Tenor drones produce a fundamental pitch one octave below low A. Bass drones produce a fundamental pitch two octaves below low A. However, both drones produce higher frequency pitches called overtones. The first overtone of each is the next A up. So a tenor drone’s first overtone is the same pitch as the chanter’s low A. The bass drone’s first overtone is the same pitch as the tenor drone’s fundamental. The second overtone of each is an E. So the second overtone of a tenor drone is an E with the same frequency as the E on the chanter.
These overtones, when present with enough amplitude to be heard, manifest as a pleasant ringing sound that seems to hover over the top of the overall drone sound. Many may often hear this ringing only transiently as their pressure fluctuates enough for the ringing to fluctuate in and out. Overtone tuning is very sensitive and here’s why.
Say your chanter tunes at low A = 480 Hz, a common pitch in modern piping. This means your tenors should tune to half that at 240 Hz and the bass tunes at half that, 120 Hz. Say we are tuning our tenor drones and one is at 240 Hz but the other is at 245 Hz. They are out of tune. What you will hear is a beating frequency of 5 Hz, the difference between the two frequencies: 245 – 250 = 5; this is the wawawawawa sound produced by out of tune drones. The overtones produce their own beating frequency. For example, our 240 Hz tenor drone will have an E overtone frequency of 720 Hz. The tenor drone playing at 245 Hz will have an E overtone frequency of 735 Hz. The beating frequency between the E overtones is 735 – 720 = 15 Hz. Therefore, if you can hear this beating frequency it will sound very out of tune. That’s fifteen wawawawa in one second! If you tune the second drone down from 245 to 241 Hz, the fundamental beating frequency between the two tenor drones is now 241 – 240 = 1 Hz and the E overtone beating frequency is now 723 – 720 = 3 Hz. The beating frequencies are smaller (not quieter) so our drones are getting closer in tune.
What does this have to do with drone locking? Well, if you can’t hear the overtone frequencies all that well then you don’t have to worry about their faster beating frequency. All you have to do is get your drone fundamental beating frequency small enough that it sounds as if the drones are in tune. I believe many pipers have often favored bass dominant pipes because they feel they “lock” in tune better. Locking is piper code for drones staying in tune for a long period of time without the need for retuning. I postulate that the perception that bass dominant pipes lock better is due to the lower amplitude in overtone frequencies that make their overtone beating frequencies harder to hear. Thus, the illusion of drone locking is simply due to not being able to hear one’s drones go out of tune because the fundamental beating frequency is still too small to hear and the overtone beating frequencies are too quiet to hear. Note the difference in the words used. Too small to hear means the wawawawa is so slow it can’t be discerned. Too quiet to hear means regardless of how fast it is, you cannot hear it.
I offer an audio sample to guide your understanding. This is made possible by a bum reed the manufacturer has already replaced. This bum reed needed a replacement because it sounds terrible. It produces this huge, nasty overtone that just hurts to listen to. Which makes it a great reed to prove my point, you can definitely hear the fundamental beating frequency along with an overtone beating frequency. You may need to turn up the volume to a setting that is generally considered too loud to be able to discern both beating frequencies. Notice how much smaller the fundamental beating frequency is relative to the high pitched, grating overtone beating frequency. Even near the end of the audio file when the drones are pretty close to in tune, you hear the overtone beating frequency go in and out as I try to find the perfect tuning spot for the second drone. It’s almost impossible and so I will never use this reed in public or even in private, hence why I asked for a replacement.
I have received a copy of Mode Locking and the Highland Bagpipe by John Kidd and Peter J. Lindstrom published in Sonus, Vol. 32 No. 2, 2012. I found a couple of statements from the article interesting, they are as follows:
“Preliminary measurements have shown that the effect is real. The phenomenon has not yet been quantified by detailed measurements of instruments of our design. The instruments to be measured must be of this design because those made in the traditional manner, and not modified, will not mode lock.”
“Pipes with abrupt changes in cross section of the drone interiors and cylindrically bored stocks will not mode lock.”
To paraphrase, “single reed” mode locking is specifically the coherence, if you will, of the fundamental with the overtones and occurs very quickly, within the first second of playing a tone on an instrument. “Multiple reed” mode locking is the coherence between two instruments, e.g. two tenor drones.
Mode lock = Phase lock + Frequency lock
By measuring the frequency of the two tenors of the specially designed pipe they determined it took over 30 seconds for them to frequency lock. They made no determination for phase locking.
“Instruments made in the traditional way do not mode lock; however, there are several examples of modified pipes with tapered, but not flared, stocks that have mode locked.” Examples given in the article include: John MacFadyen’s Hendersons (mode locked in 20 minutes), Colin MacMellan’s (Lellan’s?) MacDougals, and Robertson pipes in generally (mode locked in 20 to 30 minutes) due to tapered stocks.
MacDougal designed the bell of the drones (a low pass filter) to allow only the fundamental and a couple overtones to pass. It is also claimed that MacDougals exhibit papered (tapered?) stocks and internal bore chamfering. Mode locking occurs in about 20 minutes.