In short, Bill H is right. Basically, it does not matter at all what type of wood pipes are made of, rather it matters how that wood reacts to machining. Woods that, due to their grain and other factors, yield a very smooth bore produce a brighter tone than woods that yield a grainy bore.
The factual part:
I can add some actual “I have done this” experience here. I will keep it short, write me a PM for more detail if interested. I made 10 identical Northumbrian smallpipes chanters in a variety of woods. These all had gun drilled bores, as these bores are cylindrical, would be as close to identical as possible. The woods ranged from African blackwood and ebony (both brightest, the blackwood being just a touch more so), to Honduras rosewood, bubinga, hard maple, mesquite, cherry, walnut, pecan and white oak (in more or less that order of descending brightness).
Based on the notion that bore smoothness at the micro-level was the answer, I then, on advice of another maker, shellaced the bore of some of the duller chanters and ran the gun drill through carefully to remove any excess shellac, the idea being to only fill in the pores and tear out areas. Sure enough, all the ones I shellaced did in fact come out brighter. For example, the walnut was now brighter than the cherry.
This was all with the same reed. No, I made no recordings and have since done away with the evidence in one way or another (rental sets or interesting kindling).
The “what I think” part:
Northumbrian pipes having small bores makes the bore smoothness that much more critical than uilleann, I believe, as a small open grain or tear out is a larger % of the total bore volume than on a larger bore instrument. So it makes sense that the larger the bore, the less difference the wood makes.
I personally use dark woods like blackwood, ebony, and ziricote, because (a) they sound good, (b) they look good with imitation ivory and any metal, and (c) they are easily repairable (try replacing a knocked off key block on an oak chanter so that it is not detectable!). Grainless light colored woods like box would be fairly easy to repair as well.
Disclaimer:
I did not make a glass chanter. I think that is Bruce Childress’s realm!