In this exercise, the key signature has two flats but it's marked as C minor. There's a footnote that simply says 'modal key signature'. How do I work out which mode to use in my harmonisation?
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You don't need to know which mode you need to use in order to complete this exercise. You simply follow the chord symbols on the bottom.
I would hazard a guess that "ic" means the "cadential" version of the i chord and would therefore be i 6/4, but consult what the book says "ic" is before committing your answer.
Following the chord symbols on the bottom strictly will eventually lead to you using a B natural (in the V chord) and an E natural (in the I chord). At this point, fuhgheddaboudit mode-wise--no mode of any major scale contains Eb, E, and F.