Size of Drum and Pitch/Tone

My question is whether, all else being equal, a 16 x 16 tom has a pitch (and general tone) twice as deep as an 8 x 8 tom, and therefore also if a 12 x 12 tom has a pitch/tone exactly in the middle of the two.

Simple math would seem to suggest this direct correspondence between drum size and pitch/tone, but I have to wonder whether this is one of those instances where simple math is too simplistic. Maybe the correspondence between drum size and pitch/tone requires more complex math than this. Anybody know?

My question is born of the frustration over always being caught between the desire to play a small, simple set and to have all the drums around me that I may want. Toms especially have a tendency to accumulate. I really like cutting high pitched toms, and for years have lugged around a set of concert toms, but I also want the classic tom thud, so lug those around too. My fantasy has therefore long been to limit myself to three toms, one really high pitched and cutting, another floor with a powerful thud, and the third exactly in the middle. I think I could get used to playing a more streamlined set like this while still being able to get the gist of the sounds I want.

Realistically, I doubt I'd want the three toms to be 8 x 8, 12 x 12, and 16 x 16. I think the small cutting tom might be even smaller than 8 x 8, especially in depth, while the middle tom might have its width and depth adjusted correspondingly. However, I'm now wondering whether the math works as directly as this, or whether it's all more complicated.

Just fantasizing about reducing clutter while still having the minimum variety I'd rather not go without.
 

larryace

"Uncle Larry"
I'd say no.

Like you I go for a high, medium and low tone for my 3 toms. I just go with whatever respective tom gets me what sound I want, size be damned. Things don't have to be perfectly mathematical to be musical. But hey, if you wanted to do it by the numbers, nothing wrong there either.

Doing some calculations, it's not as cut and dried as you may think. 16 times 16 is 256, 8 times 8 is 64, which is only 1/4 of 256. From your post, it sounds like you are looking for a high tom with half the internal volume of the low tom. Which works out to be a little bigger than a 13 x 9. Which sounds too big to be a high tom. So the numbers don't always have a direct relationship like it seems on the surface. I think internal volume is what you were initially thinking about.
 

DrumEatDrum

Platinum Member
As mentioned, no, the math isn't that simple.

But I get the basic drift.

I think that's why I settles on using 10" and 12" toms, with a 16" floor time many, many years ago, before it caught on as a thing to to.

The 10" gives me the high end cut, the 16" the low end boom and the 12" just fits nicely in-between the two.
 

wildbill

Platinum Member
I think head tension plays as big a part as diameter.
A small drum tuned low can sound lower pitched than a larger drum tuned high.
 

GruntersDad

Administrator - Mayor
Staff member
I think the volume of a 16 x 16 is a lot m ore than twice the 8 x 8. See the formula above. or google volume of a cylinder, and do the math.
 
Thanks all, I was suspecting that the math is more complicated.

To further complicate my question (and make this even more overly scientific) I'm now wondering what ratios we would want for "matched" toms of different sizes and pitches.

In the example I used in my original post, I suggested that one tom might be double the pitch of another tom, with the middle tom being I guess three-quarters of it. But doesn't music (and I guess harmonics) usually work in thirds and divisions or multiples thereof rather than in halves, quarters, and doubles? If so, again to make this all disgustingly scientific, might we not theoretically want our toms to be related to one another by some divisions or multiples of thirds? If not, what kind of ratios among them would we look for? Halves, quarters, and doubles somehow strike me as the wrong ratio.

To put this is practical playing terms, as said I love my high-pitched cutting concert toms, and I can't imagine a 10" regular tom coming close. These give me a real Cuban/Latin sound, much sharper than other toms. However, their sound is so distinctive that no way can they be played in conjunction with the other toms, as in a Hawaii 5-0 roll around the toms. They have to be played separately or not at all. What I keep wondering is whether I can replace them with a small regular tom that is simultaneously capable of being used for the Cuban/Latin but can also work with my regular toms, albeit with some acceptable compromises on both ends.

Yeah, I know, in the real world we handle these things with trial and error, and Lord knows that's how I operate. Everything I have is cobbled together. However, one day I'd like to buy or possibly even commission exactly what I want, and I'm curious about the science of it.
 

GruntersDad

Administrator - Mayor
Staff member
Buy an electronic kit and tune it as such. Drums are not like guitar strings.
 

