1789edo

1789 EDO divides the octave into equal steps of 0.67 cents each. It is the 278th prime edo. Perhaps the most notable fact about 1789edo, is the fact that it tempers out the jacobin comma (6656/6655), which is quite appropriate for edo's number. Although there are temperaments which are better suited for tempering this comma, 1789edo is unique in that it's number is the hallmark year of the French Revolution, thus making the temperance of the Jacobin comma on topic.

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1789

Theory

1789edo can be adapted for use with the 2.5.11.13.29.31 subgroup.

Table of selected intervals

Step	Name	JI Approximation or Monzo
0	Unison	1/1 exact
25	28-thirds comma	[65 -28]
61	Lesser diesis	128/125
576	Major third	5/4
677	Jacobin naiadic	13/10
822	Jacobin superfourth	11/8
1789	Octave	2/1 exact

Temperaments

The "proper" Jacobin temperament for 1789edo is a maximally even mode of 967 notes, originating from the 822\1789 11/8-superfourth as a generator. The mode is closely related to 20/37 maximally even mode of 37edo which uses 17\37 superfourth as its generator, and 967/1789 can be represented as a stack of 46 20/37 patterns merged with one 47/87 cycle arising out of 87edo.

Since 1789edo contains the 2.5 subgroup, it can be used for the finite decimal temperament - that is, where all the interval targets in just intonation are expressed as terminating decimals. For example, 5/4, 25/16, 128/125, 32/25, 625/512, etc. This rings particularly true for the French attempts to decimalize a lot more things than we are used to today.

This property of 1789edo is amplified by poor approximation of 3 and 7, allowing for cognitive separation of the intervals (or whatever is left of it at such small step size).