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Well, you might have to define what you mean by "harmonize" exactly in order for me to answer your question best.

If by harmonize you meant that every note in the major scale sounds restful and pleasant against one primary chord, then the answer is no (certain notes will be dissonant compared to a given chord according to natural rules). If you mean, can any note in a major scale sound restful and pleasant with one of the three primary chords in a key, then the answer is "yes".

The three primary chords in a key produce all 7 notes in a major scale.

(F) The F is in parenthesis because it creates a tritone with B-very dissonant)

C G D

A E B

F C G

C D E F G A B C

To put it in very simple terms, without going deeper into the theory of how this works, or even how to generate good chord progressions, match the scale tone of a melody to one of the three chords in order to harmonize a melody. There is often more than one choice especially if you want to use secondary chords as variety.

If you meant how any notes combine together as harmony then any of the twelve tones can combine with a given chord- it depends on how much dissonance you want to express and depends on how you want to structure your voice leading.

I hope this answers your question.

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Q: Can a primary chord harmonize every note of a melody in a major key?
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