The pulse

"I've got a good sense of rhythm," nearly everyone says. And tapping your foot to a familiar song really is easy: the song leads the foot. It gets harder when nobody is leading. A drummer keeps time even when the rest of the band stops. So does a pianist playing alone. Nobody is clicking in their ear, and if they speed up, only the audience will notice.

This chapter is set out as a training log. Every section has a drill with a measurement: the course works out, in milliseconds, how evenly you tap and which way you drift. All the results collect in a log at the end of the chapter, where you can see what has got better. Tap with Space, the big button on the screen, any key on the computer keyboard or a key on a MIDI keyboard. Count in your head if it helps, but there is no need to count out loud: here your hands do all the work.

Drill 1. The test

We start with an honest test. Below is a metronome. It gives you four clicks to get going, then eight more to tap along with, and then it goes quiet. Your job is to keep tapping at the same tempo until the silence is over. Before you start, place a bet: what will you do without the metronome?

The dots on the graph are your taps. The zero line in the middle is where the click should have been. A dot above it means you tapped early, a dot below it late. While the metronome is clicking, the dots usually stay close to zero: your ear has something to hold on to. In the silence the drift begins. The dashed line shows your own tempo in the silence. If it climbs, you were speeding up and every tap came a little sooner than it should have. If it falls, you were slowing down.

The "Your taps next to the click" button replays the attempt, but with clicks where the silence was. That way you can hear the drift: at first your taps merge with the clicks, then they start to fall behind or run ahead.

Hardly anyone passes this test perfectly the first time, and that is fine. Below we take apart what a sense of rhythm is made of, and at the end of the chapter you take the same test again.

Pulse and beat

Think back to the clicks in the test: they came at equal distances, and not one of them was late. Music is built on an even grid like this. Notes can be long or short, but all of them are measured against it. This steady series of ticks that we hear or feel under the music is called the pulse, and each tick of the pulse is a beat.

Sometimes you hear the pulse directly: the click of a metronome, the kick drum in a dance track, the bass in a march. More often nobody plays it at all. It is implied. When you tap your foot to a song, you are tapping a pulse that may not exist as a separate part in the recording: your brain works it out from the melody and the chords.

The first drill is the simplest: tap with the metronome. After the count-in, tap on every click. The card shows how many milliseconds early or late you are on average and how widely your taps are scattered.

With the click, not after it

Look at the dots after the exercise. If almost all of them sit below the line, and all by the same distance, you were most likely tapping after the click: waiting for it and then answering. That way you will always be late, by exactly your reaction time. A musician does not play like that. They know when the next beat is due and land on it together with the click, not after it.

For that you don't catch the click. You feel the gap. After two or three beats you already know how long it is, and your hand starts down early to meet the next beat. Many people find it helps to move the hand smoothly, like a conductor: not a jab at the moment of the click, but a movement that reaches its lowest point together with it.

Curiously, people tapping along to a metronome usually come in slightly before the click, by a few tens of milliseconds. This well-studied effect is called negative asynchrony. Its causes are not fully understood. One explanation is that the signal from the finger takes longer to reach the brain than the signal from the ear. So a small lead is not a mistake. A wide scatter is.

Tempo: beats per minute

Beats can come slowly, like steps on a stroll, or fast, like running. How fast the pulse goes is called the tempo. It is measured in beats per minute. The short form is BPM, and you will see those three letters in every DAW, on every metronome and on every drum machine. This course writes BPM throughout.

You don't have to type the tempo in as a number. You can tap it. Many DAWs and drum machines have a tap tempo button: tap it at the speed you want, and the program does the sum. Below is a tap tempo like that, except that it also shows how evenly you tap. Each bar is one gap between taps. A bar going up means the gap was longer than average, a bar going down that it was shorter.

Try tapping the tempo of a favourite song while you play it in your head. Then press "Hear this tempo" and compare. Next, tap sixteen times in a row, trying to hold one tempo: the widget compares the first half with the second and tells you whether you are speeding up or slowing down. Remember your spread in milliseconds. The log at the end of the chapter keeps every run of eight taps or more, and from them you can see how the spread changes from one session to the next.

Beats and milliseconds

Tempo and the length of a beat are two sides of one number. A minute has 60,000 milliseconds, and if 120 beats fit into it, each one gets 60,000 / 120 = 500 ms. At 60 BPM a beat lasts exactly a second, at 100 it lasts 600 ms, at 150 it lasts 400 ms. The faster the tempo, the shorter the beat.

