Fourier Toy

http://toxicdump.org/stuff/FourierToy.swf

by alxndr • 13 years ago

348 70 13 years ago

zoba• 13 years ago

This is very cool and reminds me of something I've wanted for a long time: a tool like this that is used to make sound. The synthesizers I've used seem predisposed to making a certain type of sound, however, something like but which gives you complete control of the wave form, should give you complete freedom when creating sounds. Maybe I've been looking at the wrong synths... Neat though :)

gosub• 13 years ago

Try pure data. You can fill a table (an array) with whatever function you like, and then use the tabosc4~ object to generate a signal with that as the waveform of a single cycle.

anigbrowl6• 13 years ago

What you want is an additive synthesizer. Usually these contain a lot of fairly high level 'helpers' rather than control over every individual sine wave, because while 8 sine waves are fun to play with full sound sculpting requires more, and applying envelopes, LFOs and other modulation sources to 64 (or 128 or 356 or 512...) sine waves rapidly becomes tedious.

You could easily make one with (or download a premade one for) Reaktor or Synthmaker (now called Flowstone DSP) or Max/MSP. Kyma is another system for doing so, but very expensive as it's hardware based. Pd/Puredata is free, albeit ugly. Various plugins exist, from VSTi's to rack extensions for Propellerheads' Reason. If you're feeling brave/patient and you want to do it in a hardware instrument, then you can get hold of a Kawai K5000 for only a few hundred $. If you're code-inclined (ugh* ) then try Supercollider or Csound. A related but slightly orthogonal techniques is spectral manipulation using tools such as Metasynth (Mac, $$$) or Coagula (Win, free). Neither of these latter two have seen an update for a long, time, reflecting the general lack of popularity of this technique.

(All these Italicized words are well-known product names, BTW that should come at or near the top in any search engine)

Also, check out http://amaranthaudio.com/ for Cycle which is new and impressive, though a bit clunky last time I checked. I'm hardware based but this is the first instrument I've seen in a while that could draw me back to the PC. I'm sure there's a bunch of iPad apps too, but not having an iPad I only check that platform occasionally.

Additive synthesis is a lot of fun but because there are so many harmonics to play with it's very easy to go astray and end up making clangorous noises that are not particularly musical or natural sounding; of course this makes them an automatic go-to for sci-fi noises, but the problem is that everything sounds unnatural in much the same way, if you see what I mean - the brain says 'ah, that's a very unnatural arrangement of harmonics' and gives up for all but the simpllest cases, much as it decides that poorly-designed FM sounds are quite noisy or that distorted sounds certainly involve a lot of clipping. It's still interesting territory for any sound nerd to explore, but don't expect m/any of your friends/loved ones to share your enthusiasm for such esoteric timbres.

* writing code is a rather masochistic approach to producing sounds IME.

squidfood2• 13 years ago

I'll add SynthEdit, because the demo version is fully-featured, intuitive, standalone and free.

If you just want to do it by numbers without interface, and get as mathematically crazy as you like, R has some simple "turn a timeseries to a wav file" libraries.

Also to add: quite a few ipad apps that let you sketch in either a wave form or a spectrum, then turn knobs on it like a synth. Addictive Synth is one that lets you draw spectra freehand; WaveGenerator lets you put in various surfaces or even pictures and "listen" to them. This specific method is called "Wavetable Synthesis".

smrtinsert• 13 years ago

Back in my day, real men had to buy all these damn synths! My fave setup was to use additive synths for a lead, analog for the bass/strings/background texture, and fm for chunky mid ranges.. Worked really well... I kind of missing having all that crap.

nitrogen3• 13 years ago

You can do additive and additive-like synthesis with ZynAddSubFX, but instead of using per-harmonic envelopes and shift amounts, you can control the bandwidth and spacing of each harmonic.

To mimic an existing sound, such as an organ, I once used audio software to plot the FFT of the original sound, then manually entered the amplitudes of the fundamental and harmonics in a ZynAddSubFX XML instrument definition. I'd like something that automates that process.

