[brsrmbrz] Hydrogen times phi

To avoid harmonics, aliens (or humans) should broadcast (or listen) at the frequency of the hydrogen line times the golden ratio, not "hydrogen times pi" has mentioned in the movie Contact.  Phi is the most irrational number.  In contrast, pi is unusually close to harmonics at 22/7 and 355/113.  The frequencies of hydrogen times phi are, depending on whether one multiplies or divides, 2298.264784206 MHz and 877.8590324196 MHz, falling in the UHF band of microwave radio.

For frequencies more at human scale, divide by some high power of phi.  Phi^44 yields 1.1 seconds.

Or divide the Planck frequency by some high power of phi.  Planck time multiplied by phi^207 yields 0.98 seconds.

Or, broadcast gravitational waves.  It is vaguely possible that some natural process causes harmonic coupling between EM radiation and gravitational radiation.