## the beginnings of a beautiful era for audio dsp

xoxos
Mr Entertainment

12013 posts since 29 Apr, 2002, from i might peeramid

you come and go, you come and go. amitabha xoxos.net free vst. neither a follower nor a leader be
tagore "where roads are made i lose my way"
where there is certainty, consideration is absent.
sinkmusic
KVRAF

6095 posts since 28 Apr, 2004, from france
It looks beautiful, Xoxos !
stanlea
KVRAF

4792 posts since 11 Feb, 2005, from Bordeaux France
indeed !
You can't always get what you waaaant...
MackTuesday
KVRist

453 posts since 11 Jul, 2004, from Southern California, USA
Go to https://www.desmos.com/calculator. Copy and paste the following equation.
Code: Select all
((a+\cos x)\cos n+\left(b\sin x\right)\sin n)/\sqrt{(a+\cos x)^2+\left(b\sin x\right)^2}

Click on the "all" button next to "add slider".

For the a and b sliders, change the range from [-10,10] to [0,1].

Now you can fiddle with the kinds of waveforms this scheme generates. a is the offset of the ellipse from center. b is the roundness of the ellipse. n is the angle through which the ellipse is rotated.

My coordinate system is different from xoxos' because I didn't follow his code, but the results are essentially the same.

It looks like the waveform at n is the derivative of the waveform at n+pi/2. But that would mean the function is its own fourth derivative, and we know that can't be. Trying to figure this out...
camsr
KVRAF

6755 posts since 16 Feb, 2005
It could do with a way to solve the DC offset problem. Somehow find a way to get the integral for the period and subtract it from the output. Although this might pose problems with modulation of the oscillator parameters.
Miles1981
KVRian

1284 posts since 26 Apr, 2004, from UK
MackTuesday wrote:It looks like the waveform at n is the derivative of the waveform at n+pi/2. But that would mean the function is its own fourth derivative, and we know that can't be. Trying to figure this out...

sin and cos have this characteristics, so maybe yours as well? Haven't looked at the equation.
MackTuesday
KVRist

453 posts since 11 Jul, 2004, from Southern California, USA
Miles1981 wrote:
MackTuesday wrote:It looks like the waveform at n is the derivative of the waveform at n+pi/2. But that would mean the function is its own fourth derivative, and we know that can't be. Trying to figure this out...

sin and cos have this characteristics, so maybe yours as well? Haven't looked at the equation.

It works for simple sinusoids, but when your periodic signal has harmonics, there's no way for any nth derivative of the signal to be equal. It's because differentiation is like a high-pass filter: it strengthens harmonics by an amount proportional to frequency. For the fourth derivative, it goes like f^4.

I compared waveforms at n with their true derivatives at n-pi/2. It looks like the true derivatives are high-pass versions of the "quasi-derivatives".

I'm tempted to say rotation acts like some kind of allpass filter.

Maybe someone could whip up some Fourier spectra? I don't have the time right now.
Last edited by MackTuesday on Sat Mar 04, 2017 10:35 am, edited 1 time in total.
Miles1981
KVRian

1284 posts since 26 Apr, 2004, from UK
But in your equation, you don't have any coeff in your trigonometric functions, so depending on the square root (basically I can only think of |a| == |b|), you will have the fourth derivatives being equal to your original signal.
MackTuesday
KVRist

453 posts since 11 Jul, 2004, from Southern California, USA
Miles1981 wrote:But in your equation, you don't have any coeff in your trigonometric functions, so depending on the square root (basically I can only think of |a| == |b|), you will have the fourth derivatives being equal to your original signal.

Yeah, the division and the square root make things quite messy. Look at the Fourier transform of (cos t)/(cos t + 2) and you'll see what I mean. Also when you take the square root of pretty much anything, you end up with a shit ton of harmonics all over the place.

Oh also, if the function were as simple as a A sin + B cos, the waveforms would just be sinusoids. You wouldn't be getting any of the shapes we're getting.
xoxos
Mr Entertainment

12013 posts since 29 Apr, 2002, from i might peeramid
'out' vst here for frequency analysis -
http://xoxos.net/temp/blackout.zip

spectra are what you'd expect by looking, harmonics roll off. thanks to desmos i noticed that a saw is possible with angle at 1.5.
you come and go, you come and go. amitabha xoxos.net free vst. neither a follower nor a leader be
tagore "where roads are made i lose my way"
where there is certainty, consideration is absent.
MackTuesday
KVRist

453 posts since 11 Jul, 2004, from Southern California, USA
DAFX is accepting papers. Due date is 31 March, not much time, but you might be interested to know.
parricide
KVRer

18 posts since 21 Nov, 2010
we can already do these things, and the 3D object version is pretty much just wavetable synthesis.

the concept of adjusting shapes to create the waveform is new to me though, but personally i would prefer to visualise the waveform as a waveform while making adjustments, but the shape method could be very attractive to some people.
stratum
KVRian

1438 posts since 29 May, 2012
In the 'Instruments' forum there is another thread documenting some chaotic features of the method, and that involves some kind of feedback, if I recall correctly.
~stratum~
xoxos
Mr Entertainment

12013 posts since 29 Apr, 2002, from i might peeramid
MackTuesday wrote:DAFX is accepting papers. Due date is 31 March, not much time, but you might be interested to know.

ty for that, and to the french persons, appreciated!

i'll just leave this here, you never know
https://xoxos.bandcamp.com/album/dope-beats-for-suckers

it's difficult to imagine that this method has evaded precedence, i think somehow the interests of this commercial field are responsible.
you come and go, you come and go. amitabha xoxos.net free vst. neither a follower nor a leader be
tagore "where roads are made i lose my way"
where there is certainty, consideration is absent.
MackTuesday
KVRist

453 posts since 11 Jul, 2004, from Southern California, USA
(retracted)
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