I tune organs professionally, and in the US most instruments are tuned to equal temperament. For the performance of pieces originally composed on unequal-tempered instruments, though, something is lost on equal-tempered organs: the movement through harmonic progressions on unequal temperaments creates a dramatic tension between consonance and dissonance, with dissonance increasing the farther you get from the more "in-tune" keys and decreasing as the progression returns to them. Similarly, pieces composed in keys that are some distance away from the "purest" key, gain their own distinctive colors. If you're used to equal temperament and then hear a big major chord in the temperament's home key on an organ with a historic temperament, the impact is really quite something as the thirds and fifths are much closer to the natural overtones of the unisons and the whole chord draws together into a gloriously-coherent tonality.
Pipe organs often contain stops called mutations (whose frequencies are non-integer multiples of unison-rank frequencies), and others called mixtures (where there are multiple such pipes per note, generally rather small and high-pitched). These are both intended to reinforce natural harmonics, and as such are tuned pure -- even on equal-tempered instruments! The exception is highly-"unified" instruments where one rank has been wired to play at both unison and mutation pitches (to save money and/or space); this sorta works for quints (fifths), but is pretty bad for tierces (thirds), and don't even try it with a septième (seventh).
While electronic tuners are often used to set an initial temperament on a reference rank (it can also be set by listening to the contrasting rates of the differential waves between fourths and fifths), we generally tune other ranks to the reference rank, listening to the differential waves created by the two ranks to discern in/out-of-tuneness. For mixtures and mutations, the trick is to be able to recognize differential beating with partials of the reference rank that are higher than the fundamental; and for very high pitches, listening for sub-harmonics comes into play (frequencies can align in a way that creates the illusion that they are harmonics of a fundamental that's not actually being played, and our brains fill in the fundamental; this phenomenon is sometimes used to create the illusion of extremely low "resultant" Pedal-division ranks sounding an octave lower than the root of the fifth that the pipes are actually playing, and the use of an independent pure-tuned quint rank produces the most convincing result).
>Why are D-sharp and E-flat considered to be two different notes?
Officially, it's only on paper.
It kind of makes the key signatures come out more sensible because you don't want to have a signature where there are both sharps & flats in one key.
>electronic tuners are often used to set an initial temperament on a reference rank
>tune other ranks to the reference rank, listening to the differential waves created by the two ranks to discern in/out-of-tuneness.
The equivalent on guitar is to use the tuner for reference on the high E string only, then tune the low E to match perfectly by ear. You're going to be hearing a lot of these two, and they better be able to make you happy to begin with.
Then tune the middle 4 strings according to what the hands will be doing in relation to the reference strings, as well as who you will be playing with and how they are tuned.
Without an electronic tuner a single tuning fork is enough for this, and it's actually better than having a set of 6 forks at the nominal even tempered frequencies.
E=329.6 is the fork you want so you don't have to fret the high string to match an A=440 fork.
Pipe organs often contain stops called mutations (whose frequencies are non-integer multiples of unison-rank frequencies), and others called mixtures (where there are multiple such pipes per note, generally rather small and high-pitched). These are both intended to reinforce natural harmonics, and as such are tuned pure -- even on equal-tempered instruments! The exception is highly-"unified" instruments where one rank has been wired to play at both unison and mutation pitches (to save money and/or space); this sorta works for quints (fifths), but is pretty bad for tierces (thirds), and don't even try it with a septième (seventh).
While electronic tuners are often used to set an initial temperament on a reference rank (it can also be set by listening to the contrasting rates of the differential waves between fourths and fifths), we generally tune other ranks to the reference rank, listening to the differential waves created by the two ranks to discern in/out-of-tuneness. For mixtures and mutations, the trick is to be able to recognize differential beating with partials of the reference rank that are higher than the fundamental; and for very high pitches, listening for sub-harmonics comes into play (frequencies can align in a way that creates the illusion that they are harmonics of a fundamental that's not actually being played, and our brains fill in the fundamental; this phenomenon is sometimes used to create the illusion of extremely low "resultant" Pedal-division ranks sounding an octave lower than the root of the fifth that the pipes are actually playing, and the use of an independent pure-tuned quint rank produces the most convincing result).