It's called harmonics, if you change your embouchure enough you can finger a low C and play C above it, then G above that, then C again and you can keep on going and different harmonics come out the higher you go.
This is because the note 'C' is made up of lots of notes, all coming together, The main harmonics are the C itself, then G and and E. Which so happens to be a C major chord!
I think the change in timbre or tone is the emphasis upon different harmonics. One player could therefore produce a brighter sound by naturally producing more of said harmonics or certain ones, than another player. Have I stumbled on something here?
Is a brighter tone made by increasing the amount of 2nd harmonic in the note? Is a darker tone made with increasing the amount of harmonics that don't fit into the major scale. Does a bright tone have a major emphasis? does a dark tone have a minor emphasis?
Food for thought, especially for scientists.
Got a bit off track, I don't think it's helpful at your stage, as Roger said it could cause you to 'pinch'. Not so helpful later on.
It's good you can do it though, I'd stick to using the octave key as again like Roger says it makes the shift between octaves a lot easier. A way you can check your intonation is that when you produce a harmonic, it is going to be in tune with the note you were previously playing (to a better extent than the saxophone). If you then play that harmonic with a correct fingering, you have a nice self created reference pitch to hit.
It could be too much to work on if your embouchure and throat isn't up to it yet, but I think it's quite important to have an awareness about pitching and the quirks of your saxophone from the beginning.