The curvature of a harp

Factual Questions
1

Here’s a harp:

Wikipedia is hosting that pic, so if someone changes it, here’s a Google-Images search for “harp” that’ll show you lots of similar examples.

My question concerns the curvature of the brace holding the top ends of the strings. Why are there inflection points part way from the bass strings to the, um, short strings? The brace curves more and more steeply downward, then halfway to the short strings the trend reverses and the brace starts pulling out of its dive, even to the point of regaining height. And then, very close to the player’s head, there’s another inflection point where the brace reduces its rate of climb just a bit. The varying thickness of the brace along its length accentuates this a bit, but it’s still apparent even if you look at the curve traced out by the string anchor points.

It seems like one should expect a curve with no inflection points from one edge of the harp to the other.

2
3

If all of the strings were the same density and tension, then you’d want an exponential shape, with the length doubling every octave.

Exponential shapes get impractical pretty quickly, so they do vary the density and tension of the strings. But there are also limits on how much they can vary both of those. So there’s still a vestige of the exponential shape, there.