Well, there may have been some thought to generally placing the elements of common diads on the opposite sides of the keyboard (that would be one good way to keep the striking levers far apart), but you might be thinking of the Dvorak keyboard. In that arrangement, all of the common English vowels are in the home row under the left hand, and the most common consonants are on the home row under the right hand. Since English words tend to a more-or-less consonant-vowel-consonant rhythm that would tend to make a left-right-left rhythm when typing.

(BTW, the only well-known studies that show that Dvorak's keyboard layout are superior are the ones conducted by Dvorak himself, and he had a financial stake in a venture promoting his keyboards.)