Waveform Specification

Input for wigout is given in the form of a datafile. The first row of the input datafile (see below) is the id for the segment, followed by the segment type. (Only the wiggle type is used in this paper. For others, see [4, 5].) The second row refers to the duration in samples of the segment, and the third to the amplitude of the segment. The columns refer to: 1) the initial value for the variable; 2) its maximum value; 3) its minimum value; and 4) the increment by which it changes upon each iteration.

Below is an example of an input data file of two segments:

# 1st input datafile for wigout
w0 wiggle     # id, type
50 100 50 5   # duration (init., max, min, inc)
-20588 20588 -20588 2422.11 # amplitudes     

w1 wiggle     # id, type
67 67 33 1.7  # duration (init., max, min, inc)
796 796 -796 106.133333 # amplitudes

So, for each of the variables (duration, and amplitude), one can set the range, increment of change, and starting value. Upon every iteration of the state, each variable changes by its increment, until it reaches its minimum or maximum value, whereupon its increment changes its sign. This process results in a cycle length, which can be calculated by numCycles=2*(max-min)/rate. Using this formula, segment w0 has a cycle length of 20 for its duration and 34 for its amplitudes; and segment w2 has a cycle length of 40 for its duration and 30 for its amplitudes.

Below are the 1st and 600th iterations of an 8-segment waveform, followed by their FFTs. The iterations are about 7 seconds apart in time.

It should be apparent from the above plots that the iterative change of variables (which is the procedural paradigm of wigout) generates significant differences in frequency and spectrum over time.

Below is a plot of the changing base frequency from state 1 until state 836 of the above waveform:

As you can see in the above plot, the changing base frequency manifests some periodicities by its regularity of peaks and troughs.

In presenting the above FFT plots and the changing base frequency plot, I would like to show you how wigout allows for significant changes of base frequency that are simultaneous with significant changes in timbre. This, more than anything else, is what I, as a composer of music, am attracted to in wigout.