Oh, one more thing to add (sorry for posting so much, there’s nothing I love more than a leisurely Saturday morning breakfast and posting on Piano Tell… 😅
So, back to the question of why an AC causes a drop in RH.
Normally — say, outside in the open air — if the temps drop, the RH increases and if the temps rise, the RH decreases. This is because cooler air can ‘hold’ less moisture, and hotter air can hold more moisture. That’s why many climates are more humid in the summer and less in the winter. (But not deserts, I don’t know anything about deserts and someone else can chime in on that matter).
So you would think that AC, i.e., cooling the air, should cause the RH to rise.
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.
Any kind of movement of air can contribute to a drying effect, hence the AC causing a (usually beneficial) drop in humidity even though the temp dropping would otherwise cause a rise in humidity.
In a desert climate, this is different because it’s so much drier outside and I don’t know how the parameters are different. (It’s also why I am super curious about whether @rogerch is in a desert or desert-like climate)
With regard to heating, it’s already less humid, and on top of the air being moved around by the air handler (the fan) the air is also being heated. So even though an increase in temps outside lead to an increase in overall RH, indoors with the heat on, it leads to an overall decrease in RH because the air is being in both artificially warmed, and artificially moved around — both of which result in a drop in RH.
So basically, HVAC systems, whether in heating or cooling mode, usually result in a drop in humidity. It’s just that in the summer, this is usually beneficial for pianos because the starting point is a higher RH. But in the winter, the starting point is already a lower RH, so usually the drop in RH caused by heating is bad for pianos.
So, in conclusion (you all thought I’d never finish!) absolute humidity is important and relevant, but it’s relative humidity that has the more direct impact in the piano.