So I am not sure if the problem I am having is a technical limitation of PD or if I am calculating something wrong.

I figured out I could add two square waves, one twice the frequency and half the amplitude to get a sawtooth wave. but it doesn't work.

I know there is a phasor~ object to get a sawtooth, just trying to figure something out before I try it in hardware.

if a square has odd harmonics I think at the same ratio as a saw has it's even harmonics then why can't I add two squares, one that is the base freq for all my odd harmonics and one that is X2 freq and half amplitude to get all of my even harmonics?

forgot to say I tried this in pd and I get something that sounds a lot like a sawtooth, but graphed out looks like a 3 step ladder sawtooth instead of a smooth line going from 0 to 1.

As an example, let's look at a square at 100Hz and one at 200Hz (doubled frequency):

1st 3rd 5th 7th 9th 11th <-- Harmonic number (odd only)
100 300 500 700 900 1100 <-- frequencies
200 600 1000 1400 1800 2200

Add these together and you get the frequencies in this order:

100 200 300 500 600 700 900 1000 1100 etc.

You can see that you're missing frequencies at 400 and 800 just from that, and of course there would be more the further up you go.

Also, if you just think about it as discreet amplitude values, a full scale square wave without anti-aliasing will only have values at -1 and 1, and one at half amplitude will have -.5 and .5. Adding these together will only give you values of -1.5, -.5, .5, and 1.5. This couldn't possibly produce a smooth ramp with only four values (well, except for a frequency of samplerate/4).

You can do the opposite, however. If you take two sawtooths at the same frequency and amplitude, offset the phase of one, and subtract them you'll get a pulse wave. The amount of the offset determines the width of the pulse. There is some bias issues, though. I guess that's not exactly the opposite, but kind of. That's the cheap trick Reason's Subtractor uses to get pulse waves.

ok that makes sense.

The reason I was trying to figure out how to put squares of together to make a saw was because I was trying to figure out how to do it with cheap hardware that only produces square waves (555 timers, 40106 switches) combined with a multiplexor/divider chip.

as for pulses in PD I like.

[phasor~] [0-1]
| |
[fexpr~ $x1 > $x2]

the 0-1 adjusts the PW.

thanks

@noizehack said:

[phasor~] [0-1]
| |
[fexpr~ $x1 > $x2]

the 0-1 adjusts the PW.

thanks

You don't want to use [fexpr~] for this. [fexpr~] is considerably more cpu intensive, and this works perfectly fine as [expr~ $v1 > $f2].

I agree for simple pulse waves this is better than the phase-offset approach I mentioned above. However, if you want band-limited pulses, using the phase-offset approach with band-limited sawtooth waves (via table lookup) is relatively simple and efficient. Of course, this has nothing to do with your original problem. I just thought maybe you were confusing this method with the one you were trying to do.