Piping Today #84, 2017.

In the last two Theory Top-Up articles, I shamelessly — shamelessly — manufactured an analogy comparing subtle flavour overtones in beer to the overtones (harmonics) in music.  I went even further in the most recent issue and asked our beleaguered editor to insert a prominent image of a bottle of beer in order to lure unsuspecting readers into an article that may have initially seemed of little interest.  It was an astonishingly cheap trick but if more readers came away with a better understanding of harmonics and the music they produce, perhaps the end justifies the means.

Do you have the tolerance for a third round?  I hope so, because there’s no putting that genie back in the beer bottle.  For this issue, I want to talk about how we pipers — whether or not we’re conscious of it — use the harmonics in our drones to fine-tune our chanters; and how that differs from the way in which guitars, accordions, banjos, pianos and most pipe organs (among other instruments) are tuned.  You might not believe it at first but a well-tuned bagpipe is in fact more in tune with itself than the professionally tuned Steinway & Sons grand piano currently sitting on stage at Carnegie Hall.  (Yes, really.)

But first: more beer.  I’m going to go way out on a very short limb and assume that those of you who drink beer have at least some awareness that certain types of beer pair better with certain foods than others.  (The same is true, of course, for wine and other beverages.)  According to an impressive online chart by the Brewers Association1, Double/Imperial IPAs are best enjoyed with any of the following: smoked beef brisket, grilled lamb, Southern chicken-fried steak, sharp and rich American artisanal blue cheese and very sweet desserts such as carrot cake, caramel cheesecake or crème brûlée.  These are highly specific suggestions, and I bet things could get even more specific if there were a chart listing individual brands of Double/Imperial IPAs.

  1. To view the entire chart, have a look at the brewers association craft beer food guide here.

•Queen City Brewery’s Gregarious Scotch Ale paired with Bonnieview Farm’s Ben Nevis farmstead sheep cheese.

You may find yourself reacting to all this as I did: thinking this sort of information is eye-rollingly snobbish but also feeling curious enough to actually go out and try one or two of these pairings.  The point I want to make, however, is that some beers have particular flavourings that “harmonise” better with certain types of food — the combinations of flavourings enhance each other and are particularly pleasing.  It’s not that you can’t enjoy a Double/Imperial IPA while eating fish and chips, it’s just that the aforementioned foods will make the beer + food experience even more rewarding for your tongue.

By contrast, there are beers that seem to be designed to be more flexible and succeed with a wide array of foods.  I don’t actually know for sure but I tend to assume larger, more commercial pale lagers such as Stella Artois, Heineken, Budweiser etc., deliberately avoid any strong flavour profile in order to be enjoyed — or at least not clash — with most foods.  They seem to head more in the direction of one-beer-fits-all-meals.  Regardless of what you think of this type of beer, the idea certainly succeeds on a vast commercial scale.

Let’s get back to bagpipes:  we pipers, when we do our job well, generally tune our pipe chanters in such a specific manner that they can only really play perfectly in tune in one or two keys: A and D (sounding B-flat and E-flat on modern Highland pipes).  We do this by consciously or subconsciously matching each note on the chanter to the corresponding note in the harmonics of our drones.  If you’ve forgotten what those harmonics are, the chart below will remind you of the fundamental of a Highland bass drone, along with the first eight harmonics (or overtones).

Except for our D and F-sharp, every note of our chanter’s scale is heard in the first eight harmonics of the bass drone, though not always in the same octave as the chanter.  (The D and F-sharp are also present in the harmonic series but are higher in pitch and less audible.)  These harmonics are sounding at all times when the bass drone is being played and they are notes that we all hear whether or not we’re conscious of that fact.  Further, our tenor drones produce the exact same harmonics as the bass drone but an octave higher.  Thus, it makes sense that our bagpipe as a whole will sound best when the individual notes of our chanters are perfectly tuned to the corresponding harmonics.  If we tune our chanter’s E so that it is sharper or flatter than the Es coming through in the harmonics, the instrument will not sound as “pure” or as “sweet”.  A chanter that’s perfectly tuned to the drones is not unlike a craft beer whose flavour profile beautifully matches a particular food.

This is all well and good, but there’s a catch to this system of tuning: when you tune your chanter this carefully, as most of us do, it is really only perfectly suited to playing in the general key of A.  Thankfully this tuning also works very well for the key of D.  But stray farther from the keys of A and D and things will start to sound a little squirrelly, especially if you start adding in harmonies.  For example, when two in-tune Highland pipers play a low-A and an E together, the result is a very smooth, powerful harmony.  But if they were to play a low-G and a D together — which is the same exact interval as A and E (a “perfect fifth”) — things will sound more unsettled, a little wonky. 

