Reading Response: Math in relation to Music and Computer Science.

In this week’s reading response, I would like to focus on the inverse comb filter, an audio tool that reinforces pitches through a clever use of time delays. In summary, we can create an echo effect by replaying an audio with a short delay (say, half a second delay) while the original audio plays; usually, the second audio signal is damped in volume to give the illusion of a fade-out.

The inverse comb filter uses the same feedback loop, but sets the time delay to something miniscule—on the order of milliseconds—that our ears no longer perceive echos. Rather, the component sine waves of the audio signals combine additively or destructively depending on their relative frequency to the delay duration. In turn, depending on the delay setting, the inverse comb filter can reinforce certain pitches and dampen other signals.

Why do I feel so inspired to write about this audio-processing tool?

Because it’s an example of how the digital computer transformed a very simple physical and natural phenomenon (an echo) into something completely different in form and nature (a pitch-filtered signal). It’s also my first experience with an auditory perception phenomenon in which the echos, at a certain setting of delay duration, lose their semantics as echos and rather invoke a new sensory experience as pitches.

Moreover, it’s an elegant demonstration of the combination of math, computer science, and music/acoustics:

1. The computer program transforms music through a very simple process. Programmatically, the computer programs to generate echos vs. implement an inverse comb filter are almost identical. Phenomenally and perceptibly, the effects are completely different. Thus, the computer program also transforms our perception of the music in a very fundamental sense (not just aesthetically! but also functionally!)
2. Math enables us to understand what is happening physically. With the understanding that audio signals can be decomposed into sums of sine waves, we can apply a discrete Fourier transform to the audio before and after filtering to find that certain sine frequencies have been amplified!
3. With the mathematical model in mind, we can now go back to the program to modify the sounds we generate and begin to aesthetically shape our audio composition.