A common feature of arrangements, especially in jazz, is reharmonization. This is the practice of changing the harmony underneath a melody.
But how does it work?
You should know by now that a chord is built of 3 or more notes, typically stacked in thirds. This means that for any given note there are at least 3 triads containing said note. Here’s a case study of all the possible triads that have a C5:
C major: C major (I), A minor (vi), F major (IV)
F major: C major (V), A minor (vi), F major (I)
Bb major: C minor (ii), A diminished (vii0), F major (V)
Eb major: C minor (vi), Ab major (IV), F minor (ii)
Ab major: C minor (iii), Ab major (I), F minor (vi)
Db major: C diminished (vii0), Ab major (V), F minor (iii)
G major: C major (IV), A minor (ii), F# diminished (vii0)
Notice that C augmented isn’t listed in any of the keys above. That’s because augmented chords only occur in minor keys as a III+ chord. Augmented chords are the only symmetrical triad, meaning C augmented, E augmented, and G#/Ab augmented all contain identical notes: C, E, G#/Ab.
The ability to quickly identify different possible harmonizations for a note is critical for any arranger/composer.
Let’s try three different harmonizations for the first phrase of the star spangled banner: