Elegiac refers either to those compositions that are like elegies or to a specific poetic meter used in Classical elegies. The Classical elegiac meter is a dactylic hexameter and pentameter following.
The "elegy" was originally a classical form with few English examples. However, in the mid-18th century, Thomas Gray wrote "Elegy Written in a Country Church-yard (http://www.thomasgray.org/cgi-bin/display.cgi?text=elcc)" (published 1751). That poem inspired numerous imitators, and soon both the revived Pindaric ode and "elegy" were commonplace. Gray used the term "elegy" for a poem of solitude and mourning, and not just for funereal ("eulogy") verse. He also freed the elegy from the Classical elegiac meter.
Afterward, Samuel Taylor Coleridge argued that the elegiac is the form "most natural to the reflective mind," and it may be upon any subject, so long as it reflects on the poet himself. Coleridge was quite aware of the fact that his definition conflated the elegaic with the lyric, but he was emphasizing the recollected and reflective nature of the lyric he favored and referring to the sort of elegy that had been popularized by Gray. Similarly, William Wordsworth had said that poetry should come from "powerful emotions recalled in tranquility" (emphasis added). After the Romantics, "elegiac" slowly returned to its narrower meaning of verse composed in memory of the dead.
The three selections from Ovid, all from the Amores, are in elegiac couplet, a meter created by the early Greek lyric poets for a variety of themes (drinking, military, history, dedications, epitaphs, laments, and love poems) and to be accompanied by music on the flute.
While the meter of Roman elegy is almost totally derived from its Greek originals, it is original to the Romans in its treatment.
The elegiac couplet, particularly as Ovid composed it, tends to be sense contained, in that each line of verse presents a complete idea.
With his first solo album, Elegiac Cycle, that voice becomes even more pronounced, and announces Mehldau as one of the most cerebral pianist/composers currently working, while producing a work of great beauty and haunting melody.
This is not music that swings, but music that once again extends the boundaries of what we have come to think of as jazz.
Elegiac Cycle is nearly neo-classical in its way, and I don't mean "classical" as in Ellington and Armstrong, but as in Schumann and Satie.