Voussoir arches were circular back in Roman times, since then, other shapes have been used. The pointed arch was invented so that church vaulting arches of different spans could meet at the top. This avoided the complex (in stone at least) intersections of circular arches.
Later, for aesthetic reasons, cycloidal and elliptical arches were used. Brunel build a notorious elliptical arch at Maidstone which many people thought would fail. It is still carrying rail traffic to this day.

Parabolic arches really only came into their own since the introduction of reinforced concrete.

As a side issue, the arches used by the Marsh Arabs to construct their Mosques of rushes, appear to be either parabolic or elliptical.

And GUEST, if you care to read the thread in it's entirety instead of going off half cocked you will find some musiacl references.