I'm getting into music theory and was going along good until I came to interval inversions. I think I understand it for chords, in a C Major you wouldn't play the original root, but the C two octaves up (the second octave being the original octave) right? I don't understand how this applies to single note inversions though. I know all of them, that a fifth becomes a fourth and a second a seventh and whatnot, but I don't understand them. Can someone help me out?

Chord inversions mean that a note other than the root is the lowest sounding note. Often in chord notations they are shown by what is called 'slash' chords. For instance. The C chord in first inversion has E as the lowest sounding note and is shown like this: C/E.
Second inversion has the fifth as the lowest sounding note, in a C chord that would be G and the chord would be shown as C/G. If you have a 7th and it is the lowest sounding note then that would be a 3rd inversion: C/B. All other note placements in the chord have to do with other aspects of the music at hand... in other words, what the melody note is and what voice placement has been used in the previous chord.

As far as interval inversion, you're right, 2nd's become 7th's and 5th's become 4th's and 3rd's become 6th. In these cases you should be mindful of the 'quality' of the inversion. In other words MAJOR 2nd inverted becomes a MINOR 7th. MAJOR 3rd becomes MINOR 6th. The Perfect intervals stay perfect. DIMINISHED becomes AUGMENTED.

This is all well and good, but please try to always apply a practical situation to everything you learn in music theory, that way it will improve your playing and understanding of music, and it will help you remember.

It's really very easy. If you've got two notes, like C and G, they can be arranged to form two intervals. If you put the G on top, then you'll get a fifth. If you put it on the bottom, it's a fourth. That's the essence of it. If you did the same with C and E you could go C-D-E, a major third, or E-F-G-A-B-C, which is a minor sixth. You just move the top note to the bottom (or the other way around, I think).

someone will hate me for this, but here it goes:

interval inversions sum up to nine, ie

a fourth, like G to C, ("4") will become a fifth ("5"), C to G.
4 + 5 = 9. this works works for every interval: a third (3) becomes a sixth (6). 3 + 6 = 9.

as for the other interval qualities (major, minor, augmented, diminished) they "become their opposite" so to speak, ie. major becomes minor, augmented becomes diminished and vice versa. perfect stays perfect.

That's handy. I think I know them all by now through repetition, but it's still a good trick.

so with a c major chord, C E G C E, the interval would be, E G C E C?

so do intervals only matter with chords?

so with a c major chord, C E G C E, the interval would be, E G C E C?

so do intervals only matter with chords?
I'm going to assume that in this post your use of the word "interval" is a mistake and you mean "inversion"?

An interval is two notes sounding at the same time. So... one of them as to be the lowest and one the highest. If you change the order, making the lowest the highest then you have inverted the order and you and an inversion.

In your example the first chord would be a C chord in root postion. The second one is a C chord in first inversion.

so with a c major chord, C E G C E, the interval would be, E G C E C?

so do intervals only matter with chords? You wouldn't normally invert a chord that had the octave and tenth in it (like the one you posted). You would take a simple chord that didn't span more than an octave and move the lowest note up an octave to get the chord's first inversion. Telling someone that you're playing a C chord, first inversion, will let them know that the third is now in the root and the C has moved to the top of the chord. It doesn't make much sense to try to figure out the possible inversions of a chord that isn't in its simplest form (just three or four notes -- stacked thirds, usually). When you're duplicating notes and making chords that span more than an octave you've already come up with your own voicing (a the way you've arranged the notes in a chord).

If you wanted to find the possible inversions of a C chord you would just take a C major triad (C E G) and nothing else, then cycle through the inversions. C E G, E G C, G C E. You might also do it with a four note chord: C E G B, E G B C, G B C E, B C E G.

ahh i see, it all makes sense now. Thank you very much BassChuck and lemur+

actually one more question, is the first inversion the original chord? for the c major triad would the first inversion be (CEG) or is it (EGC)?

I believe the the first inversion is the first permutation of the original chord, and the original chord doesn't have a number.