music theory

Back to basics - the Key to Music

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Having started my series of blogs about the theory of music with time signatures, the next logical step is to look at key signatures and the way composers use them. I know many amateur musicians have no formal training in music theory, so we’ll begin with the absolute basics. You’re welcome to skip ahead through sections you already know, or use them as a refresher.

The geography of key signatures

Let’s begin with the layout of key signatures. In most recorder music we rarely venture beyond three sharps or flats but it does no harm to check out the entire range of keys, especially as they are all interconnected. For starters, the key signature always appears directly after the clef and before the time signature. This pattern of clef then key signature is repeated on every line as a handy reminder.

Key signatures contain either sharps or flats - never a mixture of the two - and they always appear in the same order and layout. For sharps this order is F C G D A E B and for flats it’s B E A D G C F. Knowing this means you never need to think about exactly which sharps or flats are in your key signature. For instance, if there are three sharps they will always be F, C and G - no exceptions.

Perhaps the easiest way to learn this it to remember the following phrase, in which the first letter of each word gives you the order of the sharps:

Father Charles Goes Down And Ends Battle

To remember the order of the flats, all you need to do is reverse the phrase;

Battles Ends And Down Goes Charles’ Father

Now let’s take a look at the layout of the sharp and flat key signatures in the two clefs we use most when playing the recorder. The sharps and flats are kept close together on the stave and apply to every instance of a note - not just the ones which appear on the same line or space.

Now you know the order of the sharps and flats we need to look at the keys themselves.

Major and minor

As you’re probably aware, every key signature is connected to a major key and a minor key. For instance, a key signature of one sharp could be G major, but it could also be E minor. The latter is often known as the relative minor of G major because it is related by having the same key signature.

We’ll look at the difference between major and minor keys in a moment, but first let’s familiarise ourselves with the pattern of these keys.

You may have heard other musicians talk about a cycle or circle of 5ths without really understanding what this means. This term is often used because each new key signature is five steps away from its neighbours. For instance, if you count up five notes from C (always include the note you’re counting from the note you’re counting to in the five: C-D-E-F-G) you reach the note G. This is the distance between each of the keys when you either add another sharp or reduce the key signature by one flat.

This is most clearly illustrated by looking at it in a circle. The major keys are shown on the outside of the circle and the minor ones inside. By working around from the top of the circle in a clockwise direction, a 5th at a time, you progress from one key signature to another, ultimately returning back to C major. It’s with noting that there’s some duplication at the bottom of the circle, where we reach the really extreme keys. For instance, D flat and C sharp sound the same, but you can have a key signature for either note - one has five flats, the other has seven sharps.

As recorder players, we’re unlikely to be worried by G flat major too often, but it’s useful to be aware of the existence of these extreme keys and to understand how they relate to each other. I would still recommend you practise scales in some of the more extreme keys to gain a fluency with the less commonly found sharps and flats. That way, when you encounter a stray D flat somewhere you won’t be thrown by it and have to stop and think about where to find it. Earlier this year I wrote a blog post about using scales and arpeggios in your practice - if you haven’t already read it, you can find it here.

Identifying your keys

It’s all very well knowing you’ve got four sharps to play in your music, but next you need to know the name of that key. Again, there’s a quick and easy way to work this out without having to memorise every single one. Let’s look at the major keys first:

For sharp major keys, the name of the key is a semitone above the last sharp of the key signature. So if you have four sharps, the last one is D sharp and therefore you’re in E major.  Likewise, if the last sharp in your key signature is E sharp, the key is F sharp major.

For flat major keys, it’s even simpler - the name of the key is the penultimate flat of the key signature. Therefore, if you have two flats (B and E) you are in B flat major and if there are five flats (BEADG) you’re in D flat major. Admittedly this solution doesn’t work for F major, which only had one flat, but it’s one of the most common keys in recorder music so I dare say you’ll probably remember that one!

OK, that’s the major keys dealt with, but how to identify your minor keys? If your piece is in a minor key, there are will almost certainly be extra accidentals (usually sharps or naturals) dotted around in the music. We’ll look at the reason for these later. These should immediately alert you to the fact that the music is in a minor key, and you’ll probably be able to hear the different character of the music too. To figure out which key it is, use the rules I mentioned above to identify which major key is associated with that key signature. From there it’s an easy enough step to work out the related minor key, which is three semitones lower. So if the major key is G major, those three semitones are G to F sharp, F sharp to F natural and F natural to E. Your related minor key is E minor.

So you can see these rules in action, here are all the key signatures together:

Quick refresher - tones and semitones

Before we go on to look at major and minor keys in more detail it’s worth having a quick recap on tones and semitones. In western music the semitone is the smallest distance between two neighbouring notes - the equivalent of moving between neighbouring black and white keys on the piano. From a non-keyboard player’s perspective, a semitone is the distance between a natural note and its flat or sharp neighbour - e.g. D to D sharp.

A tone is a step wider - two semitones - as you can see from the keyboard illustration below. Semitones are shown in red, while tones are shown in blue.

These two intervals are the building blocks for all major and minor scales, creating the sounds we hear in major and minor keys. It’s important to understand the distinction between these if we’re going to understand the difference between the different types of scales.

Shades of major and minor

We often talk about music being in major or minor keys but have you thought about the difference between the two? We’ll get into the technical differences in a moment, but the most important distinction is the way they make the music feel. One of the ear tests often given in music grade exams is making the distinction between major and minor when listening to music, and teachers often ask students to decide if the music makes them feel happy (major) or sad (minor). This is, of course, a huge oversimplification - there are plenty of sonorous, serious pieces of music in major keys, or lively dances in minor keys. Perhaps a better distinction might be to think of music in a minor key as having a ‘darker’ sonority and major as being ‘brighter’. Let’s have a listen to some examples:

One of the most joyful and energetic examples of recorder music in a major key is Vivaldi’s Concerto, RV443, played here on the descant recorder by Lucie Horsch.

