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A Pipers Guide to Music

A Highland Pipers Guide to Music


 

Part three       Transposition

 

The cycle of fifths

 

If you’ve followed me this far you have the makings of an understanding of what key you are playing your GHB, smallpipe or border pipe chanter in. What we are going to tackle now is what happens if you decide to play on your GHB chanter music written out for instruments in other keys – D, G, C, F Bflat - fiddle music, for instance, might be in any of these or other keys. We will look at music that can be played on the GHB chanter using the process known as ‘transposition’; converting the notes of one key into those of another. This music will at first look alien; we are going to explore how to come to terms with it.

 

First, let’s go back to the key signatures we had:

Fig 10 [ from Fig 3]

 

Fig 11 [ from Fig 6]

 

Fig 12 [ from Fig 9]

And to the scales they relate to, in reverse order

 

G         A         B         C[#]     D         E          F#        G        

                                                D         E          F#        G         a          b          c#        d

 

                                                                                                a          b          c#        d etc

 

It is clear there is a pattern here and we have discerned above what it is; each scale is related to the one before and after by a fifth. What happens if we extend this sequence beyond the bounds of our chanter, maintaining the same major scale? [intervals of tone-tone-semitone-tone-tone-tone-semitone-tone]

We can do this in both directions, of course. Going down a fifth from G brings us to C.

C         D         E          F          G         A         B         c

The F here must be ‘natural’ [dropping the sharp from the key signature]; the key signature is ‘empty’. [note that this is what our fiddler reads when they see GHB music – hence the strange sounds they produce playing what in the hands of a GHB piper is a normal tune].

 

Let’s stop there for a moment and go from A in the opposite direction;

A fifth up from A brings us to E; to maintain the major scale intervals we must raise the D to D#, adding a fourth sharp symbol to the key signature.

E          F#        G#       A         B         C#       D#       E

 

A fifth up from E is B and again to preserve the major scale intervals we must add another sharp, this time to the A.

B         C#       D#       E          F#        G#       A#       B

 

At this point things start to get bewildering; a fifth up from B is F# and to maintain the major scale starting here we must raise the seventh note, which is E. Now, on a fixed tuning instrument, like a piano, or for that matter a bagpipe chanter, raising the E by a semitone brings us to F. However, music written in the key of F# writes E# instead. [For obscure reasons which are actually crucial to understanding bagpipe tuning, this E# is not actually the same as F, but we’ll leave that aside for now]

F#        G#       A#       B         C#       D#       E#        F#

A fifth up from F# brings us to C#; here we have the same problem as with F# major, only concerning the note B; it must be written B# [although this is nominally the equivalent of C]

C#       D#       E#        F#        G#       A#       B#       C#

 

This means we now have a scale with seven sharps in the key signature [pianists really do have to read such things ocassionally]. We should stop here and go back to our C major scale. What happens if we go down a fifth from C?

We are brought to the note F. Can we build a major scale on F?

F          G         A         B         C         D         E          F

Now the interval between the A and B is a tone when for a major scale it should be a semitone; we need to lower the B by a semitone which we do by using the ‘flat’ sign [for convenience I’m going to write this b]

Thus, where we had an ‘empty’ key signature for our C major scale, we now have one flat for our F major. You can probably predict how this will go – each fifth we go down, from F to Bflat, to Eflat, to Aflat, to Dflat, to Gflat to Cflat we add another flat to the key signature; You can probably write out these scales for yourself, taking care to always preserve the major scale intervals. Note that by the time we reach Dflat we have [again, nominally] reached the same scale as C# [and thus Gflat=F#, Cflat = B] [Again, piano works do exist written in Gflat, six flats].

Let’s now write out the names of all these keys, starting with C#/Db:

 

C#/Db, F#, B, E, A, D, G, C, F, Bb, Eb, Ab, Db/C#

In 12 steps we have returned to our starting point; this cycle is called ‘the circle of fifths’.

If we were to count in fifths from a C# at the very bottom of the piano keyboard we would end up on a C# 7 octaves above where we started [most normal piano keyboards don’t have that many notes]. [4]

 

In Fig 6 we saw a tune written out in the key of D; the notes of this tune are such that we can play it on a GHB chanter; however, here is another version of the tune which we cannot play on the GHB chanter.

 

Fig. 13

 

Our fiddle player will have no difficulty playing from this music; they will, however, be playing a fifth lower than before. For a piper to play along, they will need a different chanter, one whose ‘six-finger’ note is D, rather than A. A GHB piper could play this D chanter reading from the GHB music, ‘pretending’ they were playing in the usual way; the only difference would be that they were now playing a fifth lower.

