Wiener entropy

To expand the dynamic range, the Wiener entropy is measured on a logarithmic scale, ranging from 0 to minus infinity (white noise: log1=0; complete order: log0=minus infinity). The Wiener entropy of a multi-harmonic sound depends on the distribution of the power spectrum (see figure below).

A narrow power spectrum (the extreme of this is a pure tone) has a large, negative Wiener entropy value; a broad power spectrum has a Wiener entropy value that approaches zero.  The amplitude of the sound does not affect its Wiener entropy value, which remains virtually unchanged when the distance between the bird and microphone fluctuates during recording. Yet, the entropy time series (or curve) of a song motif is negatively correlated with its amplitude time series. This is because noisy sounds tend to have less energy than tonal sounds.  A similar phenomenon has also been observed in human speech, where unvoiced phonemes have low amplitude.

Wiener entropy may also correlate with the dynamic state of the syringeal sound generator, which shifts between harmonic vibrations and chaotic states. Such transitions may be among the most primitive features of song production and maybe of song imitation.