In contrast, the Welsh traditional lullaby Suo Gan is very poignant and thoughtful, but is still unmistakably in a major key.

And now two examples of music in a minor key. The first movement of Bach’s Double Violin Concerto is in D minor but is still full of life and energy, yet it definitely has a darker feel.

Perhaps one of the archetypal pieces of minor key music is Elgar’s melancholic Cello Concerto, composed soon after the end of World War I. The opening is heart wrenchingly sad, but even here there are moments of vivacity in the scherzo.

What’s the difference?

While we respond differently to music in major and minor tonalities, it’s also useful to understand the technical distinction. The key difference is the distance between the first and third notes of the scales, although as we will see there are other distinctions too. In a major scale, the distance between notes 1 and 3 is a major third. By contrast, in a minor scale the interval (distance) between these same notes is a minor third.

A minor third is made up of three semitones, while a major third is a semitone wider. Why not play the two examples below and hear the difference for yourself?

Of course there are other differences too, so let’s take a moment to look at the make up of major and minor scales.

Major scales

Major scales come in just one variety and the notes are the same whether the scale is ascending or descending. As you can see from the red boxes in the example below, each major scale contains two intervals of a semitone - between notes 3 and 4, and again between notes 7 and 8.

Minor scales

The minor scale has three different sub-species, as you can see below. The natural minor includes just the notes contained within the key signature. A natural minor scale is fundamentally the Aeolian Mode, but modes are a rabbit hole I’ll save for a future occasion or you might still be reading at midnight!

Like the major scale, the natural minor contains two semitones, but this time they occur between notes 2 and 3 and again between notes 5 and 6.

The Harmonic Minor scale tends to be the one most people learn first, although it’s used less than the other two in western classical music. When children begin preparing for grade exams they have to learn scales and arpeggios from memory and I think many teachers start with harmonic minors simply because they’re easier to memorise. This is practical solution, even if melodic minors are arguably more practical use in the music we tend to play every day.

As you can see in the example below, in a harmonic minor scale note 7 is raised by a semitone - in this case the F becomes an F sharp. This creates a semitone between note 7 and the key note, which creates a clear sense of pulling one’s ear towards the scale’s final destination.

The addition of this accidental also creates another interesting interval, marked here with blue circles - is an augmented second. This stretched shape in the musical line creates a more exotic feel - much like the melodic shapes you’d hear in the tune from a snake charmer’s flute.

If you want to hear the harmonic minor scale in use, Gustav Holst’s Beni Mora contains oodles of them from the outset. It was inspired by the music he heard on a visit to Algeria and instantaneously feels exotic to western ears, despite its orchestral soundworld.

Finally, we have the Melodic minor scale which is the variety we meet most often in the music we play. As you can see in the example below, both the 6th and 7th notes are raised by a semitone on the way upwards, and lowered back to their native pitch as the scale descends again. This means the semitones occur in different places on ascent and descent, but the effect is a very easy ‘melodic’ sound.

The Overture to Mozart’s opera Don Giovanni is a beautiful example of minor scales in action, definitely rooted in the dark, melancholic toneworld of the minor key. In this recording, 33 seconds in we hear small sections of melodic minor scales (listen out for those exotic augmented seconds) and and 1 minute and 12 seconds there are chains of melodic minor scales, rising and falling in the flutes.

A Baroque quirk

Having talked about minor key signatures and the way minor scales are constructed I should perhaps mention one small glitch in the system. This occurs specifically in minor keys with flats in the key signature and mostly in Baroque music. As we’ve seen already, in a melodic minor scale (the type which occurs most frequently in Baroque music) about 50% of the time the 6th note of the scale is raised by a semitone. Therefore from the perspective of someone writing out music, or engraving plates for printing, there will be lots of occasions when you have to insert an accidental. Because of this it’s not unusual to find music from this period where the final flat of the key signature (looking at it from our 21st century perspective) is omitted.

For example, this extract from Barsanti’s G minor recorder sonata has only one flat in the key signature. Had the E flat been included, the engraver would have then needed to add flat accidentals for all the notes circled in red. Of course, the other side of the coin is that he or she then needed to add E flats in for all the notes circled in blue! One could argue for or against this Baroque practice, but it’s important to know about its existence when trying to understand the key your music is written in.

The false relation

No, this isn’t one of those family friends you always called ‘uncle’ when you were a child, even though he was really nothing of the sort! Instead it’s the name for a harmonic curiosity that crops up in early music; in particular repertoire from 16th and early 17th century England. You’ll often find it in music by Tallis and Byrd but Henry Purcell had a penchant for this piquant effect too.

You remember I talked earlier about the way a melodic minor scale has raised 6th and 7th notes as it ascends, returning them to their original pitch again as the music descends? Well, occasionally composers created melodic lines which did both at the same time. Sometimes you’ll get a direct clash as the raised 7th and lowered 7th occur simultaneously, creating one of those ‘double take’ moments as you try to figure out if someone played a wrong note. On other occasions it’ll just be a ‘near miss’ and the effect isn’t quite so astringent. There’s nothing to be done here, except to check the score to reassure yourselves that all is well and then simply enjoy the exotic clash in the music!

As you can see in this short extract from Byrd’s Ave Verum Corpus, a G sharp and G natural come into direct contact, albeit fleetingly, in bar 37. The music is in A minor, so the tenor line has the raised 7th note of the melodic minor scale (leading upwards to A), while the bass has the G natural which is descending. The fact that the two happen simultaneously creates a beautiful, piquant discord.

