 # Are there systems that adjust to produce perfect tuned chords?

I’ve been curious if errors introduced by tempered tuning necessary to fit a scale into a piano, might be corrected in some circumstances.
I imaging harmonizing singers and string quartets adjust their tuning to eliminate beat frequencies that the tempered piano scale might introduce. Don’t some guitar chords have perfect tuning?

It would be a fairly simple test to setup a controller for a listening test, that maintained the chord root note (or perhaps an inner note of the chord to minimize average shift) , while adding a bit of bend to the other notes for perfect fractional ratios.

I tried a little math exam of the notes in a C Major, from a MIDI notes table:

C major tempered freq.
C 261.63
E 329.63 (C x 5/4 = 327)
C-E tempered scale ratio 1.2599)
G 392.00 (C X 3/2 = 392.445)
(C-G tempered scale ratio 1.4983)

An academic paper examining scales noted:
The equal-tempered fifth consists of seven half-steps (700 cents), which is a completely acceptable approximation to a perfect fifth (702 cents). Similarly, the equal-tempered fourth consists of 5 half-steps (500 cents), which is a completely acceptable approximation to a perfect fourth (498 cents). Thirds are a different matter. The equal-tempered major-third is 400 cents, which is 14 cents sharp, and the equal-tempered minor-third is 300 cents, which is 15 cents flat.

Such corrections might be most noticeable playing pure tones on something like a Mellotron.

It sounds really interesting, but one question that comes to mind is how would you determine which is the root note, as, if you just take the lower note, inversions are not possible.

If you know it’s gonna be a triad for sure then you could make an algorithm that finds said root note by measuring the intervals in between said notes