6. Tuning the Resonant Drumhead – What, Why and How?

Do you ever wonder why cylindrical drums have two drumheads, what exactly does the resonant head add to the acoustics of the drum, and how exactly does it influence the sound? Well, there are two main reasons..

Firstly, a cylindrical drum with just one drumhead is very inefficient, energy wise, because as soon as the head is hit, all the energy created from the hit gets transferred into acoustic energy that leaves the drum and heads off into the space of the room or performance area. If we have a second drumhead, then a good proportion of that energy is reflected back into the drum, and the two drumheads vibrate together, holding the energy inside the drum within the air that is trapped inside. This makes drums resonate for longer, and hence in a more musical way, and allows more powerful and louder sounds to be emitted by the conservation of energy within the drum.

The second reason is owing to the sonic influence the resonant drumhead has on the drum sound. Before explaining in full, let’s just consider the vibration profile of musical strings (as in guitar) and bars (for example metal glockenspiel bars or wooden xylophone bars)… it’s an incredible phenomena of physics, but strings and plates vibrate with perfect harmonic overtones. This means that the main fundamental frequency of a string or bar is joined by many other frequencies that are harmonically related, which results in a beautiful rich tone that is much more musical than a single frequency all on its own. The additional overtones are, by a chance of physics, at perfect multiples of the fundamental frequency, so a string tuned to A at 110 Hz also vibrates at harmonics of 220 Hz, 330 Hz, 440 Hz and so on, so does a bar tuned to the same frequency. This acoustics fact is what makes string and tuned percussion instruments so musical sounding. In fact, the same principle applies to the vibration frequencies on woodwind and brass instruments too!

Now, unfortunately, single taut drumheads, or circular membranes as we call them in acoustics, do not vibrate with perfect integer harmonics, they vibrate with what we call ‘in-harmonic overtones’ that are at seemingly random overtones of the fundamental pitch, hence drums don’t sound so musical as string or woodwind instruments. Actually, much research has been done on this subject, and we see that single drumheads vibrate at seemingly random spaced overtones of the fundamental frequency, none of which are musically related to each other.

In the above diagram, we see that each frequency ratio is fixed for a single drumhead, so cannot be ‘tuned’ to have overtones at musical intervals. For example, a drumhead with a fundamental frequency of 100 Hz will have overtones at 159 Hz, 230 Hz and 292 Hz, none of which are musically or harmonically related to the fundamental.

BUT, with a resonant drumhead on the drum, this allows us to manipulate the relationship of frequencies in the drum and tune so that some of the frequencies, particularly the most powerful ones, do fall into musically related values. As a result, two-headed drums can be tuned to resonate with a much more musical tone, which gives the drums a more interesting, warm and in some respects a more ‘professional’ sound. Of course, it is not possible to make all of the drumhead frequencies harmonically related, so drums will never sound as musical in terms of pitch and resonance as guitars or clarinets, but it is a small improvement that is worth making. As a result two headed drums have become normal in pop and rock music and many drummers have learnt to tune drums until they sound good on this principle, without really having any huge need to understand the underlying science. But understanding the science helps you to understand what to listen out for, especially if you are learning drum tuning and you don’t want to wait to build up years of experience to get good at it. To hear the difference and value of the resonant head, just take off a resonant head sometime when tuning, and you’ll immediately hear the value that the second head brings, both in terms of power and tonality.

*An interesting side note is that tympani and tabla instruments, for example, are designed to have very specific shape and construction, which is another way of improving the harmonic nature of the overtones from a percussion instrument that uses circular membranes or drumheads.

So how do we go about tuning the resonant drumhead sensibly and repeatably? Well, that’s a good question and you might find lots of different approaches described online. But our published and verified research here at iDrumTune has led to a foolproof approach that really works, helps you get the best possible sound out of your drums, and ensures that you always know how to tune the top and bottom heads relative to each other so that you always get the sound you are looking for.

