In a longish feature in Slate, composer and writer Jan Swafford discusses the impossibility of tuning fixed tuned musical instruments such as keyboard instruments, guitars, harps and kettle drums.

The problem stems from the fact that a pleasing major third has a frequency ratio between the lower note (say, C) and the higher note (E) of 5/4. Three major thirds make up an octave (C-E, E-G#, G#-C). Unfortunately they don't.

(5/4)**3 should take you to C, as the higher C has twice the frequency of the lower C. But it doesn't. It takes you to 1.953125, a note that is horribly flat.

What to do? You could make the third "fatter", so that the ratio of C to E becomes 2**(1/3), or 1.2992 instead of 1.25. But many musicians find these "fat thirds" ugly.

Anyway, Swafford goes on to discuss the various ways that musicians have tried to deal with these problems and along the way makes an interesting observation:

How do [these problems] apply to instruments without fixed tuning, like violins, trombones, flugelhorns, and the human voice? They don't apply at all. Most of the time violinists, et al., tune by ear, on the fly, note by note, and chord by chord. That's why a string quartet or an a cappella choir can be better in tune with nature than a guitar or a piano can. As a high-school trombonist playing with a piano for the first time, I found adjusting to keyboard tuning a pain in the neck—without knowing why. String recitalists know that pain intimately. Meanwhile, an orchestra is made of a bunch of instruments, some of which tune naturally by ear—strings, woodwinds, brass—but also instruments in fixed, equal temperament: harp, marimbas and xylophones, harpsichord and piano, etc. What do orchestras do to harmonize all those conflicting demands? They do the best they can and try not to think about it too much. It can make you crazy.[...]

Along the way Swafford explains how on traditional tunings, each key had its own unique personality, be it D major as a key of triumph, or G minor, signalling "frenzy, despair, agitation". Given the ubiquity of guitars in modern popular music, tuniing temperament there is essentially settled, but it's worth reflecting that the raucousness of the sound is not solely due to the specifications of composers or the technique of performers.