Adatone. Punched card

3 rows: 1 = numerator, 2 = denominator, 3 = sign. Click to punch. Press Play to step columns; Bernoulli numbers map deterministically to notes.

Tempo 120 BPM

Mode

Volume

Stopped• Space/P to Play/Stop. Bottom row ON applies sign: negative inverts around C4.

Legend: Top = Numerator (pitch & velocity with log scaling), Middle = Denominator (duration via power-of-two), Bottom = Sign (shows actual sign; ON inverts if negative). Bₙ = 0 gives a rest.

Backend note: Bernoulli numbers are computed using a primitive Ada-style recurrence (ported 1:1 to JavaScript BigInt rational arithmetic). Zero Bernoulli numbers yield rests.

Show Ada-like reference routine

-- Ada-style reference for Bernoulli numbers (rational)
-- B(0) := 1
-- for m in 1..N loop
--   S := 0
--   for k in 0..m-1 loop
--     S := S + Binomial(m+1, k) * B(k);
--   end loop;
--   B(m) := -S / (m+1);
-- end loop;