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Part TWO Keys and Their Scales
Here are the three key signatures:
Fig 10 [ from Fig 3]
Fig 11 [ from Fig 6]
Fig 12 [ from Fig 9]
These three key signatures are made up of symbols known as ‘sharps’
Now let’s look at the differences in the music the non-GHB player actually sounds when he reads the GHB no-key-signature music:
Notice that in each case, the player, let’s call them a fiddler, has altered the notes that appear in the same position on the stave as the symbols in the key signature;
fig 3 the F, C and G
fig 5 the F and C
fig 8 the F
In GHB terms these notes are referred to as F, C and G without reference to whether they are sharp or not. The piper has no choice, and so no need to concern themselves with the matter. But when the fiddler reads the pipe music they take no notice of this convention and apply the rules of standard notation; they play the notes as F ‘natural’, C natural and G natural, [hence the ‘natural’ symbol F natural] and the notes sound a semi-tone lower.
Now the GHB player playing fig 1 plays the G’s as ‘naturals’, having no alternative; when the fiddler plays the version that matches the GHB version, as at fig 3, they too play G naturals, despite the fact that their key signature shows three sharps, including G sharp.
This is a crucial point because it reveals a defining difference between the music of the GHB and that of almost any other instrument commonly played in
Scales, frequencies and intervals
The word scale comes from the Italian scala-ladder. Though the notes on a musical scale go up in steps, the difference between a musical scale and a ladder is that the ‘rungs’ on a musical scale are not necessarily all the same distance apart. There are a considerable number of musical scales, differentiated by both the number of ‘rungs’ and the distances between them. Here is the GHB scale as it would be notated in conventional music:
G A B C# D E F# G A
The letters assigned to the notes of a scale represent frequencies, the rate of vibration of the source producing the sound. Now clearly, the range of frequencies generally available is not only unlimited [although human hearing limits the audibility] it is unbroken; running your finger up the fingerboard of a fiddle [while bowing the string] will give a continuously rising pitch. Even within the range of human hearing there are an infinite number of possible ‘notes’. It is a feature of human physiology, or of the nature of the universe, or of something mysterious, that we hear relationships between selections from this range. These relationships are defined by simple mathematical ratios. This is the fundamental structure upon which all music is built and to my mind is one of the wonders of the world.
The most fundamental of these relationships is that between a note of any chosen frequency and the note with twice that frequency – a ratio of 2 to 1. The space between notes of different frequencies is referred to as an ‘interval’ and the interval between these two notes is an ‘octave’. Pipers are of course, familiar with this concept, since it is built into the configuration of chanter and drones.
There is a whole sequence of these intervals, each of which determines the frequency of a possible note in a scale based on the chosen starting frequency. This matter is of profound interest but I will have to defer a discussion to elsewhere. The question for now is, how do we determine the starting frequency? Basically, if we envisage the frequency range as a sloping line on a graph, we can draw a horizontal line anywhere and call the point on the sloping frequency line where the two intersect the starting point. Exactly where this line is drawn has varied considerably throughout European history and is still being adjusted today; it varies too with the instrument. But it generally involves deciding a frequency which will be designated by the letter ‘A’. GHB players use this letter to name the pitch of their drones, but will be aware that the pitch of their ‘A’ is not the same as the ‘A’ of accordion players, for instance – the GHB is considerably higher. However, the current international convention rules that the note ‘A’ should have a frequency of 440 cycles per second [the GHB may have its ‘A’ around 460-469 or even more].
The important point here is that the octave interval, between say an ‘A’ and the note an octave higher, is so fundamental that we call this higher note by the same name. Various conventions exist for differentiating these names by adding a suffix to the letter or by changing case – hence we might have A a a’ a’’ spanning three octaves. The GHB chanter of course spans only one complete octave with an extra note beyond.
Let’s look at what happens if we start a scale on our GHB chanter with the note D. The note names are DEF#Ga [bc#d] The bracketed notes are of course ‘hypothetical’ for the GHB so this may seem an odd place to start; however, due to the particular characteristics of the GHB chanter, this is the only ‘octave’ whose intervals match those of the most common [outside the GHB world] musical scale, usually referred to as the ‘major’ or ‘Ionian’ scale. These intervals are
The major scale will have these intervals regardless of the starting note.
