10/11/2021
From past discussions in various venues, mostly Cyberpluckers I guess, we know that some people tune there highest strings a bit sharp, more to the tuner rather than the ear. The need to do so has been attributed to partial harmonics distorting the sound, but I had a palm-to-forehead moment recently, when I realized that some chords end on a third or especially a fifth interval, no octave note. That means that a trained ear is going to want to hear a pure fifth of 702 cents rather than the 700 cents of Equal Temperament (tuner default). There is also the natural tendency to want stretch the minor third from the third note to the ending fifth. When Equal Temperament stretches the Major third, it narrows the minor third that follows, leaving both intervals out of pure tuning.
For example using a G chord G-B-D-G, the G-B is a major third, B-D a minor third, and D-G a fourth. In the tuner's Equal Temperament mode, the major third is 14 cents wide, the minor third is 16 cents narrow, and the fourth is 2 cents narrow, all compared to a natural tuning in Just Intonation; what the ear would find naturally pleasing with no beating, while an impractical scheme for the majority of instruments. So what we do is flatten the top 35B note to make the G-B interval sound better, or we sharpen the top G note. The example of sharpening high notes also comes into play with chords like D Major, wherein that last D-A interval is going to beg to be improved by raising 33A slightly, yet not enough to sound really off compared to an octave lower. Another example is F Major wherein that high C finish is going to want to be raised to make a better fifth interval that stands out so clearly.
To summarize, if tuning to a tuner's default of Equal Temperament, or especially is using alternate temperaments that have an even flatter fifth interval, I would be looking to raise 32G, 33A, and 36C slightly, no more than 2 cents, probably only 1 cent. For those I would not be too critical of the octave notes sounded together, going more by how the chord sounds at the top end. The same thing can be accomplished by ear, but here I am trying to quantify it, so one can use a rule of thumb to apply to what a tuner tells us, no personal judgment or even ability to hear well involved.
The above is entirely in the context of an Oscar Schmidt chromatic. The same principles apply to other configurations, diatonic and such, but references to specific notes and positions would change while based on the same principles.