Edit: regarding spectral manipulation, there is also SpectraLayers.

ChuckMcM3• 13 years ago

You may be looking for an Analog synthesizer ( I can recommend the Arrick) or an FM synthesizer (like the DX11) which was based on Chowning's FM synthesis work at Stanford.

If you really want to create an arbitrary waveform (and I caution you that much of the timbre is in the attack and decay and harmonic filtering effects) the simplest way for non-engineers to do that is to use something like an Arduino with a Adafruit Waveshield and a scripted tool to generate .WAV files. The production path then is 'gen file, copy to SD card, stick in WaveShield and hit reset'.

jmmcd• 13 years ago

GP wants additive synthesis, not subtractive or FM.

As for copying a file to an Arduino... you know you can play wav files on your computer right?

Figs• 13 years ago

Your post prompted me to get off my ass and upload my .WAV file writer to BitBucket. I wrote it almost two years ago to do exactly what you're talking about -- generate a waveform and learn how to design my own sounds. There are a lot of sophisticated synth tools out there already, but I wanted to start from first principles and really understand what I was doing.

Here's a link to the library: https://bitbucket.org/cmcfarla/waveout

It's stupidly simple C code -- you just need to use three functions: One to open a file for writing audio, one to write a stereo sample, and one to close the file performing cleanup and bookkeeping. I included two examples -- a really basic example to just create a sine wave, and a slightly more complicated one that creates a sine wave with a panning effect.

While I've written a lot of code before, it's rare for me to put code up as open source. So, if I've missed something important, please let me know.

ryanthejuggler• 13 years ago

This is really awesome. First thing I did was try a sawtooth wave by entering sequential powers of 0.5... this had the intended effect of creating a sawtooth wave, but also the circle diagram was tracing an almost perfect circle in 2D. Really cool for discovering things like that!

gshubert172• 13 years ago

I'd like to be able to make a triangle wave, but I think the program needs to be able to input negative values for the components.

Nicely done.

anigbrowl6• 13 years ago

Yes, that was the only thing I was missing. I'm tempted to adapt this UI though, it's lovely design.

tjohns• 13 years ago

There's a triangle wave preset already available. Right click on the page to select it. It uses values: 0.75, 0, 0.083, 0, 0.03, 0, 0.015, 0

gshubert172• 13 years ago

Very helpful - thanks.

chengsun2• 13 years ago

You can change the phase by holding ctrl-shift and dragging the circle. If you want a negative value just use the absolute magnitude with the component in antiphase.

205guy• 13 years ago

Right-click the page for some pre-defined wave patterns (pulse, sawtooth, triangle, etc.)--at least it worked for me in FF.

rjgray• 13 years ago

Wow! So cool. I love the connection between the waveform and the trochoid curve on the left.

hcarvalhoalves2• 13 years ago

Try the Fibonacci sequence:

0.01, 0.01, 0.02, 0.03, 0.05, 0.08, 0.13, 0.21

It generates a beautiful wave [1].

There's also this interesting property that you can use any part of the sequence, and it will be the same wave [2].

[1] https://www.dropbox.com/s/89fg14dvsi3wuox/Captura%20de%20tel...

[2] https://www.dropbox.com/s/yu05xs10tauumgu/Captura%20de%20tel...

dnautics• 13 years ago

what phases did you use?

hcarvalhoalves2• 13 years ago

All in phase.

kylebrown• 13 years ago

Hit enter in each parameter box to update it

aadsam• 13 years ago

Well, it won't be the exact same wave, but it approaches the same wave. It's because the ratio between consecutive numbers in the Fibonacci sequence approaches phi.

zzleeper• 13 years ago

Nice findings!

By the way, try the reverse sequence (0.21 .. 0.01). I find it much more calmed and the LHS graph looks quite beautiful

wting• 13 years ago

This article and related commentary are relevant:

http://nautil.us/blog/the-math-trick-behind-mp3s-jpegs-and-h...

https://news.ycombinator.com/item?id=6683866

In fact, it looks like Lucas Viera may have used that blog post as inspiration.

anigbrowl6• 13 years ago

I think you're being downvoted because anyone who is interested in DSP already knows about Fourier transforms, they're fundamental and quite well known. Frankly, I'm surprised to find that they're new to so many HN readers.

mschuster91• 13 years ago

Fundamental if you ever finished a CS degree. Shamefully, the Wikipedia articles (German and English) aren't really good, and I dropped out of university before FFT was a topic.

