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I'm composing a traditional four-part part-writing piece with a soprano, alto, tenor and bass. The song progresses from a F Major chord to an A Major chord. In the former chord, the bass is on C, and in the latter, I want to move the bass up to C#.
My question is, would such a move be allowable (assuming no issues arose with the other voices)? I know certain movements aren't allowed, but couldn't find any information on the augmented unison interval in particular.
Yes, moving chromatically within one voice is totally fine. It's actually a secret trick composers use to get choirs to sing atonal / pantonal music. That said, if it's too chromatic, you'll have problems.
Typically in choral writing, certain movements are "not allowed" because they are difficult to "hear" in the mind before the person sings. Intervals such as tritones and augmented-seconds are both odd for this reason.
The half step motion is allowed, but you may have difficulty with voice leading. If your voices (from bass to soprano) are C/F/A/f and you go directly to A major with C#/E/A/e, the tenor and soprano move in parallel octaves, which violates the four-part voice leading rules. Same if C/A/c/f goes to C#/A/c#/e; the bass and alto move in parallel octaves. Possible solutions are C/A/c/f to C#/A/A/e, or C/F/A/f to C#/A/A/e.
If your goal is to progress to an A major chord but not necessarily to the key of A major, then C/F/A/f to C#/G/A/e (an A major 7th chord) would be acceptable; but that would be leading you toward the key of D (major or minor).
