Bastille

Bastille is a sequence of mos scales supported by 1407edo and 1789edo. It derives its name from the fact that the storming of Bastille happened on 14 July 1789, which in date format is written as 14/07/1789.

The defining characteristic of Bastille is that the generator is a "meantone" flat fifth of around 694.5 cents.

Theory

The 1407eff & 1789 temperament, named pure bastille, tempers out the jacobin comma, which brings two great French Revolution terms in one temperament. However, from a just intonation perspective, such temperament may be too complex, even for edos in the thousands. On the other hand, taking patent vals of 1407edo and 1789edo in the full 13-limit produces a temperament whose fifth is mapped to 112/75, a relatively simple interval on this scale. Comma basis for this version of bastille is {384912/384475, 41765625/41746432, 4501875/4499456, 540078539/540000000}. The common thing between the two temperaments is that fifteen stacked generators lead to 8/5, tempering out [-26 15 1⟩ = 71744535/67108864. Given the precision, such a characteristic is quite remarkable for edos in the thousands to support.