ABOUT DRUMS

The following discussion while perhaps a little technical, does not require math to understand and is  useful for tuning with more than just the RESOTUNE technology.

In the process of developing the first scientific drum clearing technology we learned a great deal about how drums resonate, that is not well documented or explained in technical descriptions of the science surrounding drum head vibrations. We want to share what we feel may be useful when trying to tune or voice drum sets using any tuning approach (even those other guys, if that's all you have).

Drum Tuning- Is it Art or Science?   

You might expect us to come down strongly in favor of science but first let's explore what we're really talking about when we discuss drum tuning.

When tuning a typical musical instrument that tuning is unambiguous regarding what note you are measuring and targeting. Also tuning to a note doesn't involve multiple adjustment lugs for one note. Drums on the other hand express multiple complex resonances and literally every lug on both the top and bottom heads will influence the actual note frequency of the fundamental (lowest) resonance. Since drum overtones are not harmonically related, they will voice different notes, typically in different octaves, expressing simultaneously. Using different weight and different tension for top and bottom heads, you can realize a near infinite palette of voicing possibilities.

Measuring and adjusting to a specific note frequency is what we normally consider tuning a musical instrument. The previous state of the art for drum tuning instead, measures a mechanical parameter like lug tension or head deflection and utilizes the relationship between tension either directly from head deflection or indirectly from lug tension to predict the head resonant frequency. The science behind this is pretty straightforward and if the rest of the drum is manufactured to a high tolerance this can get you pretty close to clear or balanced. The ability to accurately predict note frequency is unlikely but that is not most important for many applications. Using the same weight drum head adjusted to the same tension or deflection should result in a similar note frequency and sound, but this is indirect and calculated (if at all) so not very accurate.

The primary activity that we call drum tuning, has little to do with tuning to specific notes but is more concerned about making all of the lugs agree with each other. This is more correctly called "clearing" the drum head, since the note frequency of such "tuned" drums is rarely even considered.

We decline to offer specific advice regarding notes to target when tuning. That really varies from kit to kit and is often a subjective or personal choice. Instead we will describe some of the unique characteristics of how drums resonate hopefully to provide you with useful insights to assist you in making personal voicing decisions for your drum kit, and your sound. 

How to tune without a RESOTUNE  

Since most drummers don't own a RESOTUNE (yet), a quick overview of alternate tuning approaches is useful. The following exploration of the idiosyncrasies of drum resonances will be applicable to any drum tuning technique used.  

The first and simplest tuning approach is using a lug torque measuring device. In concept if all the lugs are tightened to the same torque, the head tension should be uniform and the drum head will be clear.

A second approach promises improved clearing by eliminating the variables of non-uniform lug hardware. Instead they directly measure head deflection with a dial gauge, in response to a reference force (small weight). If this technique is carefully applied you should get reasonably repeatable note tuning when using the same weight heads. It is pretty important when using this approach that you properly place the gauge relative to lugs being adjusted for measurement.

My favorite alternate tuning technique (other than RESOTUNE) can also be a little variable in result because it relies upon our short term pitch memory and manual dexterity, but I like this approach because it eliminates all the physical variables like drum head material, hardware quality, bearing edges, etc., by listening to the actual drum head vibrations. I know this approach as "tap-tuning" but it probably has other names too. Briefly stated "tap tuning" involves tapping lightly on the drum head with a finger or drum key at head locations roughly halfway between the lug being adjusted and the drum head midpoint. To suppress the lower fundamental and make it easier to hear the lug overtone, another finger is held pressed lightly down against the drum at the drum head's exact midpoint.

Each lug is then adjusted to voice the exact same pitch when tapped. One downside is that variations in the finger pressure applied at mid drum may influence the pitch slightly and human pitch memory is well, human. Some people like to sit the drum on a carpeted floor or tabletop to damp out the opposite head. This helps suppress the fundamental too but is not as effective as the finger placed lightly at mid drum on the heard your clearing.

The precision and repeatability of tap-tuning can be enhanced by using a reliable note reference. This could be something as simple as an electronic keyboard, a pitch fork, pitch pipe, or perhaps even a general purpose instrument tuner that has a reference sound output.  

