Methods to find Major thirds relative to a root.

Correct me where I go wrong.

On a Guitar, I play my E string, 1/2 it to get the octave (harmonic), 1/3 it to get the fifth, 1/4 it to get the next octave and then 1/5 it to get my first major third.

This major third is slightly flat.

And technically isn't really a third, but an 18th away from the root note.


Alternatively, I could use a violin to do it as follows.

I play my low G.

I 1/3 it and play that harmonic to find the 5th (except it is actually a 12th) to find D

I tune my d string accordingly, and do the same thing on that to find my A - now I have my 2nd (actually, from the root, a 12th on top of a 12th, which is a 23rd)

A leads to E, then to B - the Major 3rd relative to G

As a pure 5th is slightly sharper than a perfect 5th, by the time we get to B, the intonation has sharpened, and consequently we have a slightly sharper major 3rd than in equal temperament.

But this is measured not really from a 3rd, but (cumulatively) from a 45th.

Such intervals are not discernable by the human ear and for that reason I am still skeptical about the violinists ability to discern knowledgably that he is playing according to just temperament, as opposed to knowing merely that he is a bit sharp or flat of equal temperament.

An enquiring mind wishes to expand further.