Endlessly evolving keys

While I’ve talked here about the relationship between key signatures and scales, in reality it’s unusual for a piece of music to remain in one key throughout. The process of moving between different keys is modulation. In order to explain this fully a knowledge of harmony and cadences is ideally required, but again that’s a large topic for another day.

From a player’s perspective the important thing is to look out for accidentals in your music. Yes, there are certain accidentals you’d expect to find in minor keys (specifically your raised 6th and 7th notes) but if you start to encounter additional sharps or flats it’s likely the music has modulated to a new key. You need to be Hansel, following the breadcrumbs through the forest in Hans Christian Andersen’s children’s tale. Look at the clues in your music - perhaps you’re in G major, but suddenly lots of C sharps begin appearing and the likelihood is the music is moving from G into D major, which has both F and C sharp in the key signature. Or perhaps, in the same G major piece the new accidentals are D sharps. In that case E minor is a more likely destination, with the D sharps being the raised 7th note of the scale.

Music often shifts to keys that are fairly close to home - perhaps the relative minor or just a step or two around the circle of 5ths I talked about earlier. With the tools I’ve given you today you are better equipped to follow the breadcrumbs and figure out where the music has migrated to. Here’s a final example to illustrate my point. In the first page of Telemann’s Recorder Sonata in F major he moves the music through no fewer than four keys. I’ve annotated this extract with different colours to show the important accidentals and the keys the music modulates into. Some of them are fleeting, while others feel more significant. You can click on the music to see it enlarged.

Over to you…

Equipped with this knowledge, you can now take it out into the world and use it to help you understand the music you play in a deeper way. If the concept of identifying modulations seems overwhelming for now, why not simply make a point of looking at the key signatures you encounter to identify where you begin? When faced with a new piece of music, take a moment to decide which key it’s in. The key signature itself is a big clue, and this might be all you need if the music is in a major key. If you spot some accidentals too, see if they fit in the melodic scale of the minor key with the same key signature and be ready for some darker, more melancholic tones.

Did you learn something new today? If the answer is yes, I hope my words have demystified music a little more for you. But if there are still gaps in your knowledge which need filling do leave a comment below and I’ll do my best to help you. This is an ongoing series of blog posts which I hope will collectively help you gain a deeper understanding of the music you play.

Back to basics - the theory of time

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Whatever job you do for a living, the chances are you had some training at the start. Surgeons start about anatomy long before they operate on a human, and lawyers are taught the intricacies of the law before they’re sent into court to defend someone’s freedom. Likewise, a professional musician spends many years at music college or university gaining a rounded understanding of music theory and the history of the repertoire we later play and teach.

I meet many able amateur musicians who are highly qualified in their own fields of work, but have come to music making by a more circuitous route. Maybe they learnt the basics at school and returned to music making several decades later. Or perhaps they decided to learn an instrument when they retired. One common factor I frequently see is a patchy knowledge of music theory, picked up piecemeal as they’ve learnt to play new repertoire.

I also see this from a personal perspective with my photography. I’ve learnt a handful of skills to help me tweak my photographs in Photoshop, but my knowledge is far from complete. Rather than learning this complex piece of software from the ground up, I’ve picked up pieces of information as and when I need them. The result - I can do certain things, but gaps in my knowledge leave me floundering when the task in hand moves beyond my limited understanding. Even worse - I often don’t know exactly where the gaps in my understanding are, which makes them even harder to fill!

With this in mind I recently asked my Score Lines subscribers about areas of music theory where they felt they had gaps. This is the start of a new series of blog posts to help you begin to plug the holes in your knowledge and gain greater enjoyment from the music you play. Among the responses to my plea were several asking about time signatures and how they interact - especially in Renaissance music.

This seems as good a place as any to begin. So let’s dig in!

Understanding time signatures

Let’s begin with the basics - what is a time signature?

Those numbers at the beginning of our music tell us how many beats there will be in each bar. They also explain what type of beats we’ll be counting in and whether they subdivide into twos or threes. Here’s how to decode them…

Let’s begin with perhaps the most familiar time signature - 4/4.

The top number

The top number of any time signature tells you how many beats there are in each bar - in this case four. It really is as simple as that. If the top number is 2 there are two beats in the bar, if it’s 10 there are ten of them. How you feel those beats can be a touch more complex, but we’ll come to that later.

The bottom number

Now for the bottom note of your time signature. This indicates the type of beat you’re dealing with, as you can see in this table:

Now you know these two pieces of information you can at least identify the number and type of beats.

Simple and compound time

Aside from the actual beats we have in each bar, another important element to understand is whether the music is in simple or compound time. These terms refer to whether the main beats in the bar (the pulse we feel when we tap our feet in time with the music) divides into two or into three. Let’s begin by listening to two pieces which illustrate the way these feel.

Simple time

When the pulse subdivides into pairs of notes, the music is said to be in simple time. For instance, in a piece built upon crotchet beats those notes each divide into two quavers. Listen to this recording of Elgar’s famous Pomp and Circumstance March No.1 and count along to the beat - one - two, one - two. When you subdivide the beats they break down into pairs of quavers - as you can see in the extract below. This means the music is in simple time.

Simple time comes in many different forms, but if the main beat is a quaver, crotchet or minim it naturally divides into two halves. Here are a few more examples of pieces in simple time:

Gabriel Faure - Pavane, Op.50: Four crotchet beats per bar, each of which divides into two quavers.

Handel - Hornpipe from Water Music Suite No. 1: The lower number of the time signature indicates a minim beat, and these subdivide into two crotchets.

Vivaldi - Autumn from the Four Seasons, 3rd movement: Here we’re dealing with a quaver beat and each of these divides into two semiquavers.

