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