Harmony and bass

You already have a tune: in chapter 18 you wrote a phrase with a question and an answer. Play it with your right hand alone and you will hear that something is missing. The notes are right, yet it sounds like someone talking in an empty hall. It needs a floor to stand on: chords and a bass.

Chords bring a different kind of trouble. Pick them at random and they start arguing with the tune. This chapter is about keeping the peace: which chords a key has to offer, why some sound like home and others pull somewhere else, how the notes of a bar tell you which chord it needs, and what the left hand plays down below.

A tune looks for support

Here are the first four bars of Beethoven's "Ode to Joy" (1824), three times over: the tune on its own, the tune with random chords, and the tune with chords chosen from its notes. The chords in the second version come from the same key, C major, so there is not a single wrong note in them. They have simply been chosen so as not to match the tune.

In the second version the ear hears two pieces of music at once. The tune sits on, say, E and G, while the chord under it is F, A and C. Each note is fine on its own, but together they rub. The third version has only two chords, C major and G major, and the tune suddenly gains depth: every note has found its place.

Now press "Chords only" and play the "Ode" yourself: after four clicks the lit key shows which note to play. Under your fingers it is the same tune as in the first version, and it sounds completely different.

Everything that sounds at the same time as the tune, the chords, the bass and the way they change, musicians call harmony. A tune runs horizontally, and harmony stands vertically under each moment of it. The good news is that the harmony of most songs is put together from a very small set of parts. We will start with the most famous of them.

Four chords for a thousand songs

The wheel below holds the seven chords of C major. Four of them already sit in the slots on the right: C major, G major, A minor, F major. Press "Play": the chords go round in a loop, one bar each, over a beat and a bass. While the loop plays, tap chords on the wheel or hold them on the keys in any inversion. Each one goes into the selected slot, and a line on the wheel traces the path.

These four chords in this order are recognisable almost at once. You have heard them in the verse of the Beatles' "Let It Be" (1970), and most likely in a dozen other songs whose names you could not put your finger on. In the late 2000s the Australian comedy trio The Axis of Awesome turned this into an act: several dozen hits in a row over the same four chords. The video spread across the internet, and English-language reference books now sometimes call these four the Axis progression. It is a joke, not music history: the four chords belong to nobody, and songs share them the way different books share the same words.

The label "I–V–vi–IV" is read by scale degree: the chord on the first degree of the key, then on the fifth, the sixth and the fourth. An upper-case numeral is a major chord, a lower-case one minor. Written this way, a chord progression does not depend on the key. Switch the key to G or D: the letters change, the numerals and the sound do not. That is exactly how a song is moved into a key that suits the hand.

Now play with the wheel.

• Press "Start on the next chord" twice. The same four chords, but the loop now starts on A minor: vi–IV–I–V. Nothing has been added, yet the music has become more thoughtful. The first chord of a loop sounds like its anchor, and now the anchor is minor.
• Choose the preset I–vi–IV–V. This is the "fifties progression": doo-wop, early rock and roll and "Stand by Me" (1961) are built on it.
• Untick "Nearest inversions". The chords start jumping across the keyboard as whole blocks, and the loop sounds like an exercise rather than a song. With the box ticked, each note of a chord moves to the nearest note of the next one, and the hand hardly moves. This is smooth voice leading. Inversions are covered in detail in chapter 15.
• Take I out of the loop altogether, for example ii–IV–V–vi. The key starts to drift: the ear cannot tell where home is.

Play the four yourself. Take the chords in any inversion and hold each one until the next lights up.

Seven chords from one scale

Why these seven chords on the wheel? Take the C major scale, the white keys from C to B. On each note build a chord, skipping one key each time: C–E–G, D–F–A, E–G–B and so on. You get seven triads, each made only of notes of the key, without a single black key. These are the chords of the key.

Three of the seven are major (I, IV, V), three minor (ii, iii, vi) and one diminished (vii°). The same holds in every major key: in G major they are G, Am, Bm, C, D, Em, F♯°. Switch the widget to minor, and the same construction from A gives i, ii°, III, iv, v, VI, VII.

Tick "…and back to I" and go through all seven. After some chords the return to I sounds like relief, after others as if you had never left. This is how the ear sorts chords into stable and unstable ones. The colours on the buttons show three families.

• Home: I and its relatives vi and iii. vi has two notes in common with I (C and E), so A minor can stand in for C major. It sounds like home, only on a cloudy day.
• A step aside: IV and ii. They lead away from home, but are in no hurry to bring you back.
• The road home: V and vii°. Both contain B, the leading note, a semitone below the tonic. It pulls towards C so strongly that after G major it is almost impossible not to go back to C major. This is the same pull as in chapter 14, only now a whole chord is doing the pulling.

In chapter 15 these families got letters: T, S and D, for tonic, subdominant and dominant. Here hearing them matters more than naming them. A cadence at the start of each round sets the key, then a single chord plays: name its degree.

If you mix up I and vi, listen to the bottom note and to the mood: vi is minor and sadder. IV and V are harder to tell apart. Here is a hint: after V the urge to return to I is stronger. Practise this on the "Chord functions" trainer, where you can work up to six degrees.

