'Wheel-like' Mathematics (Modulating Trig Functions?)

[Chrono G. Xay]

@phion

I have personally spoken with the drum specialists at Evans--one of the big names in the drumhead industry--in the past and pitched such an idea to them- even just predicting the tension on a drum--since one of their partners, a string company called D'Addario, already has on their website an extensive table displaying values of string tension at several different tunings for dozens of the strings they sell--and they weren't interested because they were afraid of basically 'overwhelming their customers with data'. (Their exact phrase was "paralysis by analysis".) What? That's seems like a rather hypocritical thing to say, considering their partner's business practices. I've spoken with professional performers, public school and higher education percussion teachers, and they would be excited to have such a tool at their disposal.

Imagine being able to mentally prepare yourself for how your drums are going to feel before you've even submitted an order to your local music business for those new heads you want to try. Or, if you already have the feel you want and don't want to change it, what if you would like to know, scientifically, what your preferred 'feel' is? or another artist's preferred 'feel'?

 

[phion]

@phion

I have personally spoken with the drum specialists at Evans--one of the big names in the drumhead industry--in the past and pitched such an idea to them- even just predicting the tension on a drum--since one of their partners, a string company called D'Addario, already has on their website an extensive table displaying values of string tension at several different tunings for dozens of the strings they sell--and they weren't interested because they were afraid of basically 'overwhelming their customers with data'. (Their exact phrase was "paralysis by analysis".) What? That's seems like a rather hypocritical thing to say, considering their partner's business practices. I've spoken with professional performers, public school and higher education percussion teachers, and they would be excited to have such a tool at their disposal.

Imagine being able to mentally prepare yourself for how your drums are going to feel before you've even submitted an order to your local music business for those new heads you want to try. Or, if you already have the feel you want and don't want to change it, what if you would like to know, scientifically, what your preferred 'feel' is? or another artist's preferred 'feel'?

I know a couple drummers personally. I'll probably talk about this thread to them.

 

[phion]

It just occurred to me that this is a pretty common problem within functional analysis. It concerns modes of vibration.

One of the possible modes of vibration of an idealized circular drum head. These modes are eigenfunctions of a linear operator on a function space, a common construction in functional analysis.

 

[Chrono G. Xay]

That's why, as much as I'd love to calculate the damping coefficient of a membrane-shaped spring that doubles as its own mass in the mass-spring-damper system (and so be able to ascribe an actual value to 'sustain' when it comes to just the drumhead and not resonances of the air cavity or the drum shell itself), I can't--or at least *I* can't--because, for one, I don't have the knowledge to even START looking at eigenvalues/eigenvectors/etc., myself, if that's even the right road to go down!

For now I'm just content with trying to obtain a theoretical value for 'feel' (restoring force), which for what I'm trying to do is more of a static condition (for example: At 'x' displacement from rest, what is the restoring force 'F'?)

However, you can obtain an empirical value for the damping coefficient just by striking a drum at a point, noting the amount of kinetic energy imparted to the drumhead at that point (which might be best done by a machine sporting an apparatus that wields a drumstick so as to better control the striking point, velocity, impulse, et al), and as such how far the membrane is initially displaced when struck (in my opinion, the drumhead should be struck in the very center, so as to hopefully better excite the 0,1 mode as opposed to others). From there you'd analyze how the amplitude of motion the membrane makes changes as the sound decays (which might be best done with some sort of laser distance probe). When comparing data in terms of the logarithmic measure of sound pressure levels, is the damping linear, is it quadratic, or is it something else?

 

[Chrono G. Xay]

Well, *this* thread seems to have died...