Sorry, Sly, have to disagree. This is quite mistaken. Why do you think harmonic functions are taught with triads? For instance, this entire discussion:
http://en.wikipedia.org/wiki/Diatonic_function
The reason is that they are sufficient in themselves, and there is nothing "incomplete" about them.. The idea that there have to be 7ths in everything is--forgive me--a jazz guy's hangup, and not the way things work at a fundamental level. There are literally THOUSANDS of songs and pieces based on triads where harmonic function is easily apparent without needing sevenths to make it work. Sevenths are great, but they're like adding a deck to a house: the deck might make it better and give it extra value, but it doesn't make the house more complete as a house, because you already had a complete house before you started.
The way you know the functions of triads is by watching how they act. It's not at all impossible to look at a piece containing C, G, and D and figure out which one is the I. You just look at where the action is and what's happening.
I know that Richard but if you play all major scales on the set of triads that i have mention above it won't sound right. One of them as to be thought as a V7 by the melody or the b7 in the chord to be functional. Without that b7 in the melody or in the chord, it is impossible to establish a key center, that was my point on that.
