Before we discuss the qualities of different woods for traverso we have to discuss the difference between
-the listener and the
-player for this subject.
This difference is usually overlooked. The listener will not be influenced much by the vibration of the instrument.
Contrary to string instruments the traverso does not radiate its tone to the listener through the vibrations of the wood. It is the vibrations of the air in the holes that radiate the tone. To get a rough impression of this fact we may consider the following. Because of its form the wood of the traverso vibrates less then the wood of the violin. Let us assume that the vibrations are 10%. I have no measurements of this and would be pleased if somebody corrected me here. However it certainly is a lot less than 100%. The surface of a violin is roughly 1500 cm². The surface of the traverso is roughly 250cm². So about 16%. Total that gives an estimated radiation of 1.6%.
However, the player does experience the vibrations of the wood. For the player I think that they are essential. Therefore her or his way of playing will be influenced very much by this feed back!!
Then the listener will also experience this different way of playing. However, this can never be found by single note playing. Therefore blind tests using single note playing are of no value in this context!
Testing wood differences by comparing music is so difficult that it would not give simple answers either. Not only the vibration of the wood may play a role for the player. Maybe also the way the air interacts with the inside wall is different for different woods. I have no specific view on this subject however.
There are theories and evidence that the material of the flute should not matter. However, a few hundreds of years of the same sort of testimony and my own experience coinciding with that testimony convinces me that the material is essential. So it might be that the difference in woods is mainly for the player but therefore as a consequence also for the listener!
A separate issue related to woods is the question of the size of the bore when the wood shrinks over time. There is a widespread belief that the bore always shrinks when the wood ages. In my experience this is simply not so. Sometimes it shrinks sometimes it widens. I get a flute back after a few years and the head may be narrower whereas the right hand joint may be wider for instance. That this is not a simple problem may be understood by the fsollowing thought experiment.
This is not the extensive bible on what wood can be used for flutes. It is rather a short remark on what was used and what I am using. What was most used is
-coco bolo purple wood
and other hard woods that came the way of the flute maker of the time.
Of course a separate issue is Ivory!!! I use only the first three which I am going to discuss a bit now. Then I am going to make some remarks on Ivory.
The most used wood for the Beukers flute is boxwood. The original is in boxwood. The boxwood is mellow and warm. Most flutes in boxwood are softer spoken then the ones in blackwood. However, the Beukers flute carries so well also in boxwood that it is played next to any flute by well known players in concerts and is equally well heard in large churches, as recordings show.
Blackwood flutes usually are a bit more brilliant than the boxwood ones. The Beukers in boxwood is still quite mellow, but the difference is clear. It is a slightly different flute also because one has to change certain dimensions to make the flute as nicely going as the boxwood one. It is a misunderstanding to think that exactly the same dimensions should be used for the blackwood version. In my experience the flute has the flexibility of the leg of a table if one does. Good information on this topic is provided by two facts: original Ivory flutes are almost always very very thin walled and I do not know of any two original flutes in different woods with exactly the same dimensions. I have a very good uniform quality of blackwood. This implies that the blackwood flutes are extremely reliable with respect to climate changes etc. Of course anything can be ruined. However, knock on wood; I have not had any flute in blackwood with problems because of climate etc.
Ebony in a way is the most beautiful of the three woods I am discussing here. It has a very full, warm and brilliant sound. However it is most sensitive to the way the instrument is used. Also I often have a few pieces cracked before the flute is finished! Once the flute is finished and treated it is stable. For countries like Canada or Siberia I do not recommend it. Something on Ivory. I do not make full flutes in Ivory. This is not because I do not want to use Ivory. I have good, reliable sources for very old, used Ivory. However, the effort involved is difficult to insert in my normally already very pressed schedule.
When reading the following one has to keep in mind that it reflects the taste of the time as an important factor.
First half of the eighteenth century mellowness was much appreciated, so boxwood, second half the taste changes for more brilliance, and finally louder louder is the end of the nineteenth century, so Rockstro has no taste for this old stuff that is called boxwood any more. Knock on (box) wood but I very rarely have warp problems with the boxwood. My flutes have been several weeks in linseed oil, dried etc. before I finish them. I think that the eighteenth century makers did something similar (possibly even warm oil). I have taken boxwood flutes all over the world without problems. For instance wet Singapore, no problem. Dry Phoenix no problems either. But of course on a freezing day in Winnipeg nobody in his right mind leaves a wet flute outside to freeze.
So it is mainly a question of reasonable care.
(~1750) In Quantz  we find (translation by me, so no professionalism involved) "The material flutes are made from is hard wood such as: boxwood, ebony, kingwood, lignum sanctum, blackwood etcetera. Boxwood is the most used and most resilient wood for flutes. Ebony however has the most beautiful and most brilliant tone.
(~1800) In Tromlitz  we find (Translation A. Powel) They are made of various woods, such as boxwood, ebony, grenadilla, lignum vitae and the like. Those of boxwood give a pleasant but rather weak tone; they are the most durable; those of ebony, grenadilla etc. are brighter and stronger, though they require a firm and well focused embouchure. The lignum vitae also gives a good tone, but in my experience has to o little elasticity and is more subject to cracking than other woods.
(~1900) And last but not least Rockstro [ 3] Boxwood was one of the materials first used for this purpose, and it is mentioned by Mersenne(1637) as being more frequently employed than any other wood. It has many excellent qualities and some very bad ones. The tone of a boxwood flute is not surpassed in its sweetness, but no reliance whatever can be placed on this material as it absorbs moisture so readily that the bore of any wind instrument made of it is liable to continual change in its dimensions. ......... Boxwood, particularly that of Turkey has a good natural polish but because of the above mentioned defect has long ceased to be used for any but the commonest of wind instruments. The natural beauty of this wood has sometimes been barbarously destroyed by a dark brown stain. Ebony gives a fine tone at first, but it has the chief vices both of boxwood and of Jamaica cocus, being liable to change in its caliber like the former, and to cracking, like the latter. This This wood is being mentioned by Mersenne as being very good for flutes and it was once popular, perhaps on account of the extreme beauty of its appearance .....But it is no longer used for first class flutes.
There is much more on wood in Rockstro, but by that time it was the silver flute and if wood was used, hard woods like blackwood were in vogue.
 J.J. Quantz, On playing the flute, second edition, Faber and Faber, ISDN0-571-18046-9, different facsimile and translation editions. E.g. ISDN3-7618-0074-6 (and a number of other facsimiles, e.g. in Dutch, in German(original) and in French)
 J.G.Tromlitz, Ausfuehrlicher und gruendlicher Unterricht die Floete zu spielen, Facsimile Frits Knuf Buren 1973, 1985
 Richard Shepherd Rockstro, The flute. First ed. 1890, Facsimile Frits Knuf, Buren 1986 ISBN 906027507