Hi everyone

Im trying to build "complex" waveforms (squarewaves, triangle and sawtooth) using only [osc~],(im obviously avoiding trigonometry here...), i already have the relationship between frequencies for each waveform but id like to know the amplitude difference between each partial because im not getting the shapes when i look at them in an array.

if anyone can give me a table or a simple arithmetic explanation would be great.
Ill be looking for a math teacher as soon as i can afford one, i promise...

Thanks in advance.

With sawtooth and square wave, the amplitudes are 1/(harmonic number). So, with a sawtooth:

1st 2nd 3rd 4th
1/1 1/2 1/3 1/4 etc.

Remember, the first is also the fundamental.

Square waves, of course, are only the odd harmonics.

Triangle waves are trickier. The amplitudes are 1/((harmonic number)^2). And, to make matters worse, all the even harmonics are 180 degrees out of phase. But you can simulate this by giving it a negative amplitude. So the harmonics are like this:

1st 2nd 3rd 4th 5th
1/1 -1/4 1/9 -1/16 1/25 etc.

Does that make sense?

If you're only using multiple [osc~], make sure you synchronize their phases by sending a [0( to the right inlets.

makes a lot of sense, according to this book i have here the values of amplitude im getting are 6dB/oct attenuation but im still not getting the shape, either im doing something wrong or there is something wrong with the array´s properties...
i attached the patch for a sawtooth wave maybe someone can correct me, i think i got the math right...

http://www.pdpatchrepo.info/hurleur/sawtooth.pd

i just sat here for a while trying to understand what happens here, and i still don't understand,.

but for some reason, when i made a square wave by adding osc~, every 2nd odd harmonic needed to be 180 degrees out of phase.

i think i remember reading, and don't quote me on this, because it's a very old memory, but even if you don't make the waves out of phase like this, the resulting wave still SOUNDS the same. i have no idea why they don't line up properly on a graph though.

http://www.pdpatchrepo.info/hurleur/square.pd

by the way. the book you're reading probably has a formula for square waves like this, right? :

y = sin(t) + sin(3*t)/3

i have a feeling that by reading sine waves out of tables, like the pd osc~ object does, you don't perform exactly the same calculation.

again, i don't know why

Why not just do it in a wavetable using tabosc4~?

The math is essentially the same, add a bunch of sine waves with different phases and amplitudes.

http://www.pdpatchrepo.info/hurleur/sawsq-wavetable.pd

Sorry, the problem is that [osc~] uses a cosine wave, not a sine wave. So you should reset the phases at .25, not 0.

Also, setting that [metro] to update the array every 10ms is a little excessive. I get all kinds of choppy lines in the array at that speed.

thanks maelstrom!!
i changed the phase to 0.25 and voila! i got a sawtooth wave!

im guessing that was why it sounded the same but didnt look like a sawtooth in the graph, cosine waves start at 90 degrees from what ive read, ill make a video of this this is really interesting.

and @hardoff the book i was reading the amplitudes from is music, cognition and computerized sound, it didnt have a formula it just had a table of amplitudes and the one that said 6db of attenuation happened to match the results from the math Maelstrom gave me.
thanks again!

@saturno i wanted to do it with oscillators to listen, and i had no idea you could do it like that

here it is

why does the input number for phase have to be 0.25?
setting the phase to number 0 makes more sense to me if its a cosine wave... just wondering....

A cosine at phase 0 starts at the peak, whereas a sine at phase 0 starts at a zero crossing, which is what you want. Starting cosine at phase .75 (which is what I *actually* should have said) is the same as a sine wave at phase 0. Cosine at .25 is like an inverted sine wave. So it still gives you the shapes you're looking for; they're just inverted.

got it.

i did the squarewave video