Welcome to the Sound On Sound podcast where we'll be discussing the science of drums. My name is Professor Rob Toulson. I've studied the science of popular drums for over 20 years. I'm going to discuss some of the scientific theory on drums in a more user friendly way so that it can be useful to all musicians and studio engineers and of course to drummers too. So drums are often considered to be quite a simplistic musical instrument. They're often regarded as being non-musical or without pitch and it's fair to say very little detailed scientific research has been conducted on acoustics of popular drums compared to the piano, for example, or guitar or violin, which have had considerable amounts of research conducted. But actually, in reality, drums are one of the most complex and mysterious musical instruments from an acoustics perspective and most drummers will tell you and agree that they are exceptionally difficult to tune and exceptionally difficult to optimise the sound of. Nowadays it's well regarded that drums can be as musical as any other instrument. So in this podcast we'll discuss how drums create sound and how to manipulate the sound characteristics of drums so that you can get a creative edge to drum performances and recordings. We'll look at the key principles of drum acoustics and discuss some scientific aspects of drums with respect to making music and creative recording projects.

DEALING WITH MULTIPLE FREQUENCIES
Now, there's one key principle of drum acoustics that's relevant to all aspects of drum sound. It's quite a simple principle that applies to all musical instruments, but it's probably more relevant to drums and drum sound than any other instrument. So the key principle is that when you hit the drum head, many different frequencies are heard as the drum head attempts to vibrate in different ways and with different vibration shapes. So when we hear the sound of a drum, we hear multiple frequencies making up the overall sound. If you could put a strobe light on a drum at these different frequencies, you would see that each has a different vibration shape associated with it. We call these frequencies and vibration shapes vibration modes and depending on where you hit the drum, some modes and frequencies resonate stronger and louder than others. So many different frequencies are excited when we hit a drum head and two of these frequencies are hugely significant in the drum sound that we hear. It's really easy to hear the difference in these two frequencies, even if we can't see the drumhead vibration shapes themselves that they're associated with. So what are they? When hitting the drum in the middle, we mostly excite what we call the fundamental frequency of the drum. And it sounds like a boom. Let's hear it. Now if we move the drumstick over to the edge of the drum and hit the drum there, we excite what's called the first overtone frequency of the drum and it sounds more like a ping. Okay, let's hear those two together. First at the centre and then at the edge. Or three hits at the centre, three hits at the edge. So next time you're at a drum kit, try hitting your drums at the centre and then at the edge and notice the difference in sound. The same principle of vibration modes applies to many instruments, especially stringed instruments. So we can excite different vibration modes on a guitar for example. If I strum the guitar near the centre of the strings, near the sound hole, we excite much more of the fundamental frequencies of the strings. Let's hear that. Now let's hear the difference when I strum the guitar at the edge of the strings, near the bridge. Let's just hear those together, centre, then at the edge of the strings. So this acoustic principle applies to both drums and the guitar and many other instruments. Of course, we don't need to worry about this on the guitar for tuning, because we have a single tuning mechanism. However, drums are much more complicated, and we have many different locations where we can tune the drum and affect its sound. You can use a spectrum analyser to measure the different frequencies of a drum head. It's quite interesting, because with a spectrum analyser you can see the frequency peaks of the different vibration modes and you can see how the power of these peaks changes based on where you hit the drum. A few years ago, as part of my research, I created a mobile phone app called iDrumTune, which is essentially a spectrum analyser specifically designed for drums. I think this can be useful to experiment with, because you get to equate what you're hearing with the scientific data associated with the sounds. This feedback loop is really valuable for training your ears, so you can verify what exactly is causing the differences between different drum sounds that you hear. Let's go back to the drum that I initially used as an example. If I hit the drum in the centre, we get the boom sound. So let's take a reading. I can see the fundamental frequency of that drum when it's hit at the centre is about 93 Hz, which is about an F# on the musical scale. Now if I hit the drum at the edge, I can see that the edge overtone frequency is approximately 145 Hz. So we can measure the two different frequencies and see the relationship between them.

