Perhaps it would make sense to reverse time from bottom to top. Right now it reflects the standard flow of time, forward, like on a watch. But in reality, our time is only running out.
When you have a timeline going from top to bottom, it feels like it will keep going further, but if you reverse it, you see what's left — without illusion.
(Hope this doesn't sound wrong. I believe the "trimming hangnails" is an important and often overlooked job.)
I guess the "natural" base to use to get the "right" number of increments is a pointless exercise, since it ultimately bottoms out in the question of "why is a regular year as long as it is?", but if we assume a base of 2, I'm currently in my 6th log year, and hope to die comfortably into my 7th. Actuarial odds are >80% in my favor.
Extending the music analogy, we could call those powers of two "octaves", and divide it into twelve exponentially-spaced steps (i.e. 2^(years/12)).
The break even is about 75 steps (i.e. six octaves and three steps), which is about 76 years, since 2^(75/12) = 76.1.