In ring modulation two signals or spectrums are multiplied together with the result that two new but related frequency spectrums are created while the two original spectra are not present in the result. 

These new spectra are called sidebands and in the case of ring modulation are easily defined as the sum and difference of the various frequency components of the two source signals. 

This form of modulation can lead to a quite noisy and inharmonic spectrum if the two source signals are complex spectra. If one of the source signals is a pure tone the resulting timbre is much less complex.