Peter Maxwell Davies was only 26 years old when, while working as a music teacher at Cirencester Grammar School, he composed his choral and instrumental cycle for children, O Magnum Mysterium. The Fantasia taken from that work originally served as its conclusion, the solo organ providing a solemn and wordless benediction to the instrumentalists' sonatas and the choir's carols. It was subsequently published separately for solo performance and stands as a brief but impressive example of Davies' early skill, particularly in its idiomatic sensitivity—a noteworthy element, considering the composer's young age and his lack of performing experience at the organ.

The Fantasia begins with a passacaglia whose ground figure seems to demarcate the piece's sonic boundaries: it begins among the organ's lowest tones, then gradually ascends until it arrives at the upper edges of the instrument's range. The passacaglia then sets into motion a set of variations that continually gather mass and inertia until the full force of the instrument is unleashed for a grand and weighty Lento passage. The piece then diminishes by degrees until the subdued reverence of the opening is once again restored.

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