I play drums, I play a bit of piano. And when it comes to composition, you need to have some form of musical inclination, even if it is or seems, limited.
This is a weird idea, but it's one of many, and a simple but potentially good idea for composing something new out of other tunes.
Take two great popular tunes of your liking.
Say,
1.Michael Jackson - Human Nature
2.Dave Matthews - Grey Street
Ok, you may like or hate my suggestions, make your own up, i'm just spitballing here! Now, here comes the science.
STEP 1: The melody of song 1. Sing it, whether it is just the chorus melody or the verse or the bridge melody, sing one of the melodies, they're all phrased in popular music, and people like catchy phrases of melodies. If it sticks in your head and you can whistle/sing it, then it works. So take a melody and sing it.
Now, if you can understand chords and notes, that will help. If you don't have a big grasp on this, having reference material helps. If you have a keyboard or piano or instrument of sorts, listen to the melody, and try playing the rhythm of it, for starters. If you can hit the rhythm of the melody in time with it, you're onto something.
(I'm doing this in slow steps so forgive me if this is a waste of reading by some standards, Gold Cray just wanted to see how some people compose, and this is one of the methods I use when i'm stumped, not as much but it's interesting to me.)
STEP 2: Rhythm down? Awesome, you rock. Now try playing parts of the melody, even the first two notes, or the first note, just do it slow, if you have the song on reference in your mp3 player then good, keep it handy, if you have the rhythm, this part will be easier. Try assigning each note in the phrase to the rhythm in its form. Bit by bit, rewind it back if you need more, just keep building that phrase up into a melodic phrase. Eventually you have managed to play that phrase by hearing it and playing it out on the keyboard/piano/piano roll.
If you have no instruments, I suggest tapping out the rhythm and/or getting a program with a piano roll in it. This
http://www.mymusictools.com/utilities_28/pianofx_studio_20690.htm might work, it may not, but if somebody has a better non-VST source of a piano roll, then please post it.
STEP 3: SO YOU HAVE THE RHYTHM! AND THE MELODY! OF THE first phrase sorry about those caps my shift finger was sleeping. Now you want to get the chords. Now with better ear-training you can really pick out the exact chord pretty much off the bat, but when I first started, I just picked out the bass note changes underneath the melody, and then whatever that note was, in popular music, it tended to be that chord that was being played. Get the rhythm and notes down for this, you've just got yourself a chord progression with a melody to boot.
Ok, so you didn't write it yourself, but that's half the battle.
STEP FRICKIN 4: Next part, get creative. Do this with another tune, but this time, try singing the rhythm of the melody in the first tune over another tune, not the melodic part of it, chances are high it won't be in the same key. Now, take the chord progression from this second tune, and in doing so, apply the rhythm of the melody you original scored/clapped/memorized from song 1. Put it over this tune, and in correspondence to the chord progression in song 2, apply notes to the rhythm of the phrase that fit with the chords from song 2.
SO: Eventually you find yourself having a totally new song, chord progressions get used again and again, and melodic rhythms do as well, but when you take the foundations of both and shift them about, you begin to find new themes. Original & yours.
ALSO: It's good to think of this as the foundation for a theme. So you have your new melody over a different chord progression, it's yours, and you can go where ever you want with it. Take the methods above of mixing other rhythms from various tunes into different sound textures (if one rhythm in song X was on a trumpet, try putting it on a bass guitar in it's lower register in song Y).
Mixing and matching, is what is happening here. I am not suggesting to make it your sole directors choice for composing every time, but you'll be surprised at how it will improve your ear, and some of the things you will come up with, I guarantee will be awesome. Eventually you'll have such a plethora of melodic phrases and rhythms and chord progressions in your mind that you'll stop doing this consciously and it will just flow at times. Everybody get writers block though, and this is a long learning process, but it doesn't have to be a painful one.
I'm sorry, if that helps nobody then no problemo, but I figured sharing one of my many methods might at least humour you lovely people
cheers!
Chris Geehan.