Name for single repeated note

Is there a music theory term to describe when a melody revolves around one key repeated note? For example, in a piece I am playing, the melody is: F C G C Ab C Bb C. Or, in my version of "spatial awareness" ( an exercise a lot of front ensembles seem to play) , we play a blues scale, but we play a C in between each note of the scale (Eb C F C F# C G C Bb C and so on). So, in both of those situations, what would that C be called, if anything? Apparently it shows up frequently in piano music. Thank you for taking the time to help me out.

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