Finally we have Marg Hall’s Klezmer Fantasia. It may have an irregular number of beats in each bar, but each one of these splits into two quavers. We’ll come back to irregular time signatures like this again a little later…

Common time and other curiosities

While most time signatures are notated as numbers, sometimes the letter C is used. This is a historical throwback, connected to the mensuration symbols used in the 16th century and earlier, before music had bar lines. In short, C (often known as Common time) means the same as 4/4.

When the letter C is divided with a vertical line (often called Cut Common time) it usually means 2/2 time, although in early music it is occasionally also used to indicate 4/2 time. If you’re interested to learn more about this, do check out my post called Cracking the Code from 2021, where I talk in more depth about the vagaries of Renaissance notation, including the evolution from mensuration symbols to time signatures.

Occasionally you’ll also come across simplified time signatures in early Baroque music, where the composer just gives a single number. In such situations this number equates to the top number of a modern time signature. It’s up to you to look through the music and figure out which type of beats are involved. In the example shown here we’re dealing with crotchet beats so a modernised time signature would be 3/4.

Compound time

Not all music subdivides neatly into pairs of notes - sometimes the main beats divide into thirds - this is called compound time.

Let’s take a look at an example – Barwick Green, the theme music for the radio soap opera The Archers, by Arthur Wood. As you listen, note how the music has a ‘rumpty tumpty’ sort of feel, common in a lot of folk music.

If we consider the time signature of 6/8 and use the advice I gave earlier it’s easy to assume we have six quaver beats in the bar and each of these subdivides into two semiquavers.

Yes, this is true, but listen to the music again and tap along with it. Are you tapping the quaver beats? I bet you’re not! No, in this sort of music we feel a larger size of beat - in the case of 6/8 that’s two dotted crotchets in each bar. Each dotted crotchet breaks down into three quavers and that’s what makes 6/8 a compound time signature.

6/8 is probably the most familiar compound time signature, but there are others too. If you want a basic principle to work by, you should look out for time signatures where the top number is divisible by three, such as 9/8, 6/4 or even 15/8. This doesn’t apply if the top number is 3 though, as those are still simple time signatures.

Let’s do the same as before and check out some real world examples:

Bach - Fantasia and Fugue in C minor, BWV537: The time signature for this piece is 6/4, so each bar contains six crotchet beats. These are grouped into two dotted minim beats. In the first bar there are two dotted minims in the lowest voice and elsewhere the quavers are beamed together in groups of six, whose combined length is a dotted minim.

Corelli - Pastorale from Concerto Grosso, Op.6 No.9: Twelve quaver beats in each bar, but these are grouped into four dotted crotchet beats.

Putting your knowledge into practice

Knowing how to identify and translate a time signature is one thing, but that’s just the first step - now we have to put this into practice so we can actually count the music we’re playing.

Is there a difference between the pulse and beat?

This is a question I’m often asked, and the simple answer is that the pulse and beat are fundamentally the same thing. The term pulse is most commonly used to refer to the gentle throb a nurse feels for in our wrist to check how fast our heart is beating. The pulse in music has the same function, recurring at regular intervals through a piece. If you tap your foot in time with music it’s the pulse you’re tapping along with.

The term beat can often be used as a synonym for pulse in music, but it’s used in other ways too. For instance, a conductor beats the time signature with their hands or a baton, but again they’re visibly indicating the pulse or beat, just as you might by tapping your foot. You may well have heard conductors using both terms and that’s where confusion often occurs - I’m sure I’ve been guilty of doing exactly this at times!

How do I know which beat to feel/count?

Knowing which type of beat to feel when playing a piece of music is dependent on several things:

  1. The style and character of the music

  2. The tempo (speed) the composer has specified

  3. Your own level of technical proficiency.

Let’s look at three different scenarios…

Simple time signatures

When faced with a piece of music in 4/4 time, the logical approach is to count four crotchet beats in each bar - after all, that’s exactly what the time signature means. Take this extract from Handel’s Water Music, for instance. The C at the start means 4/4 time and, when played at the traditional Andante sort of speed, it makes perfect sense to feel four crotchet beats in each bar - as you can see from the beat numbers I’ve added in red.

Now let’s look at a snippet from Francesco Mancini’s Recorder Sonata No.10. Here you can see we have the same time signature but the tempo indication (Largo) is slower than in the Handel. It’s entirely possible to feel a crotchet beat in this music, but the speed will probably be around 50. For many people this will feel very slow and there’s always a temptation to rush. One alternative is to subdivide the beat in your head, counting one-and-two-and etc. as I’ve shown in the music below:

A second option is to feel a quaver beat, resulting in eight quaver beats per bar, as shown below. The metronome mark of these quaver beats would be 100 to achieve the same performance speed. This may make it easier to read the rhythms and analyse the length of the notes, but there’s a risk the music can become a bit too ‘beaty’ because you’re feeling eight pulses in each bar rather than four. It’s a matter of personal preference. If you begin counting eight quaver beats you may find you can gradually slip back into feeling the slower crotchet beat as you get to know the music better.

Minim beats

This is a thorny issue for many recorder players and a topic of conversation in many rehearsals. Look through a pile of music from the eighteenth century or later and you’ll see that most music in common time is written in crotchet beats. We spend a lot of our musical lives counting in crotchet beats and these are the notes we’re first introduced to when we begin to read music.

But this hasn’t always been the case. If you delve back into music from the 16th century and earlier you’ll find much of it is written in minim beats, or sometimes even semibreve beats. To our modern eyes this notation looks slower because there’s an absence of the smaller note values. During the first decades of the early music revival in the 20th century, music editors often sought to make this music easier to read for modern musicians by creating editions where they halved the note values. Since then the needle has swung back towards a preference for authenticity in notation, allowing us to see the composer’s original intentions. As a result most modern editions of early music now retain the original time signature.

