In this essay, Emerson is advising young people to follow the deepest spiritual guidance of their own souls in choosing what they will do with their adult lives. He is telling young people to follow their consciences and their intuition rather than tradition or what their parents say they should do. Right before the quote you cite, he speaks of great men who forged their own paths, such as George Washington, Francis Bacon, and William Shakespeare. He says that nobody could possibly teach Shakespeare to write: that was something that welled up out of his own deep soul space. Nor can anyone else write quite exactly like Shakespeare, but anyone can delve deep into their soul as Shakespeare did.
We all spring from the same universal spirit that is split (cloven means split) among a thousand different voices (people). If we can't write like Shakespeare, we can hear what his soul is saying to us and speak in a similar soul voice by looking within the soul that we have. By the same "pitch of ear," Emerson is saying that while our language will not be exactly the same as Shakespeare's, or any other great person's, it can come out of the same place. In other words, it can be the same "pitch" by being authentic and spirit-driven.
If you can hear your soul speaking, you can, like Shakespeare, reply to that voice with your own soul voice or "pitch of voice." By doing this, you can rise above mediocrity and make a difference in the world.