You might want to consider how the moons appear from the planet. "Magic" might be the easiest explanation, as it means that all three moons could orbit at the same length and appear the same size without crashing into each other. In order for all three moons to orbit at 1:2:4 and appear the same size, they would need to be increasingly large in comparison to each other. The furthest moon would be four times the size of the closest moon, or the same size as the planet! (Using standard Earth-Luna comparisons)

By contrast, if the three moons were all the same size, or if only the closest one were as large as Earth's moon, then there would be a distinct difference in appearance between the three. The second moon would appear tiny in comparison to the closest, and the furthest away would probably look like an exceptionally bring lantern when compared to the closest moon. (You could view it clearly with a telescope, of course, but you can view a lantern clearly with a telescope as well.) Note that only the closest moon would have an eclipse as we see on Earth. The second moon would probably produce a visible disk, but not darken the daylight beyond some dimming similar to light clouds. The furthest moon might not even have a recognizable difference during its eclipse.