## 8. Keys and Key Signatures

A key is the scale a piece of music treats as home, a key signature is that scale’s sharps or flats written down once at the start of the line, and the circle of fifths is what falls out when you build the same scale from each fifth in turn.

Source: https://musictheory.center/course/keys-and-key-signatures
Level: Intermediate · Materials · 6 sections
Before this: Intervals, Scales: Major and Minor

### What a Key Is

https://musictheory.center/course/keys-and-key-signatures#what-a-key-is

> Play both. They are the same six notes in the same order, and then one last note that is different each time. Only one of them sounds like it has stopped rather than been interrupted — which one feels finished?

**Plays:** First ending (C4 D4 E4 F4 G4) · Second ending (C4 D4 E4 F4 G4)

The seven-note set both phrases stay inside, climbing from C to the C above it. Neither phrase uses a note from outside this set, and neither phrase changes a single note of the other. The only difference between them is where they stop — and that alone decides whether the music sounds finished.

| Phrase | Notes it draws on | Where it stops | How it ends |
| --- | --- | --- | --- |
| First ending | C4 D4 E4 F4 G4 | C4 | Closed. The phrase has come back to the note it started from and asks for nothing more |
| Second ending | C4 D4 E4 F4 G4 | D4 | Open. The phrase stopped one note away from home, and the ear supplies the missing step for you |

**key**

**Definition.** A key is the major or minor scale a piece treats as home, named after its [tonic](https://musictheory.center/course/scales#scale-degrees) — the note of that scale the music keeps returning to and finally settles on.

Being in a key is not a property of a list of notes. It is what a piece does with them. The two phrases above contain exactly the same five pitches; the first one is in C because it leans on C, leaves it, and comes back to it, and the second one leaves that job unfinished. Play enough phrases that behave like the first and a listener stops hearing seven equal notes and starts hearing one note with six others arranged around it.

That arrangement is a hierarchy, not a set. The tonic is home; the fifth degree above it is the note that sets up the return; the seventh degree sits a [half step](https://musictheory.center/course/intervals#half-steps-and-whole-steps) below home and leans on it. A key is a scale plus that hierarchy, which is why two pieces using identical notes can be in two different keys.

A key also comes with a modality. The same seven notes will make a major key if the third degree above the tonic is the wide one and a minor key if it is the narrow one, and the whole colour of the music changes with it. Naming a key therefore takes two words: a note and a modality — C major, A minor, E flat major.

**Good to know**

- (Fact) Which note sounds like home is settled by what the ear has heard, not by anything in the notes themselves. The same seven notes will settle on different homes depending on which one the music leans towards, returns to and ends on — and a listener who has heard only half a phrase can already be wrong about it.
- (Convention) Naming a key after its tonic and its modality — C major, A minor — is a convention of Western theory, and a fairly recent one: it hardened in the seventeenth century, when the older [church modes](https://musictheory.center/course/modes#what-a-mode-is) gave way to two of them. It says nothing a listener can hear that the music has not already said.

**You already know this**

- The tonic from Chapter 7, the first degree of a scale and the note every other one is heard against — https://musictheory.center/course/scales#scale-degrees
- The major scale from Chapter 7, the seven notes a major key draws on — https://musictheory.center/course/scales#the-major-scale

**Where this goes**

- Every chord in a piece is named by the degree of the key its lowest note is built on — https://musictheory.center/course/chords

**In real music**

- Traditional — “Twinkle Twinkle Little Star” — the very last note of the tune is the one it began on, and nothing else would sound like an ending
- The Beatles — “A Hard Day’s Night” — the opening chord deliberately refuses to say where home is, and the first sung note is what settles it

**Try it on your instrument:** Play a short phrase on your instrument using only C, D, E, F, G, A and B, and end it on C. Play the same phrase again and end it on D instead. Do each three times, and notice which one leaves you wanting to add something.

[Find the key of a song you know from its chords](https://musictheory.center/tools/key-finder?c=C+G+Am+F)

**Check:** Two runs of the same little phrase, one after the other. Is the second built on the same home note as the first, or a different one?

- A different home note **(correct)** — Correct. The second run is the same shape moved three half steps up, so its home note is E flat rather than C, and three of its notes — E flat, F and B flat — were not in the first run at all. Same tune, new key.
- The same home note — The shape was the same, which is what makes this worth checking. But the second run never touched C: it started, turned and ended on E flat, and that is a different home. Play it once more and sing along with the last note of each run.
- The same notes in a different order — The order is identical — up three, back to the first, up to the fifth, and home. What changed was the pitch every one of those notes was played at, all of them by the same distance.

### Why Key Signatures Exist

https://musictheory.center/course/keys-and-key-signatures#why-key-signatures-exist

> Play the first two. They are the same climb built from two different starting notes, so they sound like one another moved. The third clip is just the pair of sounds the second climb needs that the first one never touches.

**Plays:** Climb from C (C4 D4 E4 F4 G4 A4 B4 C5) · Climb from D (D4 E4 F#4 G4 A4 B4 C#5 D5) · The two it adds (F#4 C#5)

Two bars of 4/4 in treble clef: the climb from D, written out. Between the clef and the time signature stand two sharp signs, one on the top line and one in the third space from the bottom — F and C, sharpened for the whole piece. Every F and every C printed afterwards sounds a half step higher without a sign of its own, in every octave. Written the other way, these same two bars would need a sharp drawn in front of the third note and another in front of the seventh, and so would every later F and C on the page: hundreds of signs across a piece that never once changes its mind about them. Under the staff is the order those signs are always added in.