As with the Mancini example above, you could subdivide the minim beats into crotchets. In this extract from Byrd’s Fantasia I à 4 I’ve marked up the first two bars with numbers showing the minim beats. From bar five I’ve changed that to crotchet beats and you can see how much busier it looks. If you’re trying to think about two beats for each minim that’s an awful lot of mental activity in every bar. Once again the music will be in danger of feeling too ‘beaty’ and there’s a good chance you’ll slow down too.

I know a lot of musicians find it difficult counting in minim beats, but I would argue this is largely down to a lack of familiarity. We find comfort in things we know well and unfamiliar skills will always seem harder. But if we work at it, these skills become more familiar and less scary!

One solution I sometimes hear suggested is to ‘translate’ the longer note values back into something more familiar. For instance, a minim in 4/2 would be a a crotchet beat in 4/4. It’s similar to the way we mentally convert between currencies when shopping in a foreign country. But in music we need to do it in a split second while also reading the pitch of the notes, plus accidentals, articulations and dynamics!

A better solution is to take a moment before you sight read a piece to think about the relative speeds of the different note values. Spend a few seconds looking at the minims and tapping them at your chosen tempo. Then half the speed of your tapping while looking at the semibreves. Finally, double your minim speed to tap the crotchets. Over time you’ll be able to work these out more quickly, and after a while you’ll wonder why you ever found counting in minim beats so hard!

Compound time

Having dealt with simple time, the principles are very similar for compound time. The type of note value you choose to feel while playing will depend on the character and mood of the music. Let’s look at the examples I used earlier.

With Barwick Green (The Archers theme tune) you would naturally feel two dotted crotchet beats in each bar because the tempo is Allegro. To try and feel six quavers in a bar would quickly have you tied in knots!

That said, if the music is very fast your choice of speed may be dictated by your own technical limitations. For instance, if you decided to play Barwick Green and found the quavers were too fast to play at full speed, it might be better to begin at a slower tempo, counting six quaver beats in each bar. As your fluency improves you can gradually increase the speed and eventually you’ll reach a point where you can adjust back to a dotted crotchet pulse instead of quavers.

In contrast, the Bach Passacaglia is usually played at quite a slow tempo, perhaps crotchet = 72, so you would naturally count six crotchet beats in each bar, as I’ve marked below. At this tempo the dotted minim beat would be 24, which is far slower than any mere mortal can sensibly maintain!

With both simple and compound time signatures, your choice of beat will be influenced by the tempo of the music and the character you’re trying to bring to the music. The trick is to figure out what the possibilities are and make your decision according to which feels right and/or which is easier. As you get to know the music better you may decide you prefer to feel fewer beats per bar - you’re absolutely allowed to change your mind!

Irregular time signatures

I promised to come back to unusual time signatures, such as 5/4 or 7/8. These irregular time signatures can often feel uncomfortable, purely because of their irregularity.

As humans we have two of most things - eyes, ears, legs, hands etc. and because of this we like music which has a predictable left-right-left-right sort of feel to it. Music in triple (three) time doesn’t fit this description, but it does still have a regular lilting feel (think of a waltz) which comes quite naturally.

However, a time signature like 5/4 has an instant imbalance to it. A bar with five beats cannot divide neatly into two equal halves - instead you have either 3+2 or 2+3 beats. Most composers tend to set up a regular pattern in such time signatures, only deviating from it periodically. Take this short extract from Mars from Holst’s Planets, for instance. You can clearly see the bars are broken into three beats and two beats - I’ve marked the dotted minims (three beats) with triangles and the minims with square brackets. This is very consistent in every bar.

When counting a piece like this in 5/4 you have two choices. The first is to count a consistent five crotchet beats in every bar, while the alternative is feel two unequal beats per bar - in this case a dotted minim followed by a minim. This choice will almost certainly be influenced by the speed of the music. If your metronome marks is crotchet = 100 you’re probably best off counting in crotchet beats. On the other hand, if you crotchet beat is 160 it may be easier to feel a lopsided two in a bar. What you absolutely mustn’t do is add an extra beat to turn the music into a nice, balanced 6 beats per bar!

When you have to make a decision like this it’s often best it look at the full score rather than just your own part. Seeing all the voices together can make it clearer how the music break subdivides - as you can see in the extract from Marg Hall’s Klezmer Fantasia which I’ve marked up below:

If you’re playing a piece like this in a conducted group your conductor will probably explain how the music breaks down, so do pay close attention to what they’re saying!

Time changes in Renaissance music

I’ll complete this exploration of everything related to time signatures with a look at the thorny issue of time changes in Renaissance repertoire - a topic I’m often asked about.

It’s not unusual for music from the 16th century to switch from duple (2) time to triple (3) time in the middle of a piece - and sometimes back again. Of course this happens in later music too, but Renaissance repertoire is a special case because there is usually a mathematical relationship between the two time signatures. The exact nature of this relationship is not always clear and then you have the practical matter of transitioning from one to the other to consider.

During the 16th century there were two relationships between the time signatures. At the time they had different names…

Sesquialtera

This is where a whole bar of the duple time signature is the same duration (i.e. occupies the same length of time) as the new triple time. In Victoria’s O Magnum Mysterium shown below, I’ve marked the time change in red. Treating this as a Sesquialtera, the 3/2 bars would be the same length as the preceding duple time bars (each of which is a breve long), making the new minim beat very slow.

Tripla

This is the term used when the length of the new triple time signature is the same length as half of the preceding duple time. Looking back at the Victoria example above, I think this approach works much better. The new triple time bars are then the same length as the semibreve beat (half a bar) in the duple time. As a result, the minims in the triple time section are faster than in the preceding bars.

How do I tell a Sesquialtera from a Tripla?

Wouldn’t it be wonderful if there was a clear way of knowing which piece requires which approach? Absolutely it would, but sadly notation during the Renaissance was far from consistent!

