Theory Top-Up: compound interest

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By TIM CUMMINGS.
Piping Today #99, 2019

This being the fourth consecutive Theory Top-Up article to tackle matters of rhythm and time signatures, it may now be time to pay homage to compound metres, also known as compound time signatures.  We’ve already spent a fair bit of ink looking at simple metres, which might be worth a quick review below:

Simple duple time

  • 2/4 – quicksteps, polkas, hornpipes, 2/4 marches, and some slow marches
  • 2/2 [or ‘cut time’] – reels

Simple triple time

  • 3/4 – retreat marches, waltzes mazurkas, slow marches,and slow airs
  • 3/2 – ‘triple-time’ hornpipes from the Lowland & Border tradition

Simple quadruple time

  • 4/4 [or ‘common time’] – strathspeys, 4/4 marches, and some slow marches

These simple metres all feature time signatures with either a 2, 3, or 4 as the top number, each signifying the number of pulses, or beats, in each bar of music.  The 2s and 4s on the bottom, as you may remember, represent what kind of note is assigned the beat: a half-note (or minim) or quarter-note (or crotchet), respectively.  In order for a metre to be ‘simple’, each main beat is divisible by two.  For instance, a crotchet beat, such as for 2/4, 3/4, or 4/4, can be divided into two quavers, as shown in the example below.

The above can be verbally counted as “ONE, Two”, followed by the subdivided “ONE-and Two-and”. It’s binary and very simple.

Many of you will have also encountered the term “compound metre” as being distinct from a simple metre.  Compound metres can be a little trickier to grasp at first, but the main thing to understand is that their primary beats are divided into threes rather than twos, which may explain the use of the word “compound”.  Some examples of compound metre tunes found in our ceòl beag repertoire include:

Compound duple time

  • 6/8 – jigs, 6/8 marches, slow marches, and slow airs
  • 6/4 – a few slow marches and slow airs, and some ‘hornpipes’ from the
    Lowland & Border and North West England traditions

Compound triple time

  • 9/8 – slip jigs, hop jigs, 9/8 marches, and a few slow marches and slow airs
  • 9/4 – a type of hornpipe from the Lowland & Borders and North West England

Compound quadruple time

  • 12/8 – slides, 12/8 marches,and rarely slow marches and slow airs

Compound sextuple time

  • 18/8 – Lachies Lullaby,a slow air in Donald MacLeod’s sixth collection1

Note that compound metres generally feature a 6, 9, or 12 as the top number.  But here’s the rub: whereas simple metres have top numbers that directly represent the number of beats in a bar, compound metres have top numbers that can represent both a larger beat grouping and the subdivided notes within the larger beat grouping.

This means that the rhythm of a 6/8 jig, for example, can be thought of in two ways: six individual quavers (or eighth-notes, hence the 8 on the bottom), or two triplet beats – two larger, dotted crotchet (dotted quarter-note) beats that are subdivided into three quavers (hence the term “compound”).  Jigs, when played at a speed for dancing, move along pretty quickly, making it difficult to tap your foot six times in a bar, and difficult to read:

It’s far easier to tap just once per dotted crotchet, or twice per bar, which is why we tend to notate jigs as in the next example.  As the beamed groupings suggest, the below can be counted as “ONE, Two”, just as in 2/4, but being a compound metre is instead subdivided as “ONE-and-uh Two-and-uh” (or, were you to count each quaver, “ONE two three Four five six”).  These are tertiary beats.

To get a better feel for this rhythm, some pipers invoke the following mnemonic device: “rashers and sausages”.  (NB for my fellow Americans: “rasher” is another word for a slice of bacon.)  Try saying “rashers and sausages” four times in a row without pausing in between, and you should have a good sense for the first four bars of a standard jig:

If you add eggs to your breakfast, then you’ll now be chanting a slip jig: “eggs, rashers and sausages”:

And thus we’re now in the most holy2 metre of 9/8, with three triplet beats per bar.

12/8s, you might be correctly surmising, have four triplet beats per bar.  You could add tea to the beginning of your mnemonic breakfast, but given the standard groove of a typical Irish slide, you might do even better to recite a familiar rhyme:

Alas, these spoken phrases don’t work quite so well when various quavers are dotted and offset by semiquavers, as in most 6/8 marches and other compound metre marches.  I’m hoping at this point, however, you have a good enough understanding of compound metres to make sense of the theory behind them.

A quick aside: probably the #1 most requested pipe tune of all time, Amazing Grace, is most often written in 3/4, which is how it was first printed, and how it appears in most church hymnals today.  But we pipers almost always play it more flowingly and liltingly than what a true 3/4 metre would produce; and thus, if we’re to accurately convey that in our sheet music, we’re better off writing it in 9/8:

(Remember it’s the dotted crotchet that gets the more pronounced beat in compound time; and thus the dotted minim is worth two of those beats here.)

You may be wondering: What about tunes in 6/4?  Well, theoretically speaking, this is essentially the same idea as 6/8, with two strong beats subdivided into triplets.  But the designation of the crotchet beat (the 4) suggests a ‘broader’ tempo3, perhaps a little slower and more stately than a jig, but no less lively:

Unfortunately many composers mistakenly label their music as being in 6/4 when it might be more accurately written in 3/2, or maybe in 2/4 with only three-bar phrases, or possibly with alternating metres of 4/4 and 2/4.  How do you tell the difference?  Listen to the groove and to where the strong pulses land.  Simple metres have a particular ‘squareness’ to their rhythm.  Compound metres are more easy, fluid, and flowing.  The tune Rusty Gulley, for example, has the equivalent of six crotchets in each bar, making one argument for being in 6/4.  The same goes for Neil Dickie’s The Haunting and any Breton hanter dro.  But the rhythm of all of these is fairly square – binary – with the minim being subdivided by twos (as opposed to flowing triplets).  Thus I believe it’s better to write these as being in 3/2.  The same goes for An Drochaid Chliùteach (The Crooked Bridge), which is sometimes described as a ‘slip reel’.

