Multiphonic model of split pressure-phase modes using the finite-element-method
Rolf Bader · The Journal of the Acoustical Society of America · 2004
The generation of multiphonic sounds in blown musical instruments is modeled by an eigenvalue finite-element-method (FEM) calculation. A common technique for the production of multiphonic tones is the use of complex sound-hole closing techniques, where more than one overtone spectrum appears, with fundamental frequencies being in inharmonic relations. Eigenfrequencies of a tube with both ends open are compared to eigenfrequencies of a tube with at least one sound hole open. It shows up that the tube with one open sound hole leads to additional eigenfrequencies in the tube for each node number. This is because of two possibilities of pressure curves within the tube for each node number, the pressure right and left of the hole being in phase or in opposite phase. The frequencies of equal phase form a new overtone structure which is harmonic within itself and so forms a new tone, a multiphonic. So the multiphonic model is in agreement with the Backus formula of multiphonic sounds as a combination of the tubes fundamental and multiples of the frequency difference of the zero node mode components.