# [PD] recirculating delay line reverberation time calculation

Claude Heiland-Allen claudiusmaximus at goto10.org
Mon Sep 1 16:39:59 CEST 2008

```Hi all again,

I think I found a reasonable solution, after reading around page 74 of
this document:

Introduction to Sound Processing by Davide Rocchesso

http://profs.sci.univr.it/~rocchess/SP/sp.pdf

----8<---- begin quote

In practice, once we have constructed a lossless FDN prototype, we must
insert attenuation coefficients and filters in the feedback loop. For
instance, following the indications of Jot [45], we can cascade every
delay line with a gain

g_i = a^m_i             // m_i is delay line length in samples

This corresponds to replacing D(z) with D(z/a) in (42). With this choice
of the attenuation coefficients, all the poles are contracted by the
same factor a. As a consequence, all the modes decay with the same rate,
and the reverberation time (defined for a level attenuation of 60dB) is
given by

Td = -3 Ts / log a      // Ts is 1/samplerate

----8<---- end quote

That gives a different attenuation for each delay, but such that the
"decay per sample" is constant for all of the delay lines, which makes
the reverb time calculations much easier!

gain_i = 10^(-3 * delay_i / reverbTime)

where delay_i and reverbTime are measured in the same unit (eg: ms).

Claude

Miller Puckette wrote:
> hi all,
>
> I don't think anyone knows the answer to this.  Traditionally, ever since
> Schroeder's reverberator, I think people have used delay times within a ratio
> of 1.5:1 of each other so that any old mean works OK.
>
> cheers
> Miller
>
> On Fri, Aug 29, 2008 at 10:07:30PM +0100, Claude Heiland-Allen wrote:
>> Hi all,
>>
>> Referring to Miller's book [1], and having experimented with various
>> delay times,  I'm wondering what the "average" delay time used in the
>> text is.  If all the delay times are close to equal, then using the
>> arithmetic mean as "average" gives me a reasonably accurate
>> reverberation time calculation.  But the more they differ the worse the
>> result is (comparing with measurement against my implementation).
>>
>> [1] http://crca.ucsd.edu/~msp/techniques/latest/book-html/node111.html
>>
>> Intuitively it seems that the sound recirculates more often (and is thus
>> attenuated more) through the shorter delay lines, but this is obviously
>> not taken into account with arithmetic mean.  I'm thinking something
>> like harmonic mean might be better (but I tried it and it wasn't a huge
>> improvement, nor was geometric mean).
>>
>> Any clarification would be enlightening, thanks,
>>
>>
>> Claude
>> --
>> http://claudiusmaximus.goto10.org
>>
>> _______________________________________________
>> Pd-list at iem.at mailing list
>> UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list

```