1794edo

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1794 equal divisions of the octave (1794edo), or 1794-tone equal temperament (1794tet), 1794 equal temperament (1794et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1794 equal parts of about 0.669 ¢ 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 2, 3, 6, 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. Notably, it offers a 1794 & 2016 temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).

Nonetheless, 1794edo does offer some simpler interpretations.

In the 7-limit 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.

Regular temperament properties

Subgroup Comma list Mapping Optimal

8ve stretch (¢)

Tuning error
Absolute (¢) Relative (%)
2.3 [-2843, 1794 1794 2843] 0.0892 0.0892 5.97
2.11.17.19.29.31.47 9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936 1794 6206 7333 7621 8715 8888 9965] -0.0012 0.0259 1.74

Trivia

English Wikipedia has an article on:

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