Moog Sub Phatty Waveform Purity Analysis

Recently, I have brought my Moog Sub Phatty into school to study it from the perspective of my independent study. My primary method of analysis is measuring the voltage output from the Sub Phatty's headphone jack:

The voltage data output from the synthesizer reflects the sound wave it produces; this is how sound is transferred through electronics. I was initially curious as to how the Sub Phatty's different wave forms impact the sound waves it produces. The waveshapes available are controlled by this knob:

Moog describes them, starting from the bottom left and going clockwise, as triangle, sawtooth, square, and narrow pulse waves. I decided to arbitrarily number each of the lines around the wave knob, starting from one and going to eleven in the same clockwise order. In analyzing the sound produced by the different waveforms, I wanted to assess purity. In order to quantify "purity," I measured how well each wave is fit by a sine wave curve fit. I determined this by calculating the sine fit correlation. 

The following table shows the wave number and the value of its sine fit correlation (with the bold numbers representing the waveforms named in the Moog's manual):

Wave Number:	Sine Fit Correlation:
1	0.9966
2	0.9937
3	0.9555
4	0.8839
5	0.8168
6	0.7608
7	0.8669
8	0.9122
9	0.8201
10	0.5641
11	0.3595

What was initially interesting is how pure the "triangle" wave is. While I was not surprised by the sine fit correlation of .9966 given how pure the tone sounded to me, it is interesting that it is named a triangle wave when it seems to essentially be a sine wave.
Another interesting observation is that there is not a real correlation or trend between the wave number and its sine fit correlation as I had hoped for. However, this table provides a sense of how "gritty" or impure each of the Sub Phatty's waveforms are, which can be useful in sound design. For a harsher tone, it is best to select one of the waves with a lower correlation. Hopefully this table can serve as a reference point.

Analysis of a Distortion Circuit

Building on my post about distortion, I built a distortion circuit with the help of Jon Bretan. The circuit takes in audio signal and uses transistors to distort the signal. Instead of outputting the distorted signal to a speaker, I recorded it using voltage probes. The final setup looked like this:

I recorded the voltage input (red) and the distorted signal (blue) in several different scenarios. First, I recorded the data for sawtooth, square, and triangle waves to look at how distortion uniquely effects each waveform. The data are pictured below:

100.87 Hertz Sawtooth:



100.87 Hertz Square:



100.87 Hertz Triangle:


Interestingly, the distorted waveform has a unique shape for the different input waves. The distortion is clear in the jagged and flattened parts of the blue wave, and it makes sense to see the amplitude of the distorted waveform match the general shape of the initial waveforms.  The type of distortion occurring here is called clipping, and I will be dedicating a brief blog post to this in the future. Normally, clipping results in a louder seeming wave because the top of the initial wave is "flattened" as it reaches peak intensity. However, in this circuit, the distorted sound is not amplified to a level that would make this apparent as its magnitude is significantly lower than the initial signal.

After looking at these different waveforms, I took a basic sine wave signal and recorded it at a range of frequencies to see how the frequency impacted the distortion occurring in the circuit. The following data represent the frequency range I was able to record:

59.44 Hertz Sine:

100.87 Hertz Sine:


200 Hertz Sine:



302.27 Hertz Sine:



403.48 Hertz Sine:


493.88 Hertz Sine:


I initially did not think that the effect of the distortion would not be significantly affected by the frequency of the input signal. However, looking at the data in order of increasing frequency reveals a really fascinating trend. The input signal for all the frequencies seem to be perfectly uniform, but the distorted signal at higher frequencies appears to follow a sinusoidal pattern. The peaks and troughs of the distorted signal that follow the shape of the clean signal seem to be superimposed over a sine wave. It is likely that this added oscillation is caused by the electronic components of the circuit as electric current flows through. It is interesting to see how this effect is only very clear for the higher frequency sine waves.

Works Cited:

Platt, Charles. Make: Electronics: Learning by Discovery. Sebastopol, CA: O'Reilly, 2009. Print.