So I've been playing around with sympathetic resonance in Garritan and Noire to see how it's handled. I was trying to see how I might be able to implement in future libraries (or retroactively to completed libraries). I thought I'd bring it up to some of you Physics majors - as I recall, there are many here. You might find it interesting.
I first made a midi file playing:
C4 at medium velocity, to see the waveform
C3 short at medium velocity, to see the waveform, then C3 (zero velocity) and C4 staccato at nearly same time
D3 short at med velocity, then D3 (zero velocity) and C4 staccato
Etc with E3, F3, G3, A3, A#3
This is all to see how the sympathetic harmonics are excited, and what they look like.
(Note on reading the pictures: Graph is Frequency vs Time, and the brighter the yellow, the louder the frequency.
To corroborate my intuition, I see that the open string harmonics are excited by the staccato note, and the ones that overlap are brighter. This is seen by the relatively continuous and brighter horizontal lines, and the darker lines that don't line up with the staccato note impulse.
First thing I noticed is that Garritan's harmonics have a periodic decrease in volume (you can see dashed lines). I simulated these overtones with sinewaves, and it definitely sounds more like pianoteq - Garritan is simulating (by recordings of overtones or possibly sinewaves with an LFO?) the "beating" effect -cool!
Anyway, I thought this was cool, and am now trying to break this down into samples and sinewaves to accentuate the resonant harmonics. If you're interested, I'll post some sound comparisons. Since this is a feasibility study, I have to decide if its a good enough mockup to code.