neume, n. [ from Gk pneuma, "breath." ]
Over the years, musical notation has changed in dramatic ways: From the 9th century, when music began to be written down using scratches barely resembling music, through the blockish symbols of Gregorian Chant, to the modern notation of quarter notes and fermatas of today. In the 9th century, the music looked like florid curves, haphazardly thrown onto a page, the notes indicated by blotches of ink along the lines. Toward the 11th century, the music became more refined, more blockish and easier to read and print with the technology available (re: hand-printed).
In the beginning, neumes existed not only to define the pitch of the note, but also the manner of performance, representing from one to four notes on a given syllable of sung text.
The word itself likely comes to English via the Greek pneuma, a root used often in words relating to breath or breathing (see pneumatic, pneumatocyst, &c).
Though neumes used to be the sole notation available, and it still does exist in Catholic masses in the form of Gregorian Chant, the vast majority of music is written in standard music notation.
Despite the Latin nature of pronouncing each vowel in a word, it is widely accepted to pronounce this word as "noom" or "nyoom" rather than the expected "nay-oo-meh."