9. Timbre: The Truth about Drum Shell Vibration
Updated: Oct 14, 2020
With all musical instruments, there’s a hidden quality that makes some just sound better or different to others, and some instruments which sound more suited to a certain style, genre or even the musician and their performance traits. Sometimes there’s no right or wrong; some pianists play a Steinberg, others prefer a Yamaha. Some guitarists play a Gibson Les Paul and others choose a Fender Stratocaster. But these instruments can all be tuned the same, to give the same frequencies when played and hence to allow a consistent and optimal sound every time. So if these instruments have identical tuning, what is it that makes them sound different? Well, that is all the other magical qualities of the musical instrument, which make some instruments sustain notes with a long clear tone while others sound dull and lifeless. Some instruments have rich overtones and harmonics, yet others produce sounds more like pure sinewaves. Drums, just like any other instrument, are a great example of this.
All drums sound different, given the multitude of choices for drum designs, drum shell materials, diameters and depths, the metal hardware fixed on the drum and of course the type and design of drumheads themselves. All these things influence and contribute to the resultant drum sound, in the same way that an acoustic guitar with nylon strings sounds very different to a solid electric guitar with steel strings. The term for describing the sonic differences between two instruments which are tuned the same is ‘timbre’. It’s a kind of catch all term, in that it really just means ‘everything about a musical sound not associated with tuning or performance’, and hence describing everything associated with the qualities that the instrument itself brings to the sound that we hear when it is performed.
Timbre therefore is bit of a strange term, because it is defined best by discussing what it isn’t rather than what it is! But with that in mind, it’s a very useful term to help us discuss how two seemingly similar instruments differ in their sonic characteristics.
If a musician plays the same chord in the same way on two different guitars, the timbre is what defines the difference between the two sounds
A soft middle C note on both a trumpet and a clarinet differs only by the timbre of the sounds
The difference between the sound of two singers both singing a forte (loud) A4 note is the difference in timbre of their voices
Two drums tuned to have the same fundamental and overtone frequencies differ in sound by their timbre
So, we now know that the timbre of a drum is the term that is used to describe the sonic differences between two drums that are tuned to the same frequencies and are played in the same way. That’s great, we know that timbre is therefore independent of (or not determined by) the tuning or the performance of the instrument, and so we can dig a bit deeper to understand what physical things contribute to the sonic timbre of a drum. We already gave a list at the start of the blog, including:
Size and shape of the drum
The material of the drum shell
The construction and design of the hardware attached to the drum (including lugs, tuning rods, hoops and any snare or other attachments)
The way the drum is mounted or the stand it is positioned on
The drumheads that vibrate and generate sound from the drum when hit
The drumheads are of course very important and influential, and we’ve discussed those separately in the previous tutorial specifically on drumheads. So, attempting to keep things fairly simplistic, we’re predominantly talking about the drum shell and the hardware fixed on the drum shell.
Before we start looking at the frequencies of a drum shell, it’s valuable to cover one key acoustics theory before proceeding, and that is about how weight and mass affects the frequency of an object or vibrating system (i.e. a number of objects connected together). In the video below, there’s a simple experiment with a tuning fork. Initially the tuning fork vibrates at a pure musical frequency of F4 = 173.5 Hz, as measured by the iDrumTune Pro app.
But, when you watch the video, see what happens when we add some extra weight to the tuning fork – every time we add weight the frequency of the tuning fork changes, and we see that more weight results in a lower frequency. So, with additional weight added, the tuning fork no longer vibrates at its pure musical frequency, and it would be totally useless for using as a reference pitch if it were used with some weight added. The same applies with removing weight, if we were to file the tuning fork down or saw a little bit off, then its frequency would go up. So this tells us that we need to consider the system as a whole single vibrating system and it’s not possible to just consider the tuning fork’s own frequency if it has other attachments, because as soon as we add anything to it, that frequency is gone, irrelevant, it doesn’t exist anymore. With weight added, the tuning fork has a new frequency altogether.
So why is the tuning fork experiment relevant to drums? If you think about it, a drum is exactly the same as a tuning fork with weight added. We start with a perfect clean and round drum shell, and then add lugs, hardware, hoops, tuning rods and drumheads to the drum shell. We can hence do the same experiment with a drum shell. First let’s look at how a drum shell vibrates as shown in the little animation here; the shell vibrates in and out like a circle that gradually deforms and reforms periodically.
This is how most circular or cylindrical structures vibrate when struck on axis, though we do also see more complex deform-reform shapes relating to overtone modes of going to a high level of scientific detail. *The great musical acoustics expert Professor Thomas Rossing has proven much of this theory relating to drum shell vibration, and there is some very scientific discussion in his book ‘Science of Percussion Instruments’, for those who are interested to go deeper into the shell vibration theory.
