Coupled Strings in Faust

A diagram for two coupled strings is given in Fig.H.28. A Faust template for this block diagram is displayed in Fig.D.13 and specified as follows:

 import("music.lib");
 g1 = 0.999; g2 = 0.995; P = 200; Pmax = 256; detune = 1;
 d1 = fdelay(Pmax,P-2);
 d2 = delay(Pmax,P*(1.0 - 0.01*detune)-2);
 bridgefilter = + : *(-0.5);
 g = g1;
 stringloop = ( _,+ : ((d2 <: _,_),(d1 <: _,_)) 
     : (_, (bridgefilter <: _,_) ,_) 
     : +,+) ~ (*(g2),*(g1)) ;

 process = stringloop;

where P is the fundamental period, in samples, and denotes the round-trip filtering on the string during one period. (Placeholder values are given in the Faust listing so it will compile and generate Fig.D.13.)

Note that the excitation only enters one of the string loops in Fig.D.13. This corresponds, for example, to plucking the string in the horizontal plane, say (the d1 loop), with the vertical plane (d2 loop) vibrating ``sympathetically''. More generally, the two loops may be excited by varying amounts of the excitation signal, corresponding to a physically inexact excitation plane.

As discussed in §H.11.1, the bridgefilter is of the form

where is the (real, positive) wave impedance of the string, and denotes the bridge driving-point impedance (a positive-real function of the Laplace variable ). The special case indicated in the Faust listing above, , corresponds to , which sounds similar to the following simplified diagram (shown in Fig.D.14) when g1 = g2 = g:

  stringloop = (+ <: (d2,d1) : + : *(0.5)) ~ *(g);