Subject: Re: [linux-audio-dev] math question re. tempo changes
From: est_AT_hyperreal.org
Date: ti joulu 07 1999 - 19:06:08 EST
Ack..I forgot the constant of integration which makes it:
t(b) = ln(start_tempo + k * b)/k - ln(start_tempo)/k
E
est_AT_hyperreal.org discourseth:
>
> 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
This archive was generated by hypermail 2b28 : pe maalis 10 2000 - 07:23:26 EST