[DavidWoof]

> We cannot identify the interval between two notes just by listening

He's being (purposely?)confusing here, but in context what he's saying is that you can't determine the names of intervals just by listening: i.e., you can't distinguish between an augmented fifth and a minor sixth just by listening to the two pitches.

> If you did this with any group of musicians

I think you mean any group of musicians in the modern western tradition. Not all traditions count the same way, or even treat numbers as a standard way of marking rhythm. I suspect that if you counted 1-2-3-4 to Sappho she'd just look at you funny and throw her lyre at you or something.

I'd like to be gracious and assume the author is using this weird phrasing to emphasize this universality of his points, but I honestly suspect he's being purposely obscure to emphasize his professorship.