> The big problem with trying to tune a guitar that way is that you're tuning a guitar so it's in tune when you don't press the strings, but then when you actually play it you do press down the strings.
When you press the strings, they will all press equally, playing a correct relative tune.
The big problem with trying to tune a guitar that way is that you're tuning a guitar so it's in tune when you don't press the strings, but then when you actually play it you do press down the strings. Strings 5 and 6 should be tuned slightly flat relative to the first four, the exact amount depends on your play style, but if you don't tune them a bit flat then they'll sound sharp when you're playing. If you haven't tried this yourself you might guess that it's subtle effect, but depending on your play style it can be huge.
The other problem is that the harmonics are actually 2 cents off of an equal tempered fifth, and if you tune six strings that way you'll end up 10 cents off. Your octaves will sound wrong.