In Ancient Greece, law-givers were outsiders to politics. Their only job was law and to create laws that were fair / metered / just. Somehow I think their ability to sing – to bring through them the muse’s inspiration for even-measured laws – but I’m not totally sure.
We don’t have a similar position in the modern world that I can think of.
This is around the time of Solon, after Draco (where “Draconian laws” come from and whose laws were NOT measured and even handed) around 7 BC I think. Solon is credited as the start of democracy.
Good law and music both metered and measured, although parallel courses and music came centuries earlier. There’s a rhythm to law, a ratio to law, just as there is in music. It’s a analogous link, not a cause-effect link but it’s clearly inspired.