"The Organ That Breathes" is a homecoming for composer Alex Ring Gray, whose earliest days of writing music were for his own saxophone quartet in high school, as they could not afford to purchase sheet music. After a decade of expanding into other composing mediums, Gray returns to his primary instrument with densely layered improvisations, textures, and drones; morphing his saxophone into a living, breathing reed organ. Actual organs build the through-line, with several variants (electric, reed, pipe, etc) blending and crossfading with Gray's saxophones.

Much of "The Organ That Breathes" was written and recorded during a period in which Gray had been evacuated from his home due to structural failures, which was subsequently burglarized. Living partially out of his office (Philip Glass's Dunvagen Music), he would stay late after work and through the weekends to write and record in Glass's production studio.

The importance of breathing as a woodwind player led the album to largely become a meditation on the fragility of health. Several pieces were written as cathartic reactions to loved ones' health issues (diabetes, Fahr’s syndrome, cancers), and in remembrance of ones who had passed. Others are focused on the saxophonist's own breath, intertwining Gray’s own performance practice with meditation breathing exercises. “re: meditations” showcases his and his collaborators (Seth Fox, Blake Opper, Erin Rogers) pushing their lungs to the limit in an ode to experimental saxophone legends Jon Gibson, Terry Riley, Dickie Landry, and Pharoah Sanders.

The middle of the album follows the narrative of Phaethon, the son of Sol (Helios), who begs his father to let him drive his Chariot of the Sun. After Sol reluctantly agrees, Phaethon loses control of the chariot and is struck down from the sky by Zeus in order to save the Earth from being scorched. Phaethon falls into the Eridanos River, and his path across the sky is said to have become the Eridanus constellation. These recordings gradually become processed and distorted, developing a rhythm of their own through a subtractive process of cutting away at the audio, similar to a sculptor chipping away at marble.