Understanding Waveshaping

Characterizing Waveshapers by Average Spectrum

The more parameters and the more complex the transformation has, the less easy it is to describe useful for humans the effect of a waveshaper. This is a problem for people evaluating waveshapers. Graphs and oscilloscope captures can demonstrate uniqueness and operation visually, but the focus on individual settings may miss the broad characteristics.

One approach is that taken by Tom Wiltshire in Timbral Evolution: Harmonic analysis of classic synth sounds. That maps each harmonic level in a different colour as a parameter is changed.

An approach I have trying is to record a waveshaper for the primary expected input (saw, sine, square, triangle) of that circuit at a certain frequency, say around C2 65 Hz, while each parameter is varied systematically to attempt to cover all permutations neutrally. Then a Spectrum analysis is performed, and this reveals the broad effect (assuming the waveshaper has a continuous change not modes.)

Below, I give the spectrums for a waveshape each from the Blip! and Shell waveshapers. These are below. The spectrums are interesting and reveal much about the waveshape. But the average spectrums give different information, in particular, what things in the single example spectrums are likely to be true regardless of setting?

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First, lets see what a single note example of one setting of the Blip! waveshaper looks like.

The log view on the left is good for showing the reationships between the low harmonics: in this case, like all built-in standard VCA waveshapes, the fundamental is the loudest harmonic but the early harmonics are relatively. The linear view on the right is good for seeing the trend in the higher harmonics: in this case, there is a very marked cyclic spectrum, which is what we predict from a pulse waveform: every n harmonics has a gap, depending on the width of the pulse.

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Now lets look at the average if Blip! waveshapes made while we change all the knob settings to approximate all possible waveshapes from the module. Comparing the log views that the cyclic effect of a single wave disappears on average. Remembering that the input is the same waveshape at the same frequency for both plots, it tells us that the peaks and troughs move with the breadth control. We see in the linear view that on average the early harmonics are more prominant than in our single example above: so these vary too with the pulse. We see that all the harmonics are present with their level tailing off, and that odd harmonics are fractionally louder.

(Please remember, these average spectrums are not real: any actual sound may have significant variation.)

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The harmonics around 1K are about 43 dB down compared to the fundamental on average. The harmonics around 5k are about 50dB down. The harmonics around 10k are down about 58 dB.

First, here is Shell, first an example of a single setting as shown above (it is not a Fibonnaci-like shape, btw):

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We can see for this setting the fundamental and early harmonics are much louder than in the spectrum of the single Blip! setting. For Shell the early harmonics are strong. In the log view, a less pronounced cyclical spectrum.

Next the average spectrum for the Shell waveshaper as we vary multiple parameters to attempt to get every sound.

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The harmonics around 1K are about 28 dB down compared to the fundamental on average. The harmonics around 5k are about 35 dB down. The harmonics around 10k are 40k down. On average, this waveshaper produces quite bright sounds where the early harmonics sometimes dominate the fundamental.

The notable thing is that harmonics 2,3, and 4 are almost as loud as the fundamental at 65Hz (i.e. harmonic 1): compare to the single setting, they are over twice as loud (+6dB means 2x volume). Not until the 7th or 8 harmonic does this boost go down to comparable levels with the example. the discrepency between the individual and the average suggests tha there is a lot of variation of the lower harmonics. (Other indivdual spectrums confirm this.) This reduction of the earlier harmonics is similar in effect to the approach in the CS-80 etc synths by Yamaha (in their case using a 12dB/8ve high pass filter to reduce the lower harmonics and then adding a sine in again to restore the fundamental up.)

Finally is an average spectrum for a prototype of the Rasp waveshaper:

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The harmonics around 1K are about 40 dB down compared to the fundamental on average. The harmonics around 5k are about 54db down. The harmonics at 10k are about 60dB down. On average, this is a darker sound.