programming chord shapes into FM patches

I'm wondering if there are any mathy people in here who can help me out with this, or if someone can point me in the direction of a text that deals with this directly.

What I'm trying to do in its simplest form:

2 operators.

A modulator is acting on a carrier, the carriers ratio is 1 and the modulators ratio is 1.####.

The decimal values form a chord so that the root and the interval above are both heard when playing one note. I would like to have a list of ratios for all 12 chromatic positions within one octave. Right now I can only use my ear as an approximation which is non-negotiable.

I've seen this done well in a few FM presets on different systems but I've never seen anyone talking about the technique.

you mean to get a harmonic in there that sounds like a chord?

12-tone equal temperament ratio = interval ^ (2/12)

But unless you like nasty wobbling you might be better off using just intonation to tune your operators.

Also sidebands are good to think about in terms of FM and operator frequency interaction.

you want to know the right frequencies of the modulator osc so that it's on tune with the frequencie you have on your carrier osc???

if so, i want that too :)

what i do in max is that i control the modulator osc freq. with a midi keyboard so, even if it's not not quite on tune with the carrier, the relation between every semi-tone in the modulator is always correct, giving the "right" impression when playing a scale...-

do't knwo if i'm making any sense at all :)

  On 3/27/2012 at 5:02 PM, slightlydrybeans said:

you mean to get a harmonic in there that sounds like a chord?

exactly

The great thing about FM synthesis is that the harmonic sidebands that develop are mathematically predictable.

I've attached a text by John Chowning, who formalized FM Synthesis. In it should be all of the information that you need to generate the precise harmonics you need, provided you're down to put a little work in to achieve it.

FM Theory and Applications - John Chowning.pdfFetching info...

the sidebands created are the sum and difference of the program oscillator and the carrier oscillator. harmonically related program and carrier creates harmonically related side bands. . as the index of the carrier is increased the number of sidebands also increases.

I think what you want to do is mix sinewaves like in additive synthesis. thats the way to control what you want.