D 2D
| 1 | 2 |
| | | | 1 |
|_____|_____|__|__|_____|_____
g___| |
{______|
a______| |
{____________|
So, why is g= ln(2) the best solution?
So far, we haven't scaled g, the ratio of the first "broken echo" to the
initial echo, but there is no need to keep that fixed for all allpasses/
echo generators.
In fact I believe that scaling g, possibly with ~0.382
will lead to families of optimal results for rooms
I have no proof for this though, but again its supported by data.
Replacing in the general formula
ratio a = 1 / (N+1-g)
with
ratio = 1/ (N+1-g^N)
Instead of g=ln(2) we use the simple original Go approach again where
g=1/2, we set
ratio= 1/ (N+1 -1/2^(N)) or ratio= 1/ (N+1 -2^(-N))
(wich expands with Laurent series as
1/(N(1+ln(2)) + ... ....)
and I think it is somewhere along such lines, scaling g=1/2 with each N
on a basis 1/2^x or 2^-x where ln(2) comes into play
We now should set N, which defined both the number of echoes and the
number of the nth echo generator, independently
1/ (N+1 -(1/2)^M)
and set the ratio in respect to the ratio of the next echo generator
(N+2 -(1/2)^(M+1))/ (N+1 -(1/2)^M)
or more general
(N+2 -g^(M+1))/ (N+1 -g^M)
where N is the number of echoes and m is the number of the echo generator.
I dont have any math skills to expand on this, and I would love to see
some one doing this.
Or see any other inside or discussion points.
Does anybody follow this?
Does any of this make sense to someone?
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