The Way We Tune Now - #2
On the Sensations of Tone
Previously on the program:
According to the Guiness Book of World Records, this is “fast.” Whatever it is, it’s happening approximately 20 Hz — 20 times per second. Okay, wow! That does seem “fast.” So… that’s “high frequency.” Right?
I can test this with a synthesizer.
Set phasers to “stun”
Huh! 😐
At first I hear nothing. If I put on my headphones, or play through the right system, I find that there is a sound happening. But I don’t experience it as “fast” or “high” at all… it actually reminds me of the sound that comes from the trunk of a subwoofer-armed boom-boom car:
Wait, I know what this is! This is "sub bass.” And to my ears that’s gonna be a “low frequency” sound. Right?
Maybe!
Depends on the shape of the vibration:
Stun Gun
With the wave set to “stun,” I hear that 20 Hz vibration as “low.”
But with the wave set to “massage,” will my perception change?
Let’s test it. Same speed.
Set phasers to “Massage.”
Huh! 😐
I do perceive something happening “fast!” And yet… it somehow also still tickles that first mode of perception — the one that tells me it’s “low.”
What’s going on?
Textbook: On the Sensations of Tone
I count myself as one of the many musicians of the past 150 years who stumbled across Hermann von Helmholtz’s 1863 masterpiece about the acoustics of perception On the Sensations of Tone, and found their musical life forever changed.
Helmholtz was singular in that he was qualified to draw on his expertise both as a physicist and a physician to explain a “physiological basis for the theory of music.”
At the time I discovered this book, the only “theory of music” I knew had absolutely nothing to say about physiology, and mostly consisted of covering musical scores with roman numerals.
For me, Helmholtz’s work was a revelation, and triggered a years-long fever-dream of creative productivity. Before I knew it, I had made a new record that went in a completely different direction than anything I had done before, and served as both an investigation of what I learned from Helmholtz and an elaborate personal fan-fiction of his emotional world:
… and fundamental to my newly awakened understanding was the realization that there are various words that get thrown around about music and sound to describe what is, essentially, just the air vibrating — one of them is tone.
What I talk about when I talk about “tones”
When I talk about a “simple tone,” I’m referring to a continuous vibration of air in this specific shape:
You can still call this wave a “stun” if you want, but you probably already know it as a sine wave. If the air were to vibrate in this perfect sinusoidal pattern, we would hear a simple tone.
Plot Twist:
Simple tones don’t occur in isolation anywhere in nature! Some objects like tuning forks or flutes can create a vibration that is close, but in order to truly hear a simple tone, you need to ask the machines to play it for you:
So, if pure tones don’t exist in the natural world, what function do they serve? An important one, as it turns out:
Much in the same way we might think of atoms as the building blocks of all matter, simple tones are the building blocks of every other sound.
Thus, there are two types of tones: the “simple” tone above, and everything else.
We’ll get into it. For now, that question of “high” vs “low”:
Slow and Low
As you can hear/see above, a true simple tone presents to the ear as continuous — we don’t hear the individual vibrations. I like to think this is because the shape of a sine wave is smooth… no pointy edges of any kind! In fact, sinusoidal shapes are, by definition, derived from pure circular motion:
This is a the key to understanding the puzzle of “high/low” vs “fast/slow.” The more pure the tone, the smoother the edges. And the smoother the edges, the more continuous the sensation — i.e. the less we are able to perceive the speed of the individual vibrations.
… and when the brain can’t sense the individual vibrations, it translates faster into “higher,” and slower into “lower.”
For example, when I rev the engine of a car, or turn my blender up to “puree,” I know intellectually that the apparatus is spinning faster, but I perceive the tone as getting “higher.”
This is our sensation of tone.
💧 ! 🐟
This was one of those “fish noticing the water” moments for me. I had, of course, always intellectualized rhythms and tempos in the domain of time, but tones (and pitches? and notes?) were measured in… what, even…? Position on the piano keyboard? MIDI note number? Alignment?
Even deep into music school I had never really thought about it. I just took it for granted. I would point at a key on the vibraphone and say "A.” I would tell oboist Christa that the bar was labeled “442 Hz.” Based on that reference, she might choose to tune the band “high.”
This was her business, not mine. Right?
Maybe not… Maybe consciously realizing that the stuff of tone is also the stuff of time could give me a more centered view of music overall?
A note on measurement:
Cold, clinical, and scientific, frequency is an impartial measure of how often something happens. It doesn’t care what you apply it to: use it to describe how fast a string is vibrating or how often you do your laundry. The important point is that it is a measure of the thing (not the thing itself) when that thing is cyclical 🔁 — repeating at a regular rate.
The frequency range of human hearing is defined by our ability to hear a simple tone.
Ever get a hearing test? You’re probably being played pure tones of various frequencies (and loudnesses) and being asked if you can “hear” them. For the average human, if a simple tone of any volume falls below approximately 20 Hz, it seems to disappear completely. The same happens if it rises above 20,000 Hz.
The vibration is still there, though. Just ask your dog!
Next week, on Episode #3: You can’t hide from center snare guy. Center snare guy hears everything.
Thanks so much for reading.
🔉👋 Hey, I’m Chris. I write music, and play percussion in contemporary chamber-band Alarm Will Sound. My weekly newsletter Music and Math and Feelings explores a broad range of musical topics: from just intonation to electronic music to drum corps to artist mental health.
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