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Video · Music · Math · 25 min

The Cathedral of e: Euler's Number Builds a Cathedral, One Note at a Time

Every gold line that leaves the circle becomes a stone, and every stone lands on a note. The waltz from the Continued-Fraction Suite, set for organ, orchestra and choir, is played thirteen times, and e's continued fraction, e − 2 = [0; 1, 2, 1, 1, 4, 1, 1, 6, …], sets the length of every span: 4 and 3 bars, 7, then 32, 39, 71, 465, 536 and 1001. Each is the bottom of one of the fractions closest to e, and the piece ends on 2721/1001, e to six decimal places. As it plays, a cathedral rises: 2,336 stones and sixteen stained-glass windows.

▶ The Cathedral of e: Euler's Number Builds a Cathedral, One Note at a Time Every gold line that leaves the circle becomes a stone, and every stone lands on a note. The waltz from the Continued-Fraction Suite, set for organ, orchestra and choir, is played thirteen times, and e's continued fraction, e − 2 = [0; 1, 2, 1, 1, 4, 1, 1, 6, …], sets the length of every span: 4 and 3 bars, 7, then 32, 39, 71, 465, 536 and 1001. Each is the bottom of one of the fractions closest to e, and the piece ends on 2721/1001, e to six decimal places. As it plays, a cathedral rises: 2,336 stones and sixteen stained-glass windows.

Chapters

What you are seeing: the circle is a times table of 127 points, each joined to a multiple of itself; the multiplier slides from 2 to 3 to 4 as the cycles go by, and gold lines flash on the number's accents. About 28 notes in every 100 carry an accent, because 3 − e = 0.2817…

The cathedral is an original, simplified design that follows the published dimensions of Washington National Cathedral (514 feet long, a central tower 301 feet high, three rose windows of twelve petals). It is not an official or exact model, and all sixteen windows are new designs; none of the real cathedral's windows is copied. The video is not affiliated with or endorsed by Washington National Cathedral.

Go with it

Texts, tools and credits
  • Music: Teddy Rook, from the Continued-Fraction Suite. Sound: sampled instruments (MuseScore General SoundFont) in a simulated cathedral acoustic; no live players were recorded.