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In SETI, when searching for "beacons" -- transmissions intended for us and meant to get our attention -- one must guess the appropriate frequency to search by considering what frequencies would be universally obvious to other species. This is a well known concept in game theory, where such solutions to a non-communicative cooperative game (such as a mutual search) are called "Schelling points." It is noteworthy, therefore, that when developing his eponymous units, Planck called them "natural" because they "remain meaningful for all times and also for extraterrestrial and non-human cultures." Here, I apply Planck's suggestion in the context of Schelling points in SETI with a "Planck Frequency Comb," constructed by multiplying the Planck energy by integer powers of the fine structure constant. This comb includes a small number of frequencies in regions of the electromagnetic spectrum where laser and radio SETI typically operates. Searches might proceed and individual teeth in the comb, or at many teeth at once, across the electromagnetic spectrum. Indeed, the latter strategy can be additionally justified by the transmitter's desire to signal at many frequencies at once, to improve the chances that the receiver will guess one of them correctly. There are many arbitrary and anthropocentric choices in this comb's construction, and indeed one can construct several different frequency combs with only minor and arbitrary modifications. This suggests that it may be fruitful to search for signals arriving in frequency combs of arbitrary spacing. And even though the frequencies suggested here are only debatably "better" than others proposed, the addition of the Planck Frequency Comb to the list of "magic frequencies" can only help searches for extraterrestrial beacons.