Musical Synthesis 101
1.1 Can we see what we Hear?
Audio visualization is one of the most intuitive ways to measure audio signals. Thankfully, there is a plethora of software and hardware specifically designed for audio visualization, my favorite of the group being the oscilloscope, or more specifically the vectorscope. Before we look at devices that measure sound over time, let's examine what sound looks like in a digital audio workstation, or DAW.
Instead of examining the waveform in its complete shape, we can also take a look at what a waveform looks like in real time. Previously mentioned, an oscilloscope is the perfect tool for observing a current waveform. To better understand how an oscilloscope works, take a look at the animation.
The line represents the amplitude at a point in time. Similar to how a book is read, an audio waveform is read left to right with the left most side being the earliest point in time and the right most side being the latest.
The window size can be adjusted to view the waveform closer or zoomed out to see more of the waveform. When the window size is at its smallest, notice how the waveform appears almost as a straight line.
While the oscilloscope is pretty neato, there exists another type of oscilloscope called the vectorscope. Instead of plotting amplitude over time, it instead takes in two audio signals and maps them to X and Y coordinates. The audio signal that corresponds to the X axis is the left channel, leaving the right channel to represent the Y axis.
Depicted is a cosine function representing the right (X) channel and a sine function representing the left (Y) channel. Where the two functions intersect a trace is drawn. Due to the nature of sine and cosine waves, a circle appears. On an analog vectorscope, the only thing that appears would be the circle. An interesting display of mathematics resulting from the functions of the vectorscope lies in the art of “oscilloscope music” coined by Jerobeam Fenderson in 2016 when he produced the audiovisual album Oscilloscope Music. Here is a look at one of my favorite songs in the album - Spirals. In the video, a circle is displayed and is fluctuating in size. This is done by modulating the amplitude of each signal. Later in the video Fenderson goes on to display his genius with displays of mesmerizing shapes and animations. Another spellbinding display of sinusoidal oscillations occurs when circles are played in parallel on a vectorscope. Specifically, when circles composed of frequencies related to the fundamental are played along with the fundamental. The shapes created when playing circles at frequencies with ratios related to the overtone series are very flower-like and quite beautiful.
Cymatics, defined as “a subset of modal vibrational phenomena”, derived from the ancient greek word for wave (κῦμα), is the study of visible sound and vibration. One of the more popular exhibits of cymatics lies in the research of Ernest Chladni, a musician and scientist who experimented with the phenomena found when a brass plate covered in sand is activated using a violin bow. The resonant frequencies of the plate results in what are now known as the 'Chladni Figures.' Watch ‘Chladni Figures - random couscous snaps into beautiful patterns’ by Steve Mold to see this experiment in action.
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- “Oscilloscope Music.” 2016. Oscilloscopemusic.com. 2016.
- “What Is Cymatics? Science of Visible Sound Explained.” 2017. Journey of Curiosity. 2017.
- Lehar, S.M.. (2003). “Directional Harmonic Theory: A Computational Gestalt Model to Account for Illusory Contour and Vertex Formation.” Perception. 32. 423-48. 10.1068/p5011.
- “Chladni Plates.” 2023. Dataphys.org. 2023.