I live in Montreal, Canada, where the indoors are dry in the winter and wet in the summers. In addition to humidifiers (during the winters) and dehumidifiers (during the summer), another thing that helps is to keep the indoor temperature on the cold side (less heating) in the winter and on the hot side (less AC) in the summer! I think this is the easy/stupid version of what @ShiroKuro said earlier, but it works for me. My grand piano has amazing tuning stability.
ShiroKuro But the important point is that with an HVAC, the cooling is artificial — first, warm air is blown across a cooling coil (with refrigerant) and then the air is moved around the house by artificial means — the air handler, which is like a massive fan.
This is such a good point. ACs, heat pumps, refrigerators and most of the refrigerant-coil dehumidifiers are all ultimately the same device, what differs is which direction it runs, and where the "waste heat" is placed. The AC runs ambient air over cold coils to cool the air down, and that immediately causes condensation on the surface of the coils (like filling a glass with ice and leaving it in a warm room). For an AC, that is byproduct waste water and there's usually a drip line to get rid of it. A dehumidifier works the same way, but the entire point is to draw water out of the air, and the "waste" product in this case is heat, because it's a heat pump and the heat has to go somewhere. In an AC, that waste heat is also produced, but it's re-directed outside using a big fan. For a dehumidifier, they just pump the warm, now dry air, out into the room.
Thank you @rogerch! I might be off on this point, and different ACs may work in different ways. I think ShiroKuro explained it well--*although an AC, or air conditioner (yes, I'm thinking of the ones that cool down your house) cools down the air, meaning it can now hold less water and raising the RH, (this causes the RH to rise given the same amount of moisture in the room), it must furst it pass air over a cold coil, which causes condensation out of the air onto the coil (thus reducing the moisture in the air). So it could net out differently depending on efficiency, how long the AC runs, etc.
But if you have an AC that draws in outside air, or one that is oversized and cools down the room very quickly, you could end up in a situation where higher RH air ends up replacing the warm air in your house. I'm sure a number of other things are possible too, depending on the variety of AC/heat pump setups that exist.
In my house, whenever the AC is on, the RH drops precipitously, and my dehumidifer never turns on.
*edited to correct vapor capacity
I think so. I don't have any direct experience with this, but it's been reported often that humidity swings cause tuning instability (and is one of the selling points of the Dampp-Chaser Piano Life Saver, which is a dedicated humidity control system). Presumably you get all kinds of flex/swell/shrinkage in the soundboard, bridge, pinblock and case/rim that cause this to happen.
Gombessa This right here. Very cold air holds more moisture, so if you have 15 "units" of moisture in the air, in cold air it would be only 10% RH because the air can absorb more, but in hot air it would be 80% RH, because relatively, the air is almost at saturation.
Hey Gombessa I think this is backwards. Warm air can hold more water than cool air. As temperature goes up, RH goes down if absolute humidity stays the same. At least that’s my understanding and it’s consistent with my observations where I live: as the outside temperature changes throughout the day the outside RH changes in the opposite direction.
Since you have studied humidity way more than I have I may have either misunderstood you or else I’m just wrong. What I wrote seems consistent with https://themachine.science/relative-humidity-and-temperature/
rogerch Hey Gombessa I think this is backwards. Warm air can hold more water than cool air. As temperature goes up, RH goes down if absolute humidity stays the same.
Ugh, yes you're right, I'm all in the middle of confusing myself. Warm air can hold MORE moisture than cold air, so RH goes down because it has now more capacity relative to what it could hold at a cooler temp. I have to go back and edit a few posts/responses to correct the record here 
Rubens I live in Montreal, Canada
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Oh nice! Montreal is a beautiful city. I lived there for a decade. It's amazing. Pierre Marchand is not too far away and Esmonde White as well... would love a report on Oliver's pianos with the Fandrich action one of these days.
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However, after a decade in Montreal, I could easily survive "winters" elsewhere in a t-shirt and shorts... I don't miss those -40 deg winters at all and it's not like the summers don't get hot either. I would have thought it would be hard to do optimal piano climate control under those Montreal conditions, but it sounds like you're doing just fine based on the other thread!
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Beach L168, Wish, baCh, WOW Petrof, Fake Steinway, VS
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This discussion made me curious so I moved my piano hygrometer outside and let it sit for a while.
The outside temperature was 100.9F, RH was 27% (Yes it is hot here! We have had an unusually hot summer!)
At the piano, the temperature was 77F, RH was 40%
I found a calculator that given a source temperature, source RH, and target temperature calculates the expected RH at the target temperature: https://www.markusweimar.de/en/humidity-calculator/
According to that calculator, cooling the outside air to 77F without changing the absolute humidity should result in relative humidity of 57%. That's 17% higher than the measurement that hygrometer took at the piano. From what I have learned today about air conditioners I suspect that 17% lower RH is due to condensation happening in the air conditioner. Somehow it all works out so that the RH at the piano is reasonable, and I'm fortunate that this is the case year round.
Thanks everyone educating me, this has been most interesting! 
Interesting find! I believe that being at home also contributes to a baseline RH increase indoors, too. If we aren’t home, the RH at my house stabilizes at around 40%, when we are back, even without a change in temp or climate control use, the RH typically rises (enough for the dehumidifier to kick in and bring it back down to 45%).
I think I could easily drive myself crazy worrying about RH. I have had a Piano Saver device installed (on a Yamaha C2), I try to keep the temperature below 65° F during our cold, dry winters, and below 78° F (using central AC) during the hot humid summers in northeastern Connecticut.
I also have an ultrasonic humidifier (I try to clean it frequently) in the room with the piano, but I have my doubts as to its effectiveness.
The piano seems to hold its pitch well for a few months at a time, so hopefully it's okay.
pseudonym58 I think you're doing more than enough here I definitely agree it's easy to get carried away. I certainly do, but mainly because I find it fun, and I'm interested in the data!