 

However, the task our GHB piper has set themself is to learn to play the A chanter [or, indeed, any other pitch of chanter] from music written for some other instrument [an English bagpipe collection, say, published for chanters in D]. Fig 13 is an example, and this is another:

 

Fig 14

which is our first tune, only written in the key of D rather than A.

How does our piper learn to read and play this? Basically they must understand pretty well the material we covered in the previous sections, how the chanter scale relates to the key signature. Then they must tackle the manner in which the tune is built out of the scale and how this relates to the fingering of the chanter. Once the structure of the tune in one scale can be grasped, then it will become possible to transfer this structure from one scale to another.

It’s worth reassuring ourselves that this task is made immensely easier because we have only nine notes to deal with in any one scale or structure; imagine having to learn how to apply this to all 12 keys and all seven octaves, as a pianist would have to do.

Before proceeding, let me just name the notes that appear in this music that GHB pipers may not have met before. I have labelled them as they appear in the second four bars of the tune;

F# E      D                                   c-natural          C-natural

 

Structure

We are now going to analyse how a tune is built. It is done by putting together blocks of notes, blocks which themselves consist of small patterns. Pipers who have experience of playing a number of tunes will be aware that they often find themselves playing the same little patterns repeatedly in different tunes; if you have not had this experience, then you are going to get it now, because we will begin by looking at these ‘blocks’ as they occur in the tunes we have considered so far.

 

The most fundamental of these ‘blocks’, and among the shortest is the ‘octave’. This should be no surprise, given what we have learnt so far about how music is constructed mathematically. If we understand the information contained in the key signature we can identify what this octave should be even if it does not actually appear as a ‘block’ in the tune.

Look at notes iv,v & vi in bar 1: [I shall not be counting the short bit of bar that often occurs at the beginning of a tune; this is called a ‘pick-up’; bar 1 is the first full bar.] In this case the octave is indeed the basic one of the ‘key’, D major; the block is the beginning and end of the scale of D. We can consider this as the ‘outer frame’ of our tune’s structure [although we will often step outside this outer frame].

One of the benefits of using the pipe chanter to learn this stuff is that there are only two possible octaves available; on the GHB chanter these are A-a and G-g. In our tune here they are D-d and C-c [You may find yourself wanting to play music written for an instrument that can also play an octave C#-c# - I shall not deal with that possibility now – it will cause complications which you should beware of; basically a GHB chanter cannot reproduce such music without modification.]

So, we have two octave blocks, one of which, by referring to our key signature, we have identified as forming the ‘boundaries’ of our scale. It so happens that in this tune we also have an example of the other octave, notes v & vi of bar three

C-c, the equivalent in the key of D to the GHB G-g octave.

So, by understanding the key signature and relating this to the notes of the tune, we have identified, first our ‘six-finger’ note, and then our ‘seven-finger’ note, as well as their relative octaves; that’s four notes out of nine, nearly half-way and all we’ve done is look at the key signature and two notes …

Now, in our discussion of the relationship between keys we identified the interval of a fifth as being crucial, it bearing the next closest relationship to the root after the octave. Let’s look for this interval in our D tune

We find it at bar 2, notes iii & iv. A-D. It is as if the A stands in the middle of the scale, between the D and the d. Between the D and the A in this sequence we find an F#. [7] The interval between the D and the A we know is called the ‘fifth’; that between the D and the F# is called the ‘third’, since the F# is the 3rd note in the D major scale.

So these simple mathematical ratios have built us a further subdivision of our octave; we now have D-F#-A-d

Let’s look again at this tune in A:

We can see here that the ‘block’ we have identified [bar 2, notes i- iv] is constructed from the notes A-C#-E-a, our six-finger, four-finger, two-finger and open notes. We can therefore translate this fingering into D-F#-A-d in our D major music. Together with our two octaves this gives us the knowledge to identify 6 of our nine notes.

 

Finally let’s go back to the C-c octave and look at the first four notes of bar 4 of the ‘D’ version:

The notes here are C–E-G, they have the same relationship between them as the D-F#-A group has [being the 1st, 3rd and 5th of the C octave], they translate into G-B-D on the GHB chanter and they make our total of recognisable notes up to 8.