Lots of HN readers are self-thaught hackers or come from non-theoretic backgrounds... so they likely won't have had a good explanation of it. (Speaking of which, the circle analogy is truly awesome - but how does it work in code?!)

zackkitzmiller• 13 years ago

Very much reminds me of the Spirograph I had when I was a young.

http://en.wikipedia.org/wiki/Spirograph

TheMakeA• 13 years ago

These guys are one of the reasons I love mathematics.

Check this out too: http://www.youtube.com/watch?v=QVuU2YCwHjw

Edit: Didn't realize that this was also linked to in another thread on the front page as well.

benched• 13 years ago

What determines the time/speed of each circle?

chengsun2• 13 years ago

The nth circle from the right is n times the speed of the first circle.

jonahx• 13 years ago

Why is this? Could you make it work using, say, 2n instead of n? or n^2 instead of n?

oftenwrong• 13 years ago

Doesn't work in Shumway yet.

leeoniya• 13 years ago

and probably won't for some time without an official bug report ;)

https://github.com/mozilla/shumway/issues

ZeroGravitas• 13 years ago

Though perhaps a canvas rewrite would be better?

joshguthrie• 13 years ago

Anybody got the sequence to draw Homer's head?

Reminder: http://www.youtube.com/watch?v=QVuU2YCwHjw

Serow225• 13 years ago

It would be cool if someone created the inverse of this, where you could input a signal (audio) and have it show the fft decomposition circles moving around in real time :)

spydum• 13 years ago

Isn't that approximately every Winamp visualization plugin ever created?

dualogy• 13 years ago

You sure dem younguns ever heard of Winamp?

Fingel• 13 years ago

Very nice overview of fourier transforms: http://betterexplained.com/articles/an-interactive-guide-to-...

fit2rule• 13 years ago

Beautiful .. has my 6 year old entranced. You know what he said, though? "This thing needs sound." I'm proud of him. :)

jmpe• 13 years ago

I learned about Fourier this way from an old "American Scientist" book. The writer had a very powerful remark at the end. He explained how Ptolemeus first used epicycles as a base model to explain planetary motion [edit: their paths]. The criticism that led to the demise of this model was basically "yeah, well, you can make planets have square paths this way". If someone connected the dots at that point we could have had Fourier transform a couple of hundred years earlier. Maybe we did, but the documents disappeared.

agumonkey• 13 years ago

I'd love this as an OS boot time animation.

stared2• 13 years ago

Such Fourier decomposition for an interactive quantum simulation:

http://www.falstad.com/qm1d/

(A rare piece of software not getting older with time; and in general, other Falstad's simulations are great, especially Ripple Tank for optical interference and electric circuits.)

csmuk• 13 years ago

nice. The circuit simulator is wonderful - have used it for years. In fact I actually tried to port it to .Net but never finished it.

stared2• 13 years ago

I would love to see such things rewritten to JS. And it does not sounds strange, as there are some applications based on Falstad's code, e.g. http://icircuitapp.com/.

mw67• 13 years ago

Just read that he was an orphan at age 9 and then made governor of lower Egypt at age 30 by Napoleon, what a life!

http://en.wikipedia.org/wiki/Joseph_Fourier

gbog2• 13 years ago

And he tutored Champollion at age of 11!

backprojection• 13 years ago

This is a really nice demo, but note that it's not the full Fourier series. This is only the 'sine' contribution. I'm not sure how you could expand the animation to include cosine as well.

daraul• 13 years ago

Cosine can be approximated by rotating the sine phase 90 degrees.

DonGateley• 13 years ago

Brilliant! But where's the algebra of complex numbers. :-)

Fourier Toy

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