Theory Top-Up Harmonics Part 2: continuing the discussion on overtones


Piping Today #83, 2016.

In the previous article of this series, I tried my best to introduce the phenomenon of harmonics in musical sound.  And in an effort to keep the discussion accessible to non-physicists — myself included — I first compared harmonics to something more familiar: beer.  (I confess I also hoped that writing about beer would be more likely to hold your attention.) 

To review very briefly, harmonics were compared to the subtler aromas and flavours that are present in addition to the basic beer taste:  when you take a sip of beer, you taste a fundamental beer flavour, but if you’re also paying close attention you’ll taste (and smell) other, much more subtle ‘overtones’ in the background. 

Likewise, when we tune our bass drones to A, there is the fundamental bass A that we hear most strongly; but behind it, or embedded within it, there are also many other faintly audible notes, much higher in pitch, and which adhere to a specific system as dictated by the natural laws of physics shown in diagram below:

This arrangement of harmonics (or ‘partials’), consisting of a perfect-octave, perfect-fifth, major-third, and so on, is precisely the same intervallic arrangement no matter whether it is a bass drone, a chanter’s low-A, a chanter’s E, a human voice, a ship horn, or almost any pitched sound we hear in our everyday world.  Take whatever fundamental note is being produced, and you can then add the same system of harmonics above it in order to help discover the hidden ‘flavours’ in each note as shown below.

In the previous article I also posed some questions that I promised to answer in this issue of Piping Today:  How is it we can tell the difference between a bagpipe playing a low-A, and a clarinet playing the same note?  And how is it some pipers can tell the difference between the sound of a set of Lawrie drones and the sound of a set of Henderson drones, even if the reeds, bag, player and climate etc are all constant?

The answer to those related questions involves harmonics, but maybe not in the way you may have first imagined.  Since pretty much every musical instrument produces the same exact harmonics when playing the same note, there must be some other cues that our ears are picking up on.  To answer very simply: though there are other contributing factors1, the main idea is that each instrument creates its own unique fingerprint of harmonics.  It’s not that they’re producing different harmonics, or omitting some and adding others — in fact both instruments produce exactly the same set of harmonics when they play the same note.  The difference is that some of those harmonics are more prominent to the ear than others, depending on the instrument.  Certain harmonics will be emphasised more by a clarinet, and others emphasized more by a bagpipe chanter, and our ears and brains can detect and recognise those subtle differences with impressive speed and accuracy.

1. Other cues involve the quality of both the initial ‘attack’ and the decay of a sounding note, as well as differences like added vibrato, breathe noise, and so on.  For example, the initial attack of a clarinet note differs in quality to that of that of the bagpipe, and there is a different type of breathe noise involved.

To help drive this point home, let’s return to the beer analogy:  imagine two brewers setting out to make a beer with the exact same ingredients, but with some variety in the quantities of ingredients, and with some variety in the machinery they are using to make the beer.  To be sure, their respective beers will taste similar in a fundamental way because they have all the same ingredients.  But due to variations in quantities and hardware, there will be minor differences, with one brewer’s product featuring slightly stronger hints of citrus, perhaps, and the other brewer’s product featuring a tiny bit more in the way of resinous hops.  Someone familiar with both brewers could, over time, learn to distinguish one from the other simply by detecting the subtle differences of flavour.

This a good, though imperfect analogy to how it is that we can tell the difference between the sound of a clarinet and a bagpipe chanter.  To get a little more specific, the clarinet, with a cylindrical bore not unlike that of a smallpipe chanter, tends to suppress even-numbered partials, and emphasize the odd-numbered ones, in particular the 3rd partial (the interval of an octave plus a fifth above the fundamental).2  In contrast, conically-bored pipes like those of the Highland and Border pipes, tend to emphasize all the partials more evenly than the clarinet, particularly the first 10 or so.

2. This is particularly true when the clarinet plays in its lower register (i.e. not overblown).

Again, different instruments generally produce exactly the same harmonics, but the differences lie in which of those harmonics are more perceptible than others.  Fiddles and whistles and vuvuzelas have their own unique pattern of emphasized harmonics.  And one fiddle will have extremely subtle differences relative to another fiddle.  The same is true for our chanters and drones; and also for the way your mother’s voice sounds when she’s having a relaxed conversation over a cuppa and a scone, versus how her voice sounds when the cat has knocked the heirloom vase off the table.3

3. Of course her volume and choice of vocabulary will differ, too, and both the change in volume and the new vowels heard in her new vocabulary will involve different harmonic emphases.

As an aside, the concept of emphasized harmonics also applies for different vowels when spoken or sung.  The word “peer” emphasizes many of the higher harmonics, where as “poor” brings out more of the lower overtones.  Just for fun, try saying the following sequence of words, while being careful to keep your voice at the same pitch, and see if you can hear how the accentuation of the harmonics shifts: “peer”, “pear”, “pyre”, “par”, “pore”, “purr”, “poor”.  Now try singling out only the vowels themselves, in one smooth run: “ee-eh-aye-ah-oh-oo”.  The only things that should be changing are the positions of your tongue, jaw and lips, which will be moving slightly to produce a different pattern of accentuated harmonics.  This is essentially how jaw harp players play tunes, and how Tuvan throat singers seemingly sing two notes at one time.4 

4. In the case of throat singing, the fundamental sung pitch is suppressed to the point that it is actually quieter than the individual harmonics that are being emphasised.  What sounds like very pure whistling over a very quiet low drone is in fact the natural harmonics of the voice being focused to such an extreme that they are considerably more prominent than the fundamental.

This is all to speak very, very simply and broadly, of course.  Acoustics are extremely complex, and theoretically, the harmonics produced from any single note are infinite in both number and ascending pitch.  Being able to single out and accurately map a highly specific ‘fingerprint’ of emphasized harmonics is no simple task.  But I’m hoping you get the general idea, and that’s my main goal for this article.  For those of you hungry for something more in-depth, I would encourage a visit to the “Music Acoustics” website from the University of New South Wales in Sydney here.  Better yet, find a real, live musician who knows physics, or a real, live physicist who knows music, and ask them to explain things to you at whatever level of knowledge you are coming from.

Much of this discussion may seem too abstract, too theoretical, or otherwise pointless in your life, but I would caution you against those assumptions.  Familiarising yourself with harmonics will add a whole new layer of appreciation and richness in your experience of music, as well as being to your advantage as a performer or competitor.  Being more aware of harmonics, and training your ear to hear them better, will be to your advantage both in terms of fine-tuning and in terms of setting up your instrument to have superior tone.  This knowledge will improve your overall musicianship, and give you a competitive edge (for those of you who compete). 

Tim Cummings plays, teaches, writes and publishes bagpipe musicHis Theory Top-Up series ran in Piping Today magazine for more than five years.

Theory Top-Up articles published on Bagpipe.News so far:

  1. Tunes in the key of D-Major
  2. Tunes in the key of A-Mixolydian
  3. Tunes in the key of A-Major
  4. Tunes based on a ‘gapped’ A scale
  5. Tunes based in A-pentatonic major
  6. Tunes in B-minor
  7. Double Tonic Tunes
  8. Tunes in the Dorian mode
  9. Tunes in G-Major
  10. Exotic tunes and tunes that change key
  11. Compressing tunes with low F-sharp notes
  12. Compressing tunes with high-B notes
  13. Theory Top-Up Harmonics: an introduction to the mysterious overtones in our music