Moving to the vibration analysis of a drum shell, in the video below we start with a simple drum shell, stripped of all hardware and attachments, and measure its vibration frequency by hitting it gently with a mallet. The bare shell of the drum used in this example has a frequency of about 90 Hz. Now, when we add the tuning lugs and hardware (i.e. extra weight!) the shell starts to vibrate at a lower frequency when hit by the beater - the shell vibration frequency becomes around 80 Hz with three lugs attached and 73 Hz with all six lugs attached. Adding hoops makes a huge difference too, because they not only add more mass, but they are also very rigid and actually attempt to stop the drum vibrating in the deform-reform profile, this results in a lot of new frequencies occurring in the drum as it approaches that of a complete drum which we would play in the drum kit. So with one hoop added, we have a drum that vibrates at a fundamental frequency of about 80 Hz.
It gets harder to measure the shell vibration frequency as we add more and more things, particularly the hoops which do a good job of stopping the shell from vibrating much at all, but we know one thing for sure, its vibration profile and hence the drum shell’s sound is very different with all the hardware attached. In the next video, we give a quick recap of the different shell vibration frequencies and then measure the shell vibration with the drum fully assembled, with both hoops and drumheads in place. What we see is that, with the addition of the second hoop, there is no trace of the shell vibration frequency at all; the hoops have stopped the drum shell from vibrating with an amplitude (volume) that is big enough to measure. We see lots of new frequency peaks, because the drum is now a complex vibrating system, and you can certainly hear the metalic vibration of the hoops themselves too. With the fully assembled drum, the shell is of course still vibrating and it is still providing a component to the sound of the drum, but it is very small and subtle in comparison to the volume of sound that is generated by the drumheads vibrating. This is why we can tune two drums identically, but they will still sound subtly different - the timbre of the shell, hoops, the lugs, the mounting and the style and type of drumheads themselves all give the drum a unique sound that is independent of the drum's actual tuning. But importantly, regardless of their shell material, all drums can be tuned low and all drums can be tuned high - so the drum shell has no influence of this element of the sound, which is purely to do with the drumheads and how tight they are tensioned and how evenly they are tuned.
So science tells us that the vibration of the drum shell is only really relevant when considering the whole assembled drum. It’s really not of any major value to consider the vibration frequency of a bare drum shell in terms of performance or tuning, because that frequency changes as soon as you mount or attach anything to the drum – and it’s unplayable without lugs, hoops and drumheads attached! But, of course, the vibration of the drum shell is a valuable contributor to the complete sound of the drum, that being the timbre which we discussed earlier. It’s not just the shell and hardware either, the way the drum is mounted makes a difference too. If you know that adding mass changes the frequency (and hence sound) of something, then you should be able to understand easily that where or how an instrument is held in position can have a very similar effect on changing the vibration profile and hence the sound of the instrument too. So for the same reasons, it’s no surprise that a rack tom mounted on top of a kick drum sounds subtly different to the same rack tom mounted on a snare stand. But thankfully, these things - the drum shell design, the drum material, the types of hardware and the mounting of the drum, even the shape and accuracy of the bearing edges - are all related to timbre of the sound and not what we call the tuning of the sound. It’s an important distinction to make and is one that explains why two instruments (including drums) can be tuned the same but yet sound quite different.
So the truth is, there is no scientific or creative benefit to considering the vibration frequency of the bare drum shell when tuning the drum and manipulating drumhead vibration frequencies; they have no relation to each other and bringing discussions of shell vibration frequency to discussions on tuning can just cause confusion and propagate some of the old folk-law theories about drum sound. It just doesn’t need to be made that complicated. In fact, there’s a good simple ‘equation’ to think of when considering the timbre and it’s role in musical sound and that is:
instrument sound = performance + tuning + timbre
Any instrument can be tuned and performed in many ways – but it’s not easy to change the timbre of the instrument, which is inherent of the design and manufacture of the instrument. You can’t change the timbre of a Steinway piano very easily! But with a guitar you can choose to use your preferred type of strings and with drums you can choose different hardware, mountings and drumheads heads too, so we do have some control and choices to make with regards to timbre. The best thing to do is try to read reliable reviews and where possible try different drum types for yourself, particularly drums made of different materials, to find the timbre and sonic ‘magic’ that best suits your style and musical preferences. But keep your thinking about tuning and timbre separated, as with performance, they do of course all interact creatively and if you can maximise the quality of your tuning, the timbre of your kit and the quality of your performance, then you’re maximising the individual components of the equation above, and you can be sure to be sounding great whenever you sit down to play.
We can all tell if a musical instrument is being played well, or if it is tuned badly, but as with much art and creativity, often one person’s chalk is another person’s cheese with respect to timbre, and that’s one of the many wonders of music!
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.