Subject: Re: [linux-audio-dev] math question re. tempo changes
From: est_AT_hyperreal.org
Date: ti joulu 07 1999 - 18:22:02 EST
Eli Brandt discourseth:
>
> If Paul says this one is doing the right thing for him, great, and
> there was surely something troubling about finding a natural log in
> mine. But I'm confused.
No..you were right. :)
I think I correctly solved the integral you showed..but it didn't
match your commentary or end result.
Here's a rederivation complete with explicit u-substitution:
db/dt = start_tempo + (end_tempo - start_tempo) * b/section_length
k = (end_tempo - start_tempo)/section_length
db/dt = start_tempo + k * b
dt/db = 1/(start_tempo + k * b)
t(b) = integral 1/(start_tempo + k * b) db
= integral 1/(k * u) du (u = start_tempo + k * b, db = du/k)
= ln(u)/k
= ln(start_tempo + k * b)/k
E
This archive was generated by hypermail 2b28 : pe maalis 10 2000 - 07:23:26 EST