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Video · Music · Math · 7 min

The Cathedral of Numbers: A Symphony Built from π, e, √2 and the Golden Ratio

Play pi as a beat and you hear an accent every 7 notes, and now and then 8. That rhythm, and three more like it, build this symphony for organ, orchestra and choir. The themes come from Teddy Rook's Continued-Fraction Suite: four of its numbers become four linked movements, and each number's continued fraction decides how long each phrase is, when each section changes, and where the accompaniment leans. The rose window changes with each number, and the side windows belong to the instruments: the organ lights the continued fraction, the strings rebuild the prime staircase from waves, the choir sings in Ford circles, and the brass adds 1 + 1/4 + 1/9 + … toward π²/6.

▶ The Cathedral of Numbers: A Symphony Built from π, e, √2 and the Golden Ratio Play pi as a beat and you hear an accent every 7 notes, and now and then 8. That rhythm, and three more like it, build this symphony for organ, orchestra and choir. The themes come from Teddy Rook's Continued-Fraction Suite: four of its numbers become four linked movements, and each number's continued fraction decides how long each phrase is, when each section changes, and where the accompaniment leans. The rose window changes with each number, and the side windows belong to the instruments: the organ lights the continued fraction, the strings rebuild the prime staircase from waves, the choir sings in Ford circles, and the brass adds 1 + 1/4 + 1/9 + … toward π²/6.

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  • Music: Teddy Rook, from the Continued-Fraction Suite. Sound: sampled instruments (MuseScore General SoundFont) in a simulated cathedral acoustic; no live players were recorded. Sheet music engraved with LilyPond.