Talking about tones, or pitches, or notes

In our so-called "Western" musical system we've got 12 tones, notes, or pitches (each term seems to mean something slightly different in an extraordinarily complex way). The way we name those notes, C, C#, D, etc., is complicated and it makes working with them difficult. Wikipedia describes some systems of musical notation, including one called integer notation which is particularly interesting to me, as a onetime computer science major.

In the integer notation system, you number the pitches from 0 - 11, with C being 0. This means you can do simple arithmetic to figure out the relationships between notes, rather than having to count or convert -- quick, how many tones are between A and C? How about between 9 and 0? (note that 0 acts like an Ace, it's either 0 or 12)

That sharps and flats notation is helpful when you're playing piano, because you've got that white key, black key thing going. But on the guitar, there's no inherent difference between an F barre chord on the first fret, say, and then sliding it up one fret to F#. It's keyboard bias!

When talking about the Major Scale interval pattern, people usually write W-W-H-W-W-W-H, that is, two whole tones, one half (or semi-) tone, three whole tones, then a semitone. Confusing! In integer notation you could just write 2-2-1-2-2-2-1, or you could write the C Major Scale interval pattern as 0-2-4-5-7-9-11.

Let's say we want to know the I-IV-V notes on that scale, what are they? Easy - 0, 7, 9 aka C,F,G. Just like the metric system, it's only confusing if you convert back and forth, but really there's no need to especially on a guitar.