The idea as such was first expressed by Kenneth L. Pike in 1945; though the concept of language naturally occurring in chronologically and rhythmically equal measures is found at least as early as 1775 (in Prosodia Rationalis).
Joshua Steele's disagreement, and subsequent correspondence, with Monboddo over details of the "melody and measure of speech" resulted in Steele's Prosodia Rationalis, a foundational work both in phonetics and in the analysis of verse rhythm.
In 1774 James Burnett, Lord Monboddo published the second of 6 volumes of his On the Origin and Progress of Language containing, among much else, a section dealing with "language considered as sound".