Now build these chords with your hands. Hold any of the seven on the keys, in any inversion, and the "Seven chords" widget above lights up its degree. Here the course names a chord and you play it.

Full stop, comma and a trick

Harmony can do more than stand still: it can also bring things to an end. The last two chords of a phrase decide whether it sounds like a full stop or a comma. A turn like this at the end of a phrase is a cadence, a word you already met in chapter 14. Press all four in turn.

V → I is the perfect (authentic) cadence, the strongest full stop in music: the tension of the dominant resolves into the tonic. IV → I is the plagal cadence, also a full stop, but a softer one. Stopping on V, a half cadence, sounds like a question: the music has frozen halfway, and something has to follow. And V → vi is an interrupted cadence: the ear expected home and got its cloudy twin. Composers use it to stretch a phrase for one more round.

Think back to chapter 18: the question phrase and the answer phrase. The question usually ends on V, the answer on I. Tune and harmony say the same thing: when the tune arrives on the tonic, the chord under it arrives home.

Make a full stop yourself: I, IV, V and I again. The last step, G major → C major, is the perfect cadence.

And now by ear: which of the three endings did you hear?

A song in C major ends on a G major chord and fades out. What will the listener feel?

That the song broke off and something is missing That the song came to a calm end That the key changed to G major

V is an unstable chord: it contains the leading note B, which pulls towards C. Stopping on V sounds like a question with no answer. Sometimes this is done on purpose, to leave a song hanging, but it will not be a calm ending. One chord is not enough to change the key: that takes a whole phrase in the new key.

Let the tune pick the chord

Now for the main thing: how to find chords for a tune of your own. The rule is shorter than you might think. Look at the notes in the bar, especially those on strong beats and the longest ones, and take a chord that contains them. Notes of the tune that belong to the chord are called chord tones. The rest are non-chord tones: on a weak beat they sound like movement, on a strong one like an argument.

Below is the whole "Ode", eight bars. To begin with every bar is on I. Tap a bar in the picture, then a chord underneath, or hold one on the keys. The strip on each button shows what share of the bar's notes belongs to that chord. Notes of the tune in the picture turn green if they are in the chord, and red if they are not and fall on a strong beat. Each tap plays the bar straight away with the chord you chose.

Most likely you will end up with what you heard at the start of the chapter: C major in the odd bars and G major in the even ones. The most interesting is bar 2, G–F–E–D. Two chords compete here. C major catches G and E on the strong beats, G major catches G on the first beat and D on the last. On the notes alone C major is slightly ahead, but then the first three bars sit on one chord and the music marks time. G major gives it motion, and E and F become passing notes that the tune simply walks through. That is how the "Ode" is usually harmonised. Choosing a chord is more than counting notes.

Switch to "two per bar". How often the chords change is called the harmonic rhythm. In pop music a chord most often lasts a bar. Two per bar is already livelier. In the "Ode" it lets you be more precise: in bar 4 the dotted E sits on C major, while the long D is already on G major. Just do not get carried away. If the chord changes under every note, the tune drowns.

In almost every bar two or three chords fit at once. C–E–G sits equally well over C major and over A minor, because the two chords share two notes. Then you choose not by the notes of the bar but by the story of the whole phrase: where the bass is heading, whether a chord has been repeated for too long, how the phrase ends. The last bar almost always wants I, and the one before it V or IV.

A bar has the notes A, C and E. The A falls on the first beat and is the longest. Which chord fits best?

A minor (Am) C major (C) F major (F) G major (G)

A–C–E is A minor itself: all three notes of the bar are in it. C major has C and E, but not the A that falls on the strong beat. F major has A and C, but no E. G major has none of the three.

Now without the picture. One bar plays. Tap chords, listen to how each one sits under the tune, and choose. Sometimes two answers are right, and either one counts.

Eight notes that never end

Sometimes harmony is not a trip but a circle that repeats from the beginning of a piece to its end. The most famous circle of this kind was written more than three hundred years ago.

The whole piece rests on eight bass notes: D, A, B, F♯, G, D, G, A. They come round again and again, twenty-eight times by one count. A bass like this is called a ground bass. Each note carries its own chord: D, A, Bm, F♯m, G, D, G, A. In the degrees of D major that is I–V–vi–iii–IV–I–IV–V, the same family as the "four chords", only longer.

Turn on the bass and press "Play". Then add layers: chords, the first violin, the second, the third. Each violin starts two bars after the one before and plays the same phrases. When a tune catches up with itself in another part, that is a canon, the way "Frère Jacques" chases itself in a round.

Why do three identical tunes not get in each other's way? Because they are all built on the same eight chords. Phrase A runs F♯, E, D, C♯…, and each of those notes belongs to the chord under it. Phrase B mostly repeats it a third lower. Phrase C runs in eighth notes down at the bottom of the violin's range, dipping to B3, the B below middle C, and it too lands on a chord tone on every beat. The harmony is a shared map, and the violins are three different roads across it. The widget plays only the first three phrases of the canon, in a loop. Pachelbel wrote many more, and with each one the music grows busier.

Play this bass yourself: twice through, slowly, with your left hand. D major has two sharps, and here you need the F♯.

