Selling Air, snare drum tuning

SmoothOperator

Gold Member
So, I tried out the equation for calculating the various frequencies of drums:
My suspission is that the two headed tom behaves more like a Helmholtz resonator than a vibrating column of air, since the wave length of the fundamental is so much longer than the drum.

If this were true, then the tom would essentially behave as a three spring system: top head, bottom head, air volume. If we assume the port area is equal to the port length, then the frequency of the air behaving as a spring would be.

F=(v/(2*pi*sqrt(V))

Where v is the speed of sound and V is the volume of the drum.

http://en.wikipedia.org/wiki/Helmholtz_resonance

You could add other springs to the system, shells etc. If the two heads were tuned identically, and were of the same composition, it would be essentially a two spring system.

My 12x10 was an A 110, my 14x6.5 was 117.5 Bb my 22x16 was 70.20 between F# and G, my 16x14 turned out to 70.2 which was a C#.

For my resonant head I was stuck on how to tune it, so I chose to use the interval from the next highest mode, which turned out to be a fifth. This seems much higher than usually recommended, as I got closer to that interval it did sound bad, until it was all the way in tune with the mode. After which the snare had a nice bright crisp sound. I think the differences in decay time and sound radiation work between the (0,1) mode and (1,1) mode work together to shorten the decay and make a louder thump. As a side effect it seems, the (1,1) mode of the resonant head corresponds to the (0,2) mode of batter head which seems to reinforce the effect.
http://www.acs.psu.edu/drussell/demos/membranecircle/circle.html

Overall I am fairly happy with this approach to tuning. Some things that surprised me though, was how easy it was to hit the notes tuning once I knew what they were. My new tom which kind of prompted this, went into tune easiest, I even used an electric tuner, and one of those wrenches that click when the tension is too high. I was surprised that the tom was actually lower pitched than the snare, but indeed the deeper drum has more spacial volume. The 16 and 22 were a little more difficult, I used my voice which happens to be low, to find the pitch then tuned to that for the 16, then for the 22, I had to sort of guesstimate, by this time I was getting a feel for how the drum is supposed to sound when tuned to the shell volume though, and by the end the tuner showed F#0 dead on, I suspect when in tune there is enough sustain in the fundamental to pick it up.

Another thing that surprised me was how the drums tuned to the shell volume had much less sustain. I was kind of afraid it would make for a ringee sustained drum, but the opposite occurred, I suspect, it is do to the sound energy resonating more efficiently in the (0,1) mode and not getting attenuated into the (1,1) mode.
 

SmoothOperator

Gold Member
70.20 between F# and G, my 16x14 turned out to 70.2 which was a C#.
I mistyped my 22x16 was 47.76, not 70. I wasn't satisfied with the pitch of the 16x14 this morning, so I tried tuning it down a fifth(the same as the bigger drum). This made the (1,1) mode consonant with the shell volume, and as expected from the sustain inherent in that mode the drum sang a tune, which was kind of nice for jamming solo with my sharper cymbals, kind of like a ride bass.

I was thinking why the drums were manufactured to C# and F#, I suspect it is to compensate for filling(pillow) shrinking the effective spacial volume of the bass.
 

tamadrm

Platinum Member
AAHHH....the never ending quest to quantify,that which is not quantifiable.Tuning is an art,a skill,something done with personal taste and subjectivity in mind.

Steve B
 

SmoothOperator

Gold Member
AAHHH....the never ending quest to quantify,that which is not quantifiable.Tuning is an art,a skill,something done with personal taste and subjectivity in mind.

Steve B
I don't like your taste in blog posts, why don't you post some where else buddy, unless you have a better way to quantify...
 

shemp

Silver Member
SmoothOperator....this is awesome insight. This is pure physics and it is extremely quantifiable...I suspect we could also model this as an RLC circuit probably having significant second order effects, maybe third....I have no idea at this point...but find it interesting.

