Perhaps this exists independently of the ability to sight read?

Let's hope so! This is a particular bugbear with me as, try as I might, I cannot understand musical notation in any shape or form. I think there's a defective gene, or some sort of dyslexic thing going on in what I laughingly call my brain that has been a scourge and embarrassment for my entire life. If I hated music this wouldn't be a problem of course, much less if I wasn't a pretender to the cause in terms of experimental, medieval & folkish idioms, but I console myself with the thoughts that musical notation is a comparatively recent development in terms of western history anyway, emerging with regard to the medieval scholastic tradition and developing into the music we now think of as Classical, which by definition includes all Western derived Art Music of the last nine hundred years.

Meanwhile, the non-literate Non-Art Music existed by virtue of some other process, evolving out of the melismatic modal crooning of the Indo-European hunter-gatherers which somehow sang itself into existence like birdsong and of which we still find an echo in the Irish sean nos or the Sami joik, or in the Muezzin calling the faithful to prayer, which, in turn, works its way into the Revival of British Folk Song via Ewan McColl trying to get some of that into his own singing, and urging others to do likewise. This other thing we think of as the Oral Tradition is not simply a matter of playing by ear, rather being a part of a transfigurative process of dissemination by which the thing itself undergoes a vibrant renewal with each new birth, both individually, and collectively, which is the essence of the process we might think of as being Folk Music. Once we write it down it's dead on the page; it's a relic in a museum, but not without its own persuasive mediumistic potency should we be successful in raising the spectres of ages past in that most glorious of Seances we call The Singaround, or, for those of an instrumental bent, The Session.