You have probably noticed that bars 3 and 4 here are ‘identical’ to bars 1 and 2 - ‘identical’ that is, in their structure, though they are a tone apart. Let’s look at the last three notes in bar 1 and the first four in bar 2 [and their equivalent in bars 3 and 4]

We can recognise here our octave and 5th and 3rd; but what is that note iii? Well, it’s a B, GHB pipers are familiar enough with it, though in the key of A on the GHB it plays a very different role. I am going to say little more about this note here except to observe that the sound of the notes DF#ABdBAF#D will be familiar enough to anyone who has ever listened to a 1950’s rock and roll band. The B is a ‘6th’ and is the equivalent in the key of D to the F# in the key of A.

So now we have identified all our 9 notes using the key signature and the simple intervals of 5th and 3rd.

 

The art of transposing

The whole art of transposing music for bagpipes can be described in two simple processes; first, to familiarise oneself with the relationship between these ‘structural’ intervals and the fingering that produces them and second, to identify these structural intervals in different keys.

So let’s chart these structural units in each of the keys pipers are likely to meet in most instances: we will put the familiar ‘key of A’ set at the top and work down in fifths, and next to each we will list the ‘seven-finger octave’ equivalent to that which a GHB piper has on their chanter: [8]

 

A C# E a  [ G  B  D g

D F# A d  [ C  E  G c

G B  d  g   [ F  A  c  e

C E  g  c   [ BbD  F  bb

 


Here are the last two notes of the first bar and the first four notes of the second bar of our tune in each of the keys we are considering, together with their associated 7-finger sequence from bars 3 & 4 [I have included the natural symbols as they would appear with the key signature appropriate for each key]: this pair of sequences contains all the notes on the GHB chanter.

A

                 

 

D

                 

G

                  

C

                    

 

And to complete the exercise, here’s the original tune in each of the keys:

 

A

D

G

C

Try taking other short sections and playing them from each version. Same sound, different notes…

 

For completeness’ sake, here are the other two tunes we have been considering, in all four keys: These are real challenges, since the ‘original’ keys involve scales that begin in different places – needs some thinking about; to help, I have ordered them so that the familiar GHB version is first

 

For our second tune, Robertson’s Quickstep, the original is in the ‘3-finger’ key. If French or other European pipe music is what you want to play, then you will have to master this challenge, since much of the music is written in this way. As usual, the trick here is to identify the octave interval the tune includes, and treat that as the ‘6-finger’ note; the difference is that whilst this octave forms the ‘frame of the tune, it is not the octave we should expect from looking at the key signature. Thus, the first example, our original, marked ‘D’, contains an A-a octave, and is thus written for an A chanter; the second example ‘G’ contains the octave D-d, and is written for a ‘D’ chanter - and so on. Notice that for a ‘C’ chanter this tune is written and played in F.

 

Robertson’s Quickstep

D [‘A’ chanter]

G [‘D’ chanter]

 

C [‘G’ chanter]

F [‘C’ chanter]


The last tune, Stormont Lads, is even more of a challenge, since it is written in the 7-finger key; the trick here is slightly more complex, since we must identify both octaves, treating the upper one as our 6-finger note, since the top note of the upper of the two octaves will be our highest available note. One result is that on a C chanter this tune would be played in Bflat. Fortunately, pipe music in this key is rare outside of the GHB repertoire. Playing in this way does however have one unique characteristic on the GHB chanter; it provides a true ‘major’ scale across a full octave.

 

Stormont Lads

G [‘A’ chanter]

 

C [‘D’ chanter]

 

F [‘G’ chanter]

Bb [‘C’ chanter]

 


Part Four – Transposing Minor Keys

 

Earlier in this tutorial we mentioned the issue of ‘keys’ that share their key signature with those we have discussed so far. It is now time to look at these and the implications they have for pipers learning to transpose non-GHB music.

So far, the key signatures used have been those of ‘major’ keys [the ‘Ionian mode’], that is, a scale with the intervals tone, tone, semi-tone, tone, tone, tone,  semi-tone. When playing this music on the GHB chanter, of course, we have to modify the written music by the use of ‘natural’ symbols to accommodate the fact of the ‘flat 7th’ of the chanter, giving us the scale tone, tone,  semi-tone, tone, tone, semi-tone, tone – the ‘Mixolydian’ mode.

Pipe-music, however, can be, and often is, written in other ‘modes’, as we have seen earlier. [9] The GHB chanter makes particular use of the ‘B’ scale and to a lesser extent, the ‘E’ scale.

