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In traditional tonal practice, the main melodic pitch (often in a metrically-strong position) is best supported by a chord that includes it; in other words, it is a "chord tone."
This handout summarizes some of the choices for each scale degree plus chromatic scale degrees (chromatic=outside of the key) in both the major and minor modes. Now, this is not an exhaustive list! But if you've been studying theory in a music theory sequence, this is a nice handout to have that provides lots of options for harmonization.
There are many other factors to consider, however; like syntax (grammatical "order" of chords), rhythm and meter, and effect. And if you're a jazz player, these harmonic solutions will be to "classical" for you. But for traditional tonal practice, give this a try in your own music creation process!