Detached, Factual, Thoughtful, Didactic
You might be wondering "What tone?" given how matter-of-fact (and even dry!) the narrative can be. Well, just because it isn't overly emotional doesn't mean that the novel lacks a definable tone, so let's see what's going on here.
Overall, the tone of The Fountainhead is clear and pretty unemotional. Most of the novel is filtered through the viewpoints of various characters, and they tend to repress their emotions and approach situations with an almost clinical detachment. The characters that do freak out and have meltdowns are seen as weak, while characters like Roark—who can sometime sound robotic—are seen as strong. Take this early scene with Roark, where he demonstrates his patented emotionally detached tone.
"You know," he said, "you would sound much more convincing if you spoke as if you cared whether I agreed with you or not."
"That's true," said Roark, "I don't care whether you agree with me or not." He said it so simply that it did not sound offensive, it sounded like the statement of a fact which he noticed, puzzled, for the first time. (1.1.154-5)
This quote demonstrates an almost chilling level of detachment. Roark is channelling the honey badger pretty hard here, but the fact that this is the first time he's noticed his lack of caring strikes us as edging in on sociopath territory.
The narrator also often sounds very detached and quite factual, describing emotional things in a fairly dry manner. Take this scene where the narrator describes the release of Toohey's book by adopting a factual approach.
Readers acquired erudition without study, authority without cost, judgment without effort. It was pleasant to look at buildings and criticize them with a professional manner and with the memory of page 439 [....] (1.6.6)
This narrator is saying some fairly damning things about the general readership: that readers like to acquire judgement with cost, for example. But this smack-talk is done with an ounce of emotion. "That's just the way things are," the narrator seems to be saying, "People suck."
As we noted earlier, this novel is very intellectual, so it makes sense that the narrative has a pretty thoughtful tone going on in places. Characters often try to work out tricky intellectual conundrums, or puzzles, and consider their worldviews and ideas. There are long passages where characters think and equally long passages where two characters have a good old fashioned intellectual debate. The narrator also pauses sometimes for some deep thoughts and pondering.
So he felt anger that he should find exultation only in the wilderness, that this great sense of hope had to be lost when he would return to men and men's work. (4.1.5)
The diction here ("wilderness" and "men") sounds almost biblical, and the broad ideas being explored here are capital-D Deep. This single line contains the understanding that the wilderness contains capacity for hope and happiness, while the world of men and cities takes that hope and happiness away.
Ugh. Now we're depressed. We also want to go camping.
The More You Know
Finally, The Fountainhead is pretty dang didactic. Didactic isn't the most positive of words (it can be used as an insult), but it really fits the bill here and sums up what is both good and bad about The Fountainhead's tone. The novel is definitely tries to teach its readers. This can result in interesting, informative passages and it can also result in parts that sound seriously preachy.
A couple of these educational sections include Roark's trial testimonies, and his long-winded spiel about "second-handers" on Wynand's yacht (4.11). Be forewarned.