Resonators is one of the many audio effect devices included in Live's arsenal. It's one of the more esoteric and often gets overlooked, but it sounds fantastic and once mastered, will keep creeping into your songs again and again.
A resonator is a generic word meaning anything that can exhibit resonant behavior ie. it oscillates at certain frequencies. This could obviously mean anything from a guitar string to a drum head. In the context of Ableton's Resonators device, it means an audio effect which will take the incoming signal and run it through a series of delay lines. When the delay lines are fed back into themselves they begin to ring, or oscillate, creating a series of tonal harmonics which are superimposed onto the incoming signal. The clever bit is each of the delay lines (there are 5) can be tuned chromatically so the resulting harmonics are always musically useful.
Resonators makes a wonderful sound design tool.
The Resonators device is very simple. The incoming signal first passes through a multi-mode filter and then into each resonator in parallel. Resonator I is fed with the stereo signal from the filter whilst Resonators II and IV are fed with the left channel and III and V with the right. This means the resulting resonant tones will have a nice stereo effect. The Width parameter can be used to pan the resonators to the centre if mono is desired.
The Decay parameter controls the feedback, or 'ringiness' of all the resonators together.
For tuning, Resonator I sets the root note and all the other resonators are offsets of that root note by +/-24 semitones. There are also fine tune and gain controls for each.
Each resonator is tuned relative to the first which makes it easy to tune them all to a different key.
There are two different modes, A and B. Each have their own tonal qualities and there is also a Color parameter to adjust the overall brightness of the output.
Here are some ideas to get you kick started with resonators:
Placing Resonators after a long reverb tail is a great way to make thick, drone-style atmospheres.
Resonators are used a lot in electronic music, and if you've never used one before you'll quickly have that 'so that's how they make that sound' moment. They can be used for a very obvious effect, or used more subtly to add a tuned element to any sound that didn't previously have one. It's pretty cool of Ableton to include a resonator effect as they're quite esoteric - I'm sure glad they did though!