7. Spectrum Analysis and Filtering Frequencies
Updated: Oct 14, 2020
We’re very used to seeing the audio waveform of different sounds and musical phrases, especially now that people have access to DAWs or Digital Audio Workstations such as Logic Pro X, Pro Tools and Ableton Live. Every sound waveform is unique and tells us a bit about the ‘shape’ of the sound, and by that we mean the profile of how the sound appears, how long its duration is, and how steep or how quickly it decays back to silence. The waveform is a type of graph, with volume (or more correctly amplitude) in the y-axis plotted against time in the x-axis. Here are a few examples:
So, the waveform shows us the volume profile of the sound, but it doesn’t actually tell us anything about the sound itself, i.e. what the sound’s pitch and character is. All of the information about a sound’s pitch and character is contained in what we call the ‘frequency spectrum’ which is a different type of graph plotting power (y-axis) against frequency (x-axis). Any sound waveform can be converted into a frequency spectrum graph, and any frequency spectrum can be converted into a sound waveform, using some pretty advanced mathematics known as the Fourier Transform. The frequency spectrum is really useful in audio and music processing and analysis: it is what enables an electronic guitar tuner to work accurately, it is what we look at when adding frequency equalisation (EQ) to a sound we have recorded, and it also forms the basis of many other audio processing algorithms including auto-tune, harmonic enhancers, background noise removal and the MP3 algorithm too.
In simple terms, the frequency spectrum shows all of the frequencies contained in a sound waveform and indicates which ones are most powerful, so this is really essential for tuning, especially because most electronic frequency analysers are much more accurate than the abilities of human hearing. Let's look at some examples of different sound waveforms and the associated frequency spectrum – those shown below are captured using the iDrumTune Spectrum Analyzer feature, so you can experiment yourself too with the app and different instruments if you want to investigate other sounds too:
A plain sinewave is not a very exciting sound, just a static tone that has no overtones or harmonics. Here’s an example of a 150 Hz sinewave played through a loudspeaker and captured in iDrumTune:
You can see that the sinewave gives a frequency spectrum (in the top graph) with just a single spike, meaning that only one frequency has any significant power in this sound source. Note that although the waveform is a pure sinewave shape, iDrumTune captures many more complete sine waves in 800 milliseconds than can be displayed on the width of an iPhone screen, so the display of the waveform (in the bottom graph) shows them all squashed up and a little blurred together. In fact, since 150 Hz means literally '150 sine waves per second', in 800 milliseconds (or 0.8 seconds) we can expect there to be exactly 120 complete sine waves.
Now let’s look at the waveform and spectrum of a bass guitar note played through a loudspeaker and recorded into iDrumTune. We know that the note E2 on a bass guitar represents a fundamental frequency of approximately 82.5 Hz (82.41 Hz to be precise!) and so it is no surprise to see a large frequency peak in the spectrum graph at that value. (If you don’t yet know about musical frequencies, have a look back at our previous tutorial on musical frequencies, or take a quick look at the musical frequency chart in iDrumTune.) We see more than one frequency peak with the bass guitar profile, in fact we see lots of frequencies all evenly spaced at multiples of the fundamental frequency. So, we also see frequency peaks at 163.5 Hz, 246.0 Hz and one smaller one at about 330 Hz. These extra peaks are what we call ‘overtones’ and, more specifically, when overtones are at nice even spacings (termed correctly at 'integer multiple spacings') we call them ‘harmonics’.
The harmonics are what makes a guitar sound musical to our ears where the single sinewave does not so much. Our ears like to hear multiple frequencies at mathematically separated or equal spaces and that is a big factor in how we determine if something sounds musical or not. So, the frequency spectrum allows us therefore to analyse sounds and determine components that make up the sound’s musicality and character.
A third example is the frequency profile of a human voice. Even if you are not a great singer, if you sing a very low note into iDrumTune, you’ll see the spectrum also shows fairly evenly spaced overtones. This is because the human vocal chords are also designed to generate some degree of harmonic overtones, which explains why everyone has a subtly different sounding voice and how some people can sing beautifully like a musical instrument themselves.