TUNING THE FUNDAMENTAL FREQUENCY
So having learned about the fundamental and the edge overtone frequencies, how can we use this for setting up and tuning drums? Well, most drummers tend to hit the drums near the centre when playing, so the fundamental is by far the most powerful frequency we hear in a drum performance. It may not be obvious from listening, but the top and bottom drum heads vibrate at exactly the same fundamental frequency. There's a mass of air trapped inside the drum and this causes the two drum heads to be coupled together, so they vibrate together at the drum's natural fundamental frequency. So when the batter drum head vibrates downwards, it pushes the air inside downwards, which then pushes the resonant drum head down too and the elasticity in the drum heads themselves and the air trapped inside cause the drum heads to vibrate, and this cycle repeats. So this is a principle proven by vibration theory, and you can verify it by measuring the frequency of a drum at the centre on both the top and the bottom heads. They'll always be the same centre frequency. So it's really important to think about the drum as a single instrument that is hit on the batter head and that causes all the other aspects of the drum to vibrate in unison. In fact, the drum head that you hit forces the other drum head to vibrate at certain frequencies. So if you turn the drum over and hit the resonant drum head, it's almost as if you're playing a different instrument. So it's not actually possible to tune the two heads independently of each other. They work together and create the overall sound of the drum and if you dampen one drum head in order to tune the other, you're effectively creating a different instrument again. So although this is quite a common technique, it isn't actually much help in achieving a desired drum sound. So let's explore the pitch range of a cylindrical drum. We know that changing the tension of the drum head, by tightening or loosening the drum head's tension rods, changes the frequency and pitch of a drum sound, in the same way that it does with a guitar string. So it's interesting to learn the pitch range of a particular drum. Now imagine a drum has just had two brand new heads put on it, and they're both at the point where they're really loose, but just tightened enough so they can vibrate when hit. This is essentially the lowest usable pitch of the drum. Now if we tighten either or both drum heads, then that pitch will go up. So imagine tightening both drum heads to the point where they're just about to snap, they can't take any more tension. Well, that's now the highest pitch of the drum. Let's hear that in practice. So I'm using a 13 inch tom with a coated batter head and a clear resonant head. First, I'm going to get both heads to finger tight. So I tighten the tuning rods from slack to a point where I can't tighten them anymore with my fingers. I apply this to both the batter and the resonant drum head. So I'm just tightening the drum as tight as I can with my fingers and that helps me to be confident that the drum has had the same amount of tension applied to each tension rod. Now at this point, the drum still isn't really very usable. It doesn't vibrate, the drum heads are still too slack. So what I'm going to do is just give a quarter turn to every single lug, both on the top and bottom. Okay, the drum head now vibrates. So I can take a reading with my spectrum analyser and that tells me that the fundamental frequency of the drum is 79.5 Hz. So now I'm going to adjust every tension rod on the top and bottom heads to make them just a little bit tighter. So having applied roughly the same amount of tension to each tuning rod, I can see that the drum's pitch has gone up, and let's take a reading of that. So the drum's pitch has now gone up a large amount. It's now at 117 Hz. Let's do that again and see if we can go much higher. I've now tightened all of the tension rods again, and let's take another reading. The drum's now at 153 Hz, which is almost double the original frequency, which was at 79 in the first case. So we've seen that this drum has a usable frequency range of about an octave, which is a huge amount. It means that drummers have a really large range to experiment with in deciding how they want their drums to sound. There's no particular right or wrong as to which of those is the best frequency. It depends more on the drummer's personal style and the type of music that they want to play. So you probably know that every musical note has a corresponding frequency. So if you want, it's possible to tune a drum's fundamental pitch to be on the musical scale. For example, 98 Hz is a G, 110 Hz is an A, 130.8 Hz is C. Because of the harmonic relationships of drums, it's not essential to tune to musical frequencies, but there might be some cases where depending on the music you're playing, it might be useful to tune the drums to their complement, either the key of the song or the notes of the bass guitar, for example. Moreover, it can just be really useful to know what the fundamental frequencies of drums are, in case you want to change drum heads or in case you want to keep a repeatable sound between performances and different days. So just for example, let's hear this drum tune to both G2 at 98Hz and then at A2 at 110Hz, so you can hear the difference. Here's G, 98Hz, and here's A, 110Hz.

SMOOTHING OUT MODULATION
So we've listened in detail to the fundamental frequency of the drum, now let's consider how the first overtone at the edge of the drum head is related to the drum's sound and tuning. Drummers will often listen to the edge of the drum at different locations around the perimeter of the drum head, in order to check that the sound is even at all positions. This is often referred to lug tuning, or equalising the drum head, or clearing the drum head. Now, why do they do that? Well, imagine that the drum head is actually an infinite number of strings connected across the drum head, through the centre, and between opposite sides of the rim. So, take a drum with eight lugs and there'll be four opposite pairs between the tension rods. Now, despite the drum head being a single object, it's very possible for one set of opposite pairs to be tighter or looser than another and, for instance, if we look down on the drum head, you can probably imagine that the north to south plane could be tighter than the east to west plane. In this case, the drum head won't vibrate evenly. What will happen is the drum head will attempt to vibrate at two very slightly different frequencies in two different directions. So what does that sound like? Well, if all the pairs across the drum head are tuned identically, then the drum head gives off a single smooth overtone and the drum sound has a decay that is clear and consistent. But an uneven tuning causes what we call frequency beating. Now this occurs when two similar but not exact frequencies are present at the same time. Frequency beating is also called amplitude modulation and it can be heard in an uneven drum, particularly in the decay of the drum sound. What we hear is the drum decay modulating louder and quieter at a beat frequency related to the two uneven vibration profiles. So let's have a listen to some smooth and modulating drum sounds. Here's a smooth drum sound and here's a modulating decay from an unevenly tuned drum. Let's hear another example. Smooth, modulating. Of course, drummers have known this for many years and they use their ears to hear and iron out the modulation that is caused when a drum is unevenly tuned. But it can sometimes be very difficult to hear and because of all the other frequencies that are present on a drum head, our ears can easily be fooled by what they are hearing. This makes it particularly hard to tune drums and it's why many drummers take years to understand and learn how to tune drums effectively.

