Spectral analysis of the Uilleann pipe's hard bottom D
Whenever anyone says the word 'bagpipe', what immediately comes to almost everyone's mind is Scotland and its iconic Great Highland bagpipe. While the Great Highland pipe is a wonderful instrument with a remarkable history and a unique tradition, it is in my opinion a little sad that it so absolutely dominates our perception of bagpipes. Besides the Scottish Highland pipe there are actually many, many different types of bagpipes developed in various regions of the world. It would be quite a task to even list them, though Wikipedia has done a pretty good job at that. Don't get me wrong: I love my set of Highland pipes and even though I nowadays hardly play them anymore, I would never even consider selling them! The point I am trying to make is just that other types of bagpipes are also great instruments, and that it is past time that we start thinking of 'bagpipes' as a class of distinct musical instruments that share certain features (most notably the eponymous bag), rather than only ever looking at this class's most popular member.
My personal favourite among the different kinds of bagpipes is without doubt the Irish Uilleann pipe. Compared to many other bagpipes, the Uilleann pipe is quite a complex instrument: Its chanter is (with the addition of keys) fully chromatic and can be overblown into a second octave. It can also be played staccato, where the silence between notes is obtained by covering all holes while resting the bottom end of the chanter on the piper's thigh. What I especially like about the Uilleann pipe chanter is that same note can often be played in different versions, some subtle and tender, others loud and blaring. This gives the player of the Uilleann pipe more opportunities for a dynamic and emotional interpretation of the music, which is in stark contrast to the Scottish piping tradition with its strong emphasis on accentuation through fingerwork and the technically correct execution of the latter.
Now what does it in practice mean for a note to have different versions on the Uilleann pipe chanter? It's time for an example! The best example for a note that comes in two flavors is certainly the bottom D, for which one can choose between a soft and a hard version, where the hard version is played with the same fingering as the soft one (all holes covered, chanter off the knee), but at a slightly higher bag pressure. There is some debate about which version of the bottom D should be considered the default, with some pipers liking the hard version so much that they play it exclusively, while others use either one depending on the context. I am pretty sure though that there are almost no pipers who never play the hard version. I actually feel justified in saying that the hard bottom D is something like the flagship note of Uilleann piping. It has certainly been used to great effect by James Horner in the wonderful soundtrack to Braveheart, where Horner starts off the main title with the Uilleann pipe's iconic hard bottom D.
"Main title" from the soundtrack to Braveheart (first hard bottom D at 0:18)
Two years later Horner also used the Uilleann pipe in the soundtrack to Titanic, where he again makes good use of our beloved hard bottom D.
"Hymn to the Sea" from the soundtrack to Titanic (first hard bottom D at 1:22)
So this is what the hard bottom D sounds like. But what about its soft counterpart? It's easiest to hear the difference between the two Ds in direct comparison, so I made a small recording of me simply going back and forth between hard and soft bottom D. Note that I start on the hard D.
Hard and soft bottom D in direct comparison
I think that is quite a difference: The hard bottom D is somewhat louder and more aggressive, while the soft bottom D feels soft and shy in comparison. By the way: The bottom D is not the only note for which there is a hard version. There is also a hard bottom E which is similar to the hard D in tone. It is played at the same pressure as the hard bottom D, off the knee, and with the little finger of the bottom hand down covering its hole. To illustrate the effect of the hard and soft notes in a tune, I have recorded the first phrase from the reel The Braes of Busby. Hint: The sheet music on thesession.org doesn't quite match with the version I play, but the Ds are the first and 10th note and the E is the 11th note.
First phrase of "The Braes of Busby" with all soft bottom Ds
First phrase of "The Braes of Busby" with all hard bottom Ds
First phrase of "The Braes of Busby" with all hard bottom Ds and a hard bottom E
The difference between hard and soft bottom D is subtle, but the hard bottom E is a real blare!