As you noted, the science has allowed you to find the sweet spot and now human hearing can take over and replicate the scientifically based conclusion.

The shell itself (with hardware) is a well known embodiment of a resonant cylinder having open ends...and thus specifying the effect on resonant frequency based on quarter wavelength...this is a well known musical quantity. Adding the heads adds two energy sources and storage devices that resonate together and in sympathy ( or not ) with the inherent resonant frequency of the shell system. The heads vibrate with/against each other and the shell upon application of an impulse...which is the stick hit. Of course the energy dissipates due to the internal resistance/damping of the spring in the heads and resistance/damping nature of the shell.

I'm not sure this is exactly the case as I have spelled it out, but it is a very quantifiable physical system that can also be modeled and accurately predicted.

Tuning the heads to the inherent fundamental of the shell system is not a only a good idea, it will produce the most natural tone of the drum....whether that is a desired tone is subjective....and of course none of this is required when tuning/tensioning, but it is very interesting.
 
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Andy

Administrator
Staff member
I was thinking why the drums were manufactured to C# and F#,
And what drums might these be? DW?

AAHHH....the never ending quest to quantify,that which is not quantifiable.Tuning is an art,a skill,something done with personal taste and subjectivity in mind.

Steve B
Hit - nail - head. I do the science, I have to do the science, but it's only a small part of understanding this brutally simple yet complexed instrument. The one element that all the scientific studies fail to address, is the relationship between the heads & the shell outside of simple tube/volume modelling. Equally, there's a significant concentration on the heads, most specifically, the batter head.

Let me let all the science guys into a little secret, or more specifically, a little understood set of facts. The shell produces very little sound in it's own right. If it could be measured representatively in isolation, the sound the shell produces, as a percentage of the total sound, would be minute. In all it's forms, the shell shapes the sound that the heads produce, & outside of the initial strike, almost everything else the heads produce is influenced by the shells & other elements either directly connected, or in close proximity to the drum. The listener's perception, & to some extent, the instrument itself, is shaped by the room.

The more resonant the shell (C/W all it's attachments), the greater the influence on the resultant sound, & the further away from any standardised model it becomes. The reason tuning models based purely on dimensional considerations rarely work outside of non resonant shells, is that the shell is excited in different ways, & by different frequencies. Certainly different frequencies than you'll get by tapping the shell. Just because a shell has a certain dominant tone or note, doesn't mean it's necessarily most excited by that note. Even if it is, then in a perfect model, that may detract from the dominance of the tone rather than add to it.

The straight truth is that nobody really knows what the hell is going on, & very few care. The drum craftsmen who really work with & understand constructions, do so mainly based on anecdotal evidence amassed over countless builds & experimentation. They know that a drum's sound, & how it responds to different tensioning, is a mix of many factors with greater or lesser influence. One thing's for sure, taking points in isolation, or attempting to apply a model to all circumstances, is unlikely to yield a total result, but it can form an interesting basis of a wider program of testing.
 

shemp

Silver Member
I want to respectfully and politely note that there are other scientists that would immediately disagree that this is an unquantified system...this is absolutely a quantifiable science. physical systems with a higher degree of difficulty have been quantified.

I also measure and quantify the science in a parallel but related set of products...an organization that has acquired a portfolio of patents in harnessing and using the science around this type of mechanical/acoustical behavior.

Let's please tread lightly when we apply the simplifications and hand waving...
 

SmoothOperator

Gold Member
SmoothOperator....this is awesome insight. This is pure physics and it is extremely quantifiable...I suspect we could also model this as an RLC circuit probably having significant second order effects, maybe third....I have no idea at this point...but find it interesting.

As you noted, the science has allowed you to find the sweet spot and now the human sensors can take be used to replicate the scientifically based conclusion.

For the non-believers, the shell itself (with hardware) is a very well known embodiment of a resonant cylinder having open ends...and thus specifying the effect on resonant quarter wavelength...this is a well known musical quantity. Adding the heads adds two energy storage devices that resonance together and in sympathy ( or not ) with the inherent resonant frequency of the shell system. The heads resonate together with the shell upon application of an impulse...which is the stick hit. Of course the energy dissipates due to the internal resistance/damping of the spring in the heads and resistance in the shell.

