This 'should' be easy, but I haven't found a simple general way.

I want to synchronize an envelope trigger/gate logic signal with an LFO clock. The behavior that I'm looking for is that the envelope should only trigger when the LFO triggers and the arbitrary logic signal is on. I don't want to trigger when the logic signal changes until the next lfo cycle is reached.

Try this, put the trigger/gate into the input of a Sample&Hold module, clock the module with the LFO and use the output of the S&H. Many times when synchronizing is an issue think of the S&H first. (Sometimes ANDed with the input clock to catch the end of the trigger/gate as well.) A circuit which is a bit complex to make although I vaguely remember its in the Logic workshop on Clavia's site is a so callled 'one and only one' circuit. It clocks on an LFO when a gate is present, but outputs only a single LFO clock pulse. If this is what you need check out the logic workshop. If its not there I can send you an example.

If the S&H can't in some way do the job then in general you have to think of something seriously complex.

What I really want is that the signal will only turn on if an LFO pulse arrives while the gate signal is on, but will turn off when the gate goes down. A variant (harder) would be to ensure that the gate always lasts at least some number of milliseconds. One thing I'm trying to get at (and may have just realized how to do) is to be able to sequence the number of pulses that a gate lasts for, and (perhaps independently) the number of pulses between gates.

One and only one sounds useful -- I'll have to look at it.

Here are some examples all based on a 'Set/Reset' or RS flipflop. A RS flipflop has two inputs, if a pulse arrives on the Set input the output is turned ON, if a pulse arrives on the Reset input the output is turned OFF. One thing to take note of is that the set and reset inputs cannot be ON at the same time, then the circuit doesn't know what to do. So sometimes some extra logic modules are needed to mak sure that doesn't happen. In most cases it is sufficient to 'isolate' the inputs by a pulse module set to a 1 msec pulselength.

By synchronizing the Set input with a S&H module, the flipflop can be put ON at the beginning of a LFO pulse. Then there are several ways to turn the flipflop OFF, some examples are attached. An Env module with the gate led is very handy to check if the flipflop output does what it has to do.

These are useful, esp. one and only one, a variant of which is attached. I've also attached a patch (LFO Rise Exper) where I use the reference oscillator to sync an lfo that is slower than any of the durations I want. I retrigger the lfo when the reference oscillator is on and the lfo is below a value controlled by duration seq. This triggers the held note, which turns off when the LFO drops below the duration seq value scaled by legato seq, I can thus get a pretty arbitrary pattern of durations and legato settings while syncing all notes to the reference osc.

I like the idea of using Overdrive (I'll also try WaveWrap) on top of the Perc Osc, which sounds great but has few little control possiblities.