Early in his career, Henry Cowell developed a system by which vibration ratios of intervals derived from the overtone series could be translated into rhythmic ratios. He formalized this system in his book New Musical Resources, and then applied the principles compositionally in two pieces, Quartet Romantic and Quartet Euphometric. This paper presents an analysis of Cowell's self-termed "rhythm-harmony" quartets, focusing on the rhythmic and metric structure of each quartet. In Quartet Romantic the rhythmic content of the first movement is derived from the harmonic ratios of three pre-composed harmonic themes such that the ratio of an acoustically pure interval becomes the ratio between simultaneous durational subdivisions of the whole note. In Quartet Euphometric the harmonic ratios are applied to simultaneous meters, with structural dissonance being created by Cowell's contradictory rhythmic groupings. The analyses also examine the source of the pitch material in the quartets, and correlate rhythmic and pitch structures with form. The paper concludes by examining the influence that Cowell's rhythmic innovations had on his own subsequent compositions, as well as on composers like Lou Harrison.