HARMONIC OVERTONES
Let's turn our attention now to the mysterious resonant drum head. It's not even that obvious why drums generally have two drum heads. Well, most people agree they sound better with two drum heads but why and what's the best way to set them up? To discuss the resonant drum head, we need to look at another acoustics principle relating to harmonics and overtones. It's a phenomena of physics, but strings and bars always vibrate with integer harmonic overtones. Now what that means is, is that if the fundamental pitch of a bar or a string is tuned to, let's say A at 110 Hz, we get perfect integer harmonics at multiples of that frequency. So we'll get harmonics not only at the fundamental of 110, but also at double that frequency, 220, three times that frequency, 330, four times that frequency, 440 and these harmonics create sound characteristics that we like to hear in music. Now drumheads, or circular membranes, as we call them in acoustics, do not vibrate with harmonic overtones, they don't vibrate at perfect integers. So if the drumhead is tuned to 110 hertz, it won't have those beautiful sounding harmonics at 220, 330 and 440. Instead, drumheads vibrate with overtones that are not at harmonic intervals. However, if we put a second drum head on the drum, we can start to manipulate the relationship of frequencies and tune the drum 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 than single headed drums, and that gives the drums a more interesting, warm, controlled and musical sound. The relationship between the fundamental and the overtone of the batter head can therefore be manipulated by tuning the resonant drum head. The relationship between the fundamental and overtone of a drum can even be manipulated to be a specific musical interval and this sounds rich and interesting when both are excited. We can call the relationship between the fundamental and the overtone the resonant tuning factor, or RTF for short. So if a drum has a fundamental frequency of 100Hz and an edge over tone of 150Hz, then the RTF of the drum is 1.5. 1.5 is quite a good number actually, because it represents a musical fifth and a half harmonic. It's another acoustics phenomena that if we hear two frequencies of 1.5 times apart, our brain interprets these as being harmonically related and perceives a phantom harmonic at half the fundamental, in the case of this example, at 50 Hz. So although the frequencies that are actually present are 100 and 150, our brain assumes there should have been a 50 Hz subharmonic too and this can make things sound a little bit more bassy and a little bit more powerful than they actually are. It's a trick of our ears, but it works and it makes things sound powerful and exciting. So the 1.5 RTF value is a bit of a magic number and it's amazing how drums start to sing when they have the 1.5 RTF. I suspect that when a drummer tunes their kit and it sounds just special and rich, it's often because they have with or without knowing tuned to the 1.5 RTF ratio. It's not an exact or even an essential science, but usually the RTF between 1.5 and 1.8 works pretty well and each sounds subtly different. A musical 6th is a 1.68, and this sounds quite rich in musical 2. So how do we manipulate the RTF, or the resonant tuning factor? Well there's a really simple rule based on the science of how the drum heads react. To increase the RTF, increase batter head tension and loosen the resonant head tension. To decrease RTF, loosen the batter head tension and increase the resonant head tension. So it's possible to achieve the same fundamental pitch of a drum with many different RTFs, but some just sound better and more musical than others. You do need a spectrum analyser to measure the RTF value, or some pitch perfect ears, but experiencing the difference is a really valuable thing in developing your ears for tuning and recording drums. Okay, let's hear our 13 inch tom tuned with some different RTF values. In all cases this drum is tuned with a fundamental pitch of G at 98 Hz. First we have an RTF of 1.75, which means the overtone is at 172 Hz. Next we have an RTF of 1.62, giving an overtone of 159 Hz. Now let's hear the drum tuned to an RTF value of 1.5, which represents a perfect fifth relationship between the drum's fundamental and overtone frequencies. So while we're at it, let's listen to another RTF value below 1.5. So this drum is tuned to 98 Hz with an RTF value of 1.37, which means its overtone is 134 Hz. So let's hear all four again. The first drum has an RTF of 1.75, second has an RTF of 1.62, the third has an RTF of 1.5, and the fourth has an RTF of 1.37. All drums are tuned to the same fundamental frequency of 98 Hz. For each version, you should be able to distinguish both the fundamental and the overtone frequencies and get an understanding of how the two frequencies relate to each other. Of course, a drummer can choose what the resonant relationship is for themselves, but this gives a way of measuring and repeating and ensuring that the sounds you like are the ones that you achieve whenever you're setting up a drum kit.