So much for the musical aspects of soft and hard bottom D. Let's get nerdy! As a physicist I naturally started wondering what the actual physical difference between the soft and hard bottom D is. I wondered if anyone had already looked at that but I couldn't find much on the internet. The only thing I did find was an undergraduate thesis from the Tufts University in which the author measures the amplitude of the vibration of an Uilleann pipe reed at various points on the reed's surface. This is done while the chanter is playing various notes (including both low Ds) and the result is also decomposed into normal modes of vibration. The normal modes for soft and hard bottom D look rather different, but I have no idea how to interpret this data and the author unfortunately doesn't comment on the differences between the low Ds. I think the author was mostly trying to make a connection between the spacial distribution of the vibrations' amplitudes on the reed's surface and common practical knowledge about reedmaking. Saying anything about the timbre of a sound purely by looking at the vibration of the reed is probably quite a hard task. On the other hand it is well known that it is the relative intensity of the overtones that determines the timbre of a musical instrument and lets us distinguish between different instruments playing at the exact same pitch. The difference between hard and soft bottom D should therefore also be visible when looking at the overtone intensities. Fortunately this should be fairly easy to do: All we have to do is to record both soft and hard bottom D, Fourier transform the recording from time to frequency domain and then compare the obtained spectra. So let's do it!
Here are the recordings I made. Note that I normalized the volume of both recordings to the same peak amplitude. When doing the analysis I would otherwise probably only have seen that the hard bottom D is overall louder, which is something I already knew.
Soft bottom D in isolation
Hard bottom D in isolation
The first thing I did was to just plot the amplitude of the wave as a function of time. Just to get a general idea of the two waveforms:
It's pretty hard to see anything here. It is funny though how much the actual waveform of an instrument can differ from the sine function we commonly think of. The only thing these two seem to have in common is the periodicity of the signal, but that's about it. Looking at the signal in the time domain is not very enlightening, so let's do the Fourier transform to get into frequency domain! Here is the result:
As expected we see the overtones at integer multiples of the 293.8 Hz base frequency of my bottom D(4). Overall we see that the intensity of the overtones tends to decrease with increasing frequency, though this is not a strict rule. There are some differences between soft and hard bottom D, but the picture is probably a bit too small to see details. We should zoom in. Here is the low frequency end of the spectrum:
Now this is interesting: The overtone spectra of soft and hard bottom D have remarkably different linewidths! Look at the first overtone peak at D5: It is extremely wide for the soft nottom D, but very narrow for hard version. The same is true for A6 and A7. On the other hand, the situation is reversed for A5 and and the 6th overtone (between A6 and D7). I was unable to determine a pattern in which overtones are narrower and which are wider, though I didn't try too hard and would not be surprised if there was one. I'm not quite sure how to interpret these different linewidths. I used Audacity to do the Fourier transform with a 1024 sample rectangular window. The general lineshape depends strongly on the window function and the size of the sample but while my rectangular window will result in generally fairly wide overtone peaks, this should not account for the difference in linewidth among peaks within the same spectrum. After all I produced the spectra for soft and hard bottom D using the exact same procedure. I really wonder if I'm missing something here ... ?
Going to higher frequencies, it is easy to see that the hard bottom D is dominant above 7 kHz. Starting at the A8 overtone the hard bottom D is much more intense compared to the soft D, for which some overtones are hardly visible.
This holds as we go to higher frequencies: We see some some strong hard bottom D overtones all the way up to 14 kHz, while there is not much intensity anymore for the soft D.
There are no overtones between 14 and 18 kHz, but we find some hard bottom D overtones in the region between 18 and 22 kHz, the latter being the maximum frequency for which we can extract information from the Fourier transform of a 44 kHz recording (see Nyquist-Shannon sampling theorem). I wonder if I can even hear these very high overtones ...
I don't really know what the different linewidths mean, but besides that I think it is pretty safe to say that the hard bottom D is not only overall louder (this was obvious), but also has relatively more intense high frequency overtones in the range beyond 7 kHz.
I assume that the situation is similar for soft and hard bottom E, but I should probably check that at some point in the future ... *to be continued*