We have seen that the ‘octave’ interval is the result of doubling the frequency of the ‘root’ note, the starting note, and I have mentioned that this ‘doubling’ relationship is the foundation of a series of relationships. To explore the structure of keys any further we must now consider the next relationship, the interval of the ‘fifth’ [so called from it providing the 5th note in the scale]. 
What happens then, if we start a major scale on the fifth note of this D major scale, a note [and hence a scale] having the closest relationship to our starting note? From D, the fifth [counting the D as 1] is A. Using the intervals above, a major scale on A [A major] will have these notes and intervals:
Note that to maintain the major scale intervals we must raise our seventh note by a semi-tone, in this case from g to g#.
Now, let’s go back and look at the key signatures we saw in part one.
Fig 10 [ from Fig 3]
Fig 11 [ from Fig 6]
Fig 12 [ from Fig 9]
Fig 11 has the two sharps we found in our D major scale and fig 10 has the additional g# needed to generate an A major scale. We can see a pattern emerging here. But what about fig.12?
Consider the process in the opposite direction; starting with the A major scale, our D major scale is a fifth lower [again counting the first note as 1]. Counting down five from D brings us to G and a major scale on G requires the following notes:
B-C [natural] semi-tone
We can see that the G major scale requires only the f#; hence, the key signature in fig 12 represents the scale of G major.
We thus have established the key signatures which generate the scales of G major, D major and A major; music that plays these notes and has the equivalent key signature is said to be in the ‘key’ of G, or D or A major.
So can the GHB play tunes in these three different keys?
Well, as we saw in part one, yes it can, but with one crucial proviso. If we look again at fig 2 we can perhaps identify this proviso:
We now know that the music has the key signature of A major; but what are those ‘accidentals’ before the G’s?. They are ‘naturals’ and they cancel out the effect of the G sharp sign in the key signature. They are not part of the A major scale surely?
Well, no. This is the characteristic of the GHB chanter mentioned earlier. If we start on A we do not get the conventional major scale pattern of tone-tone, semi-tone, tone, tone, tone, semi-tone; instead, the last two intervals are reversed [F#-g semi-tone; g-a tone]. A scale with this pattern of intervals is called ‘mixolydian’; but, if the tune does not include these G’s, (‘Drops of Brandy’ is an example) then the key may as well be taken as A major, since there’s nothing to say otherwise.
For the sake of completeness, a scale starting on the G of the GHB chanter gives a scale known as the ‘Lydian’ mode, a rare beast indeed. Try working out the intervals yourself. Fig 7 appears to be such a thing, but since the determining note, the C#, does not appear in this tune, it is for all practical purposes, a G major tune. There are GHB tunes that include this C#, but they almost always use this note as a ‘passing’ note, one which plays little or no determining role in the music’s character. Note that for both these non-major scales, the Mixolydian on A and the Lydian on G, the same key signature with two sharps would do to give the correct inflections to the notated notes; however, it would be more descriptive of the nature of the scale to give the major scale key signatures and apply ‘accidentals’ to readjust the notes where required, as in figs 2 and 7.
Other chanter Keys and scales
The GHB chanter is capable of playing in other keys as well as those three we have; these scales however share their key signatures with those we have studied so far. You will be aware that some GHB tunes seem to be based around the note B, for instance. ‘Brose and Butter’ is an example. The scale on B has the intervals
This scale on B is called ‘B Aeolian’: it shares its key signature, two sharps, with D major.
The scale on E is called ‘E Dorian’; see if you can figure out its intervals.
The scales on the other chanter notes [C#, F#] are so rare as to be non-existent today; I would be fascinated to hear of a GHB tune that employed them. [Since you ask, the F# scale is ‘F# Phrygian’ and the C# is ‘C# Locrian’.] 
Part Two Summary and questions:
In this part we have looked at scales, the patterns of intervals of which they are composed and the key signatures that describe them. We have also looked at the way these scales are related to each other, by the interval of the fifth.
You should now be able to write out the three major scales, A, D and G and identify their key signatures.
As a final exercise, see if you can figure out the notes, intervals and key signatures of the Aeolian scale based on the notes E, and of the Aeolian and Dorian scales based on the note A.