In the first part of this series, I used a sine wave to make a note. By changing the frequency of the note, I could make different notes and therefore a song, albeit a very boring one. The note sounded bland, a sine wave is just a pure note of one frequency.

Most instruments contain harmonics, notes that are mathematically related to the fundamental note. These harmonics give a note character. Each instrument sounds the way it does due to the way different harmonics are expressed. Compare a piano playing an "A" note with a violin playing an "A". It is the same note, yet they sound different. This is because there is a different proportion of harmonics from each instrument.

Let's change our sine wave to a saw wave, this is a wave-form that contains more harmonics and sounds different to the sine example above. 
This wave sounds different, let's have a listen:

Notice it has much more high pitched frequencies in it while still being the same note, some may describe it as a tinnier sound. This matches a lot of instruments better as it contains frequencies that they too posses in addition to the fundamental note. 

Imagine a string orchestra, there are may instruments playing the same note, to replicate this, we can make several copies of the saw wave and play them together. This alone however won't make the  sound of a bunch of strings playing, if you think, each string instrument won't be exactly in tune with the other. So I'm going to shift the pitch of each saw wave randomly a few cents (hundredths of a semitone) up and down. I will use five saw waves, each slightly out of tune with each other.

All of a sudden, this makes an interesting waveform, since the peaks don't quite fall at the same place due to the detuning, they combine and subtract in the way the waves of a string ensemble would. Have a listen:

It sounds closer to what a string ensemble would sound like, but it is still not quite right. This is because when you bow a violin, the sound doesn't suddenly play full volume, it almost fades into existence. This is where your volume envelopes come into play. But, t start with, let's just alter the attack of the instruments so they fade into being a bit gentler.

Again, each violinist will play slightly differently so I altered the attacks on each individual saw wave to simulate that.

So now we have a crude depiction of a group of instruments playing together. Many synthesisers can do this without all the work done above by altering the number of voices in each oscillator and detuning them for example in the free VSTi T-Force Alpha below:

This is only by using one oscillator, many synths come with two or three and so you can begin to imagine the depth of sound that can be created using all of them all. And that's before all the other filters and modulations that can be added, which will be described in the upcoming parts.