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The old code used the instantaneous tempo at T0 to compute where the next quarter note would be. This is incorrect, since the tempo is changing (continuously, for now) during the time represented by that quarter note. Instead, we need to add a quarter note (or technically, whatever the tempo note type is) to get a new position in beats, then compute the superclock time at that location (which will use our equations for tempo, including the use of omega, the ramp factor).
Please see the Ardour web site at https://ardour.org/ for all documentation..
For information on building ardour:
https://ardour.org/development.html