Help understanding mod matrix and shape mod

[creativespiral]

Just did a test to confirm the math behind LFO to Shape Mod... I'll add this into the Appendix F thread:

If you have a Square/Pulse Oscillator and set it to Shape Mod value of 50 using the knob, you'll get a perfect/symmetric square wave.   (0 would be narrow pulse in positive direction, 99 a narrow pulse negative direction)

Now,  using a direct LFO modulation, assuming base value is set for symmetric square (50):

TRIANGLE LFO (bi-polar)  (or Random)
Amount of 127 will swing the symmetric square perfectly to the negative pulse and then back across zero point (square) to a pulse in the positive direction, and back again. 

SQUARE LFO (uni-polar positive)  (or Saw, R-Saw)
Amount of just 64 will swing the symmetric square up to maximum shape mod setting (a narrow pulse), and then it will swing back to the zero-point of the LFO, which would result in the symmetric square.   (it will never travel in the other direction towards the opposite narrow pulse, since its unipolar)   If you were to have a LFO amount value above 64 in this scenario, you would be "clipping the upper shape mod limit"... This can produce intended or unintended results, depending on other modulations you may have going to Shape.   Also, with a Saw or RSaw LFO, the clipping will "change the shape" of the LFO... with 127amt, you'll get maxed out Shape Mod for half the cycle, and then ramp down.

The Math:

A bi-polar LFO with amount set to 127 will swing the LFO_Output from -64 to +64.
(triangle, random)   

A uni-polar LFO with amount set to 127 will swing the LFO_Output from 0 to +128
(saw, rev saw, square)

LFO_Output/128*100  += ShapeMod

[godparticle]

Ok, I've taken the info you guys have added and tried to process it.

Here is how I see a 0% shape mode on the pulse (+ direction )


This is the 100% shape mod on the pulse (- direction )


And this is the bipolar triangle LFO on the pulse(set at 50%)


I didn't draw how the triangle would affect the pulse because it would take forever, but the idea is that the pulse gets wider as it goes toward the peak(most amount/depth applied) of the triangle

Getting closer to right?

[psionic11]

Aha, there's the root of your misunderstanding.

Your first 2 graphs are incorrect.  We should not be graphing the shape mod percentage.  Instead, we want to graph the waveform itself (in red), and the LFO that affects that waveform (in green).

What you have drawn in your 2 graphs is what would be called a DC offset.

[psionic11]

A pulse wave is an artificial construct.  It is all OFF (which is zero) for a portion of the wavecycle, and then all ON for the other portion of the wavecycle.

A square wave has a pulse width of 50%.   Since 50% also means "half", this means the square wave is ON half the wavecycle, and OFF the other half.  One half of the time it is fully on, the other half it's fully off.  Easy enough.  Just remember that we are still referencing 100%.  So another way to look at it is, 50% of the time the wavecycle output is fully ON, while the other 50% of the time it is fully OFF.

So while it's tempting to think of a square wave as 50 0 50 0 50 0 50 0...  just remember it's more like ON (for 50% of the wave's cycle), OFF (for 50% of the wave's cycle), ON (for 50%), OFF (for 50%).

A single square wave cycle is 50 on 50 off.

A single cycle of a pulse width wave with a pulse width of 10 has this pattern:  10% of the time ON, 90% of the time OFF.  That's 10% of the time at full amplitude, the other 90% of the time at zero amplitude.  Again, it's tempting to think of it a 10 0 10 0 10 0...  but remember it's more like 10% of the time ON, 90% of the time OFF.  10 ON, 90 OFF, 10 ON, 90 OFF.

But it's cumbersome to write it all out as 10 ON, 90 OFF, 10 ON, 90 OFF.  If we substitute 0 for the OFF portion, we will be mixing up our units, but it looks simpler:  10 0 10 0 10 0...  It's implied that the OFF portion is the percentage left over from 100% after subtracting the ON portion:  10 0(that is, 0 or OFF for 90% of the cycle), 10 0(for 90% of the time), 10 0 (90%), 10 0(90), 10 0(90).  The implied part is in parentheses.

So, for a waveform with pulse width of 30, we like to represent it as 30 0 30 0 30 0... but again, the implied portion is left out of the representation.  In other words, it's really 30 0(70) 30 0(70) 30 0(70).  We're always referencing 100%, but implying it.

