Bug? Song tempo automation inaccurate?

[marcusgraf]

I have stumbled upon a potential inaccuracy in Ableton's tempo automation.
The time that has passed after applying a tempo automation is not what one would expect.

Here's the example:
I have created a track that slows down over 4 measures from 150 to 50 bpm using a linear fade.
When exporting the sound file and also looking at the sequence time, I get results that are not what I have expected.
The total time that has passed at measure 5 is different to when I try the same in Cubase. Also, when I try to calculate this mathematically, I get the same results as in cubase. The difference between Ableton and Cubase is already 100 milliseconds after 4 measures.

It suggests that either Ableton is not doing a real linear interpolation by design, or that it's a bug...?

See my results below:

Code: Select all

Measure			1	2	3	4	5
Beat			1	5	9	13	17
Time	(Ableton)	0	1.740	3.867	6.604	10.447
Time	(Cubase)	0	1.750	3.892	6.654	10.546
Time	(calculated)	0	1.750	3.892	6.654	10.547

To calculate the time that has passed, one has to calculate the area under the timestep curve.
To do so, use the following function:

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time = beats * 60 / (endBPM-startBPM) * log (endBPM/startBPM)

Is there a reason that Ableton is deviating from the correct mathematical approach?
And did anyone else encounter this inconsistency?

Update:
It seems that Ableton changes its tempo on every 16th note, not continuously. When changing the tempo on every 16th note, we actually get the time values that I have described above.