CONTROLLING DECAY AND DAMPING
We've now looked at three different aspects of drum acoustics and drum tuning. Those being setting the fundamental pitch of the drum, equalising the drum heads to give a clear and smooth tone and relative tuning of the batter and resonant drum heads. There's one more thing to consider, and that's controlling the decay and damping of the drum head itself. Many drumheads have advanced damping and sustained control systems built into their construction. This means that if you have the right drumheads on your kit, you really should have no need to use any additional forms of damping added to the drumheads. But sometimes you just don't have the opportunity to change drumheads in order to resolve a decay issue. For example, maybe you're playing for a different band as a one off favour, or playing a venue's house kit which is not to your taste. Maybe the venue has a big boomy space that causes your drums to ring out more than they normally would. Maybe you can't afford new drum heads, or you just don't have time to change the new drum heads at a particular moment. And there are no rules here. Maybe you'd just prefer the sound of heavily damped drumheads. A longer note allows the human ear more time to better identify with the pitch and musicality of the sound. This can sound just right for jazz and musical styles which want to carry a very clear musical pitch of the percussion performance, or for slow tempo ballads with emotive drum fills around the toms. However, long decay profiles can cause problems for drum sound and is something which many drummers, drum makers and drumhead manufacturers have long battled with. If the drum decay is too slow in comparison to the tempo of the song, it can bleed into adjacent notes, causing the drums to sound cluttered and less precise. Furthermore, if a long decay sound is not perfectly in key with the song, musical clashes can be heard between the drums and other instruments in the performance. So we've seen already that drums give off multiple frequencies when they're hit, but not always those frequencies decay at the same rate and if a drum's frequencies decay at different rates, then the character of the drum sound changes as it decays. Sometimes this is an issue, because for some drums and drumheads, the fundamental decays quite quickly, whereas the edge overtone rings out for much longer. The result is a sound that loses its deep tone quite quickly, leaving a rather thin and high frequency ring that appears less powerful and with less of a full sound character, but if there's no time to change drum heads, using o rings or damper gel applied evenly around the edge of the drum head can help tame these overtones. Let's take a listen to a drum with two different types of drum head. One has dampers built into the drum head. The other is a clear drum head. Both drums are tuned to the same fundamental and with the same RTF. Here's the damped drum head first and here's the clear drum head. We can hear that the clear drum head rings out with overtones for much longer than the damped drum head, as expected. Now let's add different amounts of damping to the clear drum head. First we'll apply some damper gel at four points around the edge, looking down on the drum in the north, south, east and west positions. If using damper gel, it can be valuable to place this at even locations around the drumhead, so that we maintain an even vibration of the drumhead itself. So let's hear the clear drumhead with four pieces of damper gel applied. Now let's add some more damper gel. Again, four more pieces in between the four that are already there. So now we have eight pieces of damper gel on the ring. Let's hear that. Now let's compare the sounds. First we hear the undamped drum. Now with four pieces applied. Now with eight pieces applied. And let's compare that to the drum head that had dampers built in too. So the differences are quite subtle, but what we can hear is that the decay of the clear drum head tends to allow the overtone to ring out a bit longer than the damped drum head and we find that as we apply damping gel to the edge of the drum head, we start to constrain and choke those overtone frequencies, to the point where it starts to sound unnatural, but of course, every drummer has their own preference on this.

SUMMARY
So now we've discussed four different aspects of drum sound, four different techniques for changing the sound of a single drum. We've talked about tuning the fundamental pitch of the drum, equalising the drum heads, tuning the resonant drum head and controlling the decay and damping of the drum head. Of course, there are many more things we can do with drums. In choosing drum heads, choosing the shell types, the different hardware and indeed tuning drums relative to each other in the drum kit, but this podcast should have given you a number of things to listen out for and control and manipulate next time you're playing or recording drums. It can be a very personal thing and all drummers and recording engineers have different perspectives on how they like drums to sound. A good suggestion is to learn about the different sound characteristics of drums and then you can make your own choices and bring your own creativity to a performance or recording session. I'll be presenting some more podcasts relating to drum science, particularly with reference to optimising the full sound of a drum kit and the science of drum sound as it applies in a recording studio space, so do check those out too when they become available. If you want to read up on these concepts, you can also visit my website, drumacoustics.com, where there are a number of pictures, diagrams and charts to help explain the concepts that I've discussed. I'm Professor Rob Toulson and this has been an RT60 Limited podcast production for Sound On Sound.

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