Re: [sc-users] Re: Resonz x Ringz (gain issues)

[Julius Smith <jos@xxxxxxxxxxxxxxxxxx>]

At 01:10 PM 12/21/2014, Alexandre Torres Porres wrote:
> ...
> There's still one thing that still intrigues me and that I'd like to ask
> the list here. Now that the math is worked out, the issue is more about
> understanding the concept of the "60 dB decay
> time".

We normally call it t60, and it depends only on R, not
resonance-frequency or gain.

> In my first message, I've showed
> how to convert to "decay time" from rq and vice-versa (given
> some frequency). In the code we see how this parameter along with
> frequency define "R".

R does not depend on frequency.

>  But in the context of
> Ringz, a so called "decay time" depends a lot on the gain
> parameter, as I see it.

Gain is often set to compensate the total energy.  A longer t60
means more energy in the impulse response, unless gain is changed to
compensate.

>  And "R" doesn't
> really define the gain parameter in Ringz. It is fixed to
> 0.5.

Yes, the gain compensation is optional.

> On the other hand, R defines the
> gain parameter in Resonz, 

I would rather say gain is chosen as a function of R.

> which always shifts according to
> both frequency & rq.

R does not depend on frequency.

>  And of course, this gain
> parameter is a lot smaller than 0.5 (so Ringz is much louder as I pointed
> here in the first message).

Right

> So now I can calculate exactly
> how much louder Ringz is. But I still do not get how "dt"
> (decay time) actually defines an exact time the filter takes to decay
> 60dB. You see? I mean, if "dt" is relates to both rq and
> "freq", shouldn't "dt" also affect the gain parameter
> like "rq" and "freq"?

I tried to state this conversion formula in my first reply (but didn't
test it, or even write down the exact version, because I was trying to do
everything in my head).  If you can derive the approximate formula I
gave involving 6.91, then you are there.

> I wonder it there's the case
> where saying this is a "60 dB decay time" parameter is not
> really accurate. In which case I hope this is corrected in the help file
> soon.

Right - Ringz defines R based on t60, so "60 dB decay time" is
right for it.  Resonz defines R as 1 - B/2, where B is bandwidh in
some units, so R is NOT defined to set t60.  By the way, I see a bug
in my first email: pi * BandwidthInHz * SamplingRateInHz makes no sense
(wrong units).  It is most likely pi * BandwidthInHz /
SamplingRateInHz, so then "radians per sample" would really
mean "pi times seconds per sample", which is pretty strange,
but pi * B / samplingRateInHz is commonly used for this situation. 
It comes from mapping 3dB bandwidth from the s plane to the z plane (not
from t60 considerations).

> Obviously I can also be just
> completely blind and ingnorant on what the "60 dB decay time"
> parameter is and works. And if so I hope you can help
> me.

It works (t60 = decay time), and 1/t60 is approximately proportional to
any reasonable definition of bandwidth, but to precisely convert Ringz's
R to Resonz's R, you need to use the conversion formula I outlined (the
approximate version may be good enough to sound the same).  If you
have trouble deriving it, let me know and I'll go find a pen and piece of
paper. :-)

- Julius

Julius O. Smith III <jos@xxxxxxxxxxxxxxxxxx>
Professor of Music and, by courtesy, Electrical Engineering
CCRMA, Stanford University
http://ccrma.stanford.edu/~jos/