
A command to create a Sound as a gammatone.
to create a Sound according to the following formula:
t^{γ–1} e^{–2π·bandwidth·t} cos (2π·frequency·t + additionFactor·ln(t) + initialPhase), 
The gammachirp function has a monotonically frequencymodulated carrier (the chirp) with instantaneous frequency
instantaneousFrequency(t) = frequency + additionFactor / (2·π·t) 
and an envelope that is a gamma distribution function. It is a theoretically optimum auditory filter, in the sense that it leads to minimal uncertainty in the joint time and scale representation of auditory signal analysis.
For faithful modelling of the inner ear, Irino & Patterson (1997) conclude that a value of approximately 1.5 * ERB (frequency) is appropriate for bandwidth. ERB stands for equivalent rectangular bandwidth. Their formula for ERB is:
ERB(f) = 6.23 10^{–6} f^{2} + 93.39 10^{–3} f + 28.52. 
To avoid aliasing in the chirp sound, a sound is only generated during times where the instantaneous frequency is greater than zero and smaller than the Nyquist frequency.
© djmw, October 13, 2016