What is the term for when a stable tone is being preceded by a previous tone and a following tone? E.g., in C major, Si-Re-Do, Re-Fa-Mi, and Fa-La-Sol.

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In a jazz context, this is usually called enclosure. This page explains it in more detail. Note that your examples are diatonic enclosures. Jazz improvisers also frequently use chromatic enclosures, where at least one of the two enclosing notes is chromatic (like A-F#-G over C major).

Another common term is changing tone.

In a classical music context (counterpoint), there's also the term cambiata which denotes a similar thing.

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