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→Harmonics
Note that to sound the harmonic correctly, you place your finger at exactly the position specified. So to ''fret'' the 12th fret, you would actually press down ''behind, not directly on top of'', the 12th fret. But for the 2nd ''harmonic'', you want to be ''directly'' over the 12th fret.
Since the guitar is tuned mostly in ascending 4ths, we can use harmonics to get what should be completely equivalent frequencies between two strings. A 4th interval is 4/3 the base frequency. The 4th harmonic of the lower string will give a frequency 4 * 4x that open string. The 3rd harmonic gives a frequency 3 * 3x that open string. Using the 4th harmonic on the lower pitched string and 3rd harmonic on the next highest pitched string should be the exact same note.
To demonstrate, the 6th string should be tuned to E, or 82.5 HZ. Sounding the 4th harmonic would give us 4 * 4x that pitch. 4 * 82.5 = 330. The 5th string should be tuned to A or 110 HZ. The 3rd harmonic is 3 * 3x that pitch. 3 * x 110 = 330. So 6th string 4th harmonic = 5th string 3rd harmonic = 330 HZ. 82.5 (E) * x 4/3 (4th interval) = 110 (A).
So if we sound the '''5th fret harmonic of the 6th string''' and the '''7th fret harmonic of the 5th string''', the same note should be ringing out. This frees up the left hand to rotate the tuners to achieve the same note. And like open strings, harmonics tend to sustain longer. This works on every pair of strings except the 2nd and 3rd strings. For these we can use the 5th harmonic of the 3rd string and the 3rd harmonic of the 1st string. That's the 3.8 fret harmonic on 3rd string and 7th fret harmonic on the 1st string.
3rd string G is 196 HZ. 196 * x 5 = 980. 1st string E is 330 HZ. 330 * x 3 = 990 HZ. But wait - 980 != 990. Unfortunate, but close enough for our purposes. If we tune the 1st string 3rd harmonic to 980, that means the 1st string is now 326 and 2/3 HZ. That's only 3 1/3 HZ away from our target of 330 HZ, and the human ear has trouble differentiating pitches within such a small window(approximately 1% off).
Once we've gotten the 1st and 3rd strings tuned together, we can use the previous 5th/7th fret harmonic technique to tune the 2nd string to the 1st string.