A coffee cup rings two notes at once too. Go around the edge, tapping with a pencil, to find the two modes. Now tap on the back and side of the handle.

Yes. Numberphile had a video on this: https://youtu.be/MfzNJE4CK_s

I discovered Matthias's channel a couple of weeks ago, great to see it here. It's wonderfully real and unpolished compared to most YT stuff and he comes across at a lovely chap.

Oh and bell is cool too!

“This isn’t a gong, it’s a pot”

He's been around for a long time; great content. Most woodworkers know him quite well.

Wow, that vid really did it for me. Amazing sounds. Thanks for digging that up.

Some people can do this with their vocal cords. Sometimes it’s more than 2 notes.

https://en.m.wikipedia.org/wiki/Overtone_singing

Such as Anna-Maria Hefele:

https://www.youtube.com/watch?v=vC9Qh709gas

This sounds more like applying resonant filter to one of the harmonics. Voice is not a pure sine hence contains "many notes".

Some of what singer from Laybach does sound 2 voice as well. In some cultures this style is a natural.

It’s not just sound, it’s literally entitled overtone singing.

FYI for anybody. Your A440 is not the only frequency. There’s every integer multiple (880, 1320, etc) as well. Different coefficients of those overtones are why you can sing “ahhh” and “eeee” at the same note but they sound different.

Polyphonic overtone singing is a technique where one or more overtones are heavily emphasized in the timbre.

This is also why major 3rds on pianos are noisy. A has a C# as it’s 5th harmonic at 2200Hz (5*440). But C#7 on piano is slightly higher at 2217.48.

That’s why if you listen close there will be a ~17Hz oscillation around C#7 when you play A4 and C#5.

It doesn't sound like that to me at all but tbh I haven't done any spectral analysis of what she's doing. But the steps she shows are very hard to do with just filtering without losing a lot of output volume and that doesn't seem to happen. It sounds like the overtones are added rather than filtered out. I'm also unaware of how you'd do the filtering from a physics perspective, unless she's able to somehow restrict certain modes from forming through muscle action.

Instead of hypothesizing, you could just look the information up lol.

Other than that, I also think you may want to hear a different polyphonic singer.

https://m.youtube.com/shorts/CEU52mO69ZA

She has a video with a spectral analyser, YT search something like "overtone singing spectral analysis".

> I'm also unaware of how you'd do the filtering from a physics perspective

It's the same thing we do when we shape our mouths to make different vowel sounds, only much more precise. The physical thing that underlies what we perceive as "vowel quality" is the frequency of spectral peaks ("formant" is the linguistics terminology). When we shape our mouths (more generally our vocal tracts) to say "aaa" versus "iii" we are creating resonances at certain frequencies.

Admittedly when creating vowel sounds the bandwidth of the resonator is pretty wide, and when we hear vowels we can still perceive "a" quality vs "i" quality with even a wide bandwidth.

What Anna-Maria Hefele and other overtone singers do is much more precise. They can get a very narrow bandwidth by controlling their vocal tracts more precisely.

I've learned to do this, it took quite a bit of time to control. I used to drive 3 hours round trip each day to and from work for years, and often used an hour or more of the trip to practice.

It's extremely calming and I have a weird side effect that when I stop, I can still hear it "in my head" - it's pretty cool actually.

Also has a text version (though of course the video illustrates the sounds better): https://woodgears.ca/physics/bell.html

As someone who is not great at visualizing this stuff, I appreciate how well this video illustrates the concept. I also appreciate the effort he was willing to put in to avoid buying a bell.

I hoped it was Matthias when I recognized the title.

He is one of my favorite science educators on yt, and that may well be because he’d likely argue that his content fills a different archetype all together.

I love his casual but data, and pen and paper equations, driven approach to development.

He creates clever contraptions to collect data to challenge hypotheses.

(A recent favorite was a sleigh and a kitchen scale to measure fan thrust.[1])

All the while without the, abhorrent to me, “ScIeNcE iS FUN!” facade inexplicably so often found in science education.

Rather, the science is simply shown for what it is, and it’s just him that is fun.

~”Let me just take an angle grinder to this steel pipe!”

I definitely recommend you check out his other channel.[2]

He split it off because he felt the content was in conflict with his main channel, or yts algo did, but I feel people who enjoy this video will also enjoy what he posts there.

[1] https://m.youtube.com/watch?v=jbJPIRurJYE

[2] https://m.youtube.com/@matthiasrandomstuff2221

If I had to choose one YT channel, I would choose his. Just great, I have learnt so much from him…

Matthias has gotten enough mileage out of his Raspberry Pi to make up for all the people that bought them and threw them into a drawer.

I did not see it clearly in the video: the 'wa wa wa' effect he refers to is due to beat frequency [1] that is produced when two frequencies are present.

Also, the video alludes to this briefly but worth repeating: if the bell (or the pipe) is perfectly circular, i.e. radially symmetric, there wouldn't be two separate modes as demonstrated (higher frequency harmonic modes would still exists at lower amplitudes, but not relevant to discussion here). Grinding the bell down on the sides is breaking the symmetry, and thus, separate modes.

Coincidentally, Joseph Fourier studied harmonics using a metal ring and a heat source, analogous to the circular bell shown here. With a heated metal ring, you can visually see the different modes (including higher harmonics).

[1] https://en.wikipedia.org/wiki/Beat_(acoustics)

It's impressive the concept of bear frequency wasn't even mentioned briefly.