Making Music
  Computer Music Software and Hardware

Look at that wave

A handful of waveforms are commonly used in synthesis, each with a distinctive wave shape and sound.

The simplest is the sine wave which we've already looked at which consists only of a single fundamental frequency.

It is often used for flute and drawbar organ sounds.

A sawtooth waveform contains all harmonics in inverse proportion to their number - with all these mathematical relationships you know something 'natural' is going on. So the 2nd harmonic is half the amplitude of the fundamental, the 5th harmonic is a fifth the amplitude and so on.

Being so rich in harmonics, sawtooth waves are commonly used for brass, strings and some woodwind sounds.

The square wave contains only odd-numbered harmonics in the same proportion as in sawtooth waves.

It produces a 'hollow' sound and is typically used for clarinets and reed instruments.

Triangle waves contain only odd harmonics, as with square waves, but at much smaller amplitudes. In fact - yes, it's more maths - the relationship is the square of the harmonic number. The 3rd harmonic has an amplitude one ninth (3x3) of the fundamental, the 5th has an amplitude of 1/25th (5x5) and so on.

Although triangle waves do contain harmonics, they are not very dominant and triangle waves sound very sine-like. Some synthesisers dispense with a sine wave in favour of a triangle waveform.

Mark this space

One of the most interesting waveforms is the pulse wave because the wave can be changed to alter its harmonic content. It looks like an offset square wave. Whereas in a square wave the upper and lower sections of a cycle are the same - square - in a pulse wave these can be varied. Technically, the upper part is called the 'mark' and the lower part the 'space'. Synth controls for adjusting them are called 'pulse width' or 'mark/space ratio' controls.

The term 'pulse width' is more intuitive but 'mark/space ratio' helps us understand what harmonics are in the wave. The mark/space ratio isn't actually a ratio between the mark and space widths but a ratio between the mark and the complete cycle. So, a square wave has a mark/space ratio of 1:2 and the mark is half of the cycle. A ratio of 1:4 means the mark width is 1/4 of the cycle, a ratio of 3/4 means it is 3/4 of the cycle and so on.

Now, a feature of pulse waves is that harmonics that are multiples of the right-hand ratio number are absent. The square wave with a 1:2 ratio has no even harmonics - harmonics 2, 4, 6, 8, 10 and so on are absent. A mark/space ratio of 1:3 would have no harmonics that are multiples of 3 - 3, 6, 9, 12 and so on.

As a pulse wave becomes narrower it becomes thinner and takes on a nasal quality. It is commonly used for oboe and harpsichord sounds.

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