In Part 2 of this series, we learned about the equal temperament scale used by non-bagpipe tuners and why it would produce a chanter scale at odds with the presence of drones. We will now learn how to create a chanter scale that will harmonize with the drones.
Instead of the equal temperament scale, the bagpipe scale utilizes the just intonation scale which maximizes harmony between the chanter notes and the drones. By understanding the relationship between the equal temperament scale and the just intonation scale we can understand how to use a standard, chromatic, non-bagpipe tuner to tune a bagpipe chanter.
It will now become apparent why the choice of tuning the drones to our low A (and high A) was such a crucial decision. The bagpipe scale is generated by simply multiplying the fundamental by improper fractions, made of small numbers for both the numerator and the denominator; fractions like 9/8 and 5/4. What follows is a table comparing the equal temperament to the just intonation scale with the bagpipe notes found in the chromatic scale highlighted in red.
This table is generated using a fundamental of 480 Hz, a common modern pitch for the bagpipe chanter low A. The 2nd and 3rd columns generate the equal temperament scale note frequencies where 480 Hz is multiplied by 2^(x/12). The 4th and 5th columns generate the just intonation note frequencies by multiplying 480 Hz by whatever improper fraction is listed in the 4th column. What should be a revelation is that the just intonation scale produces notes of the same frequency (or octaves of) the overtones produced by the drones, e.g. E, C#, and G from the bass drone overtone example in Part 2 of this series.
|Note name||x in 2^(x/12)||Frequency of ET note||Just fraction||Frequency of just note||Cents deviation|
The comparison between these two scales is necessary to understand how to use a non-bagpipe tuner based in the equal temperament scale to tune a bagpipe chanter in the just intonation scale. The space between equal temperament notes is divided into 100 pieces called cents. The size of 1 cent changes depending on which two notes you are in between because of the whole "12th root of 2" business. A non-bagpipe tuner does not report how out-of-tune your non-bagpipe is in units of Hz but in cents. What is shown in the 5th column of the table above, using the cent scale, is how out-of-tune you will need to tune the bagpipe chanter note using a non-bagpipe, equal temperament tuner in order for that note to be in tune with the drones. In short, your chanter notes must be out of tune according to the tuner to be in tune with the drones. Positive cent deviations indicate the note needs to be tuned sharp relative to equal temperament tuning and negative cent deviations indicate the note needs to be tuned flat. I've attempted to map these cent deviations onto the image of a standard non-bagpipe tuner to help elucidate where the needle should point. Small and smaller hard-to-see dots indicate graduations of 5 cents with the 20 cent marker explicitly indicated. Note that the cents deviation from the table are valid for any pitch you decide to tune your low A to as long as you set the reference pitch on your tuner to that same frequency. You can see, although it is obstructed by my red line, that the tuner in the picture is set to a reference pitch of 440 Hz.
One problem you might run into when trying to implement this method of bagpipe chanter tuning comes from a limitation of the tuner. Specifically, most instruments tune with the reference A = 44o Hz. The Korg chromatic tuner shown above allows you to just adjust the reference pitch only up to 480 Hz, but many modern bagpipe chanters tune above 480 Hz, e.g. 483 Hz. How could you then use the same tuner to tune your bagpipe chanter? Easy! If your low A is at 483 Hz, you would adjust the tuner down to 483/2^(1/12) = 455.89 ~ 456 Hz (or just see what frequency gives you the green light when you play low A). From this frequency, the tuner will no longer indicate you are playing A when it hears low A, but will instead indicate Bb. The same is true for all the other notes which will be indicated by the note above the one you're playing, e.g. C instead of chanter B, D instead of chanter C#, Eb instead of chanter D, F instead of chanter E, G instead of chanter F#, and G# instead of chanter G.
This adjustment of the tuner reference pitch down to a lower frequency is often a source of confusion among pipers in trying to communicate with one another. One piper will use the A convention (e.g. 483 Hz) to indicate their absolute tuning while another will use the Bb convention (e.g. 456 Hz) when in reality they're talking about the same thing. These waters are muddied by the existence of "Bb" or "orchestral" chanters that tune low A to 466.16 Hz, the equal temperament value of Bb when 440 Hz is used as the reference pitch (440*2^(1/12) = 440*1.0595=466.16). Some pipers will mistakenly quote their low A as being at 440 Hz, but this is not the case for these orchestral chanters, only the reference pitch of the tuner is at 440 Hz. This is proved when the tuner indicates the note is Bb instead of A. To further muddy the waters, there are actual true low A = 440 Hz chanters (e.g. Scottish border pipe chanters) where the tuner's reference pitch AND the frequency of low A are both 440 Hz. Both A = 440 Hz and Bb = 466.16 Hz are "concert" pitches in the equal temperament scale so there is additional confusion between whether one is referring to a concert Bb chanter (low A = 466.16 Hz) or a concert A chanter (low A = 440 Hz).
On a final note about the table, the inclusion of notes not in the bagpipe scale is for several reasons. 1. All the notes in the chromatic scale are needed to figure out how big a cent is between adjacent notes; not all the notes on the bagpipe scale are adjacent. 2. Maybe, someday, you'll need to play (and therefore tune) one of these other notes not usually found on the bagpipe scale: Bb, C, Eb, F, and G#. These notes are called accidentals because they are outside the key signature of the bagpipe, D-major (also referred to as A-mixolydian because our scale starts on the note A). You can hear me play a scale on a circa 1900 3/4 John Center bagpipe chanter where I include the C and F accidentals below (although the tuning of these two accidentals is subject to the tuning of the normal C# and F# notes since the accidentals are achieved by "cross fingering" C# and F#):
Lastly, I like to elaborate and where one can go from here. For instance, I used all this same theory to figure out how to tune the chanter if I instead tuned the drones to low G instead of low A which allows me to play many tunes from the Northumbrian tradition on the highland bagpipe in their proper key of G-major. Bagad bagpipe bands in Brittany have adopted the use of highland pipes with drones tuned to B instead of low A. Both of these scenarios completely change how the other notes of the bagpipe scale are tuned using an equal temperament tuner, though they still use a just intonation scale out of necessity so that they are in tune with the drones. One can now also understand older conventions of highland bagpipe tuning. In the past, D was not 4/3 of the fundamental but 27/20, meaning it would be tuned +19.1 cents sharp of equal temperament D. The modern tuning uses the cleaner 4/3 for a more harmonious sound. The 27/20 gives a twangier sound easily heard on some very old, and not so old, audio recordings. Modern tuning of the piobaireachd high G adopts the same 7/4 as the light music high G, but some older recordings show that alternate high G tunings of 9/5 at +17.2 cents sharp or 16/9 at -4.0 cents flat have been used as well. We can come to the conclusion that modern piping has settled on the smallest numbers used in the improper fractions to generate the modern just intonation scale with the cleanest sound (4/3 for D instead of 27/20), but it doesn't mean that alternate conventions (27/20 for D) are wrong or out of tune from a theoretical perspective.