A hidden gem in sound symmetry
Hi HN, author here. A few comments on how I came up with this idea. I&#x27;ve been trying to find a &quot;proper&quot; connection between audible sound and visible shape, a connection that would not only preserve all the information, but would also properly visualize the &quot;symmetry&quot; in sound, so that messy sound would turn into messy images and harmonic sound would turn into visually appealing images. The latter part is hard, as perception of &quot;musical harmony&quot; is vaguely defined and subjective. Nevertheless, after quite a few attempts, I came across a particularly simple FFT-based technique that produces impressive and unexpected results. Below is the summary of my finding.<p>Music is a temporal ornament. There are many types of ornaments, e.g. the 17 types of wallpaper tesselations, but few of them look like music. However there is one particular type of ornament that resembles music a lot - I mean those “mandala” images. I don’t know how those are produced, but I noticed a connection between those images and music:<p>- The 1st obvious observation is that a mandala is drawn in polar coordinates and is 2PI periodic. Sound is periodic too, so I thought the two facts are related.<p>- The 2nd observation is that patterns on those images evolve over the radial axis. Ans so is music is a sequence of evolving sound patterns.<p>- The 3rd observation is that a 2PI periodic function trivially corresponds to a set of frequencies. We usually use FFT to extract the frequencies and another FFT to restore the 2PI periodic function. Thus, a single radial slice of a mandala could encode a set of frequencies. If this is correct, a mandala is effectively an old school vinyl disk.<p>Putting these observations together, we naturally arrive with the idea of using ACF. More details in the linked github project.