12-TET and harmonics
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I recently found out that 12-TET tuning does not produce perfect fifths or thirds, but that most intervals are a few cents out of key. It's actually a compromise that works very well.
I wanted to think about what this means for guitar harmonics. In a guitar with good intonation, the 12th fret harmonic will sound exactly the same pitch as fretting the note on the 12th fret.
However, if I understood this correctly, playing the 19th fret harmonic (or the 7th fret, they are the same), should not produce the same note as fretting the same string on the 19th fret? The harmonic will create a Pythagorean perfect high fifth (twelfth? - 3 times the frequency of the open string), whereas the fretted note will generate the 12-TET equivalent.