The Lug Overtone  

If we look a little closer at this lug overtone used for tap tuning it will give us some useful insights into how drum heads resonate and interact with each other.

While intuition might suggest that the round shape of a drum head should be symmetrical and musical, the physics and math of how the higher overtones develop, is not so aggreable.

In most musical instrument the overtones follow the same physical path as the fundamental. Since the speed of the sound waves will be constant, multiple repeat trips over the same physical path results in a integer multiple of the fundamental frequency. These integer multiples are called harmonics and fall on octave ratios above the fundamental, in typical musical instruments.

The overtones that occur in a round drum head are instead following different physical paths across and around the drum head. As we may recall from high school geometry, the diameter or path length straight across a circle and the circumference or path around a circle differ by the mathematical constant pi (3.1415...). Since the outside rim edge is clamped and doesn't vibrate the actual lug overtone path is not the more than 3x longer path it would be at the rim edge but approximately half that, or 1.6x. This is a gross simplification of the actual math involved. The important point to take away is that the ratios are not integer multiples like all other musical instruments but contain a pi term and other less neat multiples. The overtones will not simply be the same note an octave higher so typically unrelated musically.

The specific overtone used when tap-tuning and also by RESOTUNE for lug clearing is called mode 1,1 .

Fig 1. "Lug" overtone (1,1) mode

In theory for an ideal drum head, this overtone  occurs at precisely 1.593 times the fundamental frequency. In practice when measuring real drums this ratio varies all over the place due to interaction between the mass and tension of both the the top and bottom heads. The theoretical 1.6x ratio only occurs when the top and bottom heads are identical in weight and tension. There is an upper limit to how high the overtone can range at a little over 2x the fundamental with the bottom resonant head completely removed (see fig 3). Likewise the ratio can be shifted below 1.6x by detuning the resonant head the other way. The important observations to make with real (two headed) drums is that this overtone ratio is not only not harmonically related, but it is not even a fixed ratio.

Fig 2. Fundamental or whole drum (0,1) mode

When tap tuning, the purpose of placing your finger at precisely mid drum is to damp or prevent the fundamental resonance (mode 0,1) from voicing. When this primary resonance mode is damped the energy from tapping the head will mainly excite higher overtones that have a null or node at that damped midpoint. Placing the drum on a carpeted surface damps the bottom head, this indirectly damps the fundamental in both heads and shifts the frequency in both slightly lower.

An important characteristic is that this lug overtone is basically local to the top head and only minimally influenced by the tension of the bottom head. The bottom resonant head is however not completely without influence on this opposite head lug overtone resonance. One very powerful example of this is what happens if the bottom head is removed. The lug overtone note does not change, but the actual resonance mode does. After the opposite head is removed the batter lug overtone now vibrates in resonant mode 2,1  (see image below).

Fig 3. Lug overtone (mode 2,1) with only one head mounted. 2.135x fundamental note frequency.

While the lug overtone pitch didn't change, when we removed the opposite head, the lower fundamental note shifted lower. This ratio while still not at a musical full octave spacing, will be consistently 2.1x since there is no longer a second head mass pulling the fundamental note up or down relative to the lug overtone.

This one head approach is used on "concert toms". It will deliver a much more consistent sound than two-headed drums in response to tuning, but lacks the variety of voicing possibilities available from using two heads. 

The classic orchestral drum sound comes from the tympani. This special type of one-headed drum uses a curved, sealed, rear chamber. This has the same effect as holding your finger on the drumhead midpoint while tap tuning to dampen the fundamental note. Since the rear chamber is airtight any vibration in mode 0,1 (see fig 2) would have to compress and rarify the captured air volume. Since the fundamental is now significantly damped the "thud" or lower frequency fundamental note is suppressed and the lug overtone (mode 1,1 fig 1.) dominates this drum's sound. This design gives tympani drums a more pitched or tonal characteristic sound  which facilitates playing actual notes in performance of musical compositions.

How do the two heads interact?  

At the lowest frequency fundamental resonance mode (0,1) the two parallel drum heads move together as if they were connected together. The air inside the drum acts like a fluid and couples the two heads together.

This coupling is so significant that the note frequency of this fundamental resonance is determined by the combined mass and tension of both heads together. That's why the fundamental frequency changed in the earlier example when we removed the resonant head completely.

