Drumsley

Fixed Overtones in Single-Headed Membranophones

Hi everybody,


I enjoy sharing some of my drum tuning studies, but it is rich of terminology some of you may not know. All I will say is when you read RTF, its just means the ratio between a fundamental note and the first overtone of the drum sound. RTF is a tuning system defined by Rob Toulson who did a lot of studying on cylindrical drum acoustics. I've taken his work and have expanded upon it in my own way.
If this sort of stuff fascinates you, keep reading and leave a comment if you want. This is going to be about single-headed membranophones.

Instruments such as concert toms, bongos, and congas are all single-headed drums. We know that the resonant head of a two-headed drum plays an important role in shaping the tone. When you remove that head, you lose a major point of control, leaving the batter head as your only source of adjustment. You can still raise or lower the batter head tension to change the fundamental pitch, but the timbre now depends entirely on the drum’s design, heads and construction.


The sound quality, or timbre, you hear from a conga is unique because of its shape, head, depth, and material. The same goes for bongos, timpani and concert toms. One interesting thing about single-headed drums is how consistent their overtone structure is. No matter the size or tuning, the RTF stays nearly the same every time. I was fascinated enough by this that I went around to every concert tom in my college music department to measure their RTFs. Whether it was a 6” or an 18” tom, the RTF always hovered between 2.0 and 2.4. To support my discovery, I found that Rob Toulson has already said that ideal single-head membranophones have mathematically fixed, immovable inharmonic modal ratios. “Ideal” meaning the first fundamental depends on material and physical properties (diameter, thickness, tension, etc.) and absolute even pitch around the drum head. The RTF deviations I saw going around to different concert toms could have been from uneven head pitch, size, material and other factors. Drums with two heads deviate from these ratios because the two drum heads interact through the air inside the drum.
Without a resonant head, single-headed drums have a fixed overtone behavior. Timpani overtones are consistent that way as well, but in their own way due to their entire structure, head, bowl, and enclosed air. Across different tunings and drum sizes, their overtones have consistency as well.


If you’ve played timpani, you know the best striking area isn’t in the center but somewhere between the center and the edge. There’s a sweet spot where the tone opens up. Striking directly in the center gives a dry, short sound that’s mostly the drum’s fundamental. When you move toward that sweet spot, you start exciting the overtones, and sometimes the first fundamental becomes louder than the fundamental itself. This is part of what gives timpani their blooming resonance.


On the Timpano graphs, you see I recorded both 30” and 25” drums to observe how their RTF values change across their highest, lowest, and mid tuning ranges. There was very little variation in RTF across these ranges, so the heads were tuned well. The 25” drum exhibits a short peak just below the fundamental, so I noted that frequency on the graph. I wonder if that has to do with poor tuning around the tension rods. Overall, the RTF stayed around 1.5. When we tighten the batter head on a two-headed drum, the overtone ratio shifts and that is because of the coupling between the two heads. The overtone on these single headed drums now entirely rely on all other factors. If I were to change the timpani heads to something twice as thick, would there still be consistency like we see here? Would there be the same consistency, but with a different RTF? I don’t know the answer to that yet.

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