Are square, sawtooth, triangle, etc really just made up of a bunch of sine waves? In other words, there can be no wave in the form of a rectangle, its really just a bunch of sine waves in the shape of a rectangle wave?
If true, on a typical synth, like a roland juno 6 for example, around how many sine waves do they use to make a rectangle wave sound?
I’m not sure about the sawtooth etc, but a square wave can certainly be made by adding many sine waves together. One sine wave would be at the fundamental frequency of the square wave and then other sine waves at harmonic frequencies are added in ever decreasing amounts as the harmonic frequency moves further from the fundamental. I theory it takes an infinite number of sine waves to produce a perfect square wave. It’s this multiplicity of harmonic content that makes the square wave sound ‘crunchy’. A synthesiser that uses additive synthesis would make a square wave in this way, but there are other means of generating a square wave using electronics that do not depend on sine wave addition.
On further reflection, yes, the principles of a mathematical process called Fourier synthesis (or in reverse Fourier decomposition) mean that it must be possible to construct all periodic functions, sawtooth, triangle etc, from sine waves. Fourier synthesis is way too complex to go into here. I used it in another life to create square waves which is why I jumped on that first. Again though, there are other methods that the electronic circuits of a synthesizer may use to create such waves, not necessarily by adding sine waves.
Since you mentioned the Roland Juno series specifically, famous for their DCOs (digitally controlled analog oscillators) you may find this useful as it explains how those DCOs generated the various waveforms available on the Juno series.