Figuring out Lissajous Curves
Recently, the Telequipment D66a vintage analogue Cathode Ray Tube (CRT) Oscilloscope has been pressed into service using X-Y mode to curve trace transistors, diodes, capacitors, etc. The patterns this creates on the screen are named Lissajous or Bowditch curves, named after the respective scientist who studied them. Nathaniel Bowditch in 1815 and then, independently by Jules-Antoine Lissajous in 1857 (Weisstein, 2019).
By feeding a sine into the X input and cosine into the Y input of the scope we can create a circle on the screen. This served as the starting point for many subsequent experiments (and hours) of experimentation. The process of creating music for the oscilloscope is an interesting one and often hours are spent getting “distracted” by interesting patterns created by one set-up over implementing new techniques.
Any post examining oscilloscope music would be incomplete without mentioning Jerobeam Fenderson’s compositions and work on creating Oscilloscope Music. Searching for information on Lissajous patterns on YouTube is actually how I discovered Oscilloscope Music initially. About one minute into the first video. the decision was made to take the Macbook Pro down to the lab and hook up the sound card to the Telequipment CRT scope (digital scope are not as useful for displaying complex waveforms). The reward was a complex image pattern, similar to the one created on the software scope featured in the video. The next hour was lost in playing different tracks and examining (getting lost in) the patterns created by different audio waveforms and textures.
Eager to attempt this Max was launched and a simple patch created feeding basic cycle waveforms from the left and right channels, phase and volume were then manipulated and the results were examined; the output was satisfying but simple. Fortunately Fenderson has taken the time to create some excellent tutorials (Jerobeam Fenderson, ) in Max or PD on how to start with Oscilloscope Music. Although, PDs look interesting and would be worth, Max was chosen due to previous knowledge. A sine and cosine waveform was created using a phasor and two cosine objects, one cosine was manipulated by implementing a phase shift of 90º. The resulting Lissajous pattern was a circle on the oscilloscope screen, which is a little boring on it’s own but any box with a number in it, any input in Max can be manipulated, so the very first modification was to place a number box on the phase input of the cosine waves doing this changes the phase relationship between the two waveforms, this has the result of looking like the circle is being squashed or, looking at it another way, being “rotated” in 3 dimensions. The next modification was to add a box to change the frequency of the phasor object and was rewarded by further interesting output. The cycle object was then added to dynamically change the numbers feeding into the objects.
Rotating Petal from Sound
After several hours of experimentation with various waveforms and different inputs it was back to Fenderson’s tutorial series to learn how to create more than one object on the screen simultaneously. This was achieved by using different parts of the Phasor object, i.e. when the phasor is less than 0.5 draw one object and when it is between 0.5 and 1, draw the other object. This, of course, results in half objects being drawn on the screen so it is necessary to adjust each cosine by multiplying by 2 to get a complete object. Adding offset and, what Fenderson calls a “sharp” control yielded some interesting results and it’s surprising the amount that sounds can be changed without affecting the overall visual output using this method. Future experimentation will include drawing more objects.
However, the immediate challenge was that the Telequipment D66a is a great scope but it’s definitely not portable (by today’s standards anyway). Initially I downloaded the software scope linked on Oscilloscope Music and, where as it’s great displaying the waveforms of pre-recorded music, it did not want to work with my version of Max using the soundflower interface. Therefore a simpler solution was found in using the built in Max scope and adjusting the sample and buffer parameters to get a close approximation of the analogue scope. It’s not perfect but it’s portable and good enough to experiment with. Also this allows my dBs Music BA and MA students to experiment without the need for additional equipment.
I look forward to further experimentation and composition using these techniques over the coming months.
References & Links
Emily’s Electric Oddities (2019) The LissajukeboxAvailable at: https://youtu.be/466xZ3cexMg[Accessed: 1st July 2019]
Jerobeam Fenderson (2018) Tutorials [videos]Available at: https://www.youtube.com/playlist?list=PLFgoUhNvMLro45P9uuR18wofljEaVCfvV[Accessed: 1st July 2019]
Look Mum No Computer (2018) Turn an old TV into an Oscillograph For Oscillographics!Available at: https://youtu.be/QWh4wcPNwgM[Accessed: 1st July 2019]
Weisstein, Eric W. (2019) “Lissajous Curve.” From MathWorld–A Wolfram Web Resource [online]Available at: http://mathworld.wolfram.com/LissajousCurve.html[Accessed: 1st July 2019]
Wolfram Alpha (n.d.) Lissajous CurveAvailable at: https://www.wolframalpha.com/input/?i=lissajous+curve[Accessed: 1st July 2019]