Bastille: Difference between revisions

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== Theory ==

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}. The common thing between the two temperaments is that fifteen stacked generators lead to [[5/4]]. Given the precision, such a characteristic is quite remarkable for edos in the thousands to support.

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}. The common thing between the two temperaments is that fifteen stacked generators lead to [[8/5]], tempering out {{monzo| -26 15 1 }} = 71744535/67108864. Given the precision, such a characteristic is quite remarkable for edos in the thousands to support.

[[Category:Terms]]

[[Category:Scales]]

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 == Theory ==
-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}. The common thing between the two temperaments is that fifteen stacked generators lead to [[5/4]]. Given the precision, such a characteristic is quite remarkable for edos in the thousands to support.
+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}. The common thing between the two temperaments is that fifteen stacked generators lead to [[8/5]], tempering out {{monzo| -26 15 1 }} = 71744535/67108864. Given the precision, such a characteristic is quite remarkable for edos in the thousands to support.
 [[Category:Terms]]
 [[Category:Scales]]