Maths vs. Music - Tuning and harmony

[Thumpalumpacus]

Without a reference pitch handy, the last really noticeable change for me was around 32 seconds.

Same here.
The way I, and probably everybody, detects one sound as being out of tune with another is the dissonant waves.

So I wonder if it would be easier to detect a sound that is getting closer to the original sound, if you know what I mean.
You would hear a fast wave length that gradually reduces.
I find it hard to put into words.

I think Benny has it right, that it's much, much easier to use the harmonic discrepancies in a dyad or chord than it is to identify a continuous change in a single note once it starts climbing the asymptotic hill, so to speak.