How Much a Whistle or Drum Code Can Say: A Bound on Codebook Size Against Distance

A whistle or drum code sends pre-agreed messages, so its usefulness is set by how many distinct messages can be sent reliably at a given distance. This paper treats the code as a channel: from the signal-to-noise ratio at each distance and a stated rule linking alphabet size to the signal-to-noise ratio required at a symbol error bound of 0.001, it computes the largest reliable alphabet, the number of distinct six-symbol messages, and the time one message takes. A whistle of 105 dB at 1 m supports an alphabet of 8 symbols at 500 m (262144 distinct six-symbol messages, a bound), 2 symbols at 1000 m (64 messages), and no reliable symbol at 2000 m under the stated rule. A drum of 100 dB at 1 m supports 4 symbols at 500 m (4096 messages), 2 symbols at 1000 m (64 messages), and reaches its binary limit at 1.50 km, against 1.12 km for the whistle. Every message of six symbols takes 4.0 seconds. SIMULATED, NOT MEASURED.