Re: [music-dsp] Reverb, magic numbers and random generators #2 solution?

[Scott Gravenhorst]

music-dsp@music.columbia.edu wrote:
>             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?

I am, with great interest.

>Does any of this make sense to someone?

Well, no but that's my fault.


-- ScottG

-- Scott Gravenhorst
-- http://scott.joviansynth.com/
-- When the going gets tough, the tough use the command line.
-- Matt 21:22

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Re: [music-dsp] Reverb, magic numbers and random generators #2 solution?

[gm]

    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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Re: [music-dsp] Reverb, magic numbers and random generators #2 solution?

[gm]

Am 02.10.2017 um 04:42 schrieb Stefan Sullivan:
Forgive me if you said this already, but did you try negative feedback 
values? I wonder what that does to the aesthetics of the reverb.


Stefan
yes... but it's not recommended for the loop unless it's part of a 
feedback matrix

you get half the modes and basically a hollow tone by that
you can use negative values an the AP coefficients as well which can 
sound quite different

- in reality every reflection is an inversion though
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Re: [music-dsp] Reverb, magic numbers and random generators #2 solution?

[Stefan Sullivan]

Forgive me if you said this already, but did you try negative feedback
values? I wonder what that does to the aesthetics of the reverb.

Stefan


On Oct 1, 2017 16:24, "gm"  wrote:

> and here's the impulse response, large 4APs Early- > 3AP Loop
>
> its pretty smooth without tweaking anything manually
>
> https://soundcloud.com/traumlos_kalt/whd-ln2-impresponse/s-d1ArU
>
> the autocorrelation and autoconvolution are also very good
>
> Am 02.10.2017 um 00:45 schrieb gm:
>
> So...
> Heres my "paper", a very sloppy very first draft, several figures and
> images missing and too long.
>
> http://www.voxangelica.net/transfer/magic%20numbers%
> 20for%20reverb%20design%203b.pdf
>
> questions, comments, improvements, critique are very welcome.
> But is it even worth to write a paper about that?, its just plain simpel:
>
> The perfect allpass and echo comes at *1/(N+1 -ln(2)).*
>
> Formal proof outstanding.
>
> And if you hack & crack why it's 1/(N+1 ln(2)) exactly you'll get 76.52 %
> of the fame.
> Or 99.% even.
>
> Imagine that this may lead to perfect accoustic rooms as well...
> Everywhere in the world they will build rooms that bare your name, for
> millenia to come!
> So, yes, participate please. ;)
>
> I assume it has to do with fractional expansion but that paragraph is
> still missing in the paper.
> I have no idea about math tbh.  but I' d love to understand that.
>
>
>
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Re: [music-dsp] Reverb, magic numbers and random generators #2 solution?

[gm]

and here's the impulse response, large 4APs Early- > 3AP Loop

its pretty smooth without tweaking anything manually

https://soundcloud.com/traumlos_kalt/whd-ln2-impresponse/s-d1ArU

the autocorrelation and autoconvolution are also very good


Am 02.10.2017 um 00:45 schrieb gm:

So...
Heres my "paper", a very sloppy very first draft, several figures and 
images missing and too long.


http://www.voxangelica.net/transfer/magic%20numbers%20for%20reverb%20design%203b.pdf

questions, comments, improvements, critique are very welcome.
But is it even worth to write a paper about that?, its just plain simpel:

The perfect allpass and echo comes at *1/(N+1 -ln(2)).*

Formal proof outstanding.

And if you hack & crack why it's 1/(N+1 ln(2)) exactly you'll get 
76.52 % of the fame.

Or 99.% even.

Imagine that this may lead to perfect accoustic rooms as well...
Everywhere in the world they will build rooms that bare your name, for 
millenia to come!

So, yes, participate please. ;)

I assume it has to do with fractional expansion but that paragraph is 
still missing in the paper.

I have no idea about math tbh.  but I' d love to understand that.



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Re: [music-dsp] Reverb, magic numbers and random generators #2 solution?

[gm]

Am 02.10.2017 um 00:45 schrieb gm:


Formal proof outstanding.

sorry, weird Germanism, read that as "missing" please
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Re: [music-dsp] Reverb, magic numbers and random generators #2 solution?

[gm]

Am 01.10.2017 um 18:35 schrieb gm:

Counterintutively, there is no solution for g=a for N =2 (except g=a=1);
(the solution for g=a and N=3 is 1/golden ratio )

make that phi^2 = 0.382..ect


For those who didnt follow, after all this I now postulate that

*ratio = 1/ ( N - ln(2) +1) *

with N = number of the allpass delay and ratio the allpass delay length 
ratio in respect to the loop delay


gives the ideal ratios for the smoothest reverb response for allpass 
chains and allpass + delay loops for example like in the combined structure:



[APn]->...->[AP5]-->[AP4]--+-->[AP3]-->[AP2]-->[AP1]-->[Delay]--->
^   |
|   |
<

while other ratios that follow

Na mod 1 = a*g
a = 1 / (N-g)

(lower series)
or

Na mod 1 = 1- a*g
a = 2 / (N + g)

(upper series)

with N the number of the nth impulse and g the times scaling of the 
impulse in respect to the first delayed impulse


are still of interest, for instance with
g = 1/2 and a1,2,3... = a1,2,3... *detunefactor 1,2,3...
and g = 1/golden ratio squared (0.382..)
where an additions of reziprokals like a = 0.5 for the g= 1/2 series or 
a combination

lower and upper series are also possible.

Can some ome explain the result for g = ln(2) and ratio = 1/ ( N - ln(2) 
+1) to me?

Or give a better formula or value?



BTW it doesnt mean it's the "best" reverb, musically, but it seems give 
the smoothest values
For shorter reverbs other values for instance the mixed series with 
~0.5, ~2/3, ~4/5 pluse detuning migt be better.













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