1794edo

From Xenharmonic Wiki
Jump to navigation Jump to search

1794 equal divisions of the octave creates steps of 0.668896 cents each.

Theory

Approximation of prime intervals in 1794 EDO
Prime number 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47
Error absolute (¢) +0.000 -0.283 +0.308 -0.264 -0.147 +0.275 +0.061 +0.146 -0.181 -0.146 +0.115 +0.161 -0.300 +0.188 +0.045
relative (%) +0 -42 +46 -39 -22 +41 +9 +22 -27 -22 +17 +24 -45 +28 +7
Steps (reduced) 1794 (0) 2843 (1049) 4166 (578) 5036 (1448) 6206 (824) 6639 (1257) 7333 (157) 7621 (445) 8115 (939) 8715 (1539) 8888 (1712) 9346 (376) 9611 (641) 9735 (765) 9965 (995)

1794edo's divisors are 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897.

The best subgroup for 1794 is 2.11.17.19.29.31.47. Nonetheless, we will cover some 7-limit interpretations.

In the 1794c val, 1794 2843 4165 5036], it tempers out the horwell comma and the landscape comma, supporting mutt. However, it is not better tuned than 171edo. Using the 1794bd val, 1794 2844 4166 5037], it tempers out [21 -8 -6 2, [-7 -15 6 6, [-2 -3 15 -10. This mapping of harmonic 7 is the same as 26edo's.

Remarkably, using the patent val, 1794edo tempers out the schisma.

In the 2.11.17 realm, 1794edo shares the [-67 43 -20 comma with EDOs like 148, 231, and 296. In the 2.17.19 subgroup, 1794edo tempers out the [277 -21 -45. Most notably, shares this property with 12, 24, 36, 48, as well as 855, 867, 879 and 891, with 855 being a multiple of 171. This is distantly reminiscent of the technique when 12edo's 1 and 3-step intervals, for example C# and D# counting from C, are assumed to be 17/16 and 19/16.

Trivia

English Wikipedia has an article on:

The number 1794 is known for being the fatal year of the French Revolution.