A nice introduction to historical temperaments

** EDIT **  Upon re-reading my reply, I realized this was probably off-topic regarding historical tunings.  Hopefully you do not mind that I did not erase my off-topic narrative, because I think it may add some insight into the way that pianos are tuned.  Thank you, ahead of time, for bearing with me.  Joe  * *

When I tune large grand pianos (6'10" to 9'), I tune them in equal temperament all by ear, with the possible exception of using a Korg guitar tuner as a "referee", in case I cannot get a few notes in a particular octave of the piano to sound "right" to my ears.  It is much easier to tune these larger instruments, because their generally longer strings have less inharmonicity to them.  (In addition, larger pianos tend to have better pinblocks, which make their tunings more stable.)

Aside:  On many occasions, the piano I am contracted to tune has been not tuned in years to decades; in which case, I must spend about an hour of pre-work, simply to "raise" the overall pitches of the keys, sometimes between a semitone and a whole tone, plus a little extra sharpness to about A442, in order to render a starting point that is somewhere near A440Hz after the raised pitches drift back to about A440.  (If I do not take this extra hour to raise an extremely out-of-tune piano's pitch, beforehand, my 40+ years of experience has shown that I spend more than an extra hour trying to correct additional pitches that have slipped out of tune during my tuning process.)

In contrast, when I tune smaller grands, and certainly all uprights, I use the Korg tuner to "lay the bearings" in the middle two octaves (from one octave below middle C to the first C above middle C -- C3 to C5).  This is done as a starting point.  The reason I simply rely on the Korg tuner, for these shorter pianos, is because even the lowest pitched strings are way too short, and have to be loaded down with way too much copper wrapping to lower their fundamental frequencies.  In doing so, the upper partial harmonics are completely inconsistent with the their mathematical Pythagorean harmonic frequencies.  In addition, some of the higher tones still with two wound strings (often between, say, B2 and E3) are too still thick for the amount of tension they require, and they send off these piercing ringing sounds, even though I have muted one of the two strings.

Still speaking of smaller pianos, after having laid the bearings in the middle octaves with the aid of the Korg tuner, I proceed to tune the balance of the piano's octaves by ear.  Many non-concert piano tuners would consider the instrument to be fairly in tune if they were to stop at this point.

I conclude my tuning regimen by going back, and playing various pieces on the nearly completely tuned instrument, so I may ascertain how the instrument "sounds".  Why?  Because there are various inconsistencies in all pianos that electronically aided tuning fails to solve.  My "Part III" consists of going over the entire piano as though I hadn't touched it before now -- and, by ear, perform all of the checks that piano tuners make ... to ensure that the piano is in tune with itself, as much as possible!  Often, I am amazed how these subtle checks (complementary fifths versus fourths in an octave, checking tenths, and double octaves, etc.) reveal that a piano really is NOT in tune ... when one relies of the "math" versus what the ear actually "hears" (because the overtones/partials in short pianos do not align with their mathematically pure fundamental pitches).

Enough of my rambling,

Cheers,

Joe