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A composition's tonality states the key and whether it is Major or Minor. At an early stage of composition, a key could be as simple as making an arbitrary choice, but it will have the biggest impact on the sound of your composition. If you finish your work later on and want to try  it out in different keys, you should do so, but be forewarned that it takes a fair amount of work to transpose a composition note by note into another key. The piano keyboard has been explored to death. Every possible combination has been tried and studied at this point. With that, theory can suggest the most appropriate chords. The most famous of these is the I-IV-V-vi progression (the lower case denotes a Minor chord). The Roman numerals indicate how many keys above the root the given chord is. These four chords have been proven to go together very well.  Try using a chord map to get you started.  Although this might sound too mathematical at the start, the truth is that it'll come without thinking to you once you get the basics of theory down pat. Scales are  useful tools in the creation of melody. Although melodies need to be properly felt out in order to be memorable and effective, using a scale will narrow down the notes you're conventionally supposed to use.  Make sure the scale you're using is in accordance with the chords and key you've chosen. The standard scale is a C Major scale. This scale is often used for vocal warm-ups before a performance. Some avant-garde composers in the 20th century would open up the piano itself and change the tuning of the strings, but prior to the adoption of equal temperament for keyboard instruments in the 18th century, there were numerous tunings in use. Changing all of the keys even a 16th of a step can result in a strange new experience of the piano. Be advised that messing around with a piano should only be done if you are an expert. Otherwise, you'll probably just end up sabotaging your piano for regular use. Notation is the technical language of music. If you're a serious composer, it's essential that you have at least some knowledge of notation and how to get your ideas down accurately on paper. Although it takes a little bit of time to get used to, there are fortunately lots of free online resources to help get you up to par with your notation reading and writing. If you're completely new to notation, you should try sight-reading a few basic songs on the piano until you're more used to it. There are digital notation programs that may prove easier to work with than pen and paper.

Summary:
Decide upon a tonality. Explore chord progressions leading from the root chord. Develop melodies from a chosen scale. Experiment with tuning. Record your work via notation.