Melodic Motion
If we take, for example, the key of C Major and start on C, C's tendency is to stay where it is. But if you're not just playing a drone on the tamboura, that C has energy and an inherent potential to move. There is an equal gravitational pull from the third above and the fifth below. You could just leap to the fifth below but the most common motion is stepwise, so lets talk about that for a while.
When C gets enough energy to reach escape velocity C might step down to B but the gravitational pull from C is still stronger than the G below. The A just below B is also pulling on B but not as strong as G or C. So, most likely the B will step back to C. Not only because C's pull is so strong but also because so is so close to C at only a half step away. So, proximity is a factor too.
If we had gone up to D instead, the pull from the E above D is not as strong as the C below it so most frequently D will step back to C. The pull from C on D is not as strong as the pull from C on B because D is farther at a whole step away. If we think of the motion as a space traveller and if he or she has just the right amount of energy, he will orbit around C going CDCBCDCBC until it loses energy and returns permanently to C.
If there's a little more energy then perhaps it might pass through B to A back through B and C to D making it to E. E has more power of gravitation on its neighbors than A because E is an important degree of the scale. Its a member of the first chord in the key of C. Therefore E may be able to capture our space traveler for a time. He may travel to the opposite side of the planet E if he has over shot it and visit F for a moment but F is not a member of the intergalactic coalition of first chords.
There are gravitational forces pulling on F from both of its neighbors but F is closer to E than to G so most likely E is going to win if our traveler doesn't have enough momentum in the direction of G even though G is strong than E. We can think of it like someone who gets bored easily and is also indecisive. If going in one direction for long, Spaceman Spiff will break up the monotony by changing direction a moment then change back to the original direction.
The notes in the chord are more comfortable and desirable planets to visit so when he gets there, he wants to stay longer. Our space traveler's space ship is a sentient entity like on Farscape. It's a boredom eater which, luckily, is an infinitely reneweable resource in the psyche of it's captain who is the same as our space traveler. And, incidentally, lives on excitement which is his space ship's waste product.
Once our traveller gets bored enough, his space ship starts storing the energy which is a nice relationship because when our traveler is ready to go, so is his space ship. If he's not bored enough then he could be pulled back to places he's already been. But with enough thrust he'll make it to G either directly from E and F or back the other way through B and A.
At G he's about half way from C below or the C above. The C above is a bit closer so its probably exerting more pull but our traveler has a will of his own and although he could live on the C above for a long time, he'd prefer to return to where he started. He could use his hyper space controls to transport directly to C but he'd miss out on seeing A. He's come all this way and it might be his last chance to visit there in his life so after getting excited enough about going there, he takes his ship on the trip to A.
B has almost no pull on A. B and F are weak like that. D and A have a stronger pull on their neighbors then either B or F do on theirs. The G below A has a lot more pull on it, even more than the C above so most likely he'll return to planet G. But if he over shot A to B, there won't be any way for our traveler to avoic going to the C above even if he comes back down first for a while because the governement on planet B has a law that you must eventually get a stamp on your visa which shows you've gone to the C above. Probably to encourage tourism there.
And they have a time restriction that says you must visit C in a reasonable amount of time. After which, you can go anywhere you want. If you don't visit the C above, interstellar leading tone police will chase you across the universe.
Unfortunately, if you just follow the melodic rhythm advice and the voice leading advice I've given you, you still may end up with a bunch of mediocre or just plain crappy melodies because there's one more concern that needs to be addressed: the gravitational pull of rhythmic positions on chord tones in the measure which I'll talk about in my next post.
Till then, happy composing. Below is a video of me playing classical guitar going through the most common melodic solutions. I'm wearing a "monks cowl" because I thought the music played like that sounded medieval. No, I hadn't just finished taking a shower.
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