Bass: from one note to a groove

In chapter 12 you put one bass note per bar under the "Ode". Now that you know the chords, it is clear which note: the root of the chord, the note it is built from. Under C major the bass plays C, under A minor it plays A. The bass holds the harmony up from below, and the ear recognises a chord first of all by its bass.

But a bass line is also rhythm. In electronic music, funk and rock the bass and the kick play almost as one instrument: the kick gives the hit, the bass gives that hit a pitch. The builder below makes a bass in five steps over the same chords. Work from left to right.

1. Root. One long note per bar. The harmony is clear, but the bass stands still.
2. Pulse. The same note on every beat. The bass and the kick line up, and the music gets moving.
3. Octaves. A note and the same note an octave higher, in eighth notes. The harmony has not changed, but there is twice the energy: a hallmark of disco and dance music.
4. Passing. On the last beat of the bar the bass steps towards the next root, and these notes are marked in yellow. A note that links two main notes like this is a passing note. The chords no longer stand apart: they have joined up into a line.
5. With the kick. The bass hits exactly where the kick does. Switch the kick pattern to "3+3+2", hits on the first, seventh and thirteenth sixteenths, a figure familiar from Cuban music. The bass follows it, and syncopation appears. Tap the kick's cells and the bass changes its rhythm to match.

Now tick "Bass a sixteenth behind the kick". At 100 BPM a sixteenth is 150 ms. The bass and the kick have come apart, and the low end of the track has gone loose: each hit has split in two. Sound engineers spend hours making the bass and kick hit together, and in the piano roll you can see it at once: the bass notes should sit under the kick hits. If the kick is four on the floor, the bass is often given the gaps between the hits, the eighth-note "ands". Then the two do not jostle but take turns.

Play the line with passing notes. C major, A minor, F major, G major and C major again. The last beat of each bar leads into the next chord: B to A, G to F, F♯ to G, B to C. F♯ is not in C major. It is a chromatic approach, a semitone from below, and it sounds like a little run-up.

Twelve bars of blues

One more progression, without which half the music of the 20th century would not exist. The twelve-bar blues came out of the African American music of the American South and became the foundation of rhythm and blues, rock and roll and much that followed. Three chords, twelve bars, three lines of four: I-I-I-I, IV-IV-I-I, V-IV-I-V.

While the blues plays, play along on the keyboard: the lit keys are the notes of the C blues scale, C, E♭, F, F♯, G, B♭. Almost any sequence of them will sound at home. E♭ over a C major chord is the famous "blue" note, somewhere between major and minor.

Try the variations. "IV in bar 2" is a common move called the quick change: the blues leaves home sooner. The ending V–V–I–I sounds old-fashioned, V–IV–I–V more modern. The final V in bar 12, the turnaround, sends you back for another round, just like stopping on V in a cadence. Without seventh chords the blues sounds plainer and brighter: the C chord loses its B♭, and with it the bite. The boogie bass, root, third, fifth, sixth and minor seventh up and back down in eighth notes, is what a pianist's left hand plays in boogie-woogie and early rock and roll.

Play this bass yourself: a bar under C major and a bar under F major. The pattern is the same, it just moves up a fourth.

And now the skeleton of the blues in chords: each chord the blues changes to, once.

Chords for your own tune

Now put it all together on your own tune. Below is the same widget as for the "Ode", but it opens the tune from the Notebook straight away. It takes the key and the bars of your track, shows which chords fit each bar, and writes the chords you choose and a bass into the Notebook. Here is the order to work in.

1. The last bar is I. If the tune ends on the tonic, as chapter 18 taught, that is settled.
2. The end of the first phrase is V. The question in the tune becomes a question in the harmony.
3. The other bars go by their notes. Watch the strips on the buttons: strong beats and long notes should belong to the chord.
4. Of two that fit, take the one that changes the picture. Three bars in a row on I sound like standing still, so put vi or IV in the middle.
5. Listen to the whole thing and adjust. Your ear has the last word: if a chord fits the notes but you do not like it, look for another.

You can also play chords on the keys: choose a bar and hold a chord, and it goes into that bar. When everything sounds right, press "Chords and bass to the Notebook".

Then give the bass a rhythm. The builder below is already set to the chords from the Notebook: find the step that suits the character of your track and record it.

The "Notebook now" panel at the end of the chapter shows the chords bar by bar, with hints from the notes of your tune, and the bass track in a piano roll, where you can fix any note.

Next

Now you know the seven chords of a key and can hear which of them are stable. You can build a loop of four chords, hear a cadence, choose a chord for a bar from the notes of the tune and play a bass under it, from a single note to a part locked to the kick. Your track has a tune, chords, a bass and a beat.

The next wall: every part is in place, yet together they sound like mush. The bass gets in the way of the chords, the tune drowns in the pad, and everything has the same sound. In chapter 20 each part gets its own role, its own register and its own synth sound.

The Notebook now has chords: one per bar, with a hint about which chords suit the notes of your tune. Under them is a bass track, which you can edit in the piano roll. In chapter 20 each of the four tracks will get its own sound and its own place in the form of the track.