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

There are a ton of excellent speakers made of many types of materials.  In the end, as long as a cabinet is well designed with the cabinet included in the design,  the drivers and crossovers are still more important to the overall design than the cabinet material itself. 
Again, well thought out, well designed speakers that include the cabinet material in the design. 

As to the question of the OP:  the heck if I know.

But just from user experience:  I've had tons of speakers of all sorts of designs, from the "we let the specially selected wood resonate with the music" (Shun Mook speakers), to Harbeth (Super HL5Plus),  to many MDF boxes (Hales, Audio Physic, Meadowlark, others), to Quad 63,  MBL radialstrahler with their carbon fibre petals, to Waveform (currently Mach MCs -which are almost a solid giant egg of layered MDF), to my current Thiel 3.7 and 2.7 speakers which use curved plywood cabinets.

They all sounded great!   I'm a "tone first" guy, and the MBLs have gorgeous realistic tone and presence, so do the Waveform speakers, so do my Thiels.  And I've been listening to Devore speakers quite a bit recently the O series made of plywood.

I'd say that a common thread among the "let the box resonate" speakers is a rich, full warm tone.   Though it can be hard to untangle that somewhat from the fact most of them have wide baffles, so presumably they are sending more direct sound towards you which may account for that added size and presence as much as any box resonances.

But one common characteristic among the singing box designs is that I seem to hear the box a bit more, sometimes overt, sometimes really subtle.  They rarely totally disappear as much as the more inert speakers.

I found a comparison between my Harbeth SuperHL5plus speakers and my Thiels quite interesting.  Both have beautiful organic tone.  The Harbeths being known for this.  And the Harbeths sounded rich and full - yet really open and seemed to "disappear" quite well, much better than one would expect looking at them.

But compared to the Thiels, the Harbeths had a sort of texture that ran through and behind everything, even in the space between instruments.
It didn't stick out as obvious box ringing, but when I played the same material on the Thiels, for instance an acoustic guitar quartet, the sound seemed to clean up of any blur on the Thiels.  Instrument tone was essentially as rich, but became even more distinct because of the higher precision in the sound.   All the instruments and their character that much easier to hear.  

My feeling after that (and selling the Harbeths) was that the singing box method certainly can work, but it seems to me that the most likely path to advancement in realism lies in reducing the influence from the speaker cabinet, as most designers are trying to do.

That's not to say that I automatically prefer the super dead cabinet sound.  I've fallen for the Devore O series somewhat for their richness and dynamics and they are not of the dead-box variety.  But I am also a bit more aware of the speaker than I am with speakers like my Thiels which can really be "invisible" as sound sources.

“Give it up dude, you obviously have not the slightest understanding of speaker physics. I'll await your reply with a claim of BS credentials”

I know this was targeted at someone else but if you don’t have anything productive to add to the conversation you should just skip this thread and move on. If you feel real strongly about your speaker design knowledge/skills, write a paper and send us the link. Personal insults are not welcomed here.

I see that Magico has added a new M series speaker with carbon fiber planels. Carbon fiber is very light, read: low mass. 

They have tried many other materials for their cabinets  and now choose this produce. 

Perhaps there is something to the idea that low mass high resonance is a good idea????

Magic M3 weighs a healthy 320 lbs. each! Looks like the CF “panels” are more like an esthetic touch than structural. And the (internal ) aluminum bracing is quite extensive and incredibly impressive.