Sometimes editors of modern editions will give an indication as to how they think the music should be played, showing a sort of musical equation above the score. For instance, at the change in the Victoria shown above you might see something like this:

With such a lack of clarity in the original sources the most practical approach is to try both the Sesquialtera and Tripla and see which works best. Usually one will work better than the other. In my experience the Tripla tends to occur more frequently but this is far from a fixed rule.

Practical tips for time changes

One of the questions I’m asked most often about Renaissance music is how to negotiate these sorts of time signature changes when playing. It’s all very well if you have a conductor to lead you through this minefield but I know many smaller, self-led groups struggle to figure this out. To explain the process we’ll use the Victoria O Magnum Mysterium again. Below you’ll see a short extract from the full score, which I’ve annotated, but if you’d like to refer to the whole score you can download it here.

In order to decide whether you’re going to treat the time change as a Sesquialtera (whole bar = whole bar) or a Tripla (half a bar = a whole bar of the triple time) you need to figure out the relationships between them. To explain the options you’ll see I’ve added some metronome marks. If you want to hear these speeds for yourself you can use your own metronome, or just click on the words where they’re highlighted in the text below and you’ll hear the tempi courtesy of YouTube.

Let’s begin with the Sesquialtera option…

I would normally play this piece at around minim = 120 and that means a semibreve (half a bar) = 60 and a whole bar is breve = 30. It’s very difficult to really feel 30 beats per minute as it’s so slow - that’s where a metronome can be very useful.

Looking ahead to the time change, making it a Sesquialtera means the new triple time bars (which are a dotted semibreve long) are the same length as the breve in 4/2. Now you know this, you just need to multiply the breve’s metronome mark (30) by three to find out your minim beat, which is 90. As I mentioned earlier, that means the new minim beat is still pretty slow and I find this relationship quite hard to feel instinctively.

Sesquialtera - a whole bar of the new 3/2 time signature is the same length as a whole bar of the preceding 4/2.

If the Sesquialtera doesn’t feel natural, let’s see if the Tripla works better…

Here the opening speed remains the same, but the new 3/2 bars are the same length as half a bar of the 4/2. Therefore the semibreve = 60 of the 4/2 becomes a dotted semibreve = 60 in the new 3/2. To find out the new minim beat multiply by three, which makes them minim = 180. Yes, this is a fast beat, but it makes for a livelier effect and I think it creates a more natural relationship between the two time signatures.

Tripla - a whole bar of the new 3/2 time signature is the same length as half a bar of the preceding 4/2.

The process I’ve described above is what I do when I’m preparing to work on a piece of Renaissance music like this with an ensemble. I work out the relative speeds for both Sesquialtera and Tripla and decide which seems more natural. If I’m honest, I probably opt for the Tripla more often, but it’s good to explore both.

Putting the time change into practice

Having decided which option you’re going to use, the next task is to put your decision into practice. With time and experience you may find you’ll begin to make these transitions instinctively, but I have some tips to help you get to that point. Again, I’m using the Victoria as a practical example - you can download the complete score here if you haven’t already done so.

  1. Break the piece down into sections. Having decided on your opening speed, begin by practising all sections which share the same time signature. In the case of the Victoria this means rehearsing from the beginning up to bar 52 and from bar 67 to the end. After a few repetitions the music will begin to feel familiar and you’ll develop some ‘muscle memory’ for this speed.

  2. Practise the 3/2 section separately. Now use your metronome to remind yourself of the new speed at the 3/2 and play this section. Try playing it with a minim beat or the slower one-in-a-bar dotted semibreve beat and see which feels better for you. Repeat the section several times so the speed becomes really settled in your mind. Do check back with your metronome to ensure you’re maintaining the new tempo.

  3. Now practise the transitions. This is where you combine the two time signatures. By now you should be comfortable playing the different sections, so try moving from one to the other and the muscle memory you’ve built up will carry you across the joins.

You can use this process for any piece of music with abrupt tempo changes like this, whether it’s from the Renaissance or any other period of music.

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Has this completed some of the gaps in your knowledge? Or maybe you still have questions? Answering one question often reveals other areas you’d like to know more about, so please do leave a comment below with your thoughts. My aim is always to broaden your musical knowledge and the most efficient way I can do that is by responding to your needs - I’d love to hear your ideas and requests!

How do you hemiola?

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Most recorder players feel at home playing Baroque music. After all, the period between around 1600 and 1750 was the heyday of our instrument, with composers like Handel, Bach and Telemann producing exquisite solo and chamber music for the recorder. However, there’s one rhythmic feature of Baroque music which often creates confusion and concern among recorder players - the hemiola. As we shall see, the hemiola wasn’t restricted to the Baroque period and can be found in repertoire as disparate as Susato and Brahms.

When conducting recorder ensembles, I often ask if everyone knows what a hemiola is when we encounter one. Usually, I see a handful of confident nods around the room, but these are invariably outnumbered by people who either look at me blankly or else suddenly find the floor immensely interesting! My aim today is to help lift the mists of rhythmic confusion, to assist you identifying and playing them with more confidence.

What is a hemiola?

Put simply, it’s a temporary change to the music’s regular rhythmic pattern, changing groups of three beats into groups of two. It’s always simplest to explain such concepts with musical examples so you can actually see them in practice. Take a look at this extract from Lully’s Bourgeois Gentilhomme:

The time signature gives us three beats in each bar. The first beat of the bar is the strongest, so the hierarchy of beats in bar one is strong-weak-weak. The same applies to bar 2. Now look at bars 3 and 4 and see how the rhythm changes. Instead of three crotchet beats we have three minim beats spread over two bars. With a note held across the barline, there’s no way to emphasise the first beat of bar 4, so instead stronger pulses occur every two beats, rather than every three. This is a hemiola.

