I don’t think any of the notation software can do that. I wonder if it can be done in a DAW, or something like Audacity?

I wouldn’t expect it to ever show up on Finale, although you could write it up as a feature request.

Carl Collins,

The following is not exactly what you are asking for, but it is a feature that Finale has already:

For a Measure Number Region you can choose the style ‘Time’

This is done in the dialog box Measure Number, in the pop up menu Style.

PeterT,

I thought of that but it will only show a place in time not a length in time of each measure. Perhaps that in conjunction with a non-standard time sig could work if all measures are to be the same length.  Pretty tedious if they are not. The times sig could be hidden.

it appears to me that you may be overthinking this. Concentrate on the goal instead of the method and something simpler should present itself.

The math shouldn't be that difficult. Find a common denominator that accommodates all of your timings. Although one second is obvious, can you make 10 or 20 seconds work? If 20"=whole note, then 10"=half, 5"=quarter, 1.25" = sixteenth and so on. If 16" = whole, then 1" = a sixteenth. Ok, that's a slow tempo but the formula is easy to calculate. For faster rhythms, break your 2'5" measure into sub measures using dotted bar lines. All you have to do is set a metronome mark and write your piece. You don't even have to hide your time signatures in sub measures unless you want to—with faster rhythms, time signatures will make it easier to count.