Audibility of 3rd harmonic

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If I can add a little thing about the video: When you play the fundamental on the open A string, it might be more accurate to demonstrate the 5th (12th) with the open E string, rather than fretted. You'll generate a more equal body and neck resonance -- for the purpose of this exercise. You might also consider playing the harmonics on the A string as actual harmonics. A an octave above, and A two octaves above and the 5th a 12th above. Then if you're feeling really adventurous, try to get the C#, but you'll have to go quite ponticello to make it sound well.
 
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