This article explores how Venezuelan musicians experience and speak about music's "ineffability," frequently contrasting it with the linguistically fixed state discourses about music. I approach this topic through my ethnographic work on El Sistema, a state-funded program that provides free classical music education and instruments to 900,000 young people across Venezuela. Studying the ways in which El Sistema participants experience and discuss ineffability in music captures the unpredictable, unruly, multiple, and contradictory dimensions of how they inhabit state power. Using a combined phenomenological and discursive approach, I think of music practice as simultaneously the locus of state and symbolic power, and a social experience that transcends and escapes it. I trace how young musicians appeal to the ineffability of music to make sense of their own experiences as barrio (popular sector) residents who are suspended in the cracks of polarized discourses and in the double bind of state power and its opposition. I read young musicians' determination to experience music as ineffable, or detached from the political context, as a medium for confronting the dilemma of being simultaneously dependent on and critical of a state that aims to defend their interests. In summoning musicians' verbal testimonies of music and the concepts that emerge from them as a key to understanding experiences that are thought to be ineffable, I respond to recent calls to articulate a more nuanced place for language in studies of affect and embodiment.