Major and minor

In chapter 0 there was an experiment we left unexplained. A tune was moved along the white keys, every note by the same number of keys, and it came out sadder. The shape on the keyboard was the same, and the keys were still white. So what changed?

This chapter is an experiment with one variable. The keys stay where they are, and only the starting point moves: the note the ear takes for home. That is enough to get major and minor, to hear why a tune "wants" to end on a particular note, and to take on the fourth big question of the course.

Same keys, different home

Start with the Scale and Tune buttons while home is C. Then switch to A and listen again. The keys are the same, white ones only, and the tune is built in exactly the same way: up and down by the same number of keys. Only one thing differs, the key everything starts from and ends on.

From C it sounds bright and settled, from A darker and softer. Many people hear the difference at once, even if they cannot name it. Now press "Hold home": a low home note starts sounding underneath, and you can play any white keys over it. This is a drone, a held sound in the background, like a bagpipe's or a long pad under an electronic track. Over a drone on C and a drone on A, the same key E sounds different: in the first case it is the third note from home, in the second the fifth.

The note the ear takes for home is called the tonic. Music moves away from the tonic and comes back to it, and a phrase that lands there sounds finished. The other notes only make sense next to it: "the third from home", "one step below home".

Look at the strip above the keyboard. It shows the same eight notes, but spaced honestly, by semitones. The white keys are not evenly spaced: between most neighbours there is a black key, but between E and F, and between B and C, there is none. These two short steps are coloured. When home is C, the short steps come third and seventh. When home is A, they move to second and fifth. The rungs of the ladder are the same, but the ladder starts somewhere else, and its pattern changes.

A ladder of tones and semitones

You already know how the steps work from chapter 11: neighbouring keys, counting the black ones, are a semitone apart, and keys with one key between them are a whole tone apart. Write down the steps of the white keys from C up to C: whole tone, whole tone, semitone, whole tone, whole tone, whole tone, semitone. For short, with W for a whole tone and H for a half step (a semitone), W-W-H-W-W-W-H. It adds up to six whole tones, exactly an octave.

A row of notes going up from the tonic in this pattern is a scale. The pattern itself, the set of relationships between the notes around the tonic, is called a mode. The mode with the pattern W-W-H-W-W-W-H is major.

The great strength of this pattern is that you can start it on any note. Pick D in the builder: to keep the steps W-W-H-W-W-W-H you need two black keys, F♯ and C♯. From F you need B♭. Your hand notices before your head does: the scale from D sits differently under the fingers than the one from C, yet it sounds the same, only higher.

Each note of the scale is a scale degree. The tonic is the first, or I, the next is II, and so on up to VII. The eighth is the tonic again, an octave higher. A degree's number does not depend on the note the scale starts from: in C major degree III is E, in D major it is F♯. A mode on a particular tonic is the key from chapter 11: C major, D major, F♯ major. The key signature is simply the list of black keys a key needs to keep the step pattern.

Try breaking the pattern in the builder. Turn one step into a semitone, and the total falls short of an octave, so the last note misses the tonic. To close the ladder, you have to add a semitone somewhere else. What you get is a different mode, and we will meet several of them below.

Now with your hand. First the C major scale up and down, from the notes.

G major: the same pattern from G. The seventh degree lands on the black key F♯. The sharp sits in the key signature, so the notes do not show it again.

And now without the notes. The exercise names the key and marks the tonic. Find the other seven keys yourself by counting the steps W-W-H-W-W-W-H.

Minor: the same ladder, different rungs

Back to home on A. The steps up the white keys from A are: whole tone, semitone, whole tone, whole tone, semitone, whole tone, whole tone, or W-H-W-W-H-W-W. This is minor, or more precisely the natural minor. In the builder it sits under the Minor button.

Compare the start of the two patterns: W-W… and W-H… The difference begins as early as the third degree. In major, the tonic and degree III are two whole tones apart, the major third from chapter 13. In minor they are a tone and a half apart, a minor third. Further up, minor also has lower VI and VII degrees. Play C major and C minor from the same tonic, and exactly three notes differ: E and E♭, A and A♭, B and B♭.

