Interesting question, Mujus. I generally refer to intelligence as one's ability to process and retain information. For the most part, if I see something more than once, I'll remember it for a very long time. While I may be limited in understanding theoretical process (like most of Chemistry and Physics), I can apply learned material very easily. I do have good spacial awareness, and I tend to have more, as you say it, intrapersonal intelligence. And, while I tend to get better grades in Math and Science than in English or History, I really enjoy English and History much more. But I think my intelligence more comes not only from my memory and adaptability, but my willingness to apply my ability to retain information so that I might better myself and increase in talent. I score very high on IQ tests and the like, but the value of such have begun to diminish in values. The biggest reason, being how you phrased your question. There is much to be considered in evaluating one's 'intelligence,' so I suppose that I have no right to say that I am smarter than most people. Sure, I know a bit more, but all that means is that I'm more likely to get into better colleges.
By the way, I love questions like this. It's always nice to set aside time to evaluate one's self and try to put it into words.
Oh, and I've heard the same for writing pieces. My Theory instructor applies the same philosophy. I started with harmonizing single phrases from Bach Chorales and since then, I've moved onto small Concertos. Starting with a symphony was the biggest mistake I could have made as a young composer, but I'm much more experienced now, and I'm considering starting on my first multiple movement work. What I love about it is that I now know what sounds good, and why it sounds good.