Selling Air, snare drum tuning

SmoothOperator

Gold Member
I still don't get the selling air part. Air's free! (at least for now)
But, pretty soon you'll have to have O2 tanks mounted on your SUV.

I think I was just anticipating the dull roar from the my shell is better than your shell crowd. You really couldn't test my formula by tapping on the shell without heads on it. The Helmholtz equation applies, only to a closed ported volume.

I am curious if any one else has tried calculating the frequency of their drums with that formula, and whether the frequency was reasonable for tuning.
 

larryace

"Uncle Larry"
I just don't see how any calculation could be accurate. Different amounts of hardware, hoop choice, mounting issues, tuning imperfections, pitch relationships between the batter and resonant, head thickness/muffling....too many variables stand in the way it seems. Plus the way a drumhead undulates is kind of freaky if you ever saw a slo mo video of a drumhead flapping. It seems a bit random, even though it is perfect logical, and depending where you hit the drum will pull out different freqs and make different vibration signatures. So how can one possibly take all those variables into consideration? I just have a hard time swallowing that one equation can be the same on all same sized drums.
 

MrPockets

Gold Member
I just don't see how any calculation could be accurate. Different amounts of hardware, hoop choice, mounting issues, tuning imperfections, pitch relationships between the batter and resonant, head thickness/muffling....too many variables stand in the way it seems. Plus the way a drumhead undulates is kind of freaky if you ever saw a slo mo video of a drumhead flapping. It seems a bit random, even though it is perfect logical, and depending where you hit the drum will pull out different freqs and make different vibration signatures. So how can one possibly take all those variables into consideration? I just have a hard time swallowing that one equation can be the same on all same sized drums.
Linear Differential Equations of more than one dimension is what I would use for the calculation if I knew more about D.E.s. This math has been used to solve equations with THOUSANDS of variables. You mentioned only 7.

I think that any smart person would understand that the calculation is an estimate based in a perfect scenario and would not always equal the real reading, but the answer can be very close.



I googled, "Vibrational modes of a circular membrane under tension" and found lots of articles. The math exists and it is fairly accurate to the point where it is justifiable to cite the calculation. They even include scenarios of uneven tension. The only things that I havn't seen (doesn't mean that it is not out there) are studies that involve shell and head thickness (They assume the thicknesses are constant to make the math easier, and I bet the variables get cancelled out so it doesn't matter).

The math is out there and it is accurate. However, most people agree there are elements that make the equations not ideal such as dampening and outside forces being applied ot the shell.
 

SmoothOperator

Gold Member
I just don't see how any calculation could be accurate. Different amounts of hardware, hoop choice, mounting issues, tuning imperfections, pitch relationships between the batter and resonant, head thickness/muffling....too many variables stand in the way it seems. Plus the way a drumhead undulates is kind of freaky if you ever saw a slo mo video of a drumhead flapping. It seems a bit random, even though it is perfect logical, and depending where you hit the drum will pull out different freqs and make different vibration signatures. So how can one possibly take all those variables into consideration? I just have a hard time swallowing that one equation can be the same on all same sized drums.
You didn't even mention the speed of sound in air, which quite frankly is the only variable that matters for a resonator, but we can see where your head is at, maybe a drum really is just so much glue, lacquer, metal, and plastic, but then again we aren't talking about wood blocks.

Linear Differential Equations of more than one dimension is what I would use for the calculation if I knew more about D.E.s.

I think that any smart person would understand that the calculation is an estimate based in a perfect scenario and would not always equal the real reading, but the answer can be very close.



I googled, "Vibrational modes of a circular membrane under tension" and found lots of articles. The math exists and it is fairly accurate to the point where it is justifiable to cite the calculation. They even include scenarios of uneven tension. The only things that I havn't seen (doesn't mean that it is not out there) are studies that involve shell and head thickness (They assume the thicknesses are constant to make the math easier, and I bet the variables get cancelled out so it doesn't matter).

The math is out there and it is accurate. However, most people agree there are elements that make the equations not ideal such as dampening and outside forces being applied ot the shell.

I think I would have to use PDE's to figure out a three spring system, however by tuning the fundamental mode (1,0) of two heads to approximately the resonant frequency of the cavity, it should be simplified, quite a bit.

I did tweak my bass drum a little, and it seems to me that there is probably some interaction between the air outside the head and inside, taking it down to F from F#, had more thump and less ring.
 
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shemp

Silver Member
Another interesting method might be to acoustically sweep shells by using a suitable speaker....taking into account the nonlinearities of the speaker...my guess is that the system could be used to find the resonant frequency of the volume in the shell.

If enough acoustic power was put into the shell, the wood and hardware would have an effect on the timbre ie harmonics amplitude relative to the fundamental ....the molecular structure of each wood species, I postulate, would have an effect.

Somebody somewhere has to be doing this....it seems pretty evident. I strongly suspect that, however low in output relative to the likely overwhelming nature of the volumetric effects, that the effect is audible.

The wood shell is excited when the head is struck...there is a force impulse to the wood that has a response of some sort. I surely do not have the answers but nonetheless it keeps me interested.
 

Andy

Administrator
Staff member
but we can see where your head is at, maybe a drum really is just so much glue, lacquer, metal, and plastic, but then again we aren't talking about wood blocks.
Wow, that's a tough response to a guy who's merely having difficulty getting his head around something. A pity, because this has the makings of a very interesting thread, & the information you're putting up has value. Same with your response to Steve. A counter view, no matter how ill informed you may believe it to be, should be accepted in the spirit it's offered.
 

