First off, RJ seems to have an irritating habit of making Loial use the capital "T" when discussing tree-singing as a Talent, as he does throughout EotW and TGH. I am more than convinced that Rand almost catches Loial channeling when they were on the other side of the portal stones where they meet Selene. Loial shrinking a tree into a staff has got to be the power. Men who could channel tried to weather the breaking in steddings because of their unique protections, and I would suggest that "The Longing" was merely the slower seeping of the taint into the Ogier, everything about them being slower. Generations may have passed before they felt it at all, and there have been many fewer of those for them since the breaking. Now, what does this have to do with the song. Well, when Rand goes through the crystal columns in Rhuidean, he sees some sort of celebration with the male Aiel and Ogier standing in circles and singing (I believe the ratio was 13:1, incidentally)

So, we have a link between the Aiel and Ogier, and Tinkers as well, since they're old-school Aiel. The Aiel sing their funeral dirges and battle chants, and call battle the dance. Tinkers do nothing but sing and dance (like good little hippies). Finally Ogier have the talent of tree-singing.

Now for the fun part. When Rand meets Thom in Cairhien in TGH, and first tells him of the Horn Of Valere, he also asks him about the Prophecies. Thom makes an oblique refference to there being some copies of the Kareathon Cyle in the Old Tongue that CONTAIN MUSIC. Hmmmm....

Now that the taint is lifted off the Saidin, Aiel men won't have to "go to kill the Dark One", Ogier will not have to hide in their Stedding, and all we need is to get all the elements together, and find a Tinker who knows the old tongue.