Introduction to Sound Synthesis Shaping timbre further
Ring modulation
A ring modulator multiplies two signals. The output contains the sums and differences of their frequencies and not the originals, which turns a pitched note into a metallic, bell-like or robotic tone.
Modulation at audio rate introduced ring modulation as one of three ways to modulate a carrier. Used as a sound processor, a ring modulator has two inputs and multiplies them, so its output is large only when both inputs are large, and its sign changes whenever either input changes sign. For two sine waves at 500 Hz and 200 Hz the product is exactly two sine waves, at 700 Hz and 300 Hz, which are the sum and the difference, and the output contains nothing at 500 Hz or 200 Hz.
A note from a sawtooth or a voice has many frequencies, and each one produces its own sum and difference with the modulator, so the output has up to twice as many components as the input. Unless the modulator's frequency is a whole-number multiple or a simple fraction of the note's, these components generally fall between the note's own harmonics. The tool below ring-modulates a note played on the keyboard with a sine wave, and the plot shows the calculated spectrum that results.
A ring modulator
A note played on the keyboard is multiplied by a sine-wave modulator. The modulator runs either at a fixed frequency or at a set ratio of the note's frequency, and a mix control blends the original note back in.
Listen for With a fixed modulator, every key produces a different, unrelated set of frequencies, so the intervals of a melody played on the keyboard come out different from one key to the next and each note sounds bell-like. Set the modulator to follow the note at a ratio of 2 and every key produces the same harmonic pattern, so the result keeps a clear pitch. A modulator below about 40 Hz turns the note into a buzzing, robotic sound.
Fixed and following modulators
With the modulator at a fixed frequency, the output frequencies are the note's frequencies shifted up and down by the same number of hertz. A fixed shift in hertz is a different interval at every pitch, as described in pitch and frequency, so each key gives a differently spaced set of frequencies and the intervals of a melody are not kept. When the modulator follows the note at a whole-number ratio, the sums and differences land on harmonics of a common fundamental, and every key gives the same pattern transposed. Ratios that are not whole numbers or simple fractions put the sums and differences off any harmonic series, which gives the metallic, inharmonic sound most associated with ring modulation. FM with a ratio of that kind produces inharmonic sidebands in the same way.
Uses
The circuit came from telephone and radio engineering, where multiplying a signal by a carrier moves it to a different frequency range. The composer Karlheinz Stockhausen used ring modulators to transform an orchestra live in his 1964 piece Mixtur. The BBC Radiophonic Workshop gave the Daleks of Doctor Who their voices in 1963 by ring-modulating the actors' speech with a low sine wave, and the same treatment is still a standard way to make a voice sound robotic. On a synthesiser, ring modulating two oscillators gives bells, gongs and clangorous tones, and ring modulating a drum with a sine wave adds a pitched, metallic ring.
Common questions
What does a ring modulator do?
It multiplies two signals together. For two sine waves the output contains their sum and difference frequencies and neither original, so 500 Hz ring-modulated with 200 Hz gives 300 Hz and 700 Hz. When the signals contain several frequencies, each frequency in one signal combines with each frequency in the other to produce a sum and a difference.
Why does ring modulation sound metallic?
The sum and difference frequencies are usually not whole-number multiples of a common fundamental the ear can follow, so they do not fuse into a single pitch. The result has the inharmonic quality of a bell or a struck metal object.
How were the Daleks' voices made?
The BBC Radiophonic Workshop put the actors' voices through a ring modulator with a low-frequency sine wave, around 30 Hz, which gives speech a buzzing, metallic quality. The technique is still used for robotic voices.
Why is it called ring modulation?
The original analogue circuit used four diodes connected in a ring. Modern ring modulators, including digital ones, keep the name although many use other circuits or simple multiplication.
Published Glossary