Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted in the stride-piano tradition of Willie (The Lion) Smith and Duke Ellington, yet in many ways he stood apart from the mainstream jazz repertory.
Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted in the stride-piano tradition of Willie (The Lion) Smith and Duke Ellington, yet in many ways he stood apart from the mainstream jazz repertory.
Thelonious Monk, who was a jazz pianist and composer, produced a body of work both rooted
Thelonious Monk, the jazz pianist and composer, produced a body of work that was rooted both
Jazz pianist and composer Thelonious Monk, who produced a body of work rooted
Jazz pianist and composer Thelonious Monk produced a body of work that was rooted
Jazz pianist and composer Thelonious Monk produced a body of work rooted both
both A and B, A and B should satisfy the parellelism.
In this sentence, you should use both this way: both in the tride-piano tradition of Willie Smith and in that of Duke Ellington. But if you use it like this, the sentence is wordy, in fact both is no need here.