> If you hear a sound of frequency f and others of frequency 2f, 3f, etc then there's a good chance these sounds come from the same object, due to the physical principle of resonance. And so our perception of sound evolved to reflect this...

Wow that's interesting enough to share as a standalone post, so I took the liberty! Thanks for the link!

The quoted sentence seems false to me. Most physical objects do not have naturally harmonic vibration spectra. The vibration modes are not integer multiples ofthe fundamental (except for a vibrating string). Only the finely tuned western instruments do. So this is a somewhat backwards argument.

> Most physical objects do not have naturally harmonic vibration spectra.

What is your basis for saying this?

A large number of physical objects, solids as well as hollow can be approximated as systems of springs, surfaces and tensile elements, which all have some frequency response. It isn't rare at all for a physical system to have a very sharp resonant peak in its frequency response, to the point that you'll often find mechanisms to dampen that response so the structure will survive certain inputs.

Many objects don't have audible vibration modes (infrasonic, ultrasonic, so damped that sounds are too brief and too quiet) but it doesn't mean that they don't vibrate.

what you are describing is a graph. The laplacian spectrum of a graph is arbitrary.

Every rigid object has a fundamental frequency, regardless of whether you put it on a graph.

Sure. But the other frequencies need not be integer multiples of the fundamental.

They don't have to, but usually those integer multiples will be present as well. Whether they are dominant or not is another matter but it is quite hard to design something in such a way that if it has a natural resonance at a certain frequency that integer multiples will not be present in the response spectrum.

A typical object will have multiple modes of resonance as well.

> usually those integer multiples will be present as well

"usually", under what probability model? A random 3d or 2d shape will have zero harmonic partials with probability 1. What is hard to achieve is having even a few harmonic partials. A rectangular wooden piece is painstakingly carved to have a couple of harmonic partials, in order to become a xylophone or marimba bar.

Yes, but shapes are not usually random. Bars, cylinders, cubes, rectangles, squares and circles are everywhere. That does not mean that they will have a string like attenuation curve for those higher harmonics, but they'll be there.

> Yes, but shapes are not usually random. Bars, cylinders, cubes, rectangles, squares and circles are everywhere.

While there are some exceptions, this is skewed in the modern industrial world. If we're making evolutionary scale arguments about sound perception it's a much tougher sell.

Consider one of the only objects that actually matters in this context: vocal cords. Of course it's true that many inert objects don't have audible overtones or resonate at all, but nearly all animal vocalizations do. More complex auditory processing means better ability to distinguish between kin and predators. The fact that non-living objects tend to produce sounds via the same principles is just icing on the cake.

You have the causality backwards though. It isn't saying most objects emit quantized overtones. But if you hear quantized overtones, there's a very good chance they are from the same source.

It's not just strings, either. Drum heads have varying degrees of quantized modes.

The code itself also contradicts that sentence. Notice that the first roughness graph doesn't have any local minima at rational numbers. It's only when the overtones are added to the notes (at integer multiples of the fundamental frequency) that the minima appear.

So the code thinks that human ears don't detect integer multiples specifically, they just detect sounds whose overtones line up with each other.

Good point, but our ears definitely do perceive the 2 to 1 ratio. Maybe that particular phenomenon is better analysed through the usual pschoacoustic approach of "at what point do we stop perceiving one sound and start perceiving two "?

I don't think so. If a sound persists long enough to hear its continuation, then its partials are generally going to be harmonic. Non-resonant frequencies will have a tendency to dissipate very quickly, unless they are explicitly designed to warble between resonances (like a gong or similar).

@harperlee no worries about the share, it's great to see the variety of responses on the other thread

As someone who might use these with kids: I think the problem with both of these is lack of, well, sound.

To get things, people need to hear sounds, not just see note names and pictures.

it could be argued that this is music theory, and therefore sound belongs to the realm of music practice