I'm trying to relate some different frequencies together in an experiment. Say I have 3 different frequencies, [itex] \omega_1,\omega_2, \omega_3[/itex]. Omega 3 is the large envelope, and the other two must fit inside of it, and so they are integer multiples of each other. Is there some way to express [itex]\omega_1, \omega_2[/itex] as equal approximately, or at least in terms of the third without having a mess of different constants? I've looked through some harmonic theory without much luck. All I've been able to think is(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

\omega_1 = n_1\omega_3\\

\omega_2 = n_2\omega_3\\

\omega_1 = n_3\omega_2\\

[/itex]

And just mix and match from there. What I would like though is for [itex] \omega_1\approx.\omega_2[/itex], maybe using a decomposition or something.

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