An augmented interval typically refers to an interval that has been extended or enhanced in some way. However, the term is not standard in mathematical literature.
In music theory, for instance, an augmented interval refers to an interval that is raised by a half step (or semitone) compared to a major or perfect interval. For example, an augmented fourth would be one half step larger than a perfect fourth.
In mathematics, you might refer to the term "augmented interval" informally when discussing things like augmented matrices or other structures, but the exact definition could vary based on context.
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