GetAgrippa

Platinum Member
A 16X16 has a volume of 12867.96 and an 8X8 volume of 1608.5, a 12X12 a volume of 5428.67, but you have a relative stiff wall on all sides but top and bottom where you have a viscoelastic membrane that moves. The sound produced becomes a mix of the drum head properties with certain dimensions and certain tightness and how the sound waves bounce around the stiff sides of a certain dimension drum-is my guess? Seems the pitch you hear is driven by size of the drum although you have some choice too=via the head properties and tightness, but the tonal quality is just a property of the drum= size, hardness of wood or metal of cylinder, hardware effects, how it made-stave, segment, ply??? Heck I don't have a clue-I'm winging it.
 
I haven't seen any equations dictating a drum's pitch at any given tension, but it would be a cool science experiment for you (or me). I'd buy a 12", a 14", a 16", and an 18” diameter acrylic drum (acrylic for bearing edge consistency as wood cannot do for this experiment) and the depths would be proportionally the same (let's say 12" 14" 16" and 18" just to make things easy). I'd then buy the exact same head for all drums (maybe Evans G14 for all bearing edges or Evans Hydraulic for all bearing edges; something that will produce a clearer fundamental tone with hardly any harmonic washy upper harmonics, and something without excessive external muffling [such as a dampening ring]). I’d then tension the heads on the drums with 8 lugs per bearing edge and create some sort of tension spring gauge whether it be standard or digital and place that device on each lug. I’d tension each lug on each drum to the same exact tension on the tension gauges. Theoretically the heads should be cleared (all lugs in tune with each other). I’d then measure each pitch and harmonic series of each drum. I’d repeat the process with different tension levels. In this way one could come up with an equation that dictates each drum diameter’s pitch at any given tension.
So let’s say that if an entire drum counterhoop is tensioned to 10 pounds on the drumhead and that drumhead vibrated at 55Hz on an 18” drum then I’d write that down. If the drum was 16” with 10 pounds of pressure on the drumhead counterhoop and the pitch was 65Hz then I’d write that down. Let’s say that a 14” drum tensioned at 10 pounds was 77Hz then we start to graph the rise in pitch per drum diameter. Just know that since drumheads vibrate along two planes (x axis and y axis) they have a different harmonic series than stringed instruments which vibrate one plane (x axis).
 

dboomer

Senior Member
I haven't seen any equations dictating a drum's pitch at any given tensio.

We have a winner! Drum pitch is determined by the head material and the tension. The drum diameter And volume may set range extremes but tension is the prime factor here.
 

John Lamb

Senior Member
My question is whether, all else being equal, a 16 x 16 tom has a pitch (and general tone) twice as deep as an 8 x 8 tom, and therefore also if a 12 x 12 tom has a pitch/tone exactly in the middle of the two.

I know length of a cylinder affects the pitch, but I've never heard that the width of the cylinder affects the pitch. The volume of the cylinder isn't the key point: The key point is the standing waves generated inside it.

Double the length and you get go up an octave (eg C2-C3). Triple the length and you go up an octave and a 5th (e.g. C2-G3).


That being said, the thing that drives vibration in a drum is not the shell, but the drum heads, its material and tension. Their vibration will be helped or hindered by the size/craftsmanship/material of the drum. But the width shouldn't make a big different to the contribution of the shell... but would make a big difference to the tension of the drum head.

Please, some physicist correct me if I'm wrong
 

Hollywood Jim

Platinum Member
OK, lets change the question a little bit.

I have a tom that is 12 inches in diameter and 8 inches deep.
And I have a tom that is 16 inches in diameter and 14 inches deep.
Both drums have exactly the same shell material and bearing edges.
Both drums have the same new heads, batter and reso, and all the heads are tuned to the same exact tension.

The two toms sound different. Why? What difference am I hearing?
Am I hearing a difference in tone? A difference in pitch? Why?

If both drums were 8 inches deep, would they sound exactly the same? Why?


.
 

Andy

Administrator
Staff member
Related to this thread, although not precisely to the OP, I'll be bringing some astonishing tuning revelations / observations to the forum in the coming weeks. I'm currently on the last day of our sessions, and we discovered something that has perplexed some real experts I'm currently working with. More later, as today's "extra" session is still secret, but I should get release permission soon.
 

John Lamb

Senior Member
OK, lets change the question a little bit.

I have a tom that is 12 inches in diameter and 8 inches deep.
And I have a tom that is 16 inches in diameter and 14 inches deep.
Both drums have exactly the same shell material and bearing edges.
Both drums have the same new heads, batter and reso, and all the heads are tuned to the same exact tension.

The two toms sound different. Why? What difference am I hearing?
Am I hearing a difference in tone? A difference in pitch? Why?

If both drums were 8 inches deep, would they sound exactly the same? Why?


.

