Harmonization

In music, harmonization is the chordal accompaniment to a line or melody: "Using chords and melodies together, making harmony by stacking scale tones as triads".

A harmonized scale can be created by using each note of a musical scale as a root note for a chord and then by taking other tones within the scale building the rest of a chord.
For example, using an Ionian (major scale)

Using the minor (aeolian mode) one would have:

Reharmonization is the technique of taking an existing melodic line and altering the harmony which accompanies it. Typically, a melody is reharmonized to provide musical interest or variety. Another common use of reharmonization is to introduce a new section in the music, such as a coda or bridge.

A melodic tone can often be harmonized in a variety of different ways. For example, an E might be harmonized with an E major chord (E – G♯ - B). In this case, the melodic tone is acting as the root of the chord. That same E might be harmonized with a C major chord (C – E – G), making it the third of the chord. This concept extends to ninths (E would act as the 9th if harmonized with a Dm7 chord – D – F – A – C – E), ♯fifths (E would act as ♯5 on an A♭ augmented chord – A♭ - C – E), and a wide array of other options.

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