Re: Tip on a great free reverb plugin (for lappy loopers) PSP Pianoverb

[Rainer Straschill <moinsound@googlemail.com>]

Antony sez:
> that one flew right over my head. What is the difference between the two 
>approaches?

Approach 1 (convolution):
Basically, it works like this: Theory has it that every LTI system can
be completely defined by its impulse response (the system's reaction
to an infinitely short, infinitely high spike with a finite surface
area). LTI here means "linear, time invariant". Time invariance means
that it does not matter if you send the signal now or 10ms or 1s or
whatever later (or earlier). An example of a typical effect where this
is not the case is a flanger (or, for that matter, everything
modulated by a LFO).
Linearity is that if you make the input twice as loud, the output gets
twice as loud (and that for any multiplier), and if you send in two
signals at one then the output is the sum of the processed output from
the individual input signals. An example of a typical effect where
this is not the case is a compressor (or, for that matter, everything
with something like an envelope follower).
A prime example for something LTI is a delay.
(Note that "linearity" does not mean "a flat frequency response"! In
fact, ideal EQs are linear systems).

For our application: assume you could somehow record the impulse
response of your system (in that case, the inside of a piano with the
sustain pedal depressed). Then you could record that, and by that and
a specific mathetmatical operation (faltung, or convolution) model the
system's response to the input.

There are a few drawbacks here. First, you have to record the impulse
response (but this works relatively well). Then, it only works for LTI
systems. While a piano can be considered time invariant, it is not
necessarily linear. (see below for a further discussion of that).

Approach 2 (physical modelling, as used by the PSP plugin):
the PSP plugin uses models of twelve string resonators, which
basically model the resonances of one string each. They don't say a
lot about this, but we do know its only twelve strings (of the
hundreds inside of a piano), and there doesn't seem to be any model of
the soundboard. No word on properly modelling inter string resonances.

There's limits to both approaches here:
ad 1:
the linearity is mainly a problem for very low energies transferred to
a string. If the energy falls below the value that is necessary to
establish at least one full oscillation cycle, then the behaviour of
that string changes radically, compared to the linear assumption.
And, as Per pointed out, there is a theoretical limit to how good this
can work - those nonlinearities can, by design, never be modelled in
that approach.
(btw, I found your quote from my last message rather misleading, to
say the least, Per. If you wanted to make  a statement to this regard,
please feel free to do so here or via matrix mail, but I kindly ask
you to avoid putting quotes out of context like this).

ad 2:
from just theoretically looking at this, it's not possible to tell
anything about the quality of the physical model. What can be
expected, however, is that the lack of a sufficient number of strings,
as well as the lack of a model of the soundboard, soundboard-string
interaction, sides/lid of the piano (probably only relevant for early
reflections, as there's a comparably weak coupling between those and
the soundboard).

Yours,

         Rainer