Which material sounds better for speakers construction? Wood, Ply or MDF?

Lively Harbeth cabinets color the sound. Not the way I would build. 

Best materials are composite polymers. And this is not debatable. 

As far as I'm concerned, Wilson has this nailed. Goldmund used to use composite methacrylate in the Dialogues. 

Anyone building DIY cabinets can use Corian at the very least. It's not too expensive. Or anything from McMaster's catalogue. 

Well the Harbeth " model " is the exception. The resonance of MDF is low but their cabinets are thin and " loose " which raises the resonance, so they have chosen to lower it.
In most speakers  low resonance excite the cabinet creating a very large driver. We can all relate to the example of a car with the stereo turned up load. The bass gets amplified buy the body of the car, the doors which essential are the back of the cabinet become a huge " driver ". The area of the door, perhaps 20 times larger then the driver in the door when excited will sound 20 times louder the the driver itself. 

@soundsrealaudio

I see the confusion now. You're using the term "resonance" to refer to both frequency and amplitude. 

@helomech Thanks for the comment.  I am sorry the 1.7s did not meet your requirements.  I might suggest some agonizing reappraisal, to quote a '70s 7-UP commercial.

As you clearly understand, your ROOM is the most important element in any sound reproduction evaluation.  Possibly your room was not set-up correctly for the 1.7 experiment?  I will admit that this is a real chore and may not ever be right depending upon the room.  I have years of experience doing this and can state that there are some rooms that simply do not sound right with dipole speakers.  So be it!

HOWEVER, you seem to be an open-minded individual, so might I suggest that you give it another go at a dealer who knows what they are doing in their shop and listen again to a comparable model of non-box and box speakers in the shop where they are all set-up correctly?  You might be surprised at the quality of the sound, or not.  The objective, of course, is to make sure YOUR chosen system sounds the way YOU want it to in YOUR ROOM!

Cheers!

Anyone building DIY cabinets can use Corian at the very least:
Best materials are composite polymers. And this is not debatable.


Even though Corian would work, I want anyone to be careful that might plan a diy project,  you can't grab any material because it looks dense. 
Corian is an acrylic mineral.  As long as the cabinet is thick enough, it will do a very good job 
And I'm sorry to say that composite polymers are debatable,  They can be excellent, but It very much depends on which polymer and hardening agents are used and again, how thick the material is to absorb or repel bass frequencies from within the box. Phenolic resins or some epoxy's could work also. Some of these materials sandwiched with a softer material could be excellent. 
Its not that this is wrong info, but in itself if not used properly can end in some pretty poor results. I hope this helps.