Quickly, let’s mention the different types of drumheads used on the batter and resonant side, though we’ll do a much more in depth post on drumhead choice later on. We tend to use a lighter (thinner) drumhead on the bottom resonant head, this is because it allows an additional range of tonality to be incorporated into the drum sound. We tend to use thicker heads on the top also to avoid excessive high frequency (overtone) ringing that thinner drumheads give, but it’s ok to use a thinner head on the bottom because they don’t ring out as much as the head that is being hit. Furthermore, it is possible to use identical heads on the top and bottom, but that limits the frequency range of the drum and also introduces the potential for beat frequencies if the two heads are tuned similar but not exact (similar to the beat frequencies we identified when discussing lug tuning in the previous post), so we recommend using thin resonant drumheads on the resonant side, as are supplied as standard with most brand new drum kits. But remember, THERE ARE NO FIXED RULES! If you find your resonant drumhead is giving off a sustained overtone that you just don’t like the sound of, a coated or damped drumhead on the underside may just be the solution you are looking for.

So, onto actually tuning the drumheads relative to each other: The first thing to do is ensure that both drumheads have been put on and are relatively equalised – so whatever the frequencies, go around the batter head in lug tuning mode and ensure all frequencies are within 1 or 2 Hz. Then do the same with the drum turned over for the resonant head.

Now, we want to find out what the acoustic relationship between the two heads is, and ensure that they are sensibly tuned relative to each other. Here’s the cool thing, because the resonant head has an influence on the response of the batter head, we don’t actually have to measure the frequencies of the resonant head itself, we just have to measure the batter head frequencies and see how they change when tightening or loosening the resonant head. So ultimately the resonant head controls the relationship between the batter head’s F0 and F1 frequencies. Let’s have a look at this in practice…

If we take a reading of the batter head in the centre, let’s say we get a F0 reading of 100 Hz. Now, take a reading of the batter edge frequency, let’s say it gives a reading of 160 Hz. A quick bit of maths tells us that F1 is 1.6 times greater than F0. Ok, so how is that information useful? Well, when we discussed string vibration frequencies we noticed that they tend to vibrate with exact harmonics of the fundamental, i.e. 2 or 3 or 4 times the fundamental, well perfect harmonics are not possible with drums, but musical intervals are. What are musical intervals we hear you ask? Musical intervals are those that define the gaps between frequencies in a musical scale of the space of an octave. Let’s look at this on the piano keyboard… we see from C to C there are 12 piano kets in between, but a major scale has only 8 notes, those being C-D-E-F-G-A-B-C for the scale of C Major. Well, we can see the frequency differences between each of these notes, which are all musically related to the root note. For example we call the third note in the major scale the major third (surprise surprise!) and the major 5th is the fifth note in the scale, which is G in the scale of C Major. By looking at the frequency ratios (i.e. mathematically dividing one frequency by the other), we can see the multipliers for each note in the scale, and it’s these multipliers that we suggest considering when tuning the resonant drumhead of a cylindrical drum. Here’s the list of multipliers for a single octave…

Frequencies and multipliers:

If you look back at the piano keyboard and musical frequencies we showed in a previous blog post, you can see these ratios in action. For example, see that the Major 5th of note C3 (130.8 Hz) is G3 at 196.0 Hz, and some simple math shows that 196.0/130.8 = 1.50.

Back to our example, where F1 on the batter head is 1.6 times greater than F0. Ok, we can see from our scale that 1.6 is a bit in between a perfect 5th and a perfect 6th. So assuming we want this relationship to be a perfect 5th, what would we do with the resonant drumhead? We mentioned in an earlier post that the fundamental applies equally to the batter and resonant drumhead, since they are fully coupled in their vibration mode. However, there is much less coupling between the two drumheads with respect to the F1 edge mode, which is much more localised to the batter drumhead. So, by tightening one drumhead and loosening the other, we can make the batter head’s F0 and F1 frequencies come closer together or further apart, which is pretty cool. Here at iDrumTune we’ve decided to call the relationship between the two frequencies the Resonant Tuning Factor or RTF for short, since the resonant head tuning allows us to make this value greater or smaller if we know what we are doing. In short

