# Pulse wave

## Overview

Audio: pulse wave (0:02)

pulse wave plays a pulse wave. The pulse wave figure shows the waveform of a succession of pulse waves called a pulse train.

A pulse wave consists of a harmonic series of partials in which the sound is determined by the frequency of the fundamental and by the duty cycle.

The frequency of the fundamental in a pulse wave determines how often the pulse will sound. For example, a pulse wave with a fundamental of 1Hz will make a sound once every second.

The duty cycle determines how long the pulse is on active duty, how long the sound lasts, in other words. Duty cycle is the ratio between the duration of a pulse sound and its wavelength. It can be expressed as either as a fraction or as a percentage. For example, a pulse wave with a duty cycle of 1:3 (33.33%) will make the pulse sound for one third its duration, for the remaining two-thirds of the time the pulse will be silent.

The duty cycle determines the width of the pulse. A high duty cycle produces a wide pulse wave with a distinct rectangular shape. A low duty cycle narrows the width of the pulse and changes its shape from a rectangle to a spike.

The duty cycle also determines the number of partials present in a pulse wave. A duty cycle of 33.33%, for example, produces a group of three repeated partials in which the first and second partials are present but the third partial is absent: 1 (the fundamental) 2 4 5 7 8 10 11 and so on, the partials 3 6 9 12 and so on being absent. The duty cycle also determines the amplitude of the partials although this is a tricky calculation involving a mathematical sinc function. Suffice to say that, the lower the duty cycle, the more partials there are, and the lower their amplitude compared with that of the fundamental.

pulse wave has a fundamental frequency of 20Hz and a duty cycle of 2%. A 20Hz fundamental produces a pulse wave that repeats twenty times every second. A 2% duty cycle produces 49 partials from 20Hz up to 980Hz, the fiftieth partial, 1000Hz, being absent, followed by another group of 49 partials starting at 1020Hz. The 20Hz fundamental means the wave pulses every 50ms and the duty cycle of 2% means the pulse sound lasts only 1ms, for the remainder of the 49ms it is silent.

A pulse wave is a complex and versatile sound. A pulse wave with a variable duty cycle causes the width of the pulse to vary, and the technique, known as pulse width modulation, is a feature in classic hard synths. The pulse wave synth can be used to write melody and harmony and it produces a surprisingly rich sound.

A pulse wave with a low fundamental and a low duty cycle is excellent for writing effects because its sound is rich in frequencies. An alternative name for a pulse wave in music programmes is buzz, because it has a buzzy sound. Another of its names is blip, because a pulse train sounds like a series of blips. A pulse wave is used to write all sorts of harsh and hollow effects that sound like buzzers, blips and pulses.