# Rate-Doubling Click Train cycles

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• The fourth example is a Rate-Doubling Click Train in cycles format. Whereas the auditory event associated with an isolated click is a very brief flash of an auditory figure, the auditory event associated with a train of clicks is a static tone event, provided the click rate is in the pitch range. The example shows how the isolated click figures merge to become a static tone event as the rate of clicks increases through the range 10-40 clicks per second. [The above is the text for the main page when this example is ready. 10 Feb 2011]

This example is the rate-doubling click train. It is concerned with the temporal integration mechanism in the auditory system, and the role it plays in determining whether an acoustic event is heard as a separate auditory event or is fused with adjacent acoustic events to produce a single auditory event. The distinction between acoustic events and auditory events is illustrated by the “rate-doubling” click train (RD-CT); that is, a temporally regular click train (CT) whose initial rate is 1 click/second (c/s) and whose rate of clicks doubles every two seconds until it reaches 128 c/s. Listen to audio track of the video with your eyes closed and then watch the simulation of our perceptions produced by the computational version of AIM.

Missing file: RD-CT_cycles.mov
• At rates of 1, 2 and 4 c/s, we hear each acoustic click as an auditory click, that is, a simple, transient, auditory event with no distinct pitch. At rates of 64 c/s and above, a regular stream of acoustic events fuses into a simple "tonal event" with a clear pitch corresponding to the click rate in the train. In between the low and high rates, there is a transition region around 16 c/s where the individual click events begin to merge and the perception flutters. Then, at about 32 c/s, the perception takes on a low pitch and the flutter reduces to roughness which fades away leaving a static perception as the click rate and the pitch increase to 128 c/s. Note that there is nothing in the mathematics or physics of click trains to explain why the perception should change so dramatically as the click rate increases through the range 8-32 c/s. The changes in perception reflect the operation of the temporal integration mechanism in the auditory system beyond the cochlea which converts the neural activity pattern flowing from the cochlea into the neural representation in cortex that underlies our perception of sound -- the auditory image.
• The details of the mechanism, and how it is implemented in the computational version of AIM, are presented in Chapter 3.1. It shows that one parameter -- the decay rate of the auditory image -- is largely responsible for determining when the individual auditory clicks merge to produce the perception of a tone. Briefly, it is assumed that the auditory image decays exponentially in time with a half-life of about 30 ms, so the auditory figure produced by an acoustic click fades away very rapidly after the click passes. Specifically, the magnitude of the click figure decreases to about one tenth of its initial value in a tenth of a second, and the figure fades into the floor without changing position. Thus, for isolated acoustic clicks, and trains of acoustic clicks spaced by more than 100 ms, the activity in the auditory image is limited to the region of the 0-ms vertical, and the perception is composed of isolated auditory clicks, one for each acoustic click.
• When the rate of the click train doubles from 8 to 16 c/s, the auditory clicks begin to fuse and the perception flutters. In AIM, this change occurs because the time between clicks decreases to the point where the click figure associated with the most recent acoustic click is added into the auditory image before the click figure for the preceding acoustic click has completely faded away. At this click rate, the auditory image is never empty; there is no perceptual silence between successive auditory click events. Since the click figures are all the same and they appear and fade in position without moving, successive click figures just merge in the auditory image. The perception flutters because the magnitude of the click figure is varying on a time scale where we hear changes in magnitude as changes in loudness. In other words, flutter is the perceptual correlate of rapid changes in auditory figure magnitude.
• When the pulse rate doubles from 16 to 32 c/s, and the period between acoustic clicks decreases to 31.25 ms, a second copy of the click figure appears in the auditory image because the auditory image encompasses time intervals up to about 35 ms. At this point, the perception of the rate-doubling click train takes on a faint, low, pitch and the fluttering component of the perception decreases to a roughness because the image is being refreshed more frequently and there is less variation in figure magnitude. In AIM, the position of the second auditory figure in the auditory image determines the pitch of the sound. The width of the auditory image (35 ms) is determined by the fact that the lower limit of melodic pitch is about 30 Hz.
• When the rate of the click train doubles again to 64 c/s and the period between acoustic clicks decreases to 15.625 ms, the spacing in the auditory image between the first and second click figures decreases to 15.625. At the same time, the pitch rises an octave and becomes more salient, while the roughness fades away and the tone takes on a buzzy timbre. With the final doubling from 64 to 128 c/s, the pitch rises another octave and this component of the perception becomes dominant, while the roughness fades away completely and the perception becomes effectively static, because the variation in figure magnitude is small relative to its magnitude.

In summary, the example shows how the temporal integration mechanism in the auditory system determines whether an acoustic event is heard as a separate auditory event or is fused with adjacent acoustic events to produce a single auditory event.