- **Sharps are added in this order** — F4 C4 G4 D4 A4 E4 B4
- **Flats are added in this order** — B4 E4 A4 D4 G4 C4 F4

| The problem with writing it out each time | What a key signature does instead |
| --- | --- |
| The same two letters are altered in almost every bar, and each one needs its own sign | States the alteration once, at the start of every line, and applies it to those letters in every octave until the music says otherwise |
| The reader has to notice each sign as it arrives, mid-phrase, at speed | The reader takes in the whole set in one glance, before playing a note, and then reads plain note heads |
| A page crowded with signs that carry no news hides the ones that do | A sign printed inside a bar now means something exceptional: a note from outside the key |
| Nothing on the page says which scale the music is built from | The pattern after the clef narrows the key to two — one major and the minor that shares its notes |
| A signature counted sign by sign is slow to read mid-piece | The signs always arrive in the same order — sharps on F, C, G, D, A, E, B; flats on B, E, A, D, G, C, F — and at fixed heights, so a reader knows a signature by its shape before counting it |

**key signature**

**Definition.** A key signature is the group of sharps or flats printed immediately after the [clef](https://musictheory.center/course/notation#staff-and-clefs) on every line of music, which alters those letters in every octave for the rest of the piece unless a later sign cancels them.

It is worked out, not looked up. Build the [major scale](https://musictheory.center/course/scales#the-major-scale) from the note you want as home and see which letters the pattern forced you to alter: from D, the formula puts a half step between the third degree and the fourth and another between the seventh and the octave, which can only be done by writing F sharp and C sharp. Those two sharps are D major’s key signature. The same procedure gives one sharp for G, one flat for F, and so on for all fifteen of them.

Two things follow from printing it once rather than repeatedly. The reader learns the whole alteration before the first note, so the page can be read as plain note heads at speed. And an [accidental](https://musictheory.center/course/notation#accidentals) printed inside a bar recovers its meaning: it is no longer routine bookkeeping but a signal that this note comes from outside the key, which is exactly the kind of thing a reader should notice.

A key signature identifies the notes, not the home. Two sharps means D major or B minor, and the signature cannot tell you which — for that you look at where the music starts, where the bass falls at the end, and which of the two notes the phrases keep returning to.

**Good to know**

- (Convention) A key signature is notational shorthand and nothing else. The convention belongs to Western staff notation, where it settled into its modern form in the eighteenth century; systems that write pitch by number or by syllable — Chinese jianpu, Indian sargam, tonic sol-fa — carry the same information in a single symbol or not at all.
- (Fact) A key signature adds nothing to the sound. The climb on the staff above is note for note the second clip in this section, whether its F and C are sharpened by two signs after the clef or by a sign in front of every affected note.

**You already know this**

- The sharp, flat and natural signs from Chapter 4, which a key signature applies in advance instead of one note at a time — https://musictheory.center/course/notation#accidentals
- Building a scale from its formula in Chapter 7, which is where the sharps and flats in a signature come from — https://musictheory.center/course/scales#building-any-scale

**Where this goes**

- The chords a piece is most likely to use are the seven the key signature makes available — https://musictheory.center/course/diatonic-harmony

**In real music**

- Pachelbel — “Canon in D” — every F and C in the whole piece is sharpened by the two signs at the head of the line, and the violins never see an accidental
- Beethoven — “Für Elise” — the piece is in A minor, so nothing stands after the clef, and the D sharp that opens the famous figure has to be printed as an accidental every single time it appears

**Try it on your instrument:** Open any piece of sheet music you own and look at what stands between the clef and the [time signature](https://musictheory.center/course/meter-and-groove#time-signatures). Count the signs, name the letters they sit on, then play the first bar and check that you altered every one of those letters, in whichever octave it appeared.

**Check:** The major scale built from G needs exactly one sharp to keep its pattern of steps. Which note is the sharpened one?

- F sharp **(correct)** — Correct. G A B C D E and then the seventh degree, which has to sit a half step below G. F natural is a whole step below it, so the note is raised to F sharp — and that single sharp is the whole of G major’s signature.
- C sharp — C is the fourth degree of this scale, and the formula asks for a half step from B up to it — the same half step that sits between the third degree and the fourth of every major scale. C natural is exactly that half step; sharpening it would stretch the gap to a whole step and break the pattern in the middle. C sharp belongs to D major, one fifth further on.
- G sharp — G is the note the scale is named after, so sharpening it would move home rather than fix a step. Listen to the climb again and stop on the note just before the top: that is the one the pattern had to raise.

### The Circle of Fifths

https://musictheory.center/course/keys-and-key-signatures#the-circle-of-fifths

> Play the first clip: three notes, each the same distance above the one before it. Then play the two climbs that follow, one built from the first of those notes and one from the second. Count how many notes the two climbs do not share.

**Plays:** Three notes, each the same distance up (C4 G4 D5) · The climb from the first of them (C4 D4 E4 F4 G4 A4 B4 C5) · The climb from the second (G3 A3 B3 C4 D4 E4 F#4 G4)

Start on C and build the major scale: C D E F G A B, and not one of them needs a sharp or a flat. Now go up a fifth, to G, and apply the same formula from there: G A B C D E F sharp. Six of those seven notes were already in C major. The seventh is F sharp, and it is there for one reason — the formula puts a half step between the seventh degree and the octave, so the note under G has to be F sharp rather than F. Go up another fifth, to D, and the same thing happens again: D E F sharp G A B C sharp keeps the F sharp it inherited