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I am learning RH chords, playing them along with LH chords. So right now, I'm playing 2 note RH chords. Suppose the measure calls for a C chord, and the melody note is an E note.

When playing below the melody note, do I play an E note + a B note from an E chord or do I play an E note + a C note from a C chord?

It sounds pretty good either way.

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Taking your theory further, you could , while on that E melody note, play a G# as well. Now it stops sounding so good! The E melody note is contained, as Dom says, within the C maj chord. Playing an Emaj. chord wouldn't (usually) work as the G# is not in the Cmaj. set of notes - it's not diatonic. The B sometimes works, as it makes a Cmaj.7 chord, and of course, the B is diatonic in Cmaj.

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The notes of a C major chord are C, E, and G. To fill out the chord if the melody has a E you could play the missing notes C and G. It's the simplest and most effect way of filling in the rest of the chord. There are other options though that I will explain.

If you are playing with others you have a lot more freedom in your voicing and as long as you are playing chord tones, but if you are playing alone there are certain tones you would need to imply a chord. To imply a C major chord you need at least the C and the E. You could leave out the 5th and just play C and E. You could also add the major 7th if you want too and play C and B, but you would technically be playing a CM7 chord instead of just a C major chord. You also could probably also play C and Bb to imply a C7 which depending on what you are playing may or may not make sense.

You have a lot of options and I suggest you play around with them to hear what sounds best to you.

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If you're talking about keyboard playing, beware of playing close position chords in the LH. That register can get muddy, and it's where bass lines (or maybe counter-melodies), not chords, belong.

If you want a C chord, play the notes of a C chord. Colouring it by adding the 6th (A) or major 7th (B) is harmonically neutral. The minor 7th (Bb) turns it into something with a quite different function.

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