 70 561 70 632 70 702 70 772 70 842 70 912 70 983 70 1053 70 1123 70 1193 70 1263 70 1333 70 1404 70 1474 70 1544 70 1614 70 1684 70 1755 70 1825 70 1895 70 1965 70 2035 70 2106 70 2176 70 2246 70 2316 70 2386 70 2456 70 2527 70 2597 70 2667 70 2737 70 2807 70 2878 70 2948 70 3018 70 3088 70 3158 70 3228 70 3299 70 3369   3439
49th root of 7/1	68.752 cents		0 69 69 69 138 69 206 69 275 69 344 69 413 69 481 69 550 69 619 69 688 69 756 69 825 69 894 69 963 69 1031 69 1100 69 1169 69 1238 69 1306 69 1375 69 1444 69 1513 69 1581 69 1650 69 1719 69 1788 69 1856 69 1925 69 1994 69 2063 69 2131 69 2200 69 2269 69 2338 69 2406 69 2475 69 2544 69 2613 69 2681 69 2750 69 2819 69 2888 69 2956 69 3025 69 3094 69 3163 69 3231 69 3300 69 3369   3438
50th root of 7/1	67.377 cents		0 67 67 67 135 67 202 67 270 67 337 67 404 67 472 67 539 67 606 67 674 67 741 67 809 67 876 67 943 67 1011 67 1078 67 1145 67 1213 67 1280 67 1348 67 1415 67 1482 67 1550 67 1617 67 1684 67 1752 67 1819 67 1887 67 1954 67 2021 67 2089 67 2156 67 2223 67 2291 67 2358 67 2426 67 2493 67 2560 67 2628 67 2695 67 2762 67 2830 67 2897 67 2965 67 3032 67 3099 67 3167 67 3234 67 3301 67 3369   3436
51st root of 7/1	66.055 cents		0 66 66 66 132 66 198 66 264 66 330 66 396 66 462 66 528 66 594 66 661 66 727 66 793 66 859 66 925 66 991 66 1057 66 1123 66 1189 66 1255 66 1321 66 1387 66 1453 66 1519 66 1585 66 1651 66 1717 66 1783 66 1850 66 1916 66 1982 66 2048 66 2114 66 2180 66 2246 66 2312 66 2378 66 2444 66 2510 66 2576 66 2642 66 2708 66 2774 66 2840 66 2906 66 2972 66 3039 66 3105 66 3171 66 3237 66 3303 66 3369   3435
52nd root of 7/1	64.785 cents		0 65 65 65 130 65 194 65 259 65 324 65 389 65 453 65 518 65 583 65 648 65 713 65 777 65 842 65 907 65 972 65 1037 65 1101 65 1166 65 1231 65 1296 65 1360 65 1425 65 1490 65 1555 65 1620 65 1684 65 1749 65 1814 65 1879 65 1944 65 2008 65 2073 65 2138 65 2203 65 2267 65 2332 65 2397 65 2462 65 2527 65 2591 65 2656 65 2721 65 2786 65 2851 65 2915 65 2980 65 3045 65 3110 65 3174 65 3239 65 3304 65 3369   3434
53rd root of 7/1	63.563 cents		0 64 64 64 127 64 191 64 254 64 318 64 381 64 445 64 509 64 572 64 636 64 699 64 763 64 826 64 890 64 953 64 1017 64 1081 64 1144 64 1208 64 1271 64 1335 64 1398 64 1462 64 1526 64 1589 64 1653 64 1716 64 1780 64 1843 64 1907 64 1970 64 2034 64 2098 64 2161 64 2225 64 2288 64 2352 64 2415 64 2479 64 2543 64 2606 64 2670 64 2733 64 2797 64 2860 64 2924 64 2987 64 3051 64 3115 64 3178 64 3242 64 3305 64 3369   3432