I'm not sure this is exactly the case as I have spelled it out, but it is a very quantifiable physical system that can also be modeled and accurately predicted.

Tuning the heads to the inherent fundamental of the shell system is not a only a good idea, it will produce the most natural tone of the drum....whether that is a desired tone is subjective....and of course none of this is required when tuning/tensioning, but it is very interesting.
Thanks shemp, my assumption is slightly different than what you typed above. My assumption is that the length of wave generated from the drum is much larger than four times the depth or diameter of the drum so there are no standing waves(the frequency of a shell without heads would be way off), therefore the air in the drum behaves like a spring, much like the body of an acoustic guitar or violin. Furthermore the effect of the area vs depth of the port is negligible, and there is not much "spring" effect from the interaction of the air outside the head with the air inside the shell. If there were interactions with the air outside the drum, say with a very thin head. The pitch could be lower, because that would effectively increase the spatial volume of the drum. Interactions outside the drum seemed to be negligible, much like interactions through the soundboard of a guitar can be neglected.
 

larryace

"Uncle Larry"
If a shell, with all the hardware and hoops on it...fully dressed and tensioned....produces a D note for example when struck with a mallet....and you tuned both heads to a D note.....would there be some phase cancellation going on?
 

shemp

Silver Member
No worries....it takes multiple theories and people working together to arrive at scientific conclusions. I think there is merit in both initial approaches, but I do not know the answers...and probably won't since I try to leave my day job at the office.

Still the topic is extremely interesting to me and makes the geek in me....oops I meant engineer in me....start to think and try to solve ;)

Please continue with this very interesting info!!
 

Andy

Administrator
Staff member
Let's please tread lightly when we apply the simplifications and hand waving...
We posted at the same time, so I didn't have the benefit of seeing your post, & I probably din't express myself too well. Of course the model is quantified, but in any study I've seen (& I'm not for one minute suggesting I've exhausted everything out there), the shell has been a constant, not the highly variable element I know it to be. I can think of extreme polar opposite constructions that would yield very different results, & I've never seen that factored in.

I'm not dissing the science involved, quite the opposite, but I do believe it to be just a part of the picture, with a big chunk of anecdotal evidence making up the rest of the picture, at least, when applied to drum design.
 

shemp

Silver Member
We posted at the same time, so I didn't have the benefit of seeing your post, & I probably din't express myself too well. Of course the model is quantified, but in any study I've seen (& I'm not for one minute suggesting I've exhausted everything out there), the shell has been a constant, not the highly variable element I know it to be. I can think of extreme polar opposite constructions that would yield very different results, & I've never seen that factored in.

I'm not dissing the science involved, quite the opposite, but I do believe it to be just a part of the picture, with a big chunk of anecdotal evidence making up the rest of the picture, at least, when applied to drum design.
Sure, the anecdotal evidence and design "data" or empirically gathered science is a huge part of this industry....but when someone like the OP offers us views into the science, it hurts to see folks "poo poo" it....or be disrespectful.

If I was less interested in actually playing and more interested in bringing my day job home, I could help quantify these behaviors.....but I do find it extremely interesting and enjoy postulating and kicking it around in here. I might learn something and so might other interested parties.

No disrespect Andy....let's hand the mic over to SmoothOperator ;)
 

MrPockets

Gold Member
I did a mathematical research project on the vibration of a circular membrane. I disregarded the shell for the sake of time in the presentation, but I learned lots of cool stuff.


The Bessel functions that determine the mode of vibrations: If I recall correctly some functions intersect the x-axis at the same point as another. I believe these are the modes that work well together.

Where you hit the drum can have an impact on the mode of vibration.

Someone created a linear equation to find the dominant pitch in a membrane with x lugs and each lugs specific tension.
 

