Da'shain Singing is supposed to be "wondrous" to listen to, and that suggests a lot of beautiful harmonics.

Men do the Singing, and boys can't join before they've passed puberty, so Singing don't fall into the "celestial"/"angelic" category, though Ogier Singing sounds like chirping birds, so there's a bit of that element in it too. Western harmonics, for e.g. Gregorian chants, seem totally out of place. Jordan almost certainly had in mind something Asian, like the rest of the influences behind the Da'shain. Perhaps the influence he had in mind is Indian (buddhist or even more likely jain) but I'm really not all that familiar with any traditional chanting by followers of Jainism (if they do any) so personally I imagine something quite powerful, with a very male energy, but also quiet, repetitive/rythmic and hypnotic, for example the chants of Shingon buddhist monks in Japan or something like that. Something that wouldn't feel out of place at all in woods or fields, in communication with nature. Jordan loved to listen to Japanese traditional and religious music while writing the series, so maybe it's how he imagined Singing too.

We haven't got a real Singing scene so far (or ever?), so it's hard to narrow it down more than that.