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Matt Seattle

In the fourth and last episode of this exploration of Harmonic Proportion we return to the 3:1 ratio with which we began, this time looking at three musical ideas which have been used in some pipe tunes to turn a very simple idea into something much more elaborate.


Firstly, a phenomenon which I call ‘subdominant substitution’, or more plainly put, using a melodic figure based on a D chord when you would expect an A chord (this is when the tune itself is in A). We can get away with this because the D chord contains the note A and is therefore also concordant with the drones. Here is an example:

This is Dixon’s strain 3 [of Jack Latin], but it is strain 2 in almost all other versions of the tune, both earlier and later. All of Dixon’s other strains can be harmonised with A for the whole of bars 2 and 5, though his strains 6 and 7 also have other possibilities. Anyway, if we regard the Ds in this strain as substitutions for A, then we again have the 3:1 ratio in its simplest form.

Two further examples occur in tunes well known in the Northumbrian tradition, but both with Scottish antecedents, where the D chord is used to open some strains. The first is Newmarket Races, which we looked at in Episode 2, and the second is Felton Lonnen, where bars 1, 3 and 5 of strain 1 can be harmonised |D A |

This pattern also underlies the strain which is a variation of this one, strain 6 in Peacock’s version, or strain 9 in the Northumbrian Pipers’ Tunebook version. Here is strain 1 of the NPT version transposed to A, and with chords:



You can substitute high As for the high Bs, which have been left in to show the chordal structure more clearly.


A second idea, mentioned in Episode 1, is the ‘fluid tonic’. This applies to tunes in D rather than A, which, in this particular harmonic world, are a kind of mirror image of tunes in A, in that the A chord, even though it is the drone chord, now serves as the functional dominant. Other chords which may substitute for D in these tunes are B minor and G, in the whole tune, or in some strains, or within individual strains, while F minor can substitute for A (see Watty’s Away in Episode 2). A particularly intriguing example of these substitution possibili- ties is Tail Toddle, where there was an early branching off between Northumbrian versions with strains opening on B minor and D chords and Scottish versions with strains opening on D and G chords. Dixon’s early Lasses Make Your Tails Toddle has strains opening on all three chords, but with the internal flexibility seen in early Scottish versions, while later Northumbrian versions, for the diatonically tuned Northumbrian smallpipes, open with B minor and D (transposing from the original A minor and C) and have less internal flexibil- ity. The later Northumbrian versions (e.g. Bewick and Clough) have variants of the title Little Wot Ye Wha’s Coming, paradoxically preserving the name of a Scottish song lyric which goes with the Scottish version of the tune (see Scots Musical Museum).

The widely found 2-strain Scottish version of Tail Toddle does little justice to its possibili- ties, so to remedy that situation here is an excellent 8-strain version from Flores Musicae which seems to have been skilfully edited down from the more rambling set in the McLean collection. It is also in the Rook manuscript.


The chords placed under the first two strains are more or less those underlying all subse- quent pairs, though later strains also have elements of B minor. To get back to the simple Elsie Marley structure, treat the D, G and B minor chords as mutual substitutions, likewise the A and E minor chords. It is of course possible to analyse a tune to death: the main thing is that this Tail Toddle works as a very satisfying pipe tune, but it is interesting to see how it is also structurally extremely intelligent.

This structural intelligence is the third idea we will look at, in the context of two different versions of Cut and Dry Dolly. Strain 1 of John Bell’s version, with chords, shows the simple 3:1 ratio:



There is a huge but invisible leap to Robert Riddell’s version, the tune’s only known Scottish appearance.



While the tune as a whole has been expanded into an Elsie Marley structure (3 levels of 3:1), bars 4 and 8 also have an internal 3:1 ratio, making this the only example I know of a tune which contains 4 levels of the ratio.

This may begin to sound like composing by numbers. It is not. Knowing and using these structures is a different matter from having good musical ideas, but if you do have good musical ideas, knowledge of the structures can give you ways of making ideas into coherent tunes; not the only ways, certainly, but ways which work and which were part of the craft of Border piping as traditionally practised in the past.

Footnote: Dixon’s version of Cut and Dry Dolly is subtitled ‘New Way’ and lacks this open- ing strain from Bell/Riddell. Although these two versions are later they probably represent the ‘Old Way’ which may have been abandoned because it is so similar to the opening bars of Lads of Alnwick. This speculation is supported by Dixon’s placing of the tune next to The Apprentice Lads of Alnwick .