Theory Top-Up: simple matters

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By TIM CUMMINGS.
Piping Today #96, 2019

In the last episode of Theoretically Speaking, we took an initial look at some of the theory behind rhythm and metre – specifically, decoding time signatures (or metre signatures).

In case you missed it or would like a quick refresher: time signatures are all about the organisation of beats and beat groupings in written music.  The top number of a time signature refers to the number of beats in a bar (which was compared to the number of pickets in between the support posts of a picket fence).  The bottom number refers to what note value is assigned the beat (or the width of the pickets).  Our main example was the time signature of 2/4, which was revealed to mean a rule of two quarter-note [or crotchet] beats per bar.

Also in that article was a particularly lame pun involving sheep, but I’ll spare ewe the agony of repeating it.

Today I’d like to talk a bit less about sheep, and a bit more about the 2/4 metre and others that fall into the “simple time” category.  And then I want to take a side trip to re-examine one remarkably common error involving the notation of pipe tunes that are in simple time.

But first, the term “simple time”.  Time signatures that fall into this category are those whose primary beats can each be divided by two notes of a shorter duration.  For example, in a metre of 2/4, each of those quarter-notes (crotchets) can be subdivided into two eighth-notes (quavers) as shown below:

“One, Two” followed by the subdivided “One-and Two-and”.  It’s binary.  It’s very simple.

We play a lot of tunes that fit under the simple time umbrella.  First, here is a sampling of those typically notated in simple duple time, with two primary pulses in each bar:

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

Those in simple triple time:

  • 3/8 – bourrées 3 temps [from central France, par exemple]
  • 3/4 – retreat marches, waltzes and some slow airs
  • 3/2 – ‘triple-time’ hornpipes [from the Lowland & Border tradition]

Those in simple quadruple time:

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

Generally speaking, a time signature with a 2, 3, or 4 on the top denotes a simple time metre.  Time signatures with 6, 9, or 12 on the top involve metres in compound time, a topic we’ll look at in a forthcoming issue of Piping Today.  Time signatures with 5, 7, 8, 11, etc. on the top are referred to as complex.  Those will also be investigated a little further down the road.

But let’s get back to the simple time signatures.  I like to think this is all pretty straightforward for the majority of Piping Today readers.  If you find the above concepts aren’t sinking in as well as you’d like, it’s OK!  I guarantee you’re not alone, and I’d suggest finding an experienced musician to help explain things in a way that may better match your learning style.

But I have one more item to discuss, one that may catch some seasoned pipers by surprise.  It involves the incorrect notation of a particular rhythm found in many 2/4 marches and hornpipes.

Sing this old chestnut in your head for a moment, or pick up a chanter and play it, and see if anything strikes you as not being notated as accurately as it could be.  [Go ahead, try it!]:

Any guesses?  Well, here’s another question for you: have you ever been accused of not holding that first downbeat, the dotted E, long enough?  Or have you ever accused someone else – a student or fellow bandmate, perhaps – of the same?  It’s very likely, and it’s not entirely the fault of the piper.

Still can’t figure it out?  Here’s another question: Are you giving the F# immediately following that dotted E the exact same rhythmic value as the D in the pick-up beat at the very start of the tune?  I’m guessing so, but then why aren’t those two notes written with the same note value?  Upon closer inspection, the F# has two beams, signifying a sixteenth-note (semiquaver), which gets 1/4 of a beat in this time signature; and the D has three beams, signifying a thirty-second-note (demisemiquaver), which gets 1/8 of a beat in this time signature.

This discrepancy has never stopped the world from spinning because we’ve been taught to hold that dotted E for an especially long time before snapping out the F# in the remaining nanosecond before the next beat arrives.  It’s always been a matter of style and convention.

But The Music Theory Police would sternly point out that we ought to change either the way we play that section of music, or change the way we write it.  Assuming the latter is the more palatable option – because we really like how we’re playing that bit – it would indeed seem that we need to re-think its written rhythm.  But how?

I can think of two solutions shown in the revised notation below, both of which will look a little strange to you, and the second of which is less visually cluttered, and thus gets my vote.

These are both technically correct notations for the way in which we pipers perform this familiar rhythm in a 2/4 march.  

I find, however, that the first is not only more visually cluttered, but would also confuse, momentarily at least, anyone sight-reading it for the first time.  The second looks much more like the pattern we’re used to seeing, only the E is double-dotted, and the F# is now carrying an extra beam…  “Wait, did you just say ‘double-dotted’?”  Yes, I said double-dotted.  It’s certainly less frequent in written music, but it is completely correct and for real.  The same goes for double-dotted minims, double-dotted quavers, double-dotted semiquavers, and so on.  Many of you know that one dot adds half the value of the original note to itself.  The second dot adds half of that—the other dot’s – value.  A dotted eighth note (dotted quaver) is worth 3/4s or 0.75 of a beat in 2/4 time; therefore a double-dotted eighth note is worth 7/8s or 0.875 beats in the same metre.  The double-dotted eighth note leaves room for only 1/8 or 0.125 of a beat, which is precisely the same value as the D in the pick-up beat.

If you or your computer software were to play that initial E and F# as it has always been written, ignoring stylistic convention and staying true to that single-dotted E and semiquaver F# rhythm, I guarantee someone will complain that the E is not being held long enough.  Again, this is because it is only being held for 3/4s or 0.75 of the beat.  (Subdivide that first beat into even quarters, giving the last quarter to the F#, and you’ll see what I mean.)

Clear as mud?

Never mind.  Just know that with the double-dotted rhythm, that speedy little F# is now written in a way that more accurately matches how it is played.  And now, my fellow pipers, having conveyed that special bit of knowledge, I charge you to go forth and manually double-dot all those sorry, little, falsely written, singly-dotted eighth notes in your piles and piles of 2/4 march music.  Not until every missing double-dot is avenged will our troubled, weary world find lasting peace!

One final note: if you thought the mentions of sheep in this article were inane and unnecessary ewe-phemisms, you’d be right.  But you may nonetheless appreciate the following: according to Google’s dictionary, the origins of the word ‘signature’ (as in time signature), include signatura, a late-Latin term once used to refer to the markings on sheep.


Tim Cummings plays, teaches, writes and publishes bagpipe musicHis Theory Top-Up series ran in Piping Today magazine for more than five years.


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