Zoë Blade's notebook

Beating

Not to be confused with the beat.

Beating is when two waveforms are almost, but not quite, at the exact same pitch. The difference between their two pitches can be heard as if repeating at its own rate.[1][2]

For example, if one waveform is repeating at 218 Hz, and another at 222 Hz, then you should hear them going in and out of sync every 4 Hz.

You can use this effect to tune a VCO against a reference crystal oscillator that outputs one known frequency, usually 440 Hz (A4, as per ISO 16). Simply try to make the beating as slow as possible.

A pair of linear oscillators allows the frequency of their beating to stay consistent across their whole range of pitches. In contrast, a pair of exponential oscillators instead allows fixed intervals to stay consistent across their whole range of pitches. Both types have their uses.

Pulsewidth modulation

Main article: Pulsewidth modulation.

Pulsewidth modulation is an interesting case, as it effectively achieves the same effect, but backwards. You can think of a pulse wave as two sawtooth waves playing the exact same pitch, one rising and one lowering.[3] You can use an LFO's triangle wave to slowly change the shape of the pulse wave. This is equivalent to detuning the two sawtooth waves. If the LFO repeats the modulation twice every second, then they're 2 Hz apart, and so on, as above.

References

  1. "Tune the oscillators to a close interval, smaller than a minor second, and you will be able to clearly hear the 'beat frequency.' This beating is the result of the non-linear change in current which manifests itself as an amplitude fluctuation, equal to the difference in hertz between the two signals." Electronic Music Allen Strange, 1983, ISBN 978-1-77417-031-1, p. 176
  2. "Figure 1 shows what happens when you mix two sine waves of equal amplitude, one of frequency 100 Hz, and the other of 101 Hz. The result may look surprising, but it is obvious when you think about it. The two signals are moving in and out of phase with each other so there will be times when they reinforce and there will be times when they interfere destructively. Consequently, the amplitude of the resulting waveform will range from the sum of the inputs to zero, swinging smoothly between the two. Looking at Figure 1 again, it's clear that the output is punctuated by silences. We hear this as beating, and its frequency is the same as the difference in the frequencies of the two oscillators." "Synthesizing Strings: String Machines" Gordon Reid, Sound On Sound, Feb 2003
  3. "However, if you have one of the few instruments that offer sawtooth and ramp waves, you could try combining these. I used analogue modules present in my Analogue Systems Sorceror modular synth — two RS-90 oscillators (which offer sawtooth and ramp waveforms), an RS-380 modulation controller, and an RS-160 mixer, to be precise. Bingo! When patched and programmed correctly, the result looks just like PWM, as shown in Figure 3." "Synthesizing Strings: PWM & String Sounds" Gordon Reid, Sound On Sound, Mar 2003

Synthesis: Beating | Cross modulation | Footing | Noise | Periodic waveform | Program (synthesiser) | Pulsewidth modulation