Re: Why did I piss off the headline drummer?
Very cool animations, thanks for that link JR. I did not see the equations for the circular membrane, maybe I missed them.
It's been a while since I visited that website, I believe the animations are generated from curves derived from the underlying math. I thought he listed the equations too. It is pretty clear from observation of the resonance modes what the critical variables are (mass, tension, and distance or length of waveform period). This development of overtone resonances squeezed into a round surface area explains the non-harmonic nature of the sundry overtones.
The equations I have seen are gross oversimplifications anyway so they just give you a rough idea of what variables matter and how they interact. You are right about real world complications. Damping and membrane stiffness, elasticity and density are all factors in addition to the imperfect rigidity of the rim and lugs and the coupled air columns and second heads that you mentioned. For conga heads you also have veins in the skin and variations in thickness/stiffness/density as well, which make real skins sound better than plastic skins. All of which make the waveform less sinusoidal and less precise in its pitch. Drums are more art than science at this point. Fortunately.
If there was no science to it, I would not be involved at all. I am not a musician. I do however have a patent for an invention that allows me to isolate each lug and measure them one at a time for the quality of their match to each other. Since this is patented I can share how it works. I first sweep the drum head to identify the sundry lower resonances, then at a lower resonance of the correct order (same as the animation I posted earlier) I excite the drum head with two speakers then measure the time delay/ phase of the returning waveform. I can determine from the phase of this standing wave I generate in the drumhead whether the single lug I have isolated for measurement is sharp or flat compared to the reference source.
I can't (won't) tell drummers what pitch to target, or how much to detune between the two heads (whatever sounds good to them), but i can help them with technology to "clear", or match the lugs to each other at whatever note(s) they select, and get back there again and again. I joke I only make the microscope, they must cure the disease.
Note: it's called "clear" because when the lugs are well matched to each other the entire drumhead vibrates with the least different overtones, as compared to mismatched lugs when there are multiple closely spaced but different overtones. The well cleared drum sounds more pure, while drums do not make pure notes, they can make a pure series of resonances.
The drum community is still behaving in a pre-science manner, even though technology exists to precisely quantify drum tuning, this is only half the story until the drummers are given rational targets to tune their kit to (only one manufacturer AFAIK offers a note target.. DW). It is still early days for applied science to drum tuning, but better than we were.
JR
PS: The conga is an interesting case, and perhaps of more interest to speaker guys because of how much the tuned rear chamber/port contributes to the sound. The head behaves more like the one-headed concert tom, since there is no second head to interact with.