The importance of this for drum tuning or voicing is that changing the tension of either the batter or resonant head will change the pitch of this combined fundamental resonance in both.

The lug overtone is notably different in that one half of the drum head is pushing down while the other half is pulling up so any internal pressure roughly cancels itself out and the bottom head doesn't move in strict sympathy like it does in the fundamental resonance example. As this should suggest, adjustment or tension of the bottom head lugs do not significantly affect the top lug overtone note frequency, and in real drums they don't. 

This difference in coupling is quite noticeable. If you place a RESOTUNE on top of a two head drum and excite it at the fundamental note, you can feel significant vibration by touching the bottom head. This at any of the higher overtone resonances there is very little sympathetic vibration felt.

Clearing the lugs and uniformly tensioning the batter head is very important because this is the head you strike. While this is obvious to anyone who has ever beat on a batter, where you strike the head surface determines how it responds. If you strike the drum head dead-center you get a deep thud as you drive full energy strongly into the fundamental note. As your stick hits land closer to the rim edge you excite progressively higher overtones sounding at progressively higher note frequencies.

While we have identified the strong interaction between batter and resonant head at the fundamental note, there are also subtle interactions regarding the relative tuning of the bottom head with respect to the top. Since the fundamental note is the average tension of batter and resonant heads you can realize the same fundamental note from numerous combinations of the batter head either tuned above or below the resonant as long as the combined average tension is the same.

Even though the bottom head is not being actively struck, it's lug overtone resonance will also be excited when you strike the top head. When the batter head is struck both lug overtones will voice but if the two heads have different decay rates as you would expect from using different tension and/or different mass heads, the lug overtone that decays slower and remains longer will appear to bend or pull the pitch of the drum to it. Again there are a huge number of possible combinations available but this broadly explains what is going on when you use different weight batter and resonant heads and specifically detune the resonant lug overtone above or below the batter lugs.

Other variables that can alter the relative tuning between batter and resonant heads are different head material, special surface treatments, and even non-uniform heads with added mid-head weights or outer damping rings.

I suspect a lot of the effort in unconventional head designs is to sound less bad when not properly cleared because of the apparent difficulty for so many drummers. Some head designs may be trying to pull the overtone-fundamental ratio toward something more musical. I would avoid non-standard heads until you have explored what sounds you can realize by properly adjusting conventional heads.

If if you have a steady hand and at least one good ear you should be able to clear most drums with the tap tuning techniques described.

While at first glance this may seem like an unmanageable number of possible variations, in practice you will gravitate toward a batter lug tension that gives you a good stick feel when playing. Changing the resonant head weight or tension allows you independently tweak the fundamental note (thud) and perhaps pull or bend the after ring up or down for the same batter tension.

If you don't have the ability to electronically store and recall specific tuning information after you get a drum voicing you like, consider keeping written notes with the type of heads used and whatever tension information is available. If manually tap-tuning there are sundry simple frequency references that could be used to make  that technique more repeatable.  

 Putting it all together  

To review a properly tuned/cleared 2-headed drum will have 3 important tuning related notes. The batter lug overtone, the resonant lug overtone and the combined fundamental resonance. The lower fundamental note is controlled by the tension and mass of both heads so there is no need to consider it separately as long as you manage both lug overtones.

The batter and resonant lug overtones can be the same note, but often will be tuned to different notes. The drum's "voice" will be the product of all three notes and the and relative head decays.

Science can help us precisely clear a drum head to any given note within the drums range, and digital memory (or pen and paper) allows us to return to previous tunings when desired, but ultimate selection of what notes to tune to will always remain a very personal human undertaking.    ________________________________________

A well tuned drum kit is a pleasure to play. Even if you don't have access to the latest technology, it's always worth doing the best job you can you can using whatever tools you have available. We hope this information is helpful.

Here is a link to another description of "Tap tuning.  tap tuning link

Here is a link to a comprehensive discussion of tuning and voicing drums  Prof sound

The math describing this is beyond our basic discussion but for more see  Acoustics and Vibration Animations - Dan Russell, Kettering University

I also recommend the book "Science of Percussion Instruments"  by Thomas D. Rossing for a broad technical discussion of several different types of percussion instruments.