brendan mccloskey

so I done me some research (wikipedia, stanford, synthSecrets et al); the maths gave me a headache, but I applied the general theories to a string and a soundboard model in Max. I'm posting the simple string model here, in the hope that someone with a more detailed understanding of the relevant expressions and equations will reply with "yeah, that sounds nice, I like your use of XXXXX, but woah dood you cannot do "this" because of "that"

Hi
so I done me some research (wikipedia, stanford, synthSecrets et al); the maths gave me a headache, but I applied the general theories to a string and a soundboard model in Max. I'm posting the simple string model here, in the hope that someone with a more detailed understanding of the relevant expressions and equations will reply with "yeah, that sounds nice, I like your use of XXXXX, but woah dood you cannot do "this" because of "that"

string-overtones-modelled

"yeah, that sounds nice, I like your use of XXXXX"

and then my jaw drops. Impressive work, thank you so so much for sharing.

@pid, yeah, like a reversed mandolin-zither thing, spent way too much time playing with it yesterday - today however is about refinement.......so, all you physical modelling equation heads PLEASE tell me if this can be improved. I've sat with my Amalio Burguet nylon string all morning doing A/B comparisons, and this sounds NEW AND IMPROVED, i.e. pretty damn good. The only minor issue left is the fact that, string mass/density aside (way too many equations), in a KS-model low pitches will resonate longer than higher ones due to the lengths of the delay line: >ms = low pitch, allpass) such that lowpitch = >damping, hi =

@pid, yeah, like a reversed mandolin-zither thing, spent way too much time playing with it yesterday - today however is about refinement.......so, all you physical modelling equation heads PLEASE tell me if this can be improved. I've sat with my Amalio Burguet nylon string all morning doing A/B comparisons, and this sounds NEW AND IMPROVED, i.e. pretty damn good. The only minor issue left is the fact that, string mass/density aside (way too many equations), in a KS-model low pitches will resonate longer than higher ones due to the lengths of the delay line: >ms = low pitch,  allpass) such that lowpitch = >damping, hi = 

Always loved something about that Karplus Strong sound.

In a satisfying implementation there would seem to be HF & LF damping appropriate to pitch. Brad Garton has done a bit of work in this area I believe.

Always loved something about that Karplus Strong sound.
In a satisfying implementation there would seem to be HF & LF damping appropriate to pitch. Brad Garton has done a bit of work in this area I believe.

thanks for the input. There is some HF/LF damping going on but more related to timbre than pitch - although the two are related. In my model the single string fundamental has a lopass around 5-6k, with higher overtones having a higher cutoff to allow them to ring a little longer; I'll have a look at Brad's stuff too. If you haven't already, check out my patch....as a classically trained guitarist (and poorly trained mathematician) I'm quite happy with it.

ps I agree about the Karplus-Strong appeal - I think the KS model has persisted, not just scientifically but aesthetically, because there is an underlying element of chaos in an IIR scheme

Hi Simon
thanks for the input. There is some HF/LF damping going on but more related to timbre than pitch - although the two are related. In my model the single string fundamental has a lopass around 5-6k, with higher overtones having a higher cutoff to allow them to ring a little longer; I'll have a look at Brad's stuff too. If you haven't already, check out my patch....as a classically trained guitarist (and poorly trained mathematician) I'm quite happy with it.

" in a KS-model low pitches will resonate longer than higher ones due to the lengths of the delay line: >ms = low pitch,

I don't think so-- if you play a guitar or any other stringed instrument, the low pitches (longer strings) seem to lose their energy at a lower rate than the higher strings. I suspect this is because for a given constant thickness, the shorter the sting length, then the thicker it becomes relative to its length, and therefore there's more damping.

The KS model is simple but it works so well because it's actually a reasonably accurate representation of how energy is transmitted through a string, so the idea of trying to correct for longer ring times of lower notes is really undermining the model itself.

" in a KS-model low pitches will resonate longer than higher ones due to the lengths of the delay line: >ms = low pitch, 

I don't think so-- if you play a guitar or any other stringed instrument, the low pitches (longer strings) seem to lose their energy at a lower rate than the higher strings. I suspect this is because for a given constant thickness, the shorter the sting length, then the thicker it becomes relative to its length, and therefore there's more damping. 

The KS model is simple but it works so well because it's actually a reasonably accurate representation of how energy is transmitted through a string, so the idea of trying to correct for longer ring times of lower notes is really undermining the model itself.
hope that makes sense...

Terry, exactly my dilemma. I will avoid any additional compensatory damping, with confidence now.

What you say is certainly true, and I refer to this when I mention string mass. A nylon string model is a *little* different in that the top three strings have comparable thickness (as distinct from steel string thicknesses), and with a good quality guitar (such as my own) the soundboard compensates for this phenomenon too. String shortness only becomes an issue beyond circa the 10th fret. Below this position high pitches sing out and resonate just as much as lower ones.

Lively debate, thanks for all the input and I'll now put this matter to rest.

...well, not so fast. if you do more work on it we'd like to hear. we all like to follow progress on brendan's physical (modelling) journeys.

Check out the most recent incarnation above, very nice. With the proviso that laptop speakers or cheap headphones simply will not do it justice.

string overtones modelled