This found a small number of real bugs too, for example,
this one that looked weird because of a 2to3 conversion,
but was wrong both before and after:
-        except IndexError as TypeError:
+        except (IndexError, TypeError):

And adjust the period locator accordingly.
Fitting \sin is the same mathematically, it's just conceptually more
straightforward since we're locating zero crossings anyway.

Just a little less code.  Same results.