Let’s begin with the ‘B’ scale.

B C# D E F# G a [b] [the GHB chanter does not include this note, although it is well-documented that pipers in the past have played this note using various techniques]

The intervals here are tone, semi-tone, tone, tone, semi-tone, tone, [tone]; this mode is named ‘aeolian’. Looking at the notes included in this scale we can see that an appropriate key signature would be two sharps –

 the same key signature as our D major key. How does this affect the process of transposing? Supposing, for instance we encounter the following:

‘Brose and Butter’

 

At first glance it looks like a G tune, judging by the key signature, but when we look for the octave structure we find D-d; this, then is a tune written to be played on a D chanter. We can identity our D intervals

 and we can identify what look like G intervals in the first bars of the second line but the E’s in the first line are a sign that something else is involved. The issue becomes clearer when we look at a tune like the following:

‘A Pretty Wench, and a tenant of my own’

Here we can clearly see the intervals of a scale based on the E:

 

 This is an ‘Aeolian’ mode scale; on the D chanter, E F# G A B C d [e]

with the intervals

tone, semi-tone, tone, tone, semi-tone, tone, [tone];

 

 

Both these tunes reveal however, the close link between this E mode and the G major mode; the second strain of such tunes often opens with G major intervals. In fact, in musical parlance G major is called the ‘relative major’ of E minor. [The use of the term ‘minor’ in music is a compromise that has crept in to ‘art music’; traditional music has retained the rich variety of modes.]

 

Now consider this tune –

‘Johnny Lad’

 

Here the key implied by the key signature is C and we have an octave C-c, both of which seem to imply a C chanter setting; but the second part has high d’s which means something else is involved here; the only way a GHB-type chanter can encompass this setting is if the 6-finger note is D; the tune is in fact in a mode that starts on A [on the D chanter- equivalent of E on the ‘A’ chanter]]:

Since the F# does not appear, it is undecided whether this is an Aeolian mode (tone, semi-tone, tone, [tone, semi-tone, tone, tone]- A,B,C,D,[E,F,G,a]) - or a Dorian one (tone, semi-tone, tone, [tone, tone, semi-tone, tone], A,B,C,D,[E,F#,G,a]).


Appendix I - Closing the Circle of Fifths

 

Although, when using a piano keyboard to demonstrate the relationship between the 12 fifths and the 7 octaves, we do return to the note on which we started, 7 octaves higher, this is a fudge. The discovery that this is the case has been attributed to Pythagoras. The mathematics will reveal the true situation. An octave is produced by doubling the frequency of our root note; thus the 7th octave note will have a frequency of 27=128. The frequency of a fifth is 3/2 times that of the root; thus the 12th ‘fifth’ has a frequency of (3/2) 12               =129.746337890625. The difference is now known as the ‘Pythagorian comma’; for Pythagoras, this ‘shortcoming’ was the reason why the cosmos could never be perfect and was doomed to come to an end.



[1] The ratio between the frequency of the fifth and the root is 3/2, the second term in the ‘harmonic series’ the items of which are related to each other by the simple mathematical series 2:1,3:2,4:3.5:4.6:5 etc. This series is one of the basic structures of nature; there is a profound secret here regarding the nature of the relationship between this series and the human sensitivities, which results in the universality of human musical enjoyment.

[2] Some editors will use two sharps plus a g natural in their key signature for A Mixolydian tunes.

[3] The GHB chanter might well be considered as playing three pentatonic [5-note] scales; starting on G, A and D. These scales all avoid determining the intervals between C/D and F/G by omitting either the lower or the upper notes of the pairs.

[4] See Appendix

[5] This is not, of course, how a tune is composed; that is a very different matter

[6] As usual, this is not true for every instance; we have seen that some types of scale share key-signatures; we will put this matter to one side for the time being and concentrate on ‘major’ keys.

[7] The ratio between the frequencies of the D and the F# is 4:5

[8] Although I have given three ‘new’ keys here, and in the following, you may find it easier if you concentrate your attention on only one of these until you have mastered it. Which you choose will depend on the music you have to hand; you will find that much English pipe music is written for a D chanter, and most French music for a G chanter;.You will only occasionally meet with music written for a C chanter. As for music written in other keys, you now have the tools to work it out for yourself!

[9] This system of analysis was not part of early 18th century Highland piping; Joseph MacDonald in his tutor divides his tunes by what he calls ‘Tastes’; this is a system that composers and analysers of highland [and other] music might do well to revisit.