How about a clock where day and night each take one full half, regardless of the time they take. So the hands would go very fast in northern countries during th

How about a clock where day and night each take one full half, regardless of the time they take. So the hands would go very fast in northern countries during the day and very slow at night. What unit should one use for such a clock? Is there something more intuitive than the hour for this? Maybe the angle of the sun/moon in the sky, 0 to 180? Edit: Silly idea: If this post gets traction it would be fun if we each made up our own clock.