Perceptively Beautiful - These Things

Note: I didn't mean to write an essay on the science of sound recording but it's been on my mind and it's already Thursday so this is what I've got and there's real beauty in it and, true to the mission of this communication, these things did recently inspire me. But, if you want some more typical-to-this blog/email inspiration, skip to the end. #sorrynotsorry #thatsjustthewayitisbaby #happythursday #beinspired

I’m ok, just thinking about bandwidth, how we use that term these days, and yes, I’m feeling the outer limits of my “bandwidth” some days but recently spending a lot of time under my headphones trying to understand the science of sound and I ran across this great video where Alex Knickerbocker explains sample rates for recording audio and he breaks down the “Nyquist-Shannon Sampling Theorem” which essentially gets at the idea of only using what you need to make a thing perceptively beautiful. And I was really struck by this idea: perceptively beautiful.

Let me explain.

Here’s an excerpt of the description of the theorem:

Intuitively we expect that when one reduces a continuous function to a discrete sequence and interpolates back to a continuous function… The sampling theorem introduces the concept of a sample rate that is sufficient for perfect fidelity for the class of functions that are band-limited to a given bandwidth, such that no actual information is lost in the sampling process.

I got lost in the razor sharpness of this language. But then I read it again, more slowly, considering each word, like one might when trying to enjoy a poem, and came up with another way to write this sentence.

This was my process:

continuous function

Sound can be described as a continuous function using the language of mathematics. And, may I take a moment here. Yes, declarative, not interrogative...rhetorical. Sound is not “made of math” like I keep hearing so many people say that “everything is made of math.” Many things in our world may be precisely described using the language of mathematics. Math is an abstraction layer of explaining our plane of physical existence–a re-presentation of the world. The physical is not manifested in its materiality of the imagined even though many things in our physical world were born in the imagination. Actuality and abstraction.

discrete sequence

A sampling rate, in our discussion of sound, is a discrete sequence. Audio recordings are made of a particular number of recorded slices of sound each second, similar to how a film is made of 24 images presented each second. To further explain. By count, there are more millimeters in a meter than centimeters even though they describe the same amount (length). So the millimeter is the more precise measurement. Some common sampling rates for audio are 22 kHz, 44.1 kHz, 48 kHz, 96 kHz, and so on. Therefore, a second of recorded audio, a discrete sequence, may contain 44,100 “slices” of sound per second, 48,000 slices per second and on and on. Thus, the sequence of “slices of sound” make a discrete sequence.

sufficient for perfect fidelity

It is sufficient to only record audio perceptible to humans. Fidelity in audio means basically can we hear the full spectrum of perceptible sounds clearly. High fidelity (High-Fi) provides the full spectrum of sound we can perceive whereas low fidelity (Lo-Fi) only provides a small spectrum of perceptible sound.

band-limited to a given bandwidth

The perceptible range of human hearing is, generally, 20 Hz to 22,000 Hz. This is the bandwidth of sound perceptible to humans. For recording then, the given bandwidth we limit ourselves to is 20 Hz to 22,000 Hz. Oh, sometimes we'll see this as 22 kHz meaning kilohertz (22 x 1,000 = 22,000). Metric system.

no information is lost in the sampling process

This is where it gets interesting. For example, bats communicate using ultrasonic sounds. Ultra = beyond, sonic = sound, and in context = beyond sounds that humans can perceive.

This means that in order to not lose information, that is sounds we can possible hear, we must record our discrete sequence using a sample rate of at least 44.1 kHz, which is twice the upper bandwidth limit of human perception (22 kHz), to produce a life like fidelity when we interpolate back to a continuous function. That is to say, when we re-present this sound we recorded as an audio recording.

This idea is similar to how cinematic frame rates for video are 24 frames per second vs how video was originally produced at 30 frames per second. Our eyes can only take in so much visual information per second so in the real world the edges get blurred when we move our heads. 24 frames per second provides a natural motion blur that looks closer to real life. On a technical note, audio used in video is usually presented at 48 kHz along with the 24 frames per second and the obvious math there shows why this works so well for sound to be synchronized with video when thinking in terms of a discrete sequence.

Here’s the abbreviated version of all of this: since humans can’t hear sounds below 20 Hz or above 22,000 Hertz, we don’t have to record these to provide high-fidelity sound when presented to humans at 44.1 kHz or higher.

Perceptibly Beautiful

What was fascinating to me about learning this is how perfectly mathematics describes how limited is our perception of the world around us. More importantly, that what we perceive as beautiful is a small representation of what’s around us.

Did you know that the ultrasonic sound of bats have to be slowed down by 200% when recorded at 192 kHz for humans to perceive aurally?

What’s fascinating to me is that our senses don’t even cover the bandwidth gap between the highest sounds we can hear and the slowest waves of light we can see. In other words, there are continuous functions, phenomena, we can not perceive using our physical senses. What a beautiful world. From my perception.

Thank You!

Thanks for taking a moment here with me. I very sincerely hope you and your loved ones are doing well. I hope you find something unexpected that inspires you like the mathematics of sound has inspired me recently.

Oh! Here's the video of the gerbil museum I promised to share. Oh, oh, and this video of the song a music teacher wrote about how she's dealing with "stay at home."

Until further notice,

Jeff O.

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