This gives two kinds of kinship between keys. C major and A minor share the same keys but have different tonics. Such keys are called relative: they have the same key signature, and the minor tonic is a minor third lower. C major and C minor, the other way round, share the tonic but some of their notes differ. These are parallel keys, or same-tonic keys. Watch the words here: German and Russian books use "parallel" for the first pair, the relative keys. The experiment at the start of the chapter went from C major to its relative minor, A minor. In the next section, tunes will move into the parallel mode.

Now by ear. A short tune plays in major or in minor, on a different tonic each time. Listen for degree III: the tunes in this exercise always have it. After you answer, you can hear the same tune in the other mode.

The same difference lives in chords. Take degrees I, III and V together and you get a triad: a major one if degree III is the major third, a minor one if it is the minor third. Chords get their own chapter 15. For now, a taste: three notes play one after another, then together. Major or minor?

Into minor

The most direct way to hear a mode is to take a familiar tune and change only the mode. The tonic stays put, and so does the rhythm. Every note keeps its degree, but the degree now comes from the other mode.

Beethoven's "Ode to Joy", from the Ninth Symphony (1824), is in major. Its first eight bars use only five notes, from C to G, and of the three "minor" degrees the tune contains just one: III, the E. Switch to minor: E becomes E♭, and nothing else changes. One note across the whole tune.

The second tune is the Russian folk song "Vo pole beryoza stoyala" ("A birch tree stood in the field"), known in English as "The Birch Tree". It was first printed in 1790, in a collection of Russian folk songs by Nikolai Lvov and Ivan Prach. It is in minor, and Tchaikovsky made it a theme of the finale of his Fourth Symphony. Switch it to major: C becomes C♯ and G becomes G♯. The tune stays recognisable, but its character changes: from wistful it turns almost into a dance.

The widget has one more slider, the tempo. Play the Ode in minor at 180 BPM and The Birch Tree in major at 50. Fast minor sounds agitated rather than sad, and slow major solemn or tender rather than cheerful. Remember that feeling: it will come in handy in the section on why major seems happy.

A tune in C major has been moved into C minor. Which notes could have changed?

Only E, A and B: they become E♭, A♭ and B♭ Every note moves down a minor third Only the tonic, C

The parallel minor keeps the same tonic, and three degrees change: III, VI and VII, each a semitone lower. C, D, F and G stay where they are. Moving the whole tune down a third takes it into a different key, and the mode would still be major.

The pull: why the tonic is home

At the end of chapter 13 there was an experiment: play "Twinkle, Twinkle, Little Star" and stop on the note before the last, D. Your hand wants to go on to C. The same happens with a scale: play C major slowly upwards and stop on B. Most people who grew up on European music feel their hand reaching for C on its own. B does not want to be the last note. This is the pull of the mode: unstable degrees pull towards stable ones, and the tonic pulls hardest of all.

Test it on yourself. The widget plays the home chord, so your ear knows where the tonic is, and then a short phrase. Place your bet: did it end, or is it left hanging? If it is hanging, finish it: play the note where it comes to rest.

Degree I is the most stable. III and V are a little less so: together with the tonic they make the tonic triad, the whole sound of home. The rest are unstable and pull towards the nearest stable degree: II down to I or up to III, IV to III, VI to V. VII pulls hardest of all, since it is only a semitone below the tonic. It is called the leading note, because it leads into the tonic. Degree V has a name too, the dominant; chapter 15 explains why.

The pull is not a law of physics. It is an expectation the ear has learned from thousands of tunes that end on the tonic. That is what makes it useful to a musician: you can meet the expectation and give the listener a sense of an ending, or cheat it and stretch the phrase.

Degrees are recognised by ear in the same way. First you hear a cadence, a short chord progression that puts the tonic in its place. Then a single note. Listen for where it pulls. The tonic pulls nowhere, degree V feels like firm ground with a question in it, and III like a soft middle.

Now five degrees. If you get confused, ask yourself where you want to go from the note you heard, and count the steps to the tonic.

