When carburetors are not synchronized, the engine does not sound smooth.
At first I thought this is because the frequency of each piston is different, but I guess that is not possible, since they are all connected to the same crankshaft.
So, what causes the noise when carburetors are out of sync?
Your first thought is possibly closer than you think. Basically, when carbs get out of sync, you're causing an imbalance between cylinders. One or some of the cylinders are going to fire differently from the others, thus causing a slightly different running noise then you are used to when all is in sync. The engine will not be smooth because the cylinders will not be firing the same.
Imagine a 2-cylinder engine where idle requires ~5% of the throttle.
Next, imagine that the 2 carburetors are off by ~6%.
At full throttle, you will get like 94% and 100% - barely a difference.
At half throttle, they will be like 46% and 52% - still almost equal.
Now, try to adjust the idle. One of the carburetors is 2% open, the other is 8% open and the RPM is about right.
But, this is an 1:4 ratio between the two (this effect has a separate name in mathematics).
The first cylinder not only pushes with only 1/4 force compared to the other, but also probably misfires a lot, because it is fed way below its design minimum.
The result is vibration at half the firing frequency and uneven surges when the first cylinder misfires.
The frequency part is important because the engine mount, suspension and flywheel are designed to filter vibrations above a certain frequency, usually corresponding to the proper idle.
Half of this frequency is not filtered much and shakes everything.