Milliseconds come in handy once you start working with synths and effects. Delay time and modulation rate are often set in milliseconds, and they sound best when they fit the beat. Hence an old habit of sound engineers: knowing by heart that at 120 BPM a beat is 500 ms, half a beat 250 and a quarter 125.

The metronome is set to 120 BPM. How much time passes between two clicks?

Half a second 120 milliseconds Two seconds 1.2 seconds

A minute has 60 seconds and there are 120 clicks, so each gets 60 / 120 = 0.5 s, or 500 ms. Two seconds would be 30 BPM, and 120 ms would be 500 BPM. No metronome clicks that fast.

Now by ear. The metronome plays eight clicks at one of four tempos: pick which. Neighbouring options are 30 BPM apart, a difference you can hear easily.

The tempo scale

Which tempo counts as slow and which as fast? The handiest yardstick is your own body. An adult heart at rest beats 60 to 100 times a minute. A brisk walk is about 100–130 steps a minute. Anything clearly slower than the heart feels solemn or sleepy. Anything faster than a walk feels like running.

For centuries musicians marked tempo with words, usually Italian ones: Adagio means "at ease", Andante "walking", Allegro "cheerful, lively", Presto "quick". These are tempo markings, and there are no numbers in them. The numbers on the scale below are very rough guides taken from reference books. The same word meant different things to different composers and in different centuries, which is why the bands overlap.

Press a row and you hear a tempo from inside its band. The genre rows play it on a kick drum. The "Tempo" slider moves a vertical line across all the bands at once, and the rows that tempo falls into light up. If you have already used the tap tempo, a "Your tap tempo" button appears: see where your favourite song lands on the scale.

Electronic music keeps it simpler: the tempo is a number, often written right in a track's title or description. House usually runs at 115–130 BPM, techno at 120–150, dubstep almost always around 140, drum and bass at 160–180. Dance genres keep the tempo steady for the whole track, because DJs match it when they mix one record into the next.

The easiest way to hear the pulse in this music is a kick drum on every beat. House and techno do exactly that: a hit on the bass drum on one, two, three and four. This is called four on the floor. Below is a drum machine: each cell is a quarter of a beat, and the darker cells mark the beats. The kick is already on all four. Start it, move the tempo between 115 and 130, and add a clap on the second and fourth beats.

Now guess the tempo with the options closer together: 20 BPM apart.

A pendulum with two weights

Today a metronome is an app on your phone or a button in a DAW. Two hundred years ago it was a pyramid-shaped box with a pendulum that clicked on every swing. An ordinary pendulum that swings once every 1.5 seconds (that is 40 BPM) would have to be more than two metres long. The trick of the mechanical metronome is that its pendulum has two weights: a heavy fixed one at the bottom, below the pivot, and a light sliding one at the top, on the rod. The higher you move the upper weight, the slower the pendulum swings.

Slide the weight up and down and start the pendulum. The widget works out the real physics of such a pendulum, so the marks on the scale are unevenly spaced, as on a real metronome. The scale is real too: 40, 42, 44… 208, the numbers still printed on mechanical metronomes today. The step between them grows with the tempo: at slow tempos the numbers go up in twos, at fast ones in eights.

You can check this in the widget. The blue line is the top edge of the weight, where the tempo is read. The red one is the bottom edge. The number below the weight is always larger, because the fast tempos sit lower down the rod. How much larger depends on where the weight is: see for yourself.

The weight on a mechanical metronome is moved higher up the rod. What happens?

The metronome goes slower The metronome goes faster The tempo stays the same, but the clicks get louder

The upper weight pulls the pendulum the opposite way from the lower one. The higher it sits, the weaker the pull back to the middle, and the longer each swing takes. That is why the slow tempos are at the top of the scale and the fast ones at the bottom.

The strong beat

Set the metronome in the widget below to no accent and listen for a minute. All the clicks are the same. Yet many people hear them fall into pairs or fours: "ONE-two, ONE-two". This was first described in 1894 by the psychologist Thaddeus Bolton of Clark University in Massachusetts. He gave his listeners series of identical clicks, and nearly all of them heard groups that were not there, most often of two, three, four or eight. The size of the group depended on the tempo. The ear looks for order on its own.

In music this order is set on purpose: one beat is made to stand out from the rest. Making a sound stand out is called an accent, and the beat a group begins on is the downbeat, or strong beat. The others are weak beats. The downbeat is the "one" we start counting from.

