Experiments in modal modeling

It should work on a Mac to type "make" and give it a try. For Linux, change faust2caqt to faust2jaqt, etc.

Model: N modes excited by up to M strikers

• Parameters:

  • N = number of modes max
  • M = number of strikers max (e.g., M=2 for two drum sticks)

• Modes:

  • fc
  • bw
  • g

• Strikers:

  • A = amplitude
  • D = duration = 1/bandwidth

Striker signal is presently a one-pole impulse response.

I want to convince myself with various examples (hand-edited and otherwise) that our striker model is sufficient, or decide what to add to it.

• The modalBar.dsp example in the Faust-STK port uses a sample. I would like to avoid that and go fully parametric.

• Various past efforts have used a raised cosine (variable width).

• Cascading a one-pole exponential with itself has also been used to soften the attack (t e^{-t}, t^2 e^{-t}, etc.).

• Piano-hammer models use a nonlinear spring model f = k x^p, where p is 1 for linear and higher for more nonlinear. (Higher p is higher brightness and shorter "duration".)

• Chant multiplies decaying exponentials by a "half-Hann window".

• LPC has used "multipulse" excitation, optimally choosing a sparse set of impulses in place of 1. (The first few can be relatively quiet, etc.)

• Any excitation can of course go through a "shaping filter".

  • Commuted synthesis uses this for piano-hammer modeling, with the shaping filter conditioned on striking velocity
  • (higher velocity => more bandwidth)