Now, how does this all relate to drums? Well, drums also give off very specific frequencies which the Spectrum Analyzer in iDrumTune can help us to identify and understand. Unfortunately, two-headed cylindrical drums don’t generally give off strong harmonics like the bass guitar or human voice, though drums such as tympani and tabla are designed to have a very specific shape, which allows them to exhibit stronger harmonic frequencies than most percussion instruments using circular drumheads. Regardless of this fact, there are still two very important frequencies emitted by popular cylindrical drums, as we have discussed in earlier tutorials, these are:
- The fundamental frequency, which we call 'F0' is excited most when the drum is hit at the middle and sounds like a BOOM
- The first overtone frequency of the drum, which we call 'F1' is excited most when the drum is hit at the edge and sounds like a PING
We can see and identify both of these frequencies on the spectrum plot using iDrumTune. For example, if you take a reading of a drum at the centre, F0 is excited the most as a strong frequency peak. If you take a reading at the edge, you’ll hear the difference in sound and you’ll also see the difference in the frequency peak on the spectrum graph – this is F1. If you hit the drum somewhere in between the centre and edge, you’ll see both F0 and F1 excited at the same time, which is why many drummers hit their drums slightly off centre, in order to excite more frequencies and hence achieve a richer tone when they play. Note that the fundamental frequency F0 is always the lowest frequency and F1 will always be higher by between about 1.4 - 1.8 times. The relationship between F0 and F1 can actually be manipulated by drum tuning, we recommend tuning the F1 value to be 1.5 times higher than F0; this is something we discussed more in the earlier tutorial on tuning the resonant drumhead.
Now we can see the F0 and F1 values on the frequency spectrum, we can start to use our knowledge of drum tuning to get the perfect sound we are looking for. We know that we need to analyse the F0 frequency to set the overall pitch and tone of the drum, but we use the F1 frequency to check that the drum is tuned evenly around the edge of the drumhead at each lug position.
That’s great, but sometimes (in fact very rarely, but sometimes all the same) when we try to measure F0 in Pitch Tuning mode, iDrumTune actually reads the F1 value. This is because some drums have much stronger overtones than fundamental frequencies, and this applies vice-versa too in some cases. The reason is because of the thousands of unique drums which use different drum materials, depths of drum and indeed the huge array of drumhead choices you can make. But not to worry, if you are trying to read F0 and are instead picking up F1, or vice-versa, you can use iDrumTune’s ‘Target Filter’ feature to tell the app which specific frequency you are interested in analysing at any moment in time.
Using the Target Filter is most clearly and visually described when looking at the frequency spectrum of a sound. If you take a reading of the drum slightly off-centre, you’ll get a frequency spectrum which shows the fundamental and overtone frequencies, and maybe some other little frequency peaks too. The Target Filter feature allows you to tell iDrumTune that you want it to only look for frequencies similar to F0, so if you press the Target Filter button once, the F0 value is loaded and all other frequencies are ignored. You can see this visually on the spectrum by seeing that all the other frequencies that are not close to F0 are removed. This is great if you are interested in Pitch Tuning and yet the F1 frequency keeps getting recorded accidentally in that mode.
The feature works similar for the F1 overtone frequency. If, in Spectrum Analyzer mode, you take a reading off-centre and identify both F0 and F1, you can press the Target Filter button twice to load in a filter value that is the same as the F1 frequency, and hence ignore all frequencies that are not close to F1. This is really helpful when using Lug Tuning mode if iDrumTune seems to always measure F0 when obviously you want it to only look at and measure F1.
Pressing the Target Filter button again will deactivate the feature, and you can scroll through setting the Target Filter value to F0 or F1 frequencies as you wish. A useful extra feature is that when you have the Preset Popup active (activated with the Preset Popup button in the bottom left of the screen), the Target Filter automatically loads and scrolls through the F0 and F1 values loaded in the currently selected drum kit preset.
Here's a tutorial video of iDrumTune inventor Professor Rob Toulson showing the Target Filter in action:
The Target Filter feature provides a function which is impossible for humans to perform; it can accurately ignore one aspect of a sound in order to specifically consider another aspect of the sound. As humans, this is impossible for us to do with respect to multiple frequencies in a single sound, we just aren’t able to tell our brain to ‘ignore the fundamental and only listen to the overtones’. So don’t feel bad if you find that you can’t always hear the subtleties which are being measured by iDrumTune - one of the great advantages of tuning with the help of an app is that it can perform to a much higher accuracy than our ears, and at the same time help us to continuously evaluate and develop our own hearing accuracy too.
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.