what is the sweetened tuning?
Normal guitar fretboards are built around the concept of 12-tone-equal-temperament. ("12TET")
12TET involves 12 symmetrically equivalent divisions of the octave so that each semitone is equidistant from any neighbouring semitone.
12TET is a compromise that allows for music to be played in any key with the most amount of "in-tuneness" possible without needing to resort to re-tuning for each key.
Our ears use the simplest intervals found in the harmonic overtone series ("OTS") as their gauge for what "in-tune" sounds like.
In the OTS, perfect octaves first occur between the fundamental tone and its 2nd partial (aka "1st overtone") and has a simple frequency ratio of 2:1.
In the OTS, perfect 5ths first occur between the 2nd and 3rd partials of a fundamental tone and have a simple frequency ratio of 3:2.
Maj 3rds first occur between partials 4 and 5 and have a freq ratio of 5:4.
Etc.
In a pure OTS based tuning system, POctaves, P5ths, Maj3rds, etc. do not make any audible beats and are very smooth and consonant sounding to the ear.
That smoothness is what we experience as "harmony" or "in-tuneness".
But those types of intervals are predicated on there first being a single fundamental tone governing all the other possible intervals and is really only practical to implement in drone-based music; like simple modal vamps or just intonations based upon single keys.
Modern music involves access at all times to remotely related keys and the easiest way to make this practical is 12TET.
In 12TET the *only* interval that is pure and that exhibits no audible beating is the octave (and the unison, of course).
*Every* other interval that is possible within 12TET is slightly "out-of-tune" compared to its OTS-based closest cousin.
This includes "Perfect 5ths" and "Perfect 4ths", which are not perfect at all in 12TET and are supposed to beat slightly.
That's why when you play a power chord (P5th interval) with a hi-gain tone that the upper note of the 5th sounds flat and you need to press slightly harder on that note to get it to stop beating compared to the lower note.
And that's the way that P5ths on the guitar are supposed to operate/sound by design.
In 12TET, maj 3rd intervals sound sour too, but that's the way they're supposed to sound.
Players of non-fixed-pitch-instruments, e.g. violin, routinely adjust their intervals dynamically from chord to chord to more closely resemble the pure intervals of the OTS.
On guitar, whether you're aware of it or not, we also adjust our touch slightly from chord to chord to compensate for the out-of-tuneness of 12TET.
Normally, on a properly intonated guitar, every note at each fret on each string should be as close as possible to the 12TET standard for that pitch.
I.e. Each fret divides the strings into 12 equal semitones per octave.
In order to make the sourness of 12TET on fretted guitars a bit more palatable there have been several tuning offsets designed away from 12TET that the various proponents of said offsets claim to make the overall tuning of the guitar a bit more palatable.
But even the most cleverly designed tuning offset for guitar will cause some chords and intervals to sound even more out-of-tune than they would sound in true 12TET.
It's really a game of numbers in that these tuning offsets are generally most useful for the simplest intervals and chords, i.e. for maj or and minor triads etc.
My own attitude about these types of tuning offsets is that I'd rather start from an accurate base line of 12TET and then just adjust my touch as needed to sweeten things dynamically on the fly.
But I have to admit that the Peterson "GTR" offset sounds pretty good to me right now.
I might even try it out on my big band gig tonight and see how it sits with all those other players.
