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In the English translation of Plato's Republic, he does not allow flutes to be played because they are used to play "panharmonic scales", and he says that no panharmonic scales should be played or allowed.
(He's making a metaphorical "perfect" society, and he says that panharmonics enable people to play sad music. He thinks people should only play perfect and happy music because there's no sadness in his republic.)
What is a panharmonic scale? What does it sound like?
It's not a scale per se. In Republic, Plato makes an argument that only certain modes are really worth anything: the Dorian and Phrygian.
GLAUCON: No, never. So it looks as though you have got the Dorian and Phrygian left.
SOCRATES … Leave me these two harmonies, then—the forced and the willing—that will best imitate the voices of temperate and courageous men in good fortune and in bad.
Others like the mixolydian "are even useless for helping women to be as good as they should be, let alone men."
If you are going to stick to these modes, then you need to stick to instruments like the lyre and kithara that are tuned to a particular mode (he also allows pan-pipes for the shepherd).
The flute, along with lutes and harps, can freely play any note anytime the performer wants. They are panharmonic — or sometimes translated as multi-stringed meaning they are no bound to any particular mode. In the eyes of Plato it's better not to have them at all so as not risk the drunkenness, softness, idleness, and all manner of vices other mode incite.
