the beginnings of a beautiful era for audio dsp

[Chaotikmind]

Even if the waveforms produced have nothing new, it really cool to be able to go from one to another just by tweaking a parameter (and the possible modulation linked to that as well ofc), just that is enough for me to find it useful.

[xoxos]

stratum - points in previous posts. for instance, if i repeat again, how is xoxos going to post something beneficial without receiving detraction and obfuscation? in this era, no new synthesis method is going to be overtly impressive, because it will sound similar to what we have heard for decades. the benefit of anything novel can be trivially concealed from most of the public by spin. who in the *industry* really wants an intelligent, analytic consumer body? it doesn't have to be as fantastic as my enthusiasm relates, there's still a depth of application, yes, we can do so much with it. i've been through a fair amount of methods in my years of development, we could have a party just because an old person has enthusiasm for something.

again, the sine to rounded square to perfect square is simply the projection of flattening a circular path. when in the past did you think of a square as being this? now add the other params, things open up.

anyway - off to work, in case i don't come back, i'll mention that a 3d rotation matrix is 9 multiplies of course instead of the 4 for a 2d rotation matrix (quaternions are preferable because of the derivation of angle, maybe other things afaik, but unnecessary for rotation of points, which is this). with no modulation, a constant angle should zip through a coordinate plane in all sorts of keen patterns so we ought to have some nifty harmonics.

edit: woke up, realised a 3d rotation would likely sound like fm given the extra dimension adds another frequency component :p prolly neat things to do with it still.

edit 2: i'd also like to discretise, what i said earlier was just trying to make the sentiment approachable for others.. if i could make a bling version, i'd be more likely to give it away for shock value than try to wring money out of people for it... not important but things one likes to make clear.

[xoxos]

just for fun (well, just for the erudition of those who think dsp is terribly complicated and inaccessible to the public, and beginners) here's the code for this oscillator -

angular frequency (w) is 2 * pi * freq / samplerate (see my dsp pdf or other sources for more info)

s0 and s1 are states of the quadrature oscillator. they should be initialised as s0 = 1, s1 = 0.

we begin with a 2d rotation matrix, same as you'd use for 2d computer graphics, where w0 and w1 are cosine and sine of w.

t is a temporary variable used in the 2d rotations so that the first line doesn't overwrite the value used in the second line.

Code: Select all

double t = s0;
s0 = s0 * w0 + s1 * w1;		//	circular oscillator
s1 = s1 * w0 - t * w1;

x = s0 * *in2;				//	scale
t = s1 + *in4;				//	offset
			
y = t * m0 - x * m1;		//	angle
x = x * m0 + t * m1;

*out1 = y / sqrt(x * x + y * y);

for the output, we project y onto the unit circle.. same as taking the leg of a right triangle in geometry.. we could also take the arctan2 of y and x then use the sine, but the unit circle is more cost effective

see? all very basic geometry.

a simple, flexible, meaningful and intuitive oscillator in a few lines of code. (code it like chaotikmind and you'll see how meaningful the geometry params areto timbre). we also need to antialias it, i'd recommend the polyphase filters from musicdsp for low cpu

seriously, i think most adult/teen human beings have the wherewithal to handle a 2d rotation and taking the leg of a right triangle... i am disgusted by the selfish arguments of kvr members who think creative audio dsp should be left to "professionals" because it is "so difficult" (cue your "this is inferior algorithm" arguments).

[Tale]

Code: Select all

y = t * m0 - x * m1;		//	angle
x = x * m0 + t * m1;

What are m0 and m1, or do you perhaps mean w0 and w1?

[Max M.]

Most of "those who think dsp is terribly complicated and inaccessible to the public" I met will stop at "we begin with a 2d rotation matrix".

P.S. I mean you'd get a much more insightful feedback if the thread name is "(controlling) Waveform generation via circle geometry" or so.

[xoxos]

http://xoxos.net/temp/out01.wav
http://xoxos.net/temp/out02.wav
http://xoxos.net/temp/out03.wav

modulation with an increasing effect on higher harmonics for acoustic timbres.

http://xoxos.net/temp/out04.wav
unison-like

[xoxos]

Code: Select all

y = t * m0 - x * m1;		//	angle
x = x * m0 + t * m1;

What are m0 and m1, or do you perhaps mean w0 and w1?

you should be able to infer the answer by considering the description of the algorithm. you'll feel silly for asking

[Tale]

you should be able to infer the answer by considering the description of the algorithm. you'll feel silly for asking

Well, I thought your oscilator looked interesting so I copy-pasted your code, but then it didnt work, apparently because you switched variable names midway. I have already fixed this at my end, but I thought I'd mention it, so maybe it would help others who might be interested in trying this.

But hey, if you rather call me silly than help, that's fine...

[VariKusBrainZ]

I've definately come across this idea before, though probably not being used to create a synthesiser oscillator.

[camsr]

The code example is not terribly clear, I will try to "follow along", but having undefined variables isn't helpful.

[whyterabbyt]

The code example is not terribly clear, I will try to "follow along", but having undefined variables isn't helpful.

you just dont understand how non-working code empowers non-coders.

[kryptonaut]

I think:
s1 and s2 are a pair of variables that give the x,y coordinates of a point moving in a circle.
w0 and w1 are a cos/sin pair derived from w, that determine the frequency of rotation of s1,s2 around the circle.
*in2 is an input parameter which scales the circle in the x-direction
*in4 is an input parameter which moves the scaled circle in the y-direction
m0 and m1 are another input, a cos/sin pair which rotates the moved and scaled circle about the origin. They could also perform some further scaling if (m0*m0+m1*m1) != 1
Then as we move around this rotated,moved,scaled circle, we back-project the current point onto the unit circle and return the y-coordinate of this point.

[xoxos]

But hey, if you rather call me silly than help, that's fine...

alright, it's time for you to feel silly i'll repeat what kryptonaut has said.

i described three parameters:

scale the cartesian x
offset the cartesian y
rotate the result by a set angle

scale, offset, angle. i've repeated it since the beginning of this thread.

since the two lines before say "scale" and "offset" and the line in question says "angle" on it i thought it somewhat obvious

since earlier in the very same code, the form for 2d rotation is annotated, and we have the same form here, ..it would be redundant for me to explicitly indicate that this is a 2d rotation matrix to tilt/rotate the result by a set angle.

you may intuit that m0 and m1 are respectively cosine and sine of an arbitrary angle used for the "angle" operation. intuiting that the poster has placed two "w"s upsidedown by accident may get you more sympathy from the xoxos derision brigade, it depends what you want to do today.

[stratum]

So basically xoxos is rotating an offsetted point and the result is bizzare and interesting. The resulting signal is either taken from x or y value, I guess. Whether this makes a difference or not is not stated, or I couldn't see it if it was stated. Anyway it's not difficult to try, if it's not x then it's y.

This appears to be the summary of this thread.

ps. I' have found it somewhere above, the output signal is from y

*out1 = y / sqrt(x * x + y * y);

[Tale]

scale, offset, angle. i've repeated it since the beginning of this thread.

Fair enough, and thanks for explaining.

Still, it would be nice to post a more or less working example (although one still has to wrap it in some plug-in format, but you know what I mean), especially when you argue that this shouldn't be so hard (a non-working example will almost certainly discourage a beginner).