Andy

Administrator
Staff member
Another interesting method might be to acoustically sweep shells by using a suitable speaker....taking into account the nonlinearities of the speaker...my guess is that the system could be used to find the resonant frequency of the volume in the shell.

If enough acoustic power was put into the shell, the wood and hardware would have an effect on the timbre ie harmonics amplitude relative to the fundamental ....the molecular structure of each wood species, I postulate, would have an effect.

Somebody somewhere has to be doing this....it seems pretty evident. I strongly suspect that, however low in output relative to the likely overwhelming nature of the volumetric effects, that the effect is audible.

The wood shell is excited when the head is struck...there is a force impulse to the wood that has a response of some sort. I surely do not gave the answers but nonetheless it keeps me interested.
This is a very solid & practical approach IMO, & something I've thought about myself in leu of other options we have available. We have carried out quite a bit of testing on basic variables, but never using an external means of excitement in this way.
 

SmoothOperator

Gold Member
Another interesting method might be to acoustically sweep shells by using a suitable speaker....taking into account the nonlinearities of the speaker...my guess is that the system could be used to find the resonant frequency of the volume in the shell.

If enough acoustic power was put into the shell, the wood and hardware would have an effect on the timbre ie harmonics amplitude relative to the fundamental ....the molecular structure of each wood species, I postulate, would have an effect.

Somebody somewhere has to be doing this....it seems pretty evident. I strongly suspect that, however low in output relative to the likely overwhelming nature of the volumetric effects, that the effect is audible.

The wood shell is excited when the head is struck...there is a force impulse to the wood that has a response of some sort. I surely do not have the answers but nonetheless it keeps me interested.
You could just get one of those cajons, they even come with tunable ports, I guess someone out there is thinking like me. I have a pair of wood blocks on shaped like toad and one like a cricket, I wonder what the volume of those are, they have great wood tone.
 

SmoothOperator

Gold Member
Does the resonant frequency of a shell change along with head tension or does it remain constant?
It seems with the bass drum, the looser the head the more he air outside would interact with the air inside, and behave closer to an open port, whereas if the head is tighter the head wood behave more like a piece of wood. So, the tension/stiffness of the head probably does effect the resonant frequency of the shell, looser heads lower resonant pitch, tighter heads higher resonant pitch, maybe that is what I observed tuning the bass down from F# to F. For the smaller bass when I tuned the head so that the (1,1) mode was at the C#, which is a significant drop in tension, I didn't observe a change in resonant frequency, the second mode tuned to C# pretty easily. I think there is a difference in the heads, the small bass came with a compression head, which I assume is stiff to begin with.

It seems with the bass drum, the looser the head the more he air outside would interact with the air inside, and behave closer to an open port, whereas if the head is tighter the head wood behave more like a piece of wood. So, the tension/stiffness of the head probably does effect the resonant frequency of the shell, looser heads lower resonant pitch, tighter heads higher resonant pitch, maybe that is what I observed tuning the bass down from F# to F. For the smaller bass when I tuned the head so that the (1,1) mode was at the C#, which is a significant drop in tension, I didn't observe a change in resonant frequency, the second mode tuned to C# pretty easily. I think there is a difference in the heads, the small bass came with a compression head, which I assume is stiff to begin with.
I tried the 16x14 at C/F seems to work pretty well in that range C to C#, maybe a little more sustain at C# and a little more thump at C. I think the original equation is pretty good for getting close, I wouldn't have had a clue otherwise. I was trying to tune the tom higher than the snare.

It does seem a little high pitched for the larger drums, and may depend on head stiffness. Something that is kind of disturbing is with a ten lug bass drum and fine threaded lugs it only takes like an eighth of a turn or less all the way around to drop a half step.
 
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Stroman

Platinum Member
Something that is kind of disturbing is with a ten lug bass drum and fine threaded lugs it only takes like an eighth of a turn or less all the way around to drop a half step.
That doesn't surprise me in the least, and is one of the reasons I've never put much stock in tuning methods that suggest things like "tune the bottom head one and a quarter turns tighter..." etc. I am picky enough that I tune by pitch, and increments far smaller than quarter turns affect pitch noticeably.
 

Andy

Administrator
Staff member
Something that is kind of disturbing is with a ten lug bass drum and fine threaded lugs it only takes like an eighth of a turn or less all the way around to drop a half step.
Just curious, is this a DW drum with 30TPI threaded lugs?
 

mikel

Platinum Member
Wow, that's a tough response to a guy who's merely having difficulty getting his head around something. A pity, because this has the makings of a very interesting thread, & the information you're putting up has value. Same with your response to Steve. A counter view, no matter how ill informed you may believe it to be, should be accepted in the spirit it's offered.
With you Andy. I can understand drummers getting stroppy discussing drums or technique, but squabbling over mathematical calculations???
We are mostly friendly on this forum, I don't think dismissing people as Luddites because they don't subscribe to your way of doing things is the way forward.
 
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SmoothOperator

Gold Member
Being a trumpet player as a secondary instrument, I think it is interesting that 6.5x14 worked out to Bb, and bass in approximately F. I kind of wonder what other snare's/bass frequency ranges are. I suppose I could calculate them, if I really wanted to know the answer.
 
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