So a pulse wave at 60 is represented as 60 0 60 0 60 0.  (The implied portion is 40).

[Razmo]

it's actually a little more complicated than just on/off for a certain period of a cycle... actually, what happens is that the narrower the "on" period is, then the longer "off" period has a lower amplitude and vice versa... this is what most synths does, and they do this to even out the energy of the "on" and "off" periods... so it's not just on or off, but of course it's easier to explain this way.

Normally the "on" period is called the "duty cycle"... in fact it sounds a lot more complicated than it really is for anyone who do not grasp this... what is really needed is an animated example of what is going on in realtime... that way it's much quicker to fathom... unfortunately I do not know of any such animated examples 

[psionic11]

So now, back to Shape Mod.

For a square wave, we represent as 50 0 50 0.

If we add 10 (which means leave the ON portion on for 10% more of the time), we get 60 0 60 0 60 0... (Fully ON 60% of the time, fully OFF for the remainder, which is 40% of the time).

Turning our Shape Mod by 10 units (clockwise), changes that square wave (50) to a pulse width wave with pulse width of 60 (50+10 = 60).

Turning the Shape Mod counterclockwise by 15 units results in a pulse width wave of 35:  35 0 35 0 (the 65% being implied).

In other words, turning the Shape Mod knob away from noon, and leaving it there, alters the square wave by that (pulse width) amount.

Turning the Shape Mod knob by 23 units above noon (move it from 50 to 73), gets you a pulse width wave of 73 0 73 0 73 0...  The 0 in this case implies that the wave cycle is OFF for 27% of the time.

Turning the Shape Mod counterclockwise by 11 units will result in 39 (assuming we started with a square wave).  This is the same thing as a negative change by 11.  50 - 11 = 39.

And so on.

Notice we haven't even talked about LFO yet.  I simply wanted to clear up how you are visually imagining how a pulse width waveform is represented graphically.  That's a lot of typing for now, and hopefully things are clearer now?

[Razmo]

https://www.keithmcmillen.com/blog/simple-synthesis-part-6-pulse-width-modulation/

maybe this link will help understand some of it...

[godparticle]

Right, I understand how all of that works as far as using the shape mod to make the pulse wave bigger/smaller and no LFO involved.

I was just trying to show what it was at 0 and 100% with no LFO in the first 2 images. Also going by what creativespiral mentioned:

"If you have a Square/Pulse Oscillator and set it to Shape Mod value of 50 using the knob, you'll get a perfect/symmetric square wave.   (0 would be narrow pulse in positive direction, 99 a narrow pulse negative direction)"

Also based on this image I found on PMW, even though it seems to say the opposite where 0% is negative and 100% is positive:

[godparticle]

I also found this one that looks different:

[psionic11]

I also found this one that looks different:

This is a great graphic that basically illustrates what I was saying.  With the Shape Mod knob at noon (or 5 on the graphic), you have the original waveform -- triangle in the upper graphic, square wave in the bottom graphic.

Turning the Shape Mod knob to 10 o'clock (or knob at 3) skews the triangle waveform to rise more quickly to positive max, while putting the Shape Mod knob at 2 o'clock (knob at 7) deforms the original to rise to max more slowly.

So there you have it.  Shape Mod simply deforms a single repeating cycle of the waveform into a different shape.  Each of those waveform graphics represents a single cycle.

So then what LFO does is move that knob automatically for you.  From 10 to 2 o'clock back to 10 to 2 and so on.  The resulting waveform is a continually deforming waveform morphing between the 10 o'clock position, through to the original waveform, then to the waveform at the 2 o'clock position, then back to noon, back to 10, back to noon, to 2, etc.

LFO Amount determines how wide the modulation will be -- low Amount going only from 11 to 1 o'clock, max LFO Amount going from 7 o'clock to noon to 5 o'clock.  (Or in pure knob positions, from 0 to 5 to 10 to 5 to 0, repeat).

A negative LFO Amount simply inverts the affect -- going from 10 to 5 to 0 to 5 to 10, repeat.

[godparticle]

Yeah, I understood how the shape mod worked. It was just more how amount was affecting(I think I get now) and the shape at 0 and 100%. I guess at 0 and 100% it's more like a a mostly flat line with a very, very small dip/peak