Why the difference?  To put it too simply, the G harmonic of the bass drone is naturally flatter — significantly so — than the G you might hear on a piano or pipe organ, for example.  The same is true for our C-sharp and F-sharp, but not quite to the extreme of the G.  That these harmonics are pitched the way they are is simply due to the laws of physics and the manner in which a column of air (or vibrating string) vibrates in whole-number integers.  If you sing any note, the sixth harmonic coming out of your voice will be flatter than the same note on a piano, for example.

This method of tuning an instrument based on the natural frequencies of harmonics is called “just intonation”.  Skilled singers naturally tune themselves in this way, as do professional orchestral and jazz musicians who have the ability to manipulate the tuning of their instruments while they are playing (e.g. not a piano, xylophone or fretted string instrument).

But what happens if you want to play a piece of music in the key of F, and another piece of music in the key of A-flat, and yet another in the key of E?  If you were to tune an instrument using the just intonation method, you’d need to pick just one of those keys for using the harmonics to tune the instrument.  The “home” key would resonate very sweetly, but other keys would variously sound a little “off” or even wildly out-of-tune.

But in the worlds of classical and jazz music, instruments need to be able to play in all 12 of the common Western keys and so compromises have to be made in their tuning.  Instruments with fixed tuning, like the piano, xylophone, marimba, accordion etc., are tuned in such a way so that they sound equally in-tune and equally out-of-tune in all keys.  It’s a contrived, mathematic solution to the tuning conundrum.  This system of tuning is called “equal temperament” and is so widespread that most of us have become very accustomed to its sound and don’t notice that in fact these instruments are not wholly in tune with themselves.  If you play any major chord on a professionally tuned piano, it is in fact out-of-tune but not so much that your average listener is bothered, or even notices.

All this will explain why some of you have already discovered that you can tune the low-A of your chanter to a piano — perfectly so — but your high and low-Gs will nonetheless sound very out-of-tune with the Gs on the piano.  Bagpipes and pianos use different systems of tuning for different, equally valid reasons.

So what to do if you find yourself playing with an equal-tempered instrument?  Different pipers seem to take different approaches, as there is no perfect solution.  Some tune their pipes as they have always done, using the just intonation method, and simply let the tuning discrepancies between the two instruments remain.  (Many people find a certain charm to the discrepancies.)  Others play chanters that are custom-made to be equal-tempered or find other ways of tuning their chanters to be equal-tempered.  This is not a bad option, except that any time an equal-tempered chanter is heard against the drones in a purely solo setting, several notes will sound a little out-of-tune with the drone — those notes won’t sound as sweetly as you may be used to hearing on the pipes.

• A visual representation of the variations of just intonation from equal temperament, as per a typical Scottish bagpipe chanter.  These markings are based on calculations supplied on Kinnaird Bagpipes PDF “Tuning Your Bagpipes with the Korg Chromatic Tuner”.

And then there are those like myself, who sometimes make small compromises.  I frequently find myself playing with equal-tempered instruments like the accordion, piano, guitar, banjo and pipe organ, and so have chosen to tweak the tuning of my pipe chanters so that they are neither entirely justly-tuned, nor equal-tempered.  The low and high-Gs are sharpened, as are the C-sharp and F-sharp, but to a much lesser extent than the Gs.  The chanters are dwelling somewhere in the middle of the two tuning systems and it seems to work well-enough.  For the occasions when I find myself playing entirely alone, I use tuning tape to bring specific notes back in line with the harmonics of the drones.

Have you forgotten about your beer or are you unsure of where I was going with the beer comparison?  The analogy is by no means perfect but the idea is that pairing a particular craft beer with a particular food is akin to tuning our chanters to the harmonics of the specific key of our drones (i.e. just intonation).  Lighter, more commercial pale lagers which go equally well-enough with most foods are akin to equal-tempered instruments that can play equally in-tune-enough in all keys.  Both types of beer and both types of tuning methods have their place and purpose and it’s up to you to decide which approach suits your needs and tastes the best for a particular occasion.

A quick side note: just intonation and equal temperament are only two of at least six different approaches to tuning and temperament.  For the extra-curious among you, I would suggest exploring those other systems online, or better yet with a real, live musician familiar with these different temperaments.

And now, if you’ll excuse me, I’m going put my laptop to sleep and sample a Scotch ale with aged sheep cheese…

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