No. The wider diameter will give the drum more volume - especially for the lower overtones. To make a larger diameter head vibrate at the same speed as a smaller diameter head, you'd need a lot more tension (think getting a string on a bass neck vs guitar neck) and that would affect the way in which the head vibrated, also changing the timbre - but not the fundamental. Meaning they wouldn't sound the same even at the same pitch.
 

single-ply

Senior Member
I've always thought of the head, which vibrates, as the source of the pitch. The shell is an amplifier (think marimba resonator).

The better the shell (roundness, quality of bearing edges) allows the head to produce a clearer pitch while the depth and wood quality give depth (tone) to the pitch. Compare a set of well made shelled drums to a Purecussion shell-less set. They both can be tuned to the same notes, but there is a vast difference in the quality of the sound produced. Same comparison can be made between a single headed tom to a double headed one.

This is, of course, dependent on proper tuning of the head(s) to produce a pure tone.

Just my opinion, of course, but that is how I've always thought about it.
 
I've always thought of the head, which vibrates, as the source of the pitch. The shell is an amplifier.

I've been thinking about this and other helpful comments (thanks) and I don't think it's correct to overemphasize the tightness of the head and de-emphasize the importance of the shell in determining pitch. Neither do I think that the shell is merely or even primarily the amplifier

Pitch is determined by the speed of the vibrations, with faster vibrations creating a higher pitch and slower vibrations creating a lower pitch. What's going on with head tightness, I think, is that the looser the head the more give it has when struck, and this give has the effect of slowing down the vibrations transmitted to the air beneath the head. Conversely, a tighter head transmits the vibrations pretty fast, because the head has less give, and raises the pitch. Also, not sure, but I'd guess that tighter heads cause the vibrations inside the drum to bounce around faster, which in a drum with a looser head would absorbed and slowed by the head.

I think (but am not sure) that this is why the tightness of the head has an affect on pitch. I do doubt my theory somewhat though, since according to it the harder a drum is hit, the higher the pitch, and I don't think this happens. However, maybe it actually does, but the effect of the force of the strike is so small compared to the tightness of the head that we don't notice it.

Anyway, head tightness has an obvious affect on pitch.

However, I seriously doubt that it is the only thing that affects pitch. The the shape, size, and design of the receptical that receives the vibrations from strikes to the head also affects the speed of the vibrations and therefore the pitch.

I'm thinking here of a flute, an instrument I play very little. The way to raise the pitch by an octave on the flute is simply to blow harder. What seems to be going on is that blowing harder increases the speed of the vibrations of the air inside the flute, and this raises the pitch. Therefore, blowing a flute harder is analogous to a tighter drum head in that there's just more initial force transmitted to the air inside the cylinder and thus faster vibrations.

However, the notes within the octave on a flute are not raised or lowered by how hard the player blows, but by changing the shape of the cylinder, which the player does by pressing or releasing the various keys that cover the air holes. Also, tuning a flute is basically a matter of shortening or lengthening the overall cylinder. Add that the size of the "flute" itself seems to be related to pitch, with little piccolos generally being higher pitched than a flute, for example.

Anyway, if reasoning along these lines is correct, I'm pretty sure that the shell of the drum plays a large role in its pitch (as well as of course other aspects of its sound). It does because it too determines the speed of the vibrations. Generally, the larger the drum, the lower the pitch, probably because the larger the drum the more air there is that the vibrations must travel through, and this slows them down.

Of course, mere aggregate size of the air pocket inside a drum is surely not the only factor. The ratio of width to depth probably changes pitch and much else as well. Also, I'm now wondering about other aspects of drum shape. Congas, for example, are more of an oval than a cylinder shape, while bongos tend to be tapered. I wonder why this is and why almost all regular drums stick to the cylinder shape. Even more, I'm now wondering if drums could be made with a series of little doors on them analogous to the keys on a flute that could be opened and closed to change the pitch.

Oh well, just trying to think it out. Lots of good posts. Thanks.
 

John Lamb

Senior Member
The drum head works like a trampoline. The stick hits the head and the the head wavers back and forth. Each waver pushes air around, creating waves. This process is very much like a rock throw into a pond. The difference being that water doesn't compress so it stacks up making vertical waves. Air waves just compress. These waves are sound waves. They can be made bigger by the drum head or smaller. A drum then modifies the waves created by the head.

It is similar to a guitar. It is the strong that makes the sound, and the body of the guitar amplifies and modifies the waves created by the string. The tight ness of the string causes the string to shake faster in the same way the tightness on the head causes the head to vibrate faster. The speed of the vibration is pitch.

Check out this video of a snare at 3000 fps

https://www.youtube.com/watch?v=STSWLX23xqc
 
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