This particular example is about as simple as it gets with hemiolas - all five voices play the same rhythm so the effect is inescapable. Unfortunately, not all hemiolas are so obvious. If you glance at bars 6 and 7 you’ll see a very similar rhythm, but here the highest voice deviates slightly from the pattern. The overall effect is still a hemiola but slightly less clear cut.

If you find it easier to understand this concept visually I recommend watching this video, created by the Orchestra of the Age of Enlightenment, which uses different examples to help explain the hemiola further - including a juggler! The video also includes the Lully example I showed above, among others.

Why do we have hemiolas?

There are several reasons why a composer might wish to include a hemiola in his or her music - let’s look at them..

To add rhythmic interest

Shifting between groups of two and three beats brings an extra layer of variety and energy to the music. Brahms does this a lot in his music, sometimes bringing hemiola shapes into different parts independently. Recorder players don’t often get to play Brahms, but the same things happens in earlier music too. In The Fairie-round Anthony Holborne shifts endlessly between duple (2) and triple (3) time rhythms. Sometimes the parts shift between meters simultaneously, but often they work independently of each other. sometimes simultaneously. I’ve altered the colour of the notes in this extract to show the triple time rhythms in red, while the duple time rhythms are blue. Click on the image to see it enlarged. If you’ve ever tried to play the Fairie-round you’ll understand why it can be so tricky to put together!

To speed up the musical movement

When you create a hemiola you shift from having a strong pulse every three beats to one every two beats - this gives a sense of the pulse increasing in speed. I’ve added a drum line to the Lully example shown above, placing a drum beat on the stronger pulses. Notice how the speed of the pulse increases when the beat occurs every two beats rather than every three beats.

An aural guide to the music’s phrasing

This is perhaps the most important function for a hemiola, especially in Renaissance and Baroque music. While modern music can be hugely complex, early music frequently contains more consistent and predictable harmonic and rhythmic patterns. That’s not to say it can’t be surprising, but there are melodic and rhythmic features which crop up regularly - for instance trills at cadences in Baroque music.

The hemiola is one such musical feature and composers use it to flag up to the listener that we’re approaching the end of a phrase. Of course, it’s unlikely that you’ll sit there thinking to yourself, “Oh, there’s a hemiola - that must mean it’s the end of a phrase!”. But if you listen to music from this period often enough you’ll subconsciously sense the movement of the rhythm and harmony, feeling a sense of arrival as the music reaches a cadence.

The biggest clue is the rate of change in the harmonies. Very often there will be just one or two chords or harmonies in each bar. At the hemiola this alters, as the harmonies change more swiftly. For instance, listen to this short movement by Gottfried Keller and notice how the rhythm and harmony shifts up a gear just before the cadences. If you’re not sure where the cadences are, listen out for the trills which also occur then. If you’d like to follow the music as you’re listening click here.

Where do hemiolas happen?

Generally hemiolas occur in triple time music - that’s music which has three beats in each bar, say 3/4, 3/2 or 3/8. Let’s look at a few examples.

The first comes from Handel’s Music for the Royal Fireworks - a short extract from the Minuets. The music is in 3/4 time but two bars before the end of the phrase (look out for trills as these often occur at cadence points too) the harmonies change from mostly being one chord per bar to three chords spread over two bars - shown by the boxes.

If you’d like to try this example for yourself you can play among with my consort video of the minuet here.

Minuet from Handel’s Music for the Royal Fireworks - click on the image to see it larger

Now let’s take a look at a hemiola in minim beats - this time taken from Handel’s Recorder Sonata in D minor. If you look at the boxes, you’l notice the first first two beats (box 1) include notes which are predominantly from one chord - A major (A, C sharp and E). The second box contains two different chords, but the final one is once again made up almost entirely of A major.

Handel recorder Sonata in D minor, 2nd movement

As a further example, here’s a short snippet from another of Handel’s recorder sonatas - this time in C major. The time signature is 3/8 - three quaver beats (or one dotted crotchet beat) per bar. In bars 46 and 47 he changes this to have rhythmic groups of two quaver beats. The hemiola is clearest in the recorder part, where the silence on beat one of bar 47 means the emphasis inevitably shifts to the dotted quaver note on the second beat of that bar. This particular movement is littered with hemiolas just like this, introducing a delightful shift from the one in a bar feel elsewhere in the movement. You can listen to the whole movement below.

Handel Recorder Sonata in C major, 2nd movement

Of course, there’s no such thing as a rule that’s never broken, so occasionally you’ll find hemiolas in unexpected time signatures. In La Paix Handel writes in 12/8 time, but still manages to squeeze a hemiola in at the cadences! The music isn’t in triple time, but as the dotted crotchet beats each contain three quavers Handel can group those quavers in twos rather than threes, thus creating a hemiola. Take a look at the top three parts where I’ve added the boxes and you’ll once again see the beats grouped in twos - predominantly either crotchets or as pairs of quavers.

La Paix from Handel’s Music for the Royal Fireworks

Finding the hemiola in its natural habitat

Let’s take a look at the most likely locations for hemiolas…

Cadence points

In Renaissance and Baroque music hemiolas almost always occur immediately before a cadence. These are the points where the music comes to rest momentarily, giving a sense of arrival. If you’re not sure what a cadence is, think of them as the musical equivalent of punctuation in written text. When reading text aloud, the commas and full stops tell you where to take a moment to allow a point to sink in, allowing both you and your listeners a moment to breathe. A cadence has the same purpose, bringing a sense of pause or arrival in the music. Play through any of the examples I’ve shared so far today and you’ll feel this sense of arrival on the note or chord immediately following the hemiola.

When you learn a new piece of music, listen out for these moments of repose as they will guide your phrasing. If the music is in triple time (3/8, 3/4 or 3/2) or in 6/8 you may well find a hemiola in the bar or two immediately preceding these cadence points.

