Bastille: Difference between revisions

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'''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.

'''Bastille''' is a rank-2 temperament associated with the {{monzo|1426 0 -596 -15}} comma in the 2.5.7 subgroup, that is no-threes subgroup. It is extracted from a sequence of [[mos scale]]s 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 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~~.

For technical information see [[No-threes subgroup temperaments#Bastille]].

== 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~~.

Since 1407edo and 1789edo have large relative errors on harmonics outside of the 2.5.7 subgroup, there initially was no single temperament named bastille, and the term used to refer to merely a sequence of mos scales to accommodate many possible vals that 1407edo and 1789edo support. However, the temperament can be firmly defined in the 2.5.7 subgroup.

~~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 ~~[[75/56]], a relatively simple interval on this scale. Comma basis for this version of bastille is {384912/384475, 41765625/41746432, 4501875/4499456, 540078539/540000000}~~.

The defining characteristic of Bastille is that the generator is a "meantone" flat fifth of around 694.5 cents. Fifteen stacked generators lead to [[8/5]]. Given the precision, such a characteristic is notable for edos in the thousands to support.

~~It should~~ be ~~noted~~, ~~however~~, ~~that~~ in ~~no version of Bastille~~ the ~~generator~~ fifth is mapped to [[3/2]].

=== Extensions ===

The [[The Jacobins #Pure bastille|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}. Since 112/75 is called marvelous fifth, the most straightforward name for this temperament is ''[[marvelous bastille]]''.

=== MOS scales of Bastille ===

* [[1L 1s]]

* [[2L 1s]]

* [[2L 3s]]

* [[5L 2s]] - minisoft diatonic

* [[7L 5s]] - minihard m-chromatic

* [[7L 12s]] - ultrasoft m-enharmonic - can be used as a well-temperament for [[19edo]].

== Related pages ==

* [[Bastille comma]]

~~[[Category:Temperaments]]~~

~~[[Category:Jacobin]]~~

[[Category:Rank 2]]

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-'''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.
+'''Bastille''' is a rank-2 temperament associated with the {{monzo|1426 0 -596 -15}} comma in the 2.5.7 subgroup, that is no-threes subgroup. It is extracted from a sequence of [[mos scale]]s 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 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.
+For technical information see [[No-threes subgroup temperaments#Bastille]].
 == 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.
+Since 1407edo and 1789edo have large relative errors on harmonics outside of the 2.5.7 subgroup, there initially was no single temperament named bastille, and the term used to refer to merely a sequence of mos scales to accommodate many possible vals that 1407edo and 1789edo support. However, the temperament can be firmly defined in the 2.5.7 subgroup.
-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 [[75/56]], a relatively simple interval on this scale. Comma basis for this version of bastille is {384912/384475, 41765625/41746432, 4501875/4499456, 540078539/540000000}.
+The defining characteristic of Bastille is that the generator is a "meantone" flat fifth of around 694.5 cents. Fifteen stacked generators lead to [[8/5]]. Given the precision, such a characteristic is notable for edos in the thousands to support.
-It should be noted, however, that in no version of Bastille the generator fifth is mapped to [[3/2]].
+=== Extensions ===
+The [[The Jacobins #Pure bastille|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}. Since 112/75 is called marvelous fifth, the most straightforward name for this temperament is ''[[marvelous bastille]]''.
+=== MOS scales of Bastille ===
+* [[1L 1s]]
+* [[2L 1s]]
+* [[2L 3s]]
+* [[5L 2s]] - minisoft diatonic
+* [[7L 5s]] - minihard m-chromatic
+* [[7L 12s]] - ultrasoft m-enharmonic - can be used as a well-temperament for [[19edo]].
+== Related pages ==
+* [[Bastille comma]]
-[[Category:Temperaments]]
-[[Category:Jacobin]]
 [[Category:Rank 2]]