I've noticed that a piano's overall pitch will move as much as a cent in 12 hours post tuning, up or down, every string. Still perfectly in tune, but "expanded" or, sometimes, "contracted".

Is that sort of micromovement typical??

I would think so.

It's expected.

Yes. I tuned at a recording studio once and they had me tune the piano every morning and be on call in the afternoon. The piano was out of tune in the afternoon until I found out they were turning off the air conditioning at night.

Reassuring to know that variances of this magnitude are not out of the norm.

It sort of puts the mission of "perfect tuning" into context: obviously if pianos start going out of tune immediately, more or less; then the whole question of tuning precision aural or ETD becomes relative.

All we can ever do is make a piano be in tune at that moment. Once the moment has passed, there is little we can do. The skill is in making the piano drift predictably and evenly due to atmospheric changes, and not haphazardly due to unbalanced tensions amongst the different portions of the different wires.

Very well said.

Pianos are in a constant state of movement. Even in the best of conditions.

Yes. It's normal, unless it's in a magical bubble and no one plays it.

A cent is a pretty small unit. How do you know that the piano is changing pitch, rather than what you are measuring it with?

FWIW, I agree with BDB. A cent is probably within the noise level of most sensors including the ear. I would wonder if the measurement varied by more than a cent, day to day, rather than the piano's tuning.

Some of the piano tuning instruments on the market give plus or minus specs that are around .02C. I don't think the 1C difference is just the result of measurement error. Pianos drift slightly in pitch all the time depending on the amount of moving air in the surroundings, intense lighting hitting strings, and many other factors.

Pitch drift while tuning is a common problem when tuning to a fixed reference, (the tuning instrument), to a set of recorded values for the pitch of each note, (a tuning curve).

When tuning by ear you are continually referencing the note being tuned to all the significant related notes already tuned. Thus any micro-drifting will be compensated for. If you are tuning to the recorded values in a tuning instrument the notes already tuned may have drifted enough to no longer match the note being tuned. The result is a poorly tuned piano.

An instrument and tuning method that easily allows referencing the real time state of the already tuned notes would be the preferred solution.

My brother and I tried this method in the late 1970's with an instrument that used period averaging and selective filtering with a digital readout. You did not tune by watching beats between the reference values of the instrument and the note being tuned.

We stopped the project because the filtering logic was still at a too crude state. Out instrument was not good at dealing with noisy tone. On clean pianos you could tune much like you do by ear but since the plus or minus 0.1 cent accuracy was resolved very quickly, you could finesse the partial matching quickly and evaluate fine tuning stability rapidly. Also most tuners who use instruments have become so conditioned to watch beats that they are resistant to change. The market education involved is simply not worth the money possible.

A cent or even two can be the pitch difference between one single string , an unison, immediately after attack or a little later.

I once asked how one might define the pitch of a piano note, and never got a really satisfactory answer. I am sure that there is variation from one measuring method to another, as well as variations due to a number of other factors, particularly the attack, which varies from blow to blow, as well as from day to day. The conditions of the air can vary, as anyone who has attempted to tune a piano under a fan can tell. A lot of these factors can affect whatever is used to measure frequency, as well.

Everything has tolerances, which are not always studied particularly well. A tuning device which is claimed to be accurate to some degree may only be that accurate for the test that was used to calibrate it, and that may not be the same as real-world use for which it is used.

Yes, and for instance, bass string iH change depending of the force of the stroke
How much, I dont really know, but that make computations of bass strings iH difficult

I tried to analyse a few unisons with Tunelab on a cell phone

Depending of the moment, a plucked string show a loss in pitch relatively fast after a very short moment of stability (which may be due to the computation in the software , for a part)

My ususal "differnce between strings in an unisons is about 0.1 to 0,4 cts in the medium range >5th octave.

depending of the force I play during tuning that difference will be more or less pronounced. (I mean the final unison will have variances in pitch more or less large depending of the force the note is played during tuning)

But in any case trying to have perfectly the same pitch lend to an instable situation, and the dynamics only/mostly apply to the attack then (no thickening of the tone when the note is played stronger)

When the strings settle in a more stable situation, 2 shapes seem to appear : coupling between 2 strings and the last making sort of ballast. if not intended originally the final shape can be an external string low, or high, and the 2 others coupled perfectly, ore the 2 external strings coupling , and the central one a half hair lower.

If too much energy is allowed immediately at the attack, this is too much for the piano, and unless the crown is softened to death some extra energy finally move one string.

The tone can be really sharp, almost violent, with any of that shape, all depends how short you allow the attack to be.

You are dead on, as it happens. Sometimes an etd will do strange things!

Dont use only EtD then, use your ears at the same time.

And pluck the strings to hear the tinyest differences in pitch from one to the other. The etd will then confirm.

I think a piano may move way more than a cent in a day, depending of temp or even moisture more than 2 hz can be find in winter.