Temperament - Bagpipe Purity versus Classical Compromise
What we are talking about is known as Temperament, namely how we divide up the octave (or in physical terms, set the frequencies of the seven notes A to G. Or in other words how do we define a tone? From the above, it is obvious that our major scale has 6 tones (or 12 semitones) in total. So we can divide the octave using geometric (not arithmetic) intervals based on a semitone having a frequency interval of 1/12th of the octave. Without venturing into an explanation of what sounds sweet versus discordant, let us just accept that to produce perfect harmonies between notes, their frequencies should have simple geometric relationships to each other (2:1 for notes which are an octave apart, or 4:3, 3:2, 9:8, etc.). Such range of notes is called "Just". It is possible to achieve this on the pipes because its musical range is limited essentially to one octave. For a piano or any other instrument that can play several octaves and in different keys, this logical arrangement is simply not possible. The solution adopted in Western classical music (known as equal temperament, ET in the table below) is to make all the notes out of tune but not by enough that the clashes are excessively (or maybe even noticeably) discordant.
The Just temperament built into the Blair HBT-3 tuner that I use is shown below. I determined this myself by using a tone generator. I had asked Murray Blair for this information but did not get a reply. But there is no doubt that these are the ratios that are programmed into it.
Intervals of the Bagpipe Scale compared with the nearest Classical Equal Tempered Scale
| Bagpipe Note | G | A | B | C | D | E | F | G' | A' |
| Decimal Ratio to A | 0.875 | 1 | 1.125 | 1.25 | 1.33 | 1.50 | 1.67 | 1.75 | 2.0 |
| Fraction Ratio to A | 7/8 | 1 | 9/8 | 5/4 | 4/3 | 3/2 | 5/3 | 7/4 | 2/1 |
| Interval* (cents) | 231 | 204 | 182 | 112 | 204 | 182 | 84 | 231 | |
| ET Interval | 100 | 200 | 200 | 100 | 200 | 200 | 200 | 100 |
To summarise, it is the Just Temperament of the bagpipe that, together with well-tuned drones, allows it to sound so magnificent. But it also means that the bagpipe scale does not and should not sound the same as the Western classical major scale (and not just because of the bagpipe's flattened G).
On another page, I consider the question of how close to the perfect Just pitches it is possible to tune a chanter. But the next page looks at two different issues: what I call the high G and high A problems
