So in Dutch one expression for "that makes no sense" is "dat slaat nergens op", which literally translates to "that doesn't hit (slap, beat) anything". A ruder variation of that is "dat slaat als een … op een drumstel", or "that hits like a … on a drum set". For some reason I felt like sharing this trivia.
there's an amazing video on youtube about how metal bar/gong instruments (like gamelans) have different overtones, and regular western intervals instead of being consonant (like with vibrating strings) are dissonant - even perfect 5ths - and a totally different set of intervals are consonant (slendro and pelog tunings are a bit different for this reason).
thinking about it, each drum here would have totally different ideal scales to the others.
Selecting different materials would not change much. Call the frequencies \lambda_1, \lambda_2, \lambda_3...
You can prove that changing the material has no effect on the relative frequencies: \lambda_2 / \lambda_1, \lambda_3 / \lambda_1, etc. are completely independent of the material.
The shape is the determining factor; changing the materials (and hence the wave speed) just dilates the whole spectrum.
There's actually a "ring-out" slider and a "mallet" width slider under the drum already.
Ring out controls how fast the higher modes decay (basically stiff vs soft material), The mallet width controls how many modes a strike can even reach, since a real mallet can't drive the high frequency ones very hard.
No labeled presets like "wood" or "metal" though, just raw sliders. Would be a fun addition if someone wants to map a few physically sensible combos to buttons. PRs Welcome!
I've read hundreds of papers in my mathematics career, and they – good and bad – almost always blend into eachother and turn into a diffuse fog in my memory, where they're identified by "that good one by Johnson-something-I-think.. no the 90s one I think".
There are very few exceptions. Kac's drum paper is one. It's so nicely written!
https://eigendrum.com/#s=__Ap66fz1em9-NXp7_6a6-0AJu1AAiTv6gK...
If you find it interesting, a star on the GitHub repo helps a lot.
And don't forget to follow me on github, I build cool stuff!
It would be interesting if you could simulate and then print (or laser cut) your own instrument on demand.
Also you can draw your own drums! What! That's so cool
thinking about it, each drum here would have totally different ideal scales to the others.
this is cool.
You can prove that changing the material has no effect on the relative frequencies: \lambda_2 / \lambda_1, \lambda_3 / \lambda_1, etc. are completely independent of the material.
The shape is the determining factor; changing the materials (and hence the wave speed) just dilates the whole spectrum.
Ring out controls how fast the higher modes decay (basically stiff vs soft material), The mallet width controls how many modes a strike can even reach, since a real mallet can't drive the high frequency ones very hard.
No labeled presets like "wood" or "metal" though, just raw sliders. Would be a fun addition if someone wants to map a few physically sensible combos to buttons. PRs Welcome!
There are very few exceptions. Kac's drum paper is one. It's so nicely written!