Aldudénië

Elemmírë was one of the Vanyar, a people who had originally dwelt in the city of Tirion alongside the Noldor. At the time of the fall of the Trees, however, most of the Vanyar had removed from Tirion to dwell on the slopes of Taniquetil beneath the halls of Manwë and Varda. As a poet of the Vanyar (it is specifically noted that the gift of poetry was granted to the Vanyar by Manwë) Elemmírë was likely one of those who dwelt on the Holy Mountain, and therefore the Aldudénië was probably written there. However, we know of a few Vanyar who wandered more widely across Valinor, and it is not therefore impossible that Elemmírë created his work in some other part of Aman.

Given that many of the Eldar left Aman almost immediately after the destruction of the Trees, it is not entirely clear how they could all know of Elemmírë's work: the Exiles must surely have left before it was complete. Perhaps Tolkien simply means that all the Eldar who remained in Aman knew of the lament, or perhaps it later found its way across the Great Sea by some other means - for example, with the armies of the Valar at the end of the First Age.