I wrote this somewhat technical article because Bagpipe players nowadays use an electronic instrument to tune their pipes, so that all the instruments in a band sound similar to each other on each note of the scale. The instrument requires the operator to take a reading from each note and then apply an “offset” correction to decide if it is properly in tune. This is a bit mathematical and tends to confuse people who are not technically or mathematically inclined. This article tries to make clear what it is all about.
Preliminary Note: Musicians speak of the ‘pitch’ of a musical note, and engineers prefer to talk of ‘frequency’. ‘Pitch’ and ‘Timbre’ are words that describe what our ears perceive when various musical notes are played singly or at the same time as one another. They are words that describe the subjective experience people have when they listen to music. Frequency on the other hand is what we measure using scientific instruments. If a string on a violin or guitar etc. vibrates at a certain rate, say 440 vibrations per second, a classical musician will say they are hearing “A440” or “concert pitch”. It is the note called ‘A’ above the middle A note on the piano. In the middle of last century we techies used to say that the frequency of that vibration was 440 cycles per second. But in non-english speaking countries, other units were given to this vibrational speed (frequency). The Germans were always world leaders in this type of engineering, and they gave the name of a famous German scientist (Hertz) to the unit of frequency. Other countries had other names and there was a battle to arrive at standardised terminology. Somewhere around 1970, the Germans won the fight, and the whole world agreed to use the name ‘Hertz” (Hz) to describe the unit of vibrational rate, or frequency. For the record then, the number of vibrations per second (frequency) of a vibrating body or air-pressure wave is defined as the number of Hertz. 1 Hertz (Hz) is exactly equal to one cycle per second. There is no difference. It is just terminology.
Ever since early Egyptian times, or maybe earlier still, it was understood that if a number of musical notes were played, either together as a chord or rapidly after one another, they sounded better if the various notes had frequencies that were simple fractional numbers of each other. The simplest possible case is when the frequency of a particular note is exactly double that of another (a 2:1 ratio). Musicians will say they are one octave apart and they harmonise perfectly. The result is very pleasing to the ear. A frequency ratio between the two notes of 3:1 is called a perfect fifth by musicians and is also very pleasing to the ear. It’s not surprising because some of the peaks of the two sound waves impinge on the listening ear at the same instant, and at moments when they do coincide, their powers are added together. Notes in harmony boost each other.
Most modern instruments have diatonic scales. That means there are 12 steps in the octave from the lowest to the highest pitched note (Including tones and semi-tones). If we look at how the scale is put together we see that the ratio between the frequencies of each pair of adjacent notes is the same as between any other adjacent pair. This is actually not exactly the ratio that pleases the human ear most, but it is close enough to still be pleasing. Because all the intervals are the same, different instruments playing in different keys can play together and it will sound good. A scale with these intervals between notes is called an even-tempered scale and it is a good compromise which allows compatibility of different instruments playing in different keys. The average human ear accepts the slight inaccuracies in the case of most instruments
But the bagpipes are a different thing. The notes of the bagpipe chanter do not follow and even-tempered scale. The various notes are altered from the standard diatonic scale so that they will harmonize better with the drones. (For those who don’t know, the drones are the long pipes that rest on the pipers shoulder and create a deep ‘droning’ sound like a vacuum cleaner). Many pipers think the drones are fairly unimportant in the total sound produced by the pipes, but actually, I am coming to the realization that the entire scale system of the bagpipes is surely based on the characteristics of the bass drone reed. So, we should start with that reed and work up to the chanter. (The chanter is the tube with note-holes in it that the piper holds out in front of him and plays fingerings on to achieve a tune).
The sound we hear from a reed depends on three main things. (Reeds are what make the sound in the bagpipes. They consist in essence of thin wafers of reed or synthetic material that vibrate when air flows over and through them).
- The material the reed is made from
- The dimensions of the reed
- the acoustical enclosure that the reed is played in (i.e. the drone pipe itself in this case)
There is a fourth factor with reeds such as clarinet reeds where the musicians lips are directly on the reed and he/she can influence the sound the reed makes by blowing it differently. This is not relevant in the bagpipes because the reeds are enclosed within pre-tuned cavities.
Let’s get back to the bass drone reed on the bagpipes. this reed within its drone pipe and driven by a constant stream of air from the bag, vibrates at a fundamental frequency of around 115 Hz (vibrations per second). But apart from that fundamental frequency, the reed and enclosure all produce many harmonics which are multiples of the fundamental frequency, and actually, other overtones which are not exact multiples of the fundamental frequency are also produced. But ignore the stray overtones and stick to the exact harmonics for now.
The tenor drone has a fundamental (basic frequency) of exactly twice the base drone fundamental and therefore vibrates at approximately 230 Hz. It too produces harmonics and overtones and because the fundamentals of the base and tenor drones are exact multiples of each other, the harmonics and overtones will be very similar. These harmonics and overtones will therefore harmonize and produce many pleasing pressure peaks in the sound wave.
Moving up then to the chanter, the Tonic note of the scale is called low-A and that is tuned to be an exact multiple of the base and tenor drones, one octave up from the tenor drones. In other words, the low-A on the chanter is tuned to about 460 Hz. This is arbitrary and not laid down as a strict rule, and the modern trend is to increase the frequency of all the pipes to make them sound sharper and more lively.
In normal classical instruments played in orchestras, that A note is traditionally tuned to 440 Hz and that is known as concert pitch. It is however true that the trend, even in conventional instruments, is to make concert pitch a little sharper than 440 Hz.
But now, here is where the pipes are dissimilar to all the other orchestral instruments. The notes produced by the bagpipe chanter are selected to harmonise with all the rich harmonics produced by the drones and the scale notes are therefore not the same as the normal diotonic scale of classical instruments. The scale is not an even-tempered scale as explained earlier. It is instead called a just-tempered scale which is actually a more accurate division of the octave, and the notes on the chanter scale harmonize more beautifully with the harmonics of the drones to produce the full sound that bagpipe enthusiasts love so much. But here’s the rub.
Most of the electronic tuning devices we can buy, except for the very expensive ones, are all set to tune an instrument to an even-tempered scale. Because the notes of the chanter vary from those of an even-tempered scale, we need to understand that the readings of each note on a standard tuning device will be in error by the amount that the chanter note differs from the even-tempered scale. This means that we have to apply a mathematical correction to the readings we get on the electronic tester in order to tune the chanter correctly to match the drone’s harmonics. This correction is known as an offset and is given in a unit called ‘cents’ in the table issued with the instrument. The unit ‘cent’ or 1/100 th of an octave was invented more than 2 000 years ago by Pythagoras, and is simply a way of way of specifying a note far more acurately that just talking about tones and semi-tones. So for instance, the offset to be applied to the F note on the chanter is -16 cents. The F note on the chanter is close to an F# on other instruments and by applying this offset of -16 cents we will end up tuning the F to a bagpipe F and not a piano F.
Just a complication on all the above. Even with choosing chanter notes that better match the drone characteristics, it is not possible to find chanter notes that harmonize with all the available drone harmonics. This means that bagpipe manufacturers have to choose which harmonics to match their chanters to and it leaves the field open to choice. There is not total agreement between the experts which exact notes the chanter should play because it is possible to select different drone harmonics to match to, and that changes the chanter scale quite a lot. That’s why not all pipes sound the same. Some experts believe for instance that High G should be at 819 Hz and others would pitch it at 842.4 Hz. Quite a difference. Piobaireachd players apparently prefer an even lower pitch of around 770 Hz. (Piobaireach is a Gaelic word for the original classsical type of bagpipe music).