Hearing degrees is a skill for months, not for one evening. It is easiest to keep up in the "Scale degrees" trainer: it has four levels, goes up to all seven degrees in different keys, and gives you more of the ones you get wrong.

Why major sounds happy and minor sad

Why do some tunes sound happy and others sad?

You have already got part of the answer with your own hands. Happiness and sadness do not live in single notes: the same key E sounds bright over a drone on C and soft over a drone on A. The character comes from the pattern of steps from the tonic, and above all from degree III: a major third or a minor one.

But why does a major third sound "bright"? The honest answer here is that nobody fully knows. Here is what is known.

Within Western musical culture the link is strong and learned early. In 2001 psychologists in Montreal, Simone Dalla Bella, Isabelle Peretz and their colleagues, played children and adults excerpts of music in which tempo and mode were changed independently. Adults and children aged 6 to 8 called both major and a fast tempo happy. Five-year-olds heard only the tempo: the mode made no difference to their answers. Three- and four-year-olds could not tell happy from sad better than chance. In the authors' words, "tempo is mastered earlier than mode": the link between major and happy comes later, by about the age of six.

The experiment in Cameroon. In 2009 Thomas Fritz and his colleagues from the Max Planck Institute in Leipzig travelled to northern Cameroon, to the Mandara Mountains, to visit the Mafa people. They included only people who had never listened to the radio or been to church, and so had heard almost no Western music. Twenty-one listeners heard short piano pieces meant to sound happy, sad or scary, and for each one chose the matching face from a set of photographs. The Mafa recognised all three moods better than chance. Both they and Western listeners more often called the fast pieces happy and the slow ones scary. Pieces in major more often got the happy face, and pieces in minor a frightened face rather than a sad one. The mode affected the answers in both groups, but less so among the Mafa. The paper appeared in Current Biology and became an argument that some emotions in music can be understood without any exposure to it. But in these pieces the mode changed together with the tempo and other features of the music, and the effect of mode alone was not measured.

The experiment in Papua New Guinea. In 2022 Eline Smit, Andrew Milne, Hannah Sarvasy and Roger Dean tested mode on its own. They played major and minor cadences and melodies to 170 people in the Uruwa River valley, in the mountains of Papua New Guinea. There is hardly any radio or television there, and people hear Western music mainly in church, in hymns built almost entirely on major chords. Churchgoers called the major cadences happy more often than the minor ones. Among those who hear almost no Western music, there was no convincing evidence either way. With the melodies the effect was weaker still: it showed up in only one of the three groups. The authors are careful. They found "no evidence for a universal effect", and they tie the emotional sign of major and minor closely to familiarity with Western music, "although we cannot exclude the possibility of universality".

Put together, this gives a picture without big claims. In these experiments tempo works earlier and more widely than mode: five-year-olds respond to it, and so do the Mafa. The link "major is happy, minor is sad" is largely learned. Thousands of songs, films and adverts that put sad scenes in minor keep reinforcing it. It is not built in from birth as firmly as the jolt you feel at a sudden loud noise, but it is not arbitrary either.

For writing music, this leads to a practical conclusion. Mode is one control among several. Minor at a fast tempo with a dense beat sounds energetic, not mournful: plenty of dance tracks are made that way. Major at a slow tempo on a quiet pad sounds calm or solemn. You have already heard this on the tempo slider.

What did the experiment with children aged three to eight (Dalla Bella and colleagues, 2001) show?

Tempo affects the answers before mode does: five-year-olds heard only the tempo Children hear major as happy and minor as sad from birth Neither tempo nor mode affects children under ten

Five-year-olds called fast music happy whatever the mode, while children aged 6 to 8 took the mode into account too, as adults do. The link between mode and mood appears later than the link with tempo, which is one of the arguments that it is largely learned.

Seven modes on the white keys

Home does not have to be C or A. The white keys offer seven possible tonics, and each gives its own step pattern, its own mode. Medieval theory knew them by Greek names: Dorian, Phrygian, Lydian, Mixolydian. These are the church modes. The names were borrowed from the ancient Greeks, although the Greek modes with those names were built differently.

