how about starting a piece for piano.
not too complicated, but something with a definate form.
1. establish the form in advance.
2. create distinctive thematic material
don't start composing the whole thing just yet... start with some thematic ideas. let's see how you could develop them.
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for non-traditional harmony, there are a few things you could consider.
chords can be inverted for different effects (as you've noticed with the 2nd inversion effect).
harmony can be transposd on itself. what this means is that you take a chord (this is supposing that you are not working with simply major/minor chord) and transpose the entire chord structure onto every note of the original chord.
for example:
if you decided to go with a chord of C - E - F# - B - D
you would transpose the entire thing onto E, then onto F#, onto B, and finally on D.
This works well when dealing with chords that don't necessarily have a traditional directionality to them (chords that don't lead to a destination "by sound").
When building melodic material around your harmonic base, remember that too many melodic notes that are NOT part of the harmony will cut the connection between the melody and the harmony.
This is where counterpoint rules come into play: when you use a non-harmonic tone in the melody (which is the equivalent of a dissonant tone in traditional counterpoint) it should have some sort of preparation and resolution to a harmonic tone.
this could mean:
- passing note (between two notes of the harmony)
- appogiatura (unprepared non-harmonic tone that resolves down onto the harmonic tone)
- suspension (prepared note from the previous harmony that becomes dissonant to the new harmony and resolves down into the new harmony)
- neighbour tone (note that is foreign to the harmony but is surrounded on each side by the same note which IS part of the harmony)
the more distant your harmonic material is from common practice, in my opinion, the more important these principles are and their use leads to coherance in your melodic/harmonic relationship.
This is, of course, going on the assumption that you are working from a harmonic framework and assigning melodic material to that.
If you start from an entirely contrapuntal point of view, the approach will be a little bit different.
Ideally, you should be working from a number of approaches to give a truly satisfying result - harmonically, contrapuntally, and purely melodically.