Any tips on how to compose a left hand part that actually adds to the melody for piano compositions?

Good question.

I've been composing since I was a kid and I sometimes find myself asking the same question.

Anyway, here are some ideas which I can come up with:

----write in two-voice counterpoint. The best example here is Bach's Notebook for Anna Magdalena.

----write sustained chords in the left hand. Czerny's beginner books do a lot of this, but he overdoes it.

----write bass notes and after beats. That's rink-chink-chink if it's in 3/4 or rink-chink-rink-chink or rink-chink-chink-chink (Chopin nocturne in f minor, op. 55 no. 1) if it's in 4/4. George Bernard Shaw critized Verdi for overdoing this, though.

----Alberti bass. The beginning of Mozart's G major Sonata Facile is an example.

There are also numerous examples in the Clementi sonatinas.

Arpeggios in the left hand can be written with a unique twist. In the e minor nocturne, op. 72 no. 1, the arpeggios are each in two sets of triplets, but Chopin throws in a non-harmonic tone on every fifth note. In fact, if you look through the Chopin nocturnes, you will see that he made several twists on the idea of arpeggios. They don't call him the Poet of the Piano for nothing.

----repeated chords. The tarentella from the Burgmuller album, op. 100 no. 20, is an example. So is the Chopin e minor prelude, op. 28 no. 4.

----repeated chords, but with a different rhythm. "Tonight" from West Side Story is an example.

----engage both hands in church harmony, as in the second theme from the Chopin g minor nocturne, op. 37 no. 1.

A twist on this idea is to write chords in the right hand and octaves in the left hand, as in the Chopin c minor prelude, op. 28 no. 20.

----drum on a pedal point. The second theme from the Chopin Raindrop Prelude, op. 28 no. 15 is an example.

----turn it around and put the melody in the bass. The ballad from the Burgmuller album, op. 100 no. 15, is an example. So is the Chopin b minor prelude, op. 28 no. 6, and so is the Massenet Elegie.

----make the left hand do all the dirty work. Someone mentioned the Revolutionary Etude, but the Chopin prelude in G major, op. 28 no. 3 is another example.

Like I say, they don't call Chopin the Poet of the Piano for nothing.

The easiest thing to do is find places where you can use passing notes moving between the basic bass line. Though that can become a trap or stumbling block for more advanced composition.

You might get some ideas from studying Maurice Ravel's "Piano Concerto for the Left Hand":

Part I: http://www.youtube.com/watch?v=e20vW-WDQMg&feature...

Part II: http://www.youtube.com/watch?v=fDW25nrnQpk&feature...

And perhaps Chopin's "Revolutionary Etude": http://www.youtube.com/watch?v=yq_ea5RgvOI

Alberich

Listening to Scriabin may help you get ideas for that. He injured his right hand at some point in his career, so his left hand counterpoint is great.