natalini wrote:

FM is endless possibilities. I was asking myself if their are some mathematical, physical formulas that can be use for fm operators alchemy ? For example the golden ratio .

Yes, there are. It's called the Fourier Transform of the waveform. In its most basic form, going back to the mathematician & physicist Joseph Fourier in the early 1800s, it's used to break down a simple wave, such as square or saw tooth into its sinusoidal harmonics. It can be done manually for VERY simple wave shapes such as square & triangular. But once you get past that it is exceedingly complicated and must be done numerically with a computer.

For an FM synthesizer such as the Montage, the Fourier Transform must be used within the parameters of the envelope, whether that envelope is 4 stage (ADSR) or 6 or 8, or whatever the particular synth is able to model. So, for example, you can't get it to talk (yet), because the envelope is never ending.

But a constant tone can be played, input to a powerful computer with a well developed Fourier analysis engine, and the component sine waves, with their frequencies, amplitudes, feedbacks, algorithms, and so forth, printed out and generated for replay. Depending on how good the computer modelling is, you will get back a good reproduction.

But there is a deeper problem: you can only play into the computer's microphone a sound you already have. Then of course you can fiddle with the waves & algorithms to generate something quite different. With the Montage, SY77/99, DX7, you can 'invent' your own inputs and get unexpected results that could then be massaged into something to your liking. That is the advantage of FM additive synthesis, so long as you are content with the given multi-stage envelope, your imagination is the limit.

You may be able to buy a computer program to do the Fourier analysis conversion to FM modelling using the key words; Fourier, FM, and Spectral Analysis. But I suspect the best of those programs are proprietary, not for sale, and not even written about.

Thanks for replay, what I understand is that the Fourier conversion could be use for modelling existing sounds. I was thinking in my question about mathematical formula the possibility to create entirely new universe. We know that our universe is basically made of frequencies, specially electro magnetics waves. For example an electric current can generates notes in a motor or transformer and will sing a perfect fifth. I guess if the fmx engine can be use for explore these fields. The dx7 was my second synth after the ms20 and I did some amazing complex sound but it was almost by chance, it was the time I had a lot of time.

The most likely place to find examples of mathematical stuff is probably in electroacoustic/computer music. E.g., John Chowning used the golden ratio to create his composition Stria, and I believe James Dashow has explored the harmonic potential of FM.

The amplitudes of FM generated partials vary according to Bessel functions, which have many other uses in physics.

Thanks for info.