I'd add a couple points of clarification here:
1. While classic Ring Modulation does indeed produce the sum and difference of the two input frequencies, it also suppresses the input frequencies. So, for example, given two sine wave inputs, one at 300Hz and one at 200Hz, the output of the RM will only be the sum and the difference frequencies:
300 + 200 = 500
300 - 200 = 100
The original input frequencies (300 & 200) are not present in the output. Note also that the output signal consists of just two sine wave frequencies. This would give an odd two-tone sound, and not quite the clangorous, 'metallic' sound of RM as we've come to know it. For that, you need more complex input signals (more on that in a moment).
2. If we change the frequency of the second input to match the first, we get an interesting result:
300 + 300 = 600
300 - 300 = 0
In this case, the output of the RM has exactly doubled the input. This mean that you can use an RM as a frequency doubler. The catch is that it only works when two sine waves are applied.
3. When you use complex waves (saw, square, triangle, sampled waves, etc) the sum and difference of each of the wave's harmonic components comes into play, with a complex result. When complex waves are used, the RM output consists of sidebands of frequencies (similar to FM) that have a sound best described as clangerous, or metallic. The math gets complicated pretty quickly, but here's the idea using square waves as an example:
A square wave consists only of odd harmonics, so a 100Hz square wave will have a harmonic series based on odd multiples of 100: 300Hz, 500 Hz, 700Hz, 900Hz, etc.
Similarly, a 250 Hz square wave will have a harmonic series based on odd multiples of 250: 750Hz, 1250Hz, 1750Hz, etc.
By applying these two frequencies to a Ring Modulator, every harmonic of the first input frequency (100Hz) will interact with every harmonic of the second input frequency (250Hz). So, starting with the fundamental of the first frequency, the sums are:
100 + 250 = 350
100 + 750 = 850
100 + 1250 = 1350
etc.
and the differences are:
100 - 250 = -150
100 - 750 = -650
100 - 1250 = -1150
etc.
It should be noted that in this case all of the difference frequencies are mathematically negative. What actually happens is that these frequencies become phase shifted by 180 degrees, i.e. inverted, so you can simply ignore the 'minus' sign.
Returning to the discussion, perform the same set of sum and difference calculations using the third harmonic of the first input frequency (300Hz) First the sums:
300 + 250 = 550
300 + 750 = 1050
300 + 1250 = 1550
etc.
then the differences:
300 - 250 = 50
300 - 750 = -450
300 - 1250 = -950
etc.
Now do it again for the fifth harmonic, and then the seventh, then the ninth, etc. Cumbersome? Yep, but that's what Ring Modulation is doing to the square wave inputs.
There's one more thing that hasn't been mentioned yet, and that's the amplitude (level) of the harmonics. Simply put, the levels of the sum and difference frequencies will reflect the amplitude of the harmonics used in the calculations. In other words, high harmonic levels will yield high levels of sum and difference frequencies, while low harmonic levels will yield low levels of sum and difference frequencies.
Fortunately for us, we don't need to worry about the calculations; the only thing that's important is the sound. Ring Modulation gives us the capability to create sounds that are non-harmonically related - a sonic realm occupied by the likes of cymbals, chimes, gongs, bells and other 'metallic' instruments.
Ring Modulation is an extremely valuable tool in the synthesist's arsenal, IMO, and I'm pleased that Roland included it as part of the V-Synth's architecture.
- G
- gear junkie since 1980 -
