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First - I am going solely by the score but it looks like you interspersed a little of Santa Claus Is Coming To Town. Very good effort but I must say you have more work to do. I am confident though that if you can do this without playing piano, I think you have the perserverance and patience to use some of the ideas I offer --- none of them are short term solutions.
Piano writing - specific to your piece -
Requesting a pianist to play inner voices with octaves in either hands is not easy and either the octaves or the innervoice has to be rather slow.
Also, and I have noticed this with non-pianists, if you write something in one hand which you want sounded together and you cannot do it, the probability is VERY high that the pianist cannot do it either. General rule of thumb is most pianists can comfortably play an octave, some a tenth, and a few a 12th. I have a large hand span and can play tenths, consecutively at about andante.
Variation technique - your mastery-
I'd say you show some promise as the dotted quarter and some of the textures are very good ideas. Nevertheless I see you rely a little heavily on changing the accompaniment texture and key without much change to the melody for variation. Study more techniques of variation such as breaking up the melody into short motives or augmenting the note values of some parts, etc ..
Counterpoint (adding to the comments already given)-
Yes, you could use some more work on it as you write as if you want 3 or more voices but as everything is doubled or the general voice leading implies 2 voices. If this happened as a section in an orchestral piece where you want the melody brought out then this may work --- but it is not. So you have to be clearer about your intention - do you want 2, 3 or 4 independent voices? An example of a clear melody and accompaniment with pedal points is your opening harmonization of the melody.
Lastly, please study the following pieces (preferably with a teacher) -
Group I
Bach Inventions - how to write for multiple voices for keyboard and also hand distribution of voices.
Chopin - Preludes - textures sympathetic to the piano and very "pianistic"
Mendelssohn - Songs Without Words. Somewhat in between the two, but excellent piano writing.
Grieg - Lyric Pieces - more "Romantic" than the Mendelssohn but again some similarities to it.
Set II (more advanced and if you want to go further)
Well Tempered Clavier or even the organ works of Bach to see how to write multiple independent voices for keyboard. Once in awhile he writes something that seems inpossible for one hand to play but you will notice the other hand can take the note or they can be distributed between them.
Chopin Etudes - basic bible on the capabilities of piano playing. Especially helpful on arpeggios, pedaling and textures sympathetic to the piano.
Debussy Preludes - extremely useful as Debussy writes wonderully and imaginatively for the pedals. There are pitches and interval which cannot be held be the hand but through proper use of the pedal the tone (or collections of them) lingers to serve as a pedal point and create interesting overtones with the notes that proceed over it.
There is some excellent 20th and 21st century piano writing but the works from Section II are the wellspring from which many draw.
Also, you could set aside several session with a pianist to show you a few works from Set I and II to give you a better idea and then write a draft of your variation for him or her to play.
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