What all this depends on is the principle of superposition of waves. I would go and explain it, but there's a much better site here.

http://www.kettering.edu/~drussell/Demos...ition.html
The animations show things perfectly. Ignore the complex maths - what you need to know is that AT ALL INSTANTS, all the waves we're using add up. So if the signal is below the line, you are adding a minus number (ie subtracting).

What's important here is that in all cases the frequencies are the same,

apart from the last one regarding 'beats'.

Anyone who has ever tuned a guitar a few times knows this idea - you tune them until the 'pulsing' disappears, as that means they are perfectly in tune. When they are out, the two waves are going in and out of phase - so sometimes they 'pile up' (constructive interference, sometimes they 'defeat each other' (destructive interference). But what if we want things to be a little bit 'wobbly', the opposite of this?

Well, you turn that around - say we have two oscillators in our synth, both sine waves. You can create a modulating sound simply by detuning them against each other. This gives you a wobbliness - great for starting off some sort of sound for a tune.

This wobbliness is at a constant rate - sometimes desirable, sometimes not.

Question - How do we change the 'wobble rate'? And how can this be useful for synthesis?

This is just sine waves adding up/subtracting. What about waveforms that have more to offer?

dionysus Wrote:Every sound can be made up of sines

IS made of up sines.

This is Fourier's theorem.

Believe me, the maths is FUCKING HARDCORE, so we won't go there (I can't do that shit any more

).

What a thing like Voxengo SPAN or Waves PAZ analyser does (theoretically) is split the signal into its constituent frequencies - which are all sine waves - then display the amplitude/strength of each sine wave as a graph.

In practice it's not quite like that, due to various complicated physics issues, and also the fact that splitting it up into 22050 individual bands requires a LOT of CPU power and a fucking huge monitor if you want to see every individual band

It's also pointless as no eq I know of can boost a single specific frequency. And THAT is disregarding anything but integer Hz values... you get the drift

Anyway - I am aware I am going round the houses here btw - the point here is that when you analyse any sound, it is made of lots of sine

waves of different frequencies added together. This is a very useful fact!!

Let's turn this around.

If we want to achieve/create a specific sound, it must be possible to 'pile up' sine waves of certain frequencies in order to achieve the spectral distribution we want, right?

Well, yes pretty much. This is how

additive synthesis works, simply speaking.

Obviously some sounds are extremely complex, with certain 'partials' (bits of the sound being added) going in and out and up and down and so on - and there are limitations to what technology can do.

FAR more common is the opposite - subtractive synthesis.

What this does is start with a wave form that has lots of sine waves contained in it, all added up. Prove it to yourself - get your fave synth and turn everything except the oscillators off. Set those to a triangle or square wave, and view the output in a spectral analyser. Lookee there - it's made up of lots of frequencies. These are known as

harmonics as they are related to the lowest (or fundamental) frequency by a strict mathematical formula.

Here's a sawtooth wave;

Then what we do is filter away the component frequencies we don't want. So if we want a 'darker' sound, we use a lowpass filter to remove the higher frequencies, or a highpass to take away the lows if we want it 'thinner'. We can also have the filter change in frequency throughout the note, giving an 'evolving' sound (wwwooooowwwww

)

Now a sawtooth wave through a filter is - frankly - not very exciting

The trick with subtractive synthesis is to put a very interesting sound in in the first place.

One way of making the initial sound more interesting is by - you guessed it - detuning two of them! Then they add up and subtract all the time, giving a wobbly variation to the sound.

This is some (fairly unfocussed, sorry) basic background on things to take into account when synthesising. In short;

1) Waves add up - any wave is made of constituent sine waves (Fourier's theorem)

2) We use this fact to our advantage

3) We subtract what we want to

2) is where the action is. We'll get more into that when I don't have to go and practice my cornet.