
About Drums: the physics of overtones - camtarn
http://circularscience.com/about-drums
======
algesten
It's a great article, but the piano tuner in me must correct a detail about
"typical musical instruments" such as pianos. The overtones are not
necessarily perfect multiples of the base waveform and this is called
inharmonicity.

In fact, this is part of why a piano sounds like a piano and guitar sounds
like a guitar.

For any piano and especially the upright, the bass strings are actually too
short to produce any vibration of the main frequency, the only thing you are
left with are the overtones and our brains fill in the rest.

And that brain fill is actually happening across the entire range of the
instrument, our brain latches on to specific overtones depending on interval,
and the piano tuner (electronic or human), must compensate for inharmonicity
in that range.

This means the bass must be tuned lower than the middle which in turn is tuned
lower than the upper regions.

[https://en.wikipedia.org/wiki/Inharmonicity](https://en.wikipedia.org/wiki/Inharmonicity)

[http://www.precisionstrobe.com/apps/pianotemp/temper.html](http://www.precisionstrobe.com/apps/pianotemp/temper.html)

~~~
wwer
> In fact, this is part of why a piano sounds like a piano and guitar sounds
> like a guitar.

My understanding is that it is a bit more complex than that, literally!

The the final waveform is a not just

W = sum(a_i * f_i) = Psi

where a_i is the amplitude and f_i are the fundamental frequencies.

It is actually

W = sum(a_i * f_i + sqrt(-1) * (b_i * f_i))

    
    
      = Psi + i * Phi
    

Loosely, the imaginary part plays a significant role in making an instrument
sound like it.

Of course, the brain fills up a lot of stuff that is still a mystery but the
elec keyboards can set the a_i, b_i to change from "guitar" to "reed organ".

~~~
AstralStorm
That is way too simplistic as well, as this model is time invariant. Most
instruments, due to physical nature of excitation, are variable in both
frequencies and phases over time.

It is the main reason why modelling physically is the best way for realistic
results right now - lossy lumped finite element models typically - digital
waveguides are one of such models.

In such a model you can incorporate nonlinear damping and resonance functions
over time at desired accuracy.

------
adamnemecek
If you want to learn more about sound design[0], you should check out
Syntorial
[http://www.syntorial.com/#a_aid=AudioKit](http://www.syntorial.com/#a_aid=AudioKit).
It's an interactive software synthesizer that teaches you in like an afternoon
more than just about any book or video on the topic.

This tutorial series is also illuminating but it's almost too detailed
[http://sonicbloom.net/en/63-in-depth-synthesis-tutorials-
by-...](http://sonicbloom.net/en/63-in-depth-synthesis-tutorials-by-sound-on-
sound/)

You might also be interested in AudioKit
[https://github.com/audiokit/AudioKit](https://github.com/audiokit/AudioKit),
a (macOS|iOS|tvOS) framework for audio synthesis and processing.

[0] sound design is such an interesting field, as it's both vary artistic but
also extremely math/physics/cs/stats if you want.

~~~
edejong
Cheaper solution would be to try the open source Pd (PureData) in combination
with the free "Programming Electronic Music in Pd" book [1].

[1] [http://www.pd-tutorial.com/english/index.html](http://www.pd-
tutorial.com/english/index.html)

~~~
tel
Or SuperCollider or any demo of a standard synth plugin dropped into a free
VST host (like dropping a demo version of Massive [0] into Reaper [1]...
though Reaper technically not free).

[0] [https://www.native-
instruments.com/en/products/komplete/synt...](https://www.native-
instruments.com/en/products/komplete/synths/massive/) [1]
[http://www.reaper.fm/](http://www.reaper.fm/)

~~~
zdkl
Don't forget [http://overtone.github.io](http://overtone.github.io) for (live)
coding your synths, filters and effects!

------
exDM69
One item on my TO-DO list is hooking up an electric guitar to an oscilloscope
and frequency analyzer and do a video and/or blog post about the applied
physics of heavy metal guitar sound.

There are tons of tricks employed in guitar playing to create interesting
sounds by manipulating harmonics, by both the guitarist and the effect and
amplifier signal chain.

Most guitarists that use these tricks are completely unaware of the physical
phenomena involved. And the non-guitarist physics geeks always enjoy when I
give a short demo with lots of distortion and artificial and natural harmonics
tricks.