Switch the accent: every 2, every 3, every 4. The tempo and the clicks stay the same, yet the feel changes. Groups of two sound like a march, groups of three like a waltz, groups of four like most of the music around you. Then switch the accent off and tap only on the "one" you hear yourself: the widget tells you which groups you chose. After that, switch the accent back on and check whether your "one" matches the metronome's.

Now by ear. The metronome plays twelve beats with an accent. How many beats are in each group?

Next it gets harder: the accent is only a little louder, with no change of pitch, and the group does not start on the first click. Find where "one" is.

And tapping with the accent on three. The metronome marks every third beat. Tap on every beat and count "one, two, three" in your head.

How these groups are written in notation, and what "3/4 time" means, comes in chapter 8. For now it is enough that you can hear them.

A beat between the beats

A slow tempo is harder to hold than a medium one. At 60 BPM there is a whole second between clicks, and it is easy to get lost in it. Musicians deal with this by filling the gap. Instead of counting "one, two, three, four" in their heads, they count "one-and, two-and, three-and, four-and", and feel one more beat in the middle of each. Splitting a beat into equal parts is called subdivision.

Try it. The metronome clicks twice as often as the beats go by: tap on every click. Then go back to the "With the metronome" drill and tap at 80, counting "and" between the beats in your head. Your spread will most likely shrink.

The short note values these "ands" are made of, eighths and sixteenths, arrive in chapter 7. What matters here is the feeling itself: between two beats of the pulse there is room, and you can feel it.

Drill 2. Without the click

Back to the test from the start. Without a metronome nearly everyone drifts, and each person in their own way. Some speed up, some slow down, and for the same person the direction can depend on the tempo. It is worth knowing which way you go: then you can keep an eye on it.

What helps:

• Listen closely to the first beats. While the metronome is clicking, memorise not the clicks themselves but the gap between them.
• Count in subdivisions. "One-and, two-and" in your head holds the tempo better than the beats alone, especially a slow one.
• Move. Nodding your head or tapping your foot is a second pendulum that keeps going when the metronome stops.
• Don't correct with a jerk. If you notice you have rushed ahead, don't hang back waiting for the next beat: that changes the tempo all over again. Stretch the next few beats a little instead.

The exercise: eight beats with the metronome, then sixteen in silence. Afterwards the card tells you how far you had drifted by the end.

Harder: only four clicks, then twenty-eight beats of silence.

And now the silent metronome from the start of the chapter once more. Use the same settings as the first time: by default that is 80 BPM, eight clicks and sixteen silent beats. Then try another tempo: 60 and 120 drift in different ways.

Tempo in a DAW and in a MIDI file

In every DAW the project tempo sits in plain view, next to the record buttons. Everything is tied to it: the piano-roll grid, the click while you record, drum machines, delays and arpeggiators. Change the number and the whole project plays faster or slower, while the notes stay where they were in the grid.

The tempo can also change during a track. For that a DAW has a separate tempo track, where you draw in where the song speeds up, or where it slows down before the end. It can work the other way round too: musicians are recorded without a click, and the DAW's grid is then fitted to their live playing, so that it keeps breathing.

In a MIDI file the tempo is stored not in beats per minute but in microseconds per beat: a special message, FF 51 03, followed by the number in three bytes. At 120 BPM that is 500,000 µs, the bytes 07 A1 20. Look at the "Tempo and milliseconds" widget above: it shows these bytes for any tempo. If a file has no such message at all, programs take the tempo to be 120 BPM. The message can sit anywhere in a track, so the tempo in a MIDI file can change as many times as you like.

The log

Here is everything you measured in this chapter: every attempt at the silent metronome, every tap-tempo run of eight taps or more, and your best result in each exercise. Compare your first attempt with your last.

A sense of pulse grows faster from short daily practice than from one long session. The "Feeling the pulse" trainer has five levels, from plain tapping with a metronome to a slow tempo with almost no clicks. Next to it is the "Tempo by ear" trainer. Five minutes a day, and in a week the silent metronome's graph will be noticeably steadier.

Next

Now you can tell pulse, beat and tempo apart, convert BPM to milliseconds, hear the downbeat, and you know which way you drift without a metronome. But so far all your taps have been alike: one per beat, or two. In a real melody notes are long and short: one lasts three beats, two others fit into one. How to hear that, play it and write it down is the subject of chapter 7: note values, the bar and the piano roll.

Your track in the Notebook now has a tempo. Tap it in with the "Tap the tempo" button or set it with the slider, or send this chapter's tap-tempo result to the Notebook. Recording from the keyboard now runs against a click at that tempo. In chapter 7 the notes you play get their lengths and take their place in the piano roll.