Is there some mathematical formula for predicting the behavior of an LFO being fully modulated by another LFO? And of course I am not speaking of LFOs in general but of the ones in the nord.... (that is... taking into acount that the control value can only go between 64 and -64 etc....) On a similar topic... what is the formula for the velocity of a pendulum??? Any geniuses out there know it off hand??.... I want to make a patch with a quick digital popping sound that fires off at a changing rate that emulates the swing of a pendulum... I have tried to do it with an LFO controlling an LFO but it never works out quite right, which is why I am figuring maybe knowing the math would help out. Is there a better way to do than having an LFO control an LFO? Maybe I am barking up the wrong tree which is why it isn't working.

Aha!!! At last. Something I know. Yipeee!!

You can then get the velocity from the distance travelled. If you want a compound pendulum then, for small oscillations:

where k is the radius of gyration, and h is the mass' distance from the axis of oscillation.

God alone knows why I still remember this! Maybe because I used to be so afraid of my physics master? May he rest in peace.

Now how about a PING PONG BALL bouncing on a table? Would the modulus of elasticity figure in there somewhere?

Pendulum moves in simple harmonic motion for small angles.

When you say lfo modulated by another lfo do you mean the rate? If so then A=sin(wt) and w=sin(w1t) gives A=sin(sinw1t)t) where w1 is the rate of the modulating lfo. which is not solvable for t.

Unfortunately, my physics master didn't frighten me enough to make me remember the details and the formulae, but yes, Young's Modulus (which is affected by, if I recall, 26 different parameters) does figure in there somewhere.

Hmmm... woosh... over my head already! That didn't take long. Maybe math and a pendulum metaphor is not the answer for me here..... Perhaps I should take a different tactic... Imagine an event sequencer driving the gating of an AD envelope module set with a really fast attack and decay so that whatever is put through the AD module audio wise sounds like the click of the metronome.... tick tick tick tick tick etc... at whatever rate the event sequencer is moving through its 16 steps. Okay.... so the event sequencer is clicking happily along at say for instance 120 bpm. Is there any way to get the event sequencer to smoothly transition from 120bpm to 60bpm and then back to 120bpm in a cycle? That is.... back and forth between the two tempo extremes hitting all the values in between on the way.

Ideally the value of the two tempo extremes would be adjustable AND the cycling between the two extremes of bpm would also be in sync to incoming MIDI clock signal so that if a 4/4 beat synced to MIDI clock was playing (at a constant tempo) at the same time as the metronome clicking sound (with a variable tempo), the metronome sound would be back to exactly 120 bpm (or whatever the upper value was currently set to) at the beginning of the fifth bar of 4/4. (or the second bar or whatever, depending on how fast you wanted the cycling between the two bpm values to happen.)

So I hope I am making sense here!

I keep coming up empty trying to design this patch... the closest I come is to have an LFO fully modulate another LFO and then have the output of the modulated LFO go into a compare module.... then the logic signal from that drives the event sequencer. It does some neat things but not what I am looking for, mainly because I have no way of controlling the tempo extremes that the event sequencer goes through. The clicking will go from almost nothing to something complex and cool to so fast that the clicks are no longer distinguishable. It is the inbetween complex part that interests me.

I had thought that the problem was that I hadn't found some magical values for the rates of the 2 LFOs (which is why I was asking about the formulas for pendulums and LFOs controlling LFOs) but now I just think there is a better way to do it and I am too stupid to come up with it.

Anybody want to take a crack at it or have any suggestions?

Ahhh, now its a bit clearer what you mean.

Have a look at the accompanied patch. The slave signal from a clock generator is used to define the tempo of a LFO. The LFO should be set to a ration of 4:1 to get exactly the same tempo as the clockgenerator. Halving the grey slavesignal will actually also halve the tempo of the LFO, so we do that with an amplifier module and morph between full grey and half grey value with a crossfader module. The morph of the crossfader module is controlled from a control sequencer. All you have to do now is retrig the control sequencer and the LFO to the incoming midiclock sync signal and calculate the ratio between the clock generators BPM and the midiclock BPM to get the exact retriggermoment for the loop. Or do that by ear.

The clockgenerator BPM sets one tempo extreme and the amplificationfactor of the amplifier module sets the other tempo extreme. The curve drawn in the control sequencer sets the way the tempomorph evolves, getting a sinelike evolution simply draw a triangle and use a log/lin module set to log1 to easily change the curve into a sinelike curve. Then calculate the time for every step by hand, add these times together, figure out which BPM this total time would give and compared with the BPM of the clockgenerator, this would give the ratio between the midiclock BPM and the clockgenerators BPM.