When Gandalf says the Black Speech from the ring during the secret meeting in Rivendell, someone else is also speaking. Who is that? Is it the ring, or Gandalf? There is distinctly another, deeper, possibly evil voice that is echoing him. What is that? Is it Sauron?
The language spoken is the Black Speech, which Tolkien described as thus:
The Black Speech was not intentionally modeled on any style, but was meant to be self consistent, very different from Elvish, yet organized and expressive, as would be expected of a device of Sauron before his complete corruption. It was evidently an agglutinative language. [...] I have tried to play fair linguistically, and it is meant to have a meaning not be a mere casual group of nasty noises, though an accurate transcription would even nowadays only be printable in the higher and artistically more advanced form of literature. According to my taste such things are best left to Orcs, ancient and modern.
- J.R.R. Tolkien, "Words, Phrases and Passages in Various Tongues in The Lord of the Rings", Parma Eldalemberon 17, p. 11-12.
There only is a single example of "pure" Black Speech in the book, which is the writing on the ring:
Ash nazg durbatulûk, ash nazg gimbatul, ash nazg thrakatulûk agh burzum-ishi krimpatul.
One Ring to rule them all, One Ring to find them, One Ring to bring them all and in the darkness bind them.
All other occurrences in the book are simply broken words. Due to this, for the film version, a linguist, David Sato, used the broken phrases throughout the book along with some invention to create Gandalf's speech in Rivendell:
Gu kibum kelkum-ishi, burzum-ishi. Akha-gum-ishi ashi gurum. ("No life in coldness, in darkness. Here in void, only death.")
The book does state that when in Rivendell Gandalf recites the wording on the ring, and goes on to say:
The change in the wizard's voice was astounding. Suddenly it became menacing, powerful, harsh as stone. A shadow seemed to pass over the high sun, and the porch for a moment grew dark. All trembled, and the Elves stopped their ears.
Suffice to say, even though the movie speech was created by Sato, it appears Peter Jackson was trying to emulate what Tolkien suggested here. Tolkien didn't expand on the paragraph above so it seems like Jackson improvised and decided an overlay of Sauron's voice would be the best way to make the scene seem even more dark and haunting.
The voice of the Ring and Sauron in LOTR as well as Necromancer/Smaug in both parts of the Hobbit may seem similar. Back to the plot, the One Ring is a part of Sauron, so to speak. The Dark Lord put some of his evil spirit into it. In The Desolation of Smaug, taking place 60 years earlier,Gandalf realizes that the Necromancer is in fact Sauron when he (Gandalf the Grey) is caught in Dol Guldur.
The voice of Necromancer/Smaug belongs to Benedict Cumberbatch. The actor in question mentioned it in an interview promoting "The Hobbit The Desolation of Smaug". Here are some relevant links: