**ELECTRIC OPRPHEUS ACADEMY**

**SPILLING THE BEANS #1****REVERBERATION**

If one has the possibility of a large, holistic FFT ('giant') and no
real-time context is prescribed, reverberation is a simple matter. It
confines itself to the method of 'convolution'.

Two things are required: the sound that one would like to reverberate
and the pure reverberation function (impulse response) - likewise a sound.
Both sounds will be transformed in their individual spectrum; the spectra
will be modulated with each other (multiplied sample by sample), and the
result will be inversely transformed. Finished. In the VASP script it
looks like this:

A:

sfload zuverhallenderklang.wav **"load the sound in buffer
A **

FFT **"Fourier transformation**

B:

sfload raumklang.wav **"load the spatial sound in buffer
B**

FFT **"Fourier transformation**

vmul **"multiply B by A **

FFT- **"inverse transformation**

play

At first glance, it is apparent that the two components - sound and spatial
sound - are somehow equal. If one 'reverbs' Sound A with Sound B, or vice
versa, the result is the same. Since the actual link vmul
is a multiplication, and A*B is the same as B*A.

Actually, the process is 'commutative' and opens the general possibility
to arbitrarily merge two (or even more) sounds in this way. The result
will, as a rule, have a 'spatial' effect. To what extent one perceives
it as reverberation in the proper sense depends only on the character
of both components.

To identify one of both components as spatial sound (SS), a few simple
conditions have to be fulfilled:

1) SS should be relatively dense, containing
many frequencies

2) SS should have a fading progression that is not too long

3) SS should become dulled in the progression.

Naturally, one can tinker with it endlessly, get lost in the intricacies,
can recreate the acoustics of famous halls, for real-time and with moveable
positions...

It is also done like this. For the experimental work, however, rather
the systematics behind it are valuable, as well as the aspect that one
can incorporate 'space' as an integral musical element. A whole dimension
opens up here!

In this sense, a basic method of how one can derive a typical spatial
sound from a musical motif.

In the following example, a homogenous density will be brought about by
a freeze; the decay by an envelope; the reduction of the high frequency
components by a variable filter. In the VASP script it looks like this:

sfload motiv.wav

FFT

phirand

FFT-

shape.attdec 1.5sec,3.5sec

lprun.fade 6sec

Explanation:

The best and most homogenous freeze (with a natural pulse, without granular
crumbling is achieved by substituting the phases of the individual samples
in the spectrum with random values. This is done by the function phirand.
All frequencies are preserved, but are detached from any comprehensible
temporal connection - precisely a freeze. (There is even a possibility
to retain the panorama of all frequencies if it involves a stereo sound,
namely through the function xphirand).

shape.attdec applies an envelope with a logarithmic attack and an exponential
decay, in this case, 1.5 and 3.5 seconds.

lprun is a controllable low pass filter, which has several modes. The
mode .fade is the most suitable one for this purpose. The cutoff frequency
of the filter begins with the limit frequency and sinks in the indicated
time following a distance function to 40Hz.

* * *

Here is the basis so far. It might be that such a thing can be more elegantly
formulated in other programs, without having to observe the individual
steps: "reverb ding with dang."

However: From every position in this detailed process, ways lead into
totally different, adventurous directions. The simple envelope allows
itself to be substituted by a different, analytically gained one; the
merge does not have to be a simple modulation, there are also alternatives
for this. And, last but not least, although the FFT is the most important
transformation to enter into another domain, it is by no means the only
one.

akueto

G.R.

(c) Günther Rabl 2010