The above concept also applies to the very few tunes in 9/4:

Numbers and theory and mnemonics aside, what may be the most important concept to grasp is the feel, groove, and associated emotions these compound metres tend to convey, particularly in comparison to simple metres.  This is obviously a more subjective matter, but I like to think most humans experience the rhythm of compound metres as moving along more liltingly, flowingly, rollingly, or even joyfully, and sometimes gracefully4.  These descriptors, if accurate, also have the associations of emotional lightness and feeling freer and more joyful, perhaps, especially if applied to a major key.

A good experiment might be to think of your favourite tunes that are in compound metres.  What do you like about this in comparison to tunes in simple metres?  How do jigs, slip jigs, and 6/8 and 12/8 marches feel compared to polkas, reels, strathspeys, 2/4 hornpipes, and 2/4 and 4/4 marches?

Lastly, because it can often help to connect dots from outside the piping realm, I thought I’d supply some titles from other genres of music which are set in a compound metre.  Do any of the below conjure fairly consistent feelings or moods when you listen to them?  Do any of these remind you of tunes in your repertoire that are in a similar compound metre?

6/4

  • Claude Debussy: La cathédrale engloutie
  • MGMT: Electric Feel (NB this song uses a drumbeat in 2/4, which compromises some of the natural lilting of the 6/4)

6/8

  • The Beatles: Norwegian Wood
  • David Bowie: Drive-In Saturday
  • Edvard Grieg: Morning Mood (from Peer Gynt Suite No. 1)
  • Queen: We Are the Champions
  • Elvis Presley: I Can’t Help Falling in Love
  • Seal: Kiss from a Rose
  • Taylor Swift: Last Kiss and Lover
  • Trad. English: Greensleeves and Here We Come A-Wassailing

9/8

  • Johann Sebastian Bach: ‘Jesu, Joy of Man’s Desiring’
  • C. Debussy: Clair de lune
  • Radiohead: The Tourist

12/8

  • J. S. Bach: ‘Kommt, ihr Töchter, helft mir klagen’ (from the St. Matthew Passion)
  • The Beatles: You’ve Really Got a Hold on Me and Oh! Darling
  • Frédéric Chopin: Nocturne in Eb Major
  • R.E.M.: Try Not to Breathe

Theory Top-Up articles published on Bagpipe.News so far:

  1. Tunes in the key of D-Major
  2. Tunes in the key of A-Mixolydian
  3. Tunes in the key of A-Major
  4. Tunes based on a ‘gapped’ A scale
  5. Tunes based in A-pentatonic major
  6. Tunes in B-minor
  7. Double Tonic Tunes
  8. Tunes in the Dorian mode
  9. Tunes in G-Major
  10. Exotic tunes and tunes that change key
  11. Compressing tunes with low F-sharp notes
  12. Compressing tunes with high-B notes
  13. Theory Top-Up Harmonics: an introduction to the mysterious overtones in our music
  14. Theory Top-Up Harmonics Part 2: continuing the discussion on overtones
  15. Theory Top-Up Harmonics Part 3: using harmonics to fine-tune our pipes
  16. Theory Top-Up: An introduction to writing harmony for ensembles
  17. Theory Top-Up: writing harmonies of thirds
  18. Theory Top-Up: discovering chords 1 (as a basis for crafting harmonies)
  19. Theory Top-Up: discovering chords 2 (as a basis for crafting harmonies)
  20. Theory Top-Up: Elaborating on chord based harmonies
  21. Theory Top-Up: writing chord-based harmonies for slow airs
  22. Theory Top Up: harmonies that imitate uilleann pipe regulators
  23. Theory Top-Up: harmonies derived from hymns
  24. Theory Top-Up: learning tunes by ear
  25. Theory Top-Up: the signature of time
  26. Theory Top-Up: simple matters
  27. Theory Top-Up: triple time trouble
  28. Theory Top-Up: Common and Cut Time
  29. Theory Top-Up: Compound Interest
  1. This tune could just as easily be written in 6/8 with three-bar phrases. ↩︎
  2. As mentioned in the previous Theory Top-Up articles on rhythm, this particular rhythm was once known as tempus perfectum (major) [“great perfect time”] in medieval and Renaissance times.  This is because anything involving the number three was associated with the Holy Trinity.  9/8 was extra-special because it involves three triplet beats per measure. ↩︎
  3. Remember that the metre does not always dictate how fast a tune is to be played.  That’s officially the job of the tempo marking – or as is often the case of pipe tunes, the designation of “Reel”, “March”, etc. – above the first bar of music.  The metre has more to do with the organisation of natural rhythmic pulses in the music;   but there are some conventions that sometimes now suggest a particular tempo for a given piece of music. ↩︎
  4. See what I did there?  That’s right: adverbs with triplet rhythms, to drive my point deep into your subconscious.  You get more than your money’s worth on Bagpipe.news! ↩︎