Setting Chanter Intonation with a Tuner

Intervals and relevance to tuners and bagpipes:

The spacing of notes on a musical instrument, known as intervals, can be set up in a variety of ways.  Since ancient times, simple ratios have been recognized as forming pleasing intervals in music.  The octave is a 2:1 ratio.  Divisions within the octave are where the fun begins.

Today, most "normal" instruments are set up the ratio of the frequency (or pitch) of one note to the next is a constant.  This arrangement is known as "even-temperament" and was developed to allow instruments in different keys to make exactly the same pitch even though one is playing the fundamental of its scale while the other is playing the fifth, third or some other interval.  This approach is a compromise which sacrifices "purity" of pitch for versatility.  Modern tuners are (almost)  ALL based on the even-tempered scale.

Prior to about 1750, instruments were set up so that the ratio of one note to another was set up using "pure" tones based on simple ratios of frequency.  This approach is called "just-temperament" and resulted in all kinds of complications because two instruments trying to play the same "concert pitch" would not be playing quite the same frequency.

The relevance of this story to the bagpipe is inter-twined with the nature of the drone.  Based on analysis of the sonic spectrum of drones, the fundamental (lowest) frequency of the drone is based on resonance of a one fourth wavelength.  Despite what the theory might say, the observed harmonics of the drone include all integer multiples of this fundamental pitch.  For example, the bass drone might be tuned to about 117 Hz (tonic). The drone will have its second and subsequent harmonics at 234 (octave), 351 (perfect fifth), 468 (octave), 585 (major third), 702(perfect fifth), 819(harmonic minor seventh), 936 (octave) Hz, etc.  The tenor will start at 234 (tonic) and have harmonics at 468 (octave), 702 (perfect fifth), 936 (octave), 1170(major third), 1404 (perfect fifth), 1638 (harmonic minor seventh), 1872 (octave) Hz, etc.

Since the drones play constantly, it would be nice to have the chanter blend with these harmonics.  Only a "just-tempered" chanter will do this.  The parenthetic names of the intervals above reflect the position of the note on the "just-tempered" scale.   An "even-tempered" chanter will not match these pitches.  The drone pitches required by an "even-tempered" chanter would be 468, 589.64, 701.21, 833.88 Hz, etc.   Except for the tonic/octave, these pitches do not exist in any drone.  Hence tuning a chanter (by adjusting the reed and taping holes) to match the pitch suggested using an even tempered tuner cannot ever give you an intonation that will work with drones.  There will be dissonance on every note other than the tonic/octave!

So what intonation is right/best?

So far we've identified the tonic, third, fifth, seventh and octave from the "just-tempered" scale as being in the drone resonances.  The bad news is that we're not in agreement with MacNeill nor Yamane  - and we haven't yet addressed the second, fourth, or sixth intervals!

MacNeill and Yamane both hold that high G is not at 819 Hz (in our example), but really belongs at  842.4 Hz.  (This pitch is in the harmonic structure of the drones, but is based on the 36th harmonic of the bass drone!  Is in any wonder that setting high G can cause arguments?!?)  Low G is also not a simple octave below High G, but it isn't based on the harmonic seventh either! (This one is in the 16th harmonic of the bass!))

(Note: To add to the confusion, it's not clear, but possible given the source, that the high G being refered to above is not the "normal" high G but rather the piobaireach high G.  I haven't gone back to the original paper "An Acoustical Sudy of the highland Bagpipe" in the journal Acoustica, vol. 4, 1954, J.M.A. Lenihan and S. Macneill.  I'd love to see a copy of that someday or to have this point clarified.)

Yamane says that the fourth (D) belongs at the ratio of a perfect fourth. (This is present as the 16th harmonic of the bass drone.)  MacNeill says it should go quite a bit sharper in order to facilitate the maximum number of accessible pentatonic scale structures. This justification is supported based on the Phyrgian scale's use of a "limma" and "comma".  (MacNeill's version of D is present in the 27th harmonic of the bass drone.)

At least with the interval for the second and sixth, everyone agrees where it belongs!  (The second, B, is the 9th harmonic of the bass drone and the sixth, F#, is the 20th harmonic.)

(I'm not absolutely certain that the explanation above is right. If you aren't confused yet, perhaps you should be helping write this column!!)

What tuner to use?

I can't show or tell you what is "right", but I can show you how to achieve what each of MacNeill and Yamane are striving for - without buying an expensive tuner.

If you have a simple, $20, even-tempered tuner (e.g. Korg CA-10/20/30) and have your drones and chanter balanced on what you want to call "A", then note how many "cents" you are above or below "0" on the meter. With the table below, you should be able to set up your chanter to match what MacNeill or Yamane had in mind.

Let's assume that you were tuned so that you were + 10 cents (sharp) of B-flat on 449 Hz when you play Low A.  (This is about where plastic Naill's come in during the summer!)  Be sure to leave the meter set to  "AUTO" (not "MANUAL NOTE").  A well tuned Low G should be obtained at a reading of about  +6 cents (+10 cents reference - 3.91 cents is about 6 cents) and High G should be set to a reading of about +27 cents (+10 cents reference +about 17 cents).  D will be +8 cents for Yamane's scale or + 29 for MacNeill's.  (Have fun!)

Cents sharp (+) or flat (-) of reference pitch of Low A

(Note: If you have the Korg DT-3 tuner, you can autocalibrate any pitch (e.g. - low A) to read as zero, so the above readings could be taken as "absolute" and no addition/subtraction need be done.)