hello everybody,

i 've got some problem to make an abstraction which would smoothly fade from a
reverse sawtooth to a triangle and then to a sawtooth like in some analog synthesizer.
i know the J05.triangle patch but it doesn' t give a very precise shape for the sawtooths form, it' s good for making a triangle wave. usually i use separate oscillator for each waveform but i would like to make a single abstraction. i found a documentation about this subject on this pdf file :

http://www.analoguesystems.co.uk/pdf/RS95-95E.indd.pdf

in fact i' m trying to make a classical shape control

can you help me ?

Hey pouk,
what do you mean with "it doesn' t give a very precise shape for the sawtooths form" ??. If you use a "raw" [phasor~]-sawtooth you will hear tons of aliasing, so 0% and 100% of that "shapevalue" will not sound that good anyways..

i totaly agree with you but i think it' s another problem. Maybe i can use generating waveform in order to avoid aliasing. J05.triangle is a good example and may be a good solution for my problem but it doesn' t provide a complete sawtooth shape. If you test it, you will see that when you decrease the slope controls you will find a sawtooth but with a very low amplitude. The more you reach the sawtooth shape the more the amplitude decrease.
My objective is to have a sawtooth/triangle oscillator/inverse sawtooth with smooth fading between each form and same amplitudes.

Ok I see,
So you just want one parameter for the shape and a constant amp?!?
I think the idea of taking the smaller one ( ...min(,) ) of two functions that change with the [phasor~]s "phase" or "time-per-period" ( x ) is the easiest (and fastes?!)
So it's like OUT=min(f(x),g(x))
It's pretty easy if you know about vectors:
We have three points [0,0], [p,1], [1,0] laying on two lines... So lets take:

r_vect1=(p, 1), and r_vect2=(1-p, -1) that will be attached to the first one..

Now just solve: ((0, 0))+a*r_vect1=(x, f(x)) for f(x)
and solve: r_vect1+b*r_vect2=(x, g(x)) for g(x) .
In short get rid of the a and b!
Finally insert this into "OUT".

ps ...man just writing the results would have been faster...

whaou i' m a bit lost...i don' t understand how to write it in pure data. i' ve got
a low level in mathematic knowledge...please can you schematize it ? mabe i will be
able to transpose it in pure data and then understand what happen.

thank you

The last sentence in the J05.triangle.pd is the clue you're looking for here:

"If we wish instead to specify the corner location (x, y) (with x in cycles, 0<x<1) we set s = y/x and t = y/(1-x). The DC value is y/2."

You want y to be a constant that is always equal to .5. x is the location of the corner within the cycle. So just plug .5 in for y and use a slider or whatever to change x (making sure it is between 0 and 1), and there you go.

i don' t know if i understand everything. so what you say malstrom looks like something i did yet. indeed my first attempt in J05.triangle.pd was to fix a constant
for up control at 0.5 and to put a slider for down control between à an 1. if you look on the graph you will see that sawtooth got a very slow amplitude when you reach it.
in my school there are some users of reaktor and they say to me that what i am looking for is a kind of width control (name in reaktor). it looks like a symetric control like a PWM for a square wave. for example at a duty cycle of 50% your square wave is symetric. i' m looking for something like it but for a sinewave and a triangle wave.
we can find an illustration of what i am talking about at the end of p.49 and end of p.50 in the pdf that i mentionned in my first post.

..oh btw. the variable "p" I mentioned is that "pwm"-/"shape"-parameter you are looking for!

I hope these graphs will help you a little.. ...due to the limitations of painting with letters this example is for a p=0.5...

| / <- f(x) |\ 1_
| / & | \ <- g(x) => | /\ <-min(f(x),g(x))
|/___ x |__\_x |/__\___x
0 1 0 1 0 1

The last graph is the one you want to create, cause if you use a [phasor~]s signal as the x-value you kind of "play" the shape.

@pouk said:

indeed my first attempt in J05.triangle.pd was to fix a constant
for up control at 0.5 and to put a slider for down control between à an 1.

x is the position of the peak between the beginning and end of the cycle, and y is the amplitude of that peak. "Up" and "down" refer to the slopes of the triangle wave. You want y to always equal .5, but changing x is going to change both slopes. So, again, looking at the last sentence of the patch:

up = s = .5/x

down = t = .5/(1-x)

in my school there are some users of reaktor and they say to me that what i am looking for is a kind of width control (name in reaktor).

Yeah, Reaktor comes with several pre-made oscillators that just might have a "width" input. In Pd, you have to make it yourself (which is what you're doing here) or find one someone else made. The triangle one is a bit tricky, though.

we can find an illustration of what i am talking about at the end of p.49 and end of p.50 in the pdf that i mentionned in my first post.

I don't know how that oscillator is specifically working, but it looks more like phase distortion. I just recently posted a patch that emulates the Casio CZ oscillators, and the "saw" and "pulse" modes look the ones in that .pdf.

http://puredata.hurleur.com/sujet-6796-casio-oscillators

ok, i think the main problem is that i am not able to link the equation mentioned with pure data patch

"If we wish instead to specify the corner location (x, y) (with x in cycles, 0<x<1) we set s = y/x and t = y/(1-x). The DC value is y/2."

i learn a lot by looking on what happen on graph but i can' t manage to write these mathematic equation with pure data object. how can i write these equations with
boxes ? so i understand that x is the position of the corner and y is the amplitude. now if i want to change the position of the peak i need to change the slopes and if i change the slopes the amplitude increase or decrease...
so i tried to change the amplitude of the output of min~ according to the position of the peak in order to avoid low amplitude level. i know it doesn' t do what i want but
i do my best...:(

here the patch

http://www.pdpatchrepo.info/hurleur/J05.triangleGalereWidth.pd

Okay, you're over-thinking it here. All you need to do is input the slopes, and those equations give you the slopes. The patch itself is already done and doesn't need editing. Take a look at the attached.

http://www.pdpatchrepo.info/hurleur/j05.trianglepeak.pd

ok ok it' s very clear now i know who is s, t and x very useful ! great !
now i have to play with this new stuff

Maelstorm, flipp thank you for your patience !