How do "dotted-crotchet = one beat" teachers address "irregular compound" meters (e.g., 5/8)?

Question

"Ordinary" Compound Meter

1. I was taught that 6/8 time, for example, meant "six beats in a measure; the eighth note (quaver) gets one beat." Similarly, 9/8 would be "nine beats in a measure; the eighth note gets one beat."

2. Arriving at this website (SE MP&T), I encountered the approach in which 6/8 time is "two dotted quarter-notes (dotted crotchets) in triple divisions", and 9/8 is "three dotted quarter-notes in triple divisions."

"Irregular Compound"¹ Meter

1. The method by which I learned to understand compound time remains consistent for, say, 5/8 or 7/8: five (or seven) beats per measure; the eighth note gets the beat.

2. The "dotted quarter-note per beat" approach cannot remain consist for 5/8 or 7/8, so how does a "dotted quarter-note beat" teacher explain irregular compound meters like 5/8 and 7/8 to a student?

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¹ _{There's no such thing as "irregular compound" meter. I've invented the term for use in this post as a shorthand for "irregular meters that have an 8 on the bottom".}

Answer 1

There isn’t one answer, but the teaching methods for time signatures with prime top numbers can be summarized by saying we delay explaining them and then when we explain them we both refine the understanding of compound meters and address the nuances of unusual and additive meters.

When we teach a student who is closer to being a beginner that 6/8, 9/8, and 12/8 don’t actually have 6, 9, or 12 beats of 1/8 value, we’re already contradicting our first day of teaching meter when we said the top note is the number of beats and the bottom indicates which value gets the beat. When we teach compound meter, we might oversimplify by saying that 8 on bottom means it’s compound, but that’s not fully true. When we do that, we set ourselves (or some future teacher) up for having to replace that simplification with a more nuanced understanding as the student progresses and encounters meters with 8 in the bottom that are not compound.

Because there is quality literature suitable for advanced beginners that is in 3/8 meter, and we don’t always want to have to use over-edited student editions of music (at least some of us don’t), some of us choose to avoid oversimplifying at the beginning. Even if we say "when there’s an 8 on the bottom and the top is divisible by 3, then it’s compound", that’s not always going to work because 3/8 is usually simple and 9/4 usually compound. For this reason some teachers will specifically teach 6/8, 9/8, and 12/8 and not try to use a general rule for recognizing compound meters, but this has its own pitfalls.

We often make analogous oversimplifications for key signatures also. Teachers in general are challenged by how to teach basic understanding to young and beginning students in every field without having to reteach and replace understanding when students advance.

In math, for example, we couldn’t teach first graders how to add by starting with monads and groups with axioms for the binary operators and identity elements. We teach counting and whole numbers knowing full well that some of the understanding will be refined and replaced as the student learns more.

In short, across all fields, we generally teach inaccurate and incomplete information to beginners to get them started even though we know we will have to admit to having done so in the future and retrain the student with a more sophisticated understanding. Many teachers and people who study education have wanted to find ways to teach accurate information from the very beginning, and I think the best teachers work hard to be as accurate as possible as early as possible. But I’m not aware of a field where pedagogy has been developed that never requires retraining on beginner concepts as the student progresses.

Answer 2

The books I've learnt from teach "dotted-crotchet = one beat" in a compound meter, but they didn't cover irregular meters.

I've come to an understanding that irregular meters can be thought of as simply having beats of different value.

It is easier to count pulses (the subdivision unit), and these are usually used for tempi markings (PPM instead of BPM), but pulses are definitely not beats.

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For example if I were playing the simplest 5/8 groove on the drums, I'd play:

I'd think of the bass drum as hitting the on the strong beat of the bar, the snare on the medium beat, and the hi-hat as hitting on all the weak pulses.

This'd be identical to 6/8, except the last pulse is cut off and the medium beat consequently shortened.

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However if I were playing 5/4, I'd think of it quite differently. I'd play:

Which is 4/4 with an extra (medium) beat at the end. Or equivalently 2/4 + 3/4.

Answer 3

Answer to (2). It doesn't. With irregular compound times, there will not be an extra regular rhythm involved, only one rhythm every bar. Compound means (to me) that each bar can be interpreted in two ways. Read on...

Irregular time sigs. are just what it says on the tin - not regular. The top number is going to be an odd number (excluding the basic 3 and multiples thereof) so creating a 'lop-sided' rhythm.

Let's look at 6/8. So many beginners find it difficult to understand, thinking, well, it's just a re-incarnation of 3/4. Mathematically, it is. But the big difference is 3/4 has the 'beat' of a crotchet, of which there are three, giving the familiar 1 2 3 1 2 3. Whereas 6/8 is perceived as having two alternate counts: 1 2 3 4 5 6 1 2 3 4 5 6, AND 1 & & 2 & & , so could get counted in either, or both ways, depending on the tempo of the piece.

