Fwd: Tempo changes [was Re: ]

I just noticed that I sent the following test results on March 1st in 
response to a private message when I thought I was publishing them.  The 
input values labeled "Nominal" were given to me in that private message.

-----

LilyPond 2.25 accepts exact rational tempo values.

     \score {
       \fixed c' {
         \tempo 4 = #70000000/1000000
         c8
         \tempo 4 = #71190000/1000000
         c8
         \tempo 4 = #72400230/1000000
         c8
         \tempo 4 = #72523300/1000000
         c8
       }
       \midi {}
     }

These are the MIDI tempo values in microseconds per quarter note (µs/q) 
that LilyPond emits for the above input, according to the lilymidi tool. 
  I computed and rounded the quarter-per-minute (qpm) values.

     Nominal     MIDI µs/q    Approx qpm
     --------    ---------    ----------
     70             857142    70.000070
     71.19          842815    71.190000
     72.40023       828726    72.400287
     72.5233        827320    72.523328

This seems as precise as it could be.

It also seems as accurate as it could be, aside from truncating the 
final division rather than rounding it.  Truncation should please those 
who deem ending the presentation late a greater sin than ending early.
-- 
Dan