• To increase RTF: increase batter, loosen resonant head
• To decrease RTF: loosen batter and increase resonant head

Try it to see for yourself – the iDrumTune resonant head tuning feature is great for this. First take a reading of the batter head at the centre (F0) and then on the batter head at the edge (F1). The app then tells you the RTF value and indicates what to do to increase or decrease the RTF. You should be able to change the RTF value by tightening and loosening the batter and resonant drumheads as described above, so make some small changes to the tension on each lug on the top and bottom head, and try again to see how the RTF has changed, until you get the sound or the RTF value you are looking for.

The image above shows the iDrumTune Resonant Head Tuning feature. First the app informs you to hit and read the batter head in the centre (a), then take a reading at the batter head edge (b). The RTF value is then calculated and gives advice on how to adjust the batter and resonant drumheads in order to achieve a RTF value of around 1.5 (c).

Now, we suggest aiming ideally for an RTF of 1.5, for two reasons. Firstly, this represents a perfect musical fifth, which is a good place to begin with when deciding how you want your drums to sound. Secondly is a rather interesting acoustics phenomena about a ‘phantom sub harmonic’. It’s not anything to get too engrained in, but if we have a frequency and another frequency at 1.5 times the first, then our brain anticipates that these are related by an even lower frequency at 0.5 times the first frequency, which gives the sense of a low frequency power to the sound. This lower frequency isn’t actually there, it’s an illusion on our hearing, but sounds great all the same and makes us perceive the drums as having a bit of extra bottom end power (it’s also the same sneaky technique used by loudspeaker manufacturers to make very small speakers sound like they have good low-end bass response!)

Actually, it doesn’t really matter what RTF value you tune to, but it makes sense to have this somewhere between 1.3 and 1.8 and ideally to one of the musical benchmarks in that range. Higher than that starts to get towards an octave and miss out on the musical richness of an interval overtone, and lower than that starts to get too close to the main fundamental. It also makes sense to have all your drums use a similar RTF in the kit, to ensure that the tone structure of each drum is similar and consistent. The great thing about using the RTF value is that if you change drumheads, you can immediately get back to the same sound for your drums as you had before – if you use the same drumheads, the same fundamental pitch and the same RTF value, then the drum will always sound the same, day-in-day-out.

So that’s everything you need to know about the resonant drumhead, and how to use iDrumTune to quickly understand how the two drumheads are tuned relative to each other. This is really valuable for knowing that you’re in the right ballpark, for perfecting the sound of your drums, and for tuning to a repeatable sound every time you change heads or move the kit around. It’s obviously a pretty in-depth area of acoustics and drummers certainly don’t need to be acoustics experts, but we believe that a little bit of knowledge like this can really help you get the best out of your kit, and learn the more advanced elements of tuning easily and effectively. In fact, this new approach to tuning with the Resonant Tuning Factor (RTF) was recently presented and published at the 2017 Audio Engineering Society Conference in New York by iDrumTune inventor Professor Rob Toulson, so if you’d like to have a read of that article, you can go and download it here:

https://secure.aes.org/forum/pubs/ebriefs/?elib=19325

And for those really interested in the academic side of things, this approach is all based on some earlier research by Prof Toulson and collaborators, presented first at the AES New York Conference in 2009 and published by the Journal of the Acoustical Society of America in 2012, which can be accessed online here:

https://asa.scitation.org/doi/10.1121/1.3651794

We’re wishing everyone a happy time tuning their resonant drumheads! In the next tutorials we’ll look at drumheads in much more detail and move on to considering the tuning of the whole drum kit. We’ll explore different approaches to tuning each drum to have a unique and exciting sound within the kit and tuning each drum to different intervals so that your fills really stand out with an interesting and musical sound.

By Professor Rob Toulson – Professor of Musical Acoustics and Inventor of iDrumTune Pro.

iDrumTune Pro is available in the Apple and Google Play App Stores for iOS and Android.

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