Looking for a circuit that will sustain for maybe 10 seconds or so, but not hash up the signal with white noise, for playing single note slow melodic-type stuff. Will a Fuzz do this without noise? I don't want something like the EHX freeze or a feedback distortion type, just overdriven and/or compressed without the "shhhhhhhh".
This is another of those questions which pop up from time to time that seem like they should be simple, but are not because they run afoul of a natural law or two.
In this case, it's the law of conservation of energy. When you pluck a string, you put energy into it to make it vibrate. A string in a vacuum with perfectly rigid mountings on the ends that is made of a material which has no internal friction would be able to sustain for a long time. In the real world, every movement of the string leaks some of that initial "pluck" energy out into air friction and sound waves as it moves, heating from the internal bending friction, and energy coupled into the mounting points; also a pickup if it has a pickup, the energy being coupled out as the electrical power to move signal down into the controls, jacks and whatever else is there.
All of that put together makes for a constant fraction of the energy being drained out per unit time. It's the exact analog of a pendulum, which swings for a while but runs down. Some of the running-down products like sound waves and conversion to electrical signal are why you're doing this in the first place, so you can never make it ring forever, only longer by taking less energy out.
What that amounts to is that for a given initial "pluck" loading X energy in, Y% of the energy is lost per unit time. Engineers recognize this as an exponential decay, and can tell you from the value of Y (the percent of energy lost per time) how long it will take to delay to some percentage. This is also expressed as the time constant, that being the time to decay to 0.632 of its first value. After five time constants, it's generally conceded to be over with.
A given string/guitar/pickup *will* have a decay time constant of some value.
Compression sustainers fake a long sustain by taking in the signal and comparing it to some output level they want. They adjust the gain up or down to get the output to be the right level. So high input signals are lowered to the reference level, and as the note decays, the gain of the compressor is raised to make the level come out the same. In time, the compressor must lose, because it will spend all of its gain and the signal will still get smaller. The signal also gets hissier as the compressor gain goes up.
Distortion increases the apparent sustain by amplfying the signal up and clipping off the tops at some level. All of those flat tops are the same level, so the signal seems to sustain. But the string signal under it is not being sustained, just amplified and clipped. Again, eventually the signal decays down to where it can't be covered up by clipping, so the sustain disappears, and the noise from all that gain is still with you.
Both of these approaches are like shoveling sand against the tide. They do nothing about the string's energy leaking out. To get really long sustains without the noisy falling-off-the-cliff, you have to concoct some way to pump energy back into the vibrating string. All of these are feedback drivers of one kind or another.
The ebow and its ilk drive the string directly and electromagnetically. Standing in front of a cranked up amp drives the strings acoustically from the sheer air vibrations. You can also drive the mounting points of the string with a speaker coil or some transducer to shake the string mounts mechanically. These are the only ones which promise low hiss. They cooperate in the conservation of energy by feeding a supporting energy back into the string to make up for what it loses.