Bastille: Difference between revisions
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Since 1407edo is inconsistent in the 13-limit, and 1789edo is a dual-fifth system, Eliora proposes that the term ''bastille'' refer collectively to all temperaments created from vals and branchings which are supported by 1407edo and 1789edo, as different vals have different features and advantages. | Since 1407edo is inconsistent in the 13-limit, and 1789edo is a dual-fifth system, Eliora proposes that the term ''bastille'' refer collectively to all temperaments created from vals and branchings which are supported by 1407edo and 1789edo, as different vals have different features and advantages. | ||
For example, [[The Jacobins#Pure Bastille|1407eff & 1789 version of bastille]], 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 [[75 | For example, [[The Jacobins#Pure Bastille|1407eff & 1789 version of bastille]], 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}. | ||
It should be noted, however, that in no version of Bastille the generator fifth is mapped to [[3/2]]. | It should be noted, however, that in no version of Bastille the generator fifth is mapped to [[3/2]]. | ||
Revision as of 18:50, 18 January 2023
Bastille is a loose term describing a rank-2 temperament (or alternately, a rank-2 scale) produced by temperament-merging 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 characterstic of Bastille across different vals and branchings is that the generator is a "meantone" flat fifth of around 694.5 cents, and fifteen of them when stacked reach 5/4. Such a characteristic is quite remarkable for edos in the thousands to support.
Theory
Since 1407edo is inconsistent in the 13-limit, and 1789edo is a dual-fifth system, Eliora proposes that the term bastille refer collectively to all temperaments created from vals and branchings which are supported by 1407edo and 1789edo, as different vals have different features and advantages.
For example, 1407eff & 1789 version of bastille, 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}.
It should be noted, however, that in no version of Bastille the generator fifth is mapped to 3/2.