SmoothOperator

Gold Member
The reason tuning models based purely on dimensional considerations rarely work outside of non resonant shells, is that the shell is excited in different ways, & by different frequencies. Certainly different frequencies than you'll get by tapping the shell. Just because a shell has a certain dominant tone or note, doesn't mean it's necessarily most excited by that note. Even if it is, then in a perfect model, that may detract from the dominance of the tone rather than add to it.
I think springiness of the shell itself could matter, though it would be some what independent of the tone the volume of the air in the drum produces. I personally would prefer those more spherical Chinese style drums, then the helmholtz resonance would be stronger, but the craftsmen in the west are more concerned about the resonance of the shells themselves.
 

Andy

Administrator
Staff member
Sure, the anecdotal evidence and design "data" or empirically gathered science is a huge part of this industry....but when someone like the OP offers us views into the science, it hurts to see folks "poo poo" it....or be disrespectful.

If I was less interested in actually playing and more interested in bringing my day job home, I could help quantify these behaviors.....but I do find it extremely interesting and enjoy postulating and kicking it around in here. I might learn something and so might other interested parties.

No disrespect Andy....let's hand the mic over to SmoothOperator ;)
With respect, I was neither "poo pooing" it nor being disrespectful, just placing it in context from my perspective, & my perspective is the only one I can put forward. I agree that my initial post wasn't quite as well thought out as it should have been, & for that, I apologise.

As for leaning something, I couldn't agree more. I'm very open to learning, it's something I do every day. If I can pick up something that clarifies a mechanism for me, then I'm very grateful for that, & it's one of the reasons I'm here. Mic 100% handed over to SO.


the craftsmen in the west are more concerned about the resonance of the shells themselves.
You have a point there, at least, a very valid marketing observation. The fact is, most modern shell's aren't that resonant compared to the construction of other wooden acoustic instruments, although much emphasis is placed on that one aspect of design, as if it's always a good thing. In drum construction, a highly resonant shell is not always a good thing, depending on the characteristics you're seeking, but it can add wonderfully as part of a encompassing design direction.
 

Stroman

Platinum Member
This information is fascinating, without a doubt.

Intuitively, and through my limited experience, I can see the validity of the OP's hypothesis, at least as far as drum dimensions being more relevant than the pitch of the shell (ala DW). I also have experienced similar things when tuning the resonant to various intervals, particularly the way the drum starts to sound worse as you approach the note you seek, then the character changes completely when you arrive. It's interesting to see the attempt to quanitize it.

I would be curious to see how different combinations of tunings, in relation to shell size, sound in different surroundings. This has always been a trouble spot to me. I can tune well, but it is no secret that you sometimes get to a bad sounding room, and your careful tuning goes out the window. I would like to know if there is a quantifiable tuning that would sound good in the widest variety of surroundings.

Still, I'm thankful that I can tune and play drums without knowing the physics involved!
 

mikel

Platinum Member
Sure, the anecdotal evidence and design "data" or empirically gathered science is a huge part of this industry....but when someone like the OP offers us views into the science, it hurts to see folks "poo poo" it....or be disrespectful.

If I was less interested in actually playing and more interested in bringing my day job home, I could help quantify these behaviors.....but I do find it extremely interesting and enjoy postulating and kicking it around in here. I might learn something and so might other interested parties.

No disrespect Andy....let's hand the mic over to SmoothOperator ;)
Andy, Poo Pooing or disrespectful? Are we talking about the guy on this forum? Not the one I know and respect for his drum building insight and experience.
 

tamadrm

Platinum Member
I don't like your taste in blog posts, why don't you post some where else buddy, unless you have a better way to quantify...
Firstly,tough.....I'll post where ever I want to, whether you like my taste or not.

.Secondly and more importantly,that's the whole point.There is no better way to quantify something that isn't quantifiable.

Tuning is an art and a skill,that must be learned,not charted as data on some graph.

Steve B
 
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