BUG: The tension parameter does not have the expected effect on the curve

Nobody has claimed this yet.

I thought that a higher "Tension" in automation curve should make it look more like linear progression, while a lower tension should allow a smoother transition between control points. Secondly, I expected this change to occur throughout the length of the curve.

But this is not so, as can be seen from the following samples:
This is the graph with the lowest tension:

This is the same graph, with the highest tension:

But in reality, the following unexpected things happen:
1. Only the left side of the graph is affected more. The right side is hardly affected.
This is as if we have put multiple nails on a board (where the control points are),
and then threaded a string around them.
As we pull the string from left, only its portion on the left experiences the pull.
2. Increasing the tension actually relaxes the curve, which becomes more rounded (instead of sharper).
3. With the highest tension, the graph does not resemble linear progression.

Reproduce the reported automation-curve behavior using the issue's low- and high-tension samples, then trace the automation curve implementation that computes tension across control points. Compare the resulting curve shape and extent with the stated expectations; done means tension changes affect the full curve in the intended direction and the behavior is covered by a regression check.

Written by the indexing model from the issue text.