The Elven language can best be described as “musical”.
Not only in the way it sounds, but in terms of structure as well. The language takes advantage of the Elves’ unique compound vocal-cords to allow chords and harmonies to be sung by a single individual, and layers of meanings can be woven together in this way. Non-Elves who learn the language are limited to single notes and find it difficult to communicate complex concepts without the aid of musical instruments1. In contrast, learning to understand someone else speaking is no harder than any other language.
Speaking has developed into an art form in Elven society. Important speeches or documents are composed like symphonies, and especially complex presentations sometimes require multiple singers working in harmony.
The closest example of what Elven sounds like is The Diva Plavalaguna.
The Sea Elves have developed a variant dialect, modifying the tones and structure for better use underwater. With longer, sweeping notes and smooth transitions it sacrifices complexity, but a strong singer can be heard for miles underwater.
Sounds like whale-song.
The Drow have also developed their own dialect, similar to Sea Elven in that it is optimized for their environment. Drow Elven is more rapid and tends towards harsh, discordant tones and minor keys, but it is less susceptible to distortion and echoing in underground caverns.
The written form of Elvish is shared by all dialects and is also used as the standard sheet musical notation throughout the world. Transcripts of everything from famous speeches to dirty jokes have been sold to non-Elven orchestras and musicians the world over, often to the embarrassment of audience members who know the actual meaning of what is being played.
1 Perform: DC 10 (modified depending on complexity; must know the language)