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I've been doing most of the work on my first build over at a friend's workshop which he is able to keep around 45% RH but there are times when I can't make it over there and I'm itching to work on my build here at home and have been "tooling up" at Harbor Freight and Home Depot. The problem is that my basement where I have the space to work is also where my furnace resides and the RH can plummet when the furnace kicks on to heat the rest of the house. For example, lately there have been a few warmer rainy days where the furnace hasn't run so the RH went up to 41% but right now it's cold so the furnace runs a lot and the RH is down to 33%. Is there anything I can do to at least stabilize the RH?

Have you considered a humidifier? Barring that, try some tin pans of water near the boiler. The larger the surface area of water you expose, the more evaporation you will get. I never tried this, but in theory, you should be able to raise the humidity. How much? I dont know. But if you have a good rh gauge, you will!

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I use one of these in my guitar room and a larger one for the shop. The filters are replaceable and the maintenence is a no brainer

Those little humdifiers work very well. Note that the real concern is making sure that the materials are not expanded (over-size)because they contain too much water --- this is what happens when the RH is higher than 60% or so. If you glue this stuff together and the RH drops the material shrinks, and for example, the sound board is no longer large enough to cover the rim perimeter and cracks can/will occur. On the other hand if the wood is glued up when it is a bit small (low RH) there may be some change as it expands, no cracks but set-up and action can change slightly --- in the real world this happens to every guitar when ever it is taken into a performace area and the humidity is not exactly the same as where it was last set up --so setup/playability is the proverbial moving target. That said I would not be too concerned with low humidity, perhaps I would only do actual glue ups when the RH was about 45% in the build area.

During Thanksgiving week we had unusually cold weather in our area. The RH in my workshop dropped to 15%. I had planned to glue the neck to my guitar body that week, but my very tight fitting dovetail joint rattled in the slot at 15% RH. Our weather is a bit more normal now the RH in my shop is close to 40% and the joint fits properly again, so I plan to finish the gluing of the neck and bridge today.

This was the first time I experienced how big of a difference the RH could make on wood. I have an evaporative humidifier coming in the mail.

What's happening to the temp in the basement when the RH drops and the furnace is running? If the temp is going up no real change in the actual water content of the air has happened (where did it go?) and very little transfer of moisture will happen from wood to air in a short period. Relative humidity is related to the temperature and the actual amount of water in the air. As the temp goes up it can hold more water and the relative humidity drops. Keep the temp stable and I imagine too much moisture will be your problem over the long term being in a basement unless it has had a tremendous amount of waterproofing.
Instead of taking snapshots of RH peaks and troughs, I would put your RH meter in a closed box (Guitar case?) for a few weeks and let it stabilize. You may be surprized how high it is.

Tarhead --- please explain the post just before yours from John Parchem -- to my way of thinking we are concerned about the moisture left in the wood during a RH cycle, not what's in the air. BTW I can see the effect of RH change in my thinner material just in the time it takes transferring from one shop to the other, a matter of minutes. $.02

The point I'm trying to make is that changes in RH in the OP's situation may be more related to transient temperature change from the furnace cycling on and off and he needs to stabilize the temp first rather than adding more humidity right away. My experience in a Basement shop and now in an attached garage with concrete floor on subsoil is frought with battling constant high humidity migrating through the floor from the earth, not dealing with adding moisture. Being in a basement vs an above ground building are two different situations. As heated air from the above ground space leaks out it carrys water vapor with it and the replacement air is cold, low RH outside air. That's how an above ground space dries out in the winter and we get condensation and mold/rot under the insulation in our attics.

Sure, my thin, crispy dry wood moves with humidity changes. I keep project parts together in a sealed large plastic bin until they are assembled. That way transient humidity changes don't affect me. After assembly they go inside where I have things controlled. Our guest bath tub has a retractable clothes drying line where I can hang them

When it is colder outside the ability for the air to hold water goes down, so while outside there maybe a fairly high RH. When that same air is heated up in the house its ability to hold water goes up. So the relative humidity inside the house goes down. Relative humidity does not measure how much water is in the air rather its measure the amount of water in the air relative to the amount of water the air can hold. Thus the question where does the water go is not relevant. At a low RH the air has more capacity to pull moisture from wood that reached equilibrium at a higher RH at the same temperature

My guess is that the furnace turning on more is relevant only to say that it is colder outside. It is not the fact that the furnace is in the basement and it gets a little warmer in that room. My guess is the RH in the entire house has gone down Thus a humidifier, especially with the RH setting would help stabilize the RH in the basement.

Ditto -- John

One might not be able to see that larger pieces wood are loosing or gaining moisture and changing size but they are --- its just easier to see these changes when the wood is thin. The neck on John's project sure did change size. The assembly rooms at all the large guitar producers are maintained at a "low humidity setting" -- not just stablized.