Decimal: Difference between revisions

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'''Decimal''' is a temperament in both the [[dicot]] and [[semaphore]] families of temperaments. It is also [[hemipyth]], meaning that it has approximations of √2, √3, and √(3/2). It is special in that it is also an [[exotemperament]].

More precisely, it is the 7-limit temperament that tempers out both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows [[5/4]][[~]][[6/5]] to be a neutral third approximating √(3/2) and [[7/6]][[~]][[8/7]] to be a neutral semifourth approximating √(4/3). These can be equated (far more accurately) to [[11/9]] and [[15/13]], respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]].

More precisely, it is the 7-limit temperament that tempers out both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows [[5/4]][[~]][[6/5]] to be a neutral third approximating √(3/2) and [[7/6]][[~]][[8/7]] to be a neutral semifourth approximating √(4/3). These can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]].

As with many exotemperaments, it is not itself particularly useful, but it has structural value.

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 '''Decimal''' is a temperament in both the [[dicot]] and [[semaphore]] families of temperaments. It is also [[hemipyth]], meaning that it has approximations of √2, √3, and √(3/2). It is special in that it is also an [[exotemperament]].
-More precisely, it is the 7-limit temperament that tempers out both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows [[5/4]][[~]][[6/5]] to be a neutral third approximating √(3/2) and [[7/6]][[~]][[8/7]] to be a neutral semifourth approximating √(4/3). These can be equated (far more accurately) to [[11/9]] and [[15/13]], respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]].
+More precisely, it is the 7-limit temperament that tempers out both [[25/24]], the classic chromatic semitone, and [[49/48]], the septimal diesis. These two intervals have a rather similar function separating close intervals and creating "major" and "minor" triads (either pental ones splitting the perfect fifth or septimal ones splitting the perfect fourth), and tempering them out allows [[5/4]][[~]][[6/5]] to be a neutral third approximating √(3/2) and [[7/6]][[~]][[8/7]] to be a neutral semifourth approximating √(4/3). These can be equated (far more accurately) to [[11/9]] and [[15/13]] respectively, tempering out [[243/242]] and [[676/675]] and extending this temperament to the [[13-limit]].
 As with many exotemperaments, it is not itself particularly useful, but it has structural value.