On the wheel below, the twelve notes of the octave stand in a circle, and a mode is a polygon made of its notes. Choose a tonic: the white keys stay white, the polygon stays the same, and only the home arrow turns. Press "Hold home" and play on the white keys: in each mode they have a character of their own.

The easiest way to remember the modes is by how they differ from major and minor. Dorian is minor with a raised degree VI, Mixolydian is major with a lowered VII. Both are at home in folk, jazz and rock. Lydian is major with a raised IV and sounds "weightless". Phrygian is minor with a lowered II, and dark. Locrian is hardly ever used: there is no perfect fifth from its tonic to degree V, so its home is shaky.

The last button on the wheel gives five notes instead of seven. This is the pentatonic scale: a mode of five notes with no semitone steps. The major pentatonic is major without degrees IV and VII, exactly the ones that pull hardest. A ready-made pentatonic lies on the black keys. Play anything you like on them: no two notes clash a semitone apart, and everything sounds right together. That is why beginners, guitarists and teachers of music to children are so fond of improvising on the pentatonic.

What about the harmonic minor?

In the natural minor, degree VII sits a whole tone below the tonic and pulls towards it only weakly. For several centuries composers writing in minor have often raised degree VII by a semitone: in A minor they play G♯ instead of G. That gives the harmonic minor, W-H-W-W-H-1½-H, with a step of a tone and a half between degrees VI and VII. Build it in the builder: press Minor, then tap the sixth step twice (W → H → 1½) and the seventh once (W → H). That wide step is audible at once, and you cannot mistake it for anything else.

Scale mode in synths and DAWs

Many MIDI keyboards and nearly every modern DAW can do what you have just been doing in your head: keep your playing in key. This is scale mode, usually labelled Scale. You choose a tonic and a mode, and the instrument behaves in one of three ways. Highlight: the notes of the mode are marked on the keys or in the piano roll, and the rest play as usual. Scale only: keys outside the mode are silent. Snap: a key outside the mode plays the nearest note of the mode.

Set A minor and "Scale only", switch on the backing and play any keys you like, even with the flat of your hand. There will be no wrong notes. Then switch to "Snap": now every black key sounds too, but as a note of the mode. "Highlight" is the most honest of the three: it shows you where the mode is and still lets you make mistakes.

Scale mode is a good safety net when recording and when playing live. But it does not replace knowing the mode: it tells you which notes are allowed, not which one you need right now. For that you need an ear for degrees and for the pull, which you have been training above.

The key of your track

The Notebook probably already holds your tune or bass line. What key are they in? The program can make a guess. The table for this comes from 1982, from the psychologists Carol Krumhansl and Edward Kessler: they asked listeners to rate how well each of the twelve notes fits a given key. The result was a "weight" for each degree: the tonic highest, then V and III, and notes outside the key lowest of all. The classic way to guess the key is to add up how long each note sounds in the track and compare the totals with this table for all 24 keys. The closest match is most likely your key.

The bars show how long each note sounds: the tonic is the brightest, notes of the key a little darker, notes outside it grey. Choose the key that fits, and it is written to the Notebook. Then listen to the track in the other mode and, if you like it, move it there. The tune and the bass change degrees III, VI and VII, and the chords on the same degrees become chords of the new mode.

Next

Now you know why the same tune on the white keys in chapter 0 came out sadder: the tonic changed, and the pattern of steps from it became minor. You can build major and minor from any note with the patterns W-W-H-W-W-W-H and W-H-W-W-H-W-W, hear the tonic and its pull, tell major from minor, and you know where the science ends and the habits of the ear begin. And you can turn "Ode to Joy" minor with a single note.

The next wall is accompaniment. You have a tune in a key, but on its own it sounds bare. Which chords will fit under it? The answer lies in what you already know: chords are built from the notes of the mode, on its degrees. That is chapter 15.

The Notebook has learned the key of your track: the key is saved, and the "⇄" button moves the tune, bass and chords from major to minor and back, degree by degree. Chapter 15 adds a chord track built on the degrees of this key.