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I guess my next question would be what is an easy way with those two notes to find out what chord that is and what the progression is? 

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One easy way (surely not the best one!) to harmonise a given bass and melody with full chords is to look if you can harmonise everything with three chords, an idea that goes back to the 18th century: the tonic, the dominant and the supertonic, and some simple rules: The tonic (I) starts and ends the piece and can lead to all three chord types; the supertonic (ii) precedes a dominant; a dominant (V) can lead to back to the supertonic or to the tonic. Supertonic and dominant can be used as seventh chords with the seventh being resolved by going one step down, thus the supertonic seventh always leads to the dominant, the dominant seventh always to the tonic. You can use the chords in root position or inversion; the final cadence should see the dominant and tonic in root position. If the music has left the key, simply use the three chords of the new key. See e.g. Daube's Musical Dilletante for more information on this method of harmonising a melody.

If you write out which notes belong to which triads and seventh chords, you will easily see which chords can fit to the given melody/bass-combination.

There are far better methods than this one, but hardly easier ones.

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A slightly more complicated option is: 

1.  Figure out what key your melody is in. 

2.  Write all the triads that each melody and bass note pair could possibly be part of above them on the score, assuming you stick strictly to the key (don't add sharps and flats outside of the key signature, at least to start with).  Ex:  if you are in A minor, and you have an A and a C as a melody note and a bass note, you'll either end up filling out the chord to be ACE or FAC, but not F#AC, because F# is not in the key signature for A minor.  

3.  Go back and eliminate triad options using a chord progression chart to decide which of those options is best to use.  What makes something the "best" triad?  It connects smoothly to one of the triad options for the next note in the melody.  You'll want most of your triads to be in root position, with some in first or second inversion.  Some places, you may have a non-chord tone, a seventh chord, a raised leading tone, or something else that makes sense or adds interest, but doing it by process of elimination like this will get you a structure to start with that lays out the most obvious possibilities, and then you can narrow down and refine from there, or decide that you want to do something funky to spice things up.  You'll want to end on a nice cadence, so work from the end, backwards towards the beginning, as well as from the beginning forwards toward the end, and eventually you'll find you've met in the middle. 

As with a sudoku puzzle, write in ALL the good options first so you can see what you're working with and feel organized, then start eliminating by striking through, not erasing, so you can still see where you came from in case you decide, on second thought, to change directions.  When you feel pretty sure of things, write a clean copy.  

 

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