That, eventually, we all come to understand and respect.

However, with irregular time signatures, there's no simple way to split the bar evenly. So we just bite the bullet, and for 5/8, it ends up as 1 2 3 4 5, or 1 2 3 4 5 . in similar vein, 7/8 is divided into 2s and 3s. Of which there are several combinations, but never two 3s and a 1. We seem to favour 2s and 3s in most translations of time signatures. Sometimes straight 4 gets involved, but that's as far as it goes. Even in a Greek 13/4, we'd maybe count 1 2 3 4 5 6 7 8 9 10 11 12 13 (emphasis on the darker numbers).

So, translating all that into /8 times, there could be a dotted crotchet (or two!), or tied notes, which would show the splitting rhythm of the bar, and piece. Thus producing, for 5/8, for example, dotted crotchet, crotchet, or crotchet, dotted crotchet, but that's about as far as it would go, for me - on the premise I've understood the question. If not, please guide me further!

Answer 4

I was taught that 6/8 time, for example, meant "six beats in a measure; the eighth note (quaver) gets one beat."

Well, for a start, that was wrong, or you misunderstood. As wrong as saying "2/4 is four beats in a bqr, or 4/4 is eight beats".

6/8 is analogous to 2/4 with triplet 8ths. Whichever way you write it, it's ONE-and-a TWO-and-a.

(OK, this is SE, so I have to consider edge cases :-) A fast waltz, written in 3/4, is often conducted 'one in a bar'. To my mind, this makes it 'compound single', though this will attract argument. Well, what ELSE could an 'in 1' waltz be? 1/1 time is also occasionally encountered. Four quarters to a bar, but so fast as to be counted 'in 1'. 'Simple single'?

And yes, at the other end of the tempo scale a very slow 6/8 MIGHT be counted 'in 6', a very slow 2/4 MIGHT be counted 'in 4'.)

Broadly speaking, musical beats divide either into two (simple time) or 3 (compound time). 3/4 is One-and-Two-and-Three-and, 6/8 is ONE-and-a TWO-and-a.

But modern(ish) composers sometimes get more complex. They might mix up simple (2-group) and compound (3-group) beats in the same time signature! 5/8 could be grouped 2+3, a simple beat plus a compound beat, or 3+2, a compound beat plus a simple one. And the two beats are of different lengths! Equal 8th notes, but unequal beats! Groovy!

Yes, 5/8, 7/8 etc. MIGHT be a straight '5 or 7 to the bar'. But this rarely happens, rhythms just naturally fall into 2- or 3-groups. The only example I can recollect of a pounding '7 on the floor' without sub-grouping (it's written in 7/4) is the finale of Stravinsky's 'Firebird'. I'm sure there are (a few) others.

Answer 5

5/8 and 7/8 - or quintuple and septuple meters - are not irregular compound meters: they are simple meters.

Their cousins 15/16 and 21/16, although ambiguous (due to also being ways to write 3 groups of 5 16th notes and 3 groups of 7 16th notes, respectively), are ways to write the true compound meter parallels of 5/8 and 7/8.

15/16 as a compound quintuple meter is "5 dotted 8th notes in triple divisions", while 21/16 as a compound septuple meter is "7 dotted 8th notes in triple divisions".

Beam 5/8 and 7/8 in whichever way you want - 3 & 2, 2 & 3, 4 & 3, 2 & 3 & 2, 3 & 4 - it is the fact that their component 8th notes get subdivided into 2 (or 4) sub-beats and not 3 sub-beats that makes them simple meters and not compound meters.

The "dotted-crotchet = dotted quarter note = one beat" approach is already deeply flawed. This approach also fails to explain compound meters such as 6/4 and 12/16. In 6/4 time, one beat is a dotted half note instead of a dotted quarter note, while in 12/16 time, one beat is a dotted 8th note instead of a dotted quarter note.

A better rule of thumb for detecting compound meters is to check whether the top number is both divisible by 3 and not equal to 3. If both are true, then we have a compound meter on our hands (unless the beaming is like "Blue Rondo a la Turk"'s 2-2-2-3 or nastier). If at least one is false, then we probably have a simple meter on our hands (the first ambiguous case I can think of is 10/8, which can be grouped as "quintuple-pound" duple meter or as an irregular beaming like 3-3-2-2 - my experience with 8/8 is that it is generally reserved for strangely beamed measures of eight 8th notes and is therefore better thought of as a simple meter).

Answer 6

I always approach it from a conductor's point of view: some beats are longer than others. 5/8 is two beats per measure, 7/8 is three, and so on. Some beats are 50% longer.

I don't have any sources handy, but every conducting textbook I've seen approaches it this way.