[LAD] Tempo change functions.

Hello all,

What exactly is meant by a linear or exponential tempo change ?
Is the tempo a lin/exp function of time, or of score position ?

A bit of algebra leads to this:

Let 

  t = time (seconds)
  p = score position (beats)
  v = tempo (beats / second) [1]

We have 

  v = dp / dt   # by definition


If v is a linear function of t, then

  v (p) = square root of a linear fuction of p


If v is a exponential function of t, then

  v (p)  = a linear function of p


if v is a linear function of p then
 
  v (t) = an exponential function of t   


If v is an exponential function of p, then

  v (t)  = inverse of a linear function of t


So there is plenty of room for confusion...


[1] Using SI units :-)  

Ciao,

-- 
FA

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