Maximal-information audio signals have flat spectra across all frequencies

Evidence

How does this relate to an audio signal? Well, consider a sine wave; it sounds pretty boring to listen to because it is very predictable. On the other hand, a piece of music that is jumping around or an instrument whose texture is continuously changing is much more interesting to listen to because it’s more unpredictable or surprising. If we looked at the spectrum of a sine wave, we would find that all the energy is concentrated at one frequency, whereas for the more interesting music signal, it’s spread over lots of frequencies. In fact, the audio signal that carries the most information is either random noise or a single spike that happens at a time you don’t or can’t predict. Interestingly, in both these cases, the spectrum of the signal contains an equal amount of energy at all frequencies. — David M. Howard, Jamie Angus, Acoustics and Psychoacoustics, 2593

Categorization

• CANDY: Flat-spectrum signals (noise and unpredictable spikes) carry maximum information — a neat, tweetable fact.
• DEEPTHINKING: The claim that noise and unpredictable spikes both maximize information because both have uniform spectral energy is a compact, paradigm-shifting insight about how predictability maps onto spectral structure.