~~~
djaychela
I'd look forward to seeing that - I teach music tech and having done that with
a class singing a note and seeing the different harmonics in each person's
voice is interesting, and seeing that applied to a heavy guitar sound would be
interesting - as you say, there's lots that players do that they don't realise
they are doing, and it will also give an understanding of what's possible to
those who would then take that on board and use the techniques uncovered by
it.

------
maheshp
Well,

Recently I’ve been trying to figure out what is special about mridangam and
was wondering if I needed to do some analysis myself. Fortunately, I happened
to run into CV Raman’s papers analyzing the physics/acoustics/wave forms of a
mridangam that are well worth a read.

He first wrote his short paper in 1920 in Nature (almost 100 years ago)
[http://dspace.rri.res.in/bitstream/2289/2042/1/1920%20Nature...](http://dspace.rri.res.in/bitstream/2289/2042/1/1920%20Nature%20V104%20p500.pdf)

his fundamental thesis/analysis is that the way the mridangam is built is
special in that produces harmonic tones (integral multiples of frequencies)
which is highly unusual for drums therefore giving it the ability to sound
uniquely special, accompany vocal well and to be played in a smaller, softer
setting.

A good blog delving into all of this including some cool youtube videos at the
end on wave spectroscopy demos using talcum powder (related to raman) are at
[https://croor.wordpress.com/2010/11/10/cv-raman-on-
drums/](https://croor.wordpress.com/2010/11/10/cv-raman-on-drums/)

A longer version of his paper from proceedings of IIS published in 1934 is
here:
[http://dspace.rri.res.in/bitstream/2289/2047/1/1935%20Proc%2...](http://dspace.rri.res.in/bitstream/2289/2047/1/1935%20Proc%20Indian%20Acad%20Sci-A%20V1%20p179-188.pdf)

Figured some of you would be interested in this.

~~~
sn41
I have always wanted to understand the result in this paper, since it is one
of the first major publications of the first Indian to win a Nobel prize in
science. Can you point out to some more basic acoustics?

I've wondered about what similar results hold for Idakka [1], a drum played in
Kerala, and the talking drums of Western Africa [2].

[1]
[https://www.youtube.com/watch?v=kaozNblda54](https://www.youtube.com/watch?v=kaozNblda54)

[2]
[https://www.youtube.com/watch?v=B4oQJZ2TEVI](https://www.youtube.com/watch?v=B4oQJZ2TEVI)

------
dharma1
Folks at University of Edinburgh are doing some super cool stuff on physically
modeled audio, including drums.

[http://www.ness.music.ed.ac.uk/archives/systems/3d-embedding...](http://www.ness.music.ed.ac.uk/archives/systems/3d-embeddings)

------
filmor
A bit related (though much more theoretical):
[https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum](https://en.wikipedia.org/wiki/Hearing_the_shape_of_a_drum)

------
wwer
Fun fact: the waveforms shown are bessel functions, the daddy of sine (and
cosine).

------
gyrgtyn
I was really in to Supercollider a long time ago, and I remember there were
synths floating around on the mailing list that included big arrays of weird
looking values, and they somehow made drum sounds. My brain is remembering
that they were called eigenvalues, but I tried searching and didn't find much.
No idea how someone figured out or calculated the values. I think they were
impractical to calculate at runtime in supercollider.

------
madengr
Many similarities between drums and radio frequency cavities. The drums are
more interesting due to the nonlinearities of the heads and air inside.

------
bluetwo
OK, now I have a Cowboy Mouth song stuck in my head. Is there any better live
drummer than Fred LeBlanc?