Take a look at this section from Andrew Parcham’s Solo in G, where I’ve marked two hemiolas. Both come at cadence points and if you try playing the top line you’ll no doubt feel that moment of arrival on the note immediately following the hemiola. The composer would almost certainly have expected the performer to add a trill to the final dotted crotchet of each hemiola too - as you can hear in the recording below. The Allegro begins 2 minutes and 27 seconds into the video.

Andrew Parcham Solo in G

Look for trills in Baroque music

As I’ve already mentioned, cadence points are often decorated with trills in Baroque music. These aren’t always marked in the music because composers generally assumed the musicians would be familiar enough with the musical style to know where they should be added. But some did take the trouble to notate them and you’ll often find places where modern editors suggest adding cadential trills. These can be an additional way for you to spot where a hemiola may be lurking.

Look at the whole score

Perhaps the most important piece of advice I can give is to look at the whole score of the music, not just your individual part. Sometimes the hemiolas will be clear as day in your line, but, as we’ve seen in some of the examples I’ve shared, it’s often easier to spot the hemiola when looking at several parts together.

For instance, look at this extract from a Ronde by Tielman Susato. If you’re playing the top line, reading from a single part, you’d be forgiven for missing the hemiola entirely because both bars look like standard 3/2 rhythms. Cast your eye down through the score though and the hemiola becomes much clearer, with a two beat note at either end. Here the top line is simply providing rhythmic contrast, but the overall effect is definitely a hemiola.

Susato Ronde

Look for the rhythmic clues

Very often a hemiola’s effect is amplified by the use of longer notes, which have more weight or aural mass, as I like to call it. Look through any of the examples I’ve shared here and you’ll see time and again, how the composer fills one or two of the hemiola’s three parts with a longer note. This length and weight of these notes makes that section of the hemiola feel more significant, emphasising the fact that he or she is moving the musical stresses away from their usual position on the first beat of the bar.

For example, look at the last few bars of Telemann’s Concerto in C below - at the hemiola you’ll see I’ve circled the dotted crotchets in red. These notes will naturally draw the ear because they’re longer than the other note values within the hemiola. This brings the hemiola effect out effectively, especially if the quavers are kept detached and light.

Telemann Recorder Concerto in C, 4th movement

Look for consistency of rhythm through the texture.

As we’ve already seen, the hemiola rhythm doesn’t always appear in every voice, but often there will be some unanimity. Take a look at this Galliard by Anthony Holborne and you can clearly see a consistency of rhythm between the five voices. Unlike the Lully we looked at first, the parts aren’t entirely unanimous in their rhythm, but in both hemiolas several voices simultaneously have the same rhythm. Looking at the score, it becomes clear there’s a move away from the usual 1 2 3 - 1 2 3 rhythm to a hemiola pattern.

How do I play a hemiola?

Once you’ve identified your hemiola it’s very tempting to emphasise the start of all three sections to hammer the point home. Undoubtedly this will make your hemiola stand out, but it’ll likely lack subtlety!

A better approach is to think in terms of only emphasising one or two sections of the hemiola, which will result in a more subtle, musical effect. For instance, there are two hemiolas in this section of Purcell’s Chaconne from The Gordion Knot Untied. Both begin and end with dotted rhythms, which will naturally attract the most musical weight because of their longer length.

Ordinarily, the first beat of each bar would be the strongest, but here the aural mass of the dotted crotchets moves the emphasis onto the second beat of bars 52 and 59. Now you could also put some added weight onto the last beat of bars 51 and 58 to bring out the middle section of the hemiola. However, the result would be rather heavy and a better approach is to make the middle section of the hemiola light and less important. In this case I’d simply make the crotchets which fall within the second box of each hemiola short and light, creating a sense of lift and bounce. You can hear me putting this approach in practice in my consort video of this piece here.

Let’s take a look at another example, this time from Handel’s Recorder Sonata in B flat.

If you listen to this recording by David Antich you’ll hear the ensemble allow the longer notes to have some weight, but the cellist keeps the crotchets in the bassline light and separated, so as to minimise their importance and help highlight the rhythmic shift of the hemiola.

Looking beyond early music

As I said earlier, hemiolas aren’t restricted to the music of the Renaissance and Baroque - later composers used then too. One of the most famous appears in Leonard Bernsteins’s score for West Side Story and you’ll almost certainly be familiar with the shifting rhthms in America. But had you ever thought of it as a hemiola? You will now! Take a listen - the famous melody line begins around one minute and fifteens seconds into the video below.

Another example occurs in the opening bars of the Concierto de Aranjuez by Joaquin Rodrigo. The solo guitarist opens the whole work with the rhythmic pattern shown below - a clear hemiola in 6/8 time.

As I said at the beginning, Brahms wrote hemiolas too and you’ll find them dotted about endlessly in his music. Very often he chooses to write hemiolas independently in different voices but in this example, from his Intermezzo No.1 for piano, he shows them very clearly together. Normally in 6/8 time the quavers would be grouped in threes (as they are at the beginning of the extract) but on the second system here he writes a series of crotchets - notes worth two quavers - to create a series of hemiolas.

Johannes Brahms Intermezzo No.1 for piano

Are the hemiola mists clearing?

I hope my explanations and all these musical examples have helped you to understand the hemiola better. Don’t be afraid of them, but just be aware of their existence when you meet pieces where the note patterns are grouped in threes. Take every opportunity to consult the score, as you’re more likely to see them there, and don’t hesitate to experiment with your phrasing and articulation in bars you think may be hemiolas. These fascinating rhythmic patterns don’t bite and they can bring more variety, light and shade into your performances.

Finally, if you have a trick for spotting or dealing with hemiolas which I haven’t mentioned please do leave a comment below so we can share our ideas and musical knowledge.