#1
My guitar teacher told me that we never use the terms "tenths, twelves," etc when we talk about the next octave. I asked why, he told me he didn't even know, so I assume that it's just for identification purposes or something. So does anyone know the real reason why this is, if there is one?
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#3
I think it's because 10th is the same as the third, and it doesn't really affect the chord other than accenting that note a bit more. The same goes for 5th/12th. Things like the 9th, 11th etc actually add something new to the chord which is why we consider them worth naming
#4
When you have an interval larger than an octave it usually has the same harmonic purpose as the interval formed an octave below, therefore when doing a bare bones analysis of a chord, say involving the notes C4, E5, and G6 (Octave ranges), its still a C major chord, regardless of the Major 10ths and stuff that are formed from it.

But, when adding a 7th or 9th to a major/minor chord, you should definitely include it, as its part of the tonality of the chord. Plus, CM7add2, or addX might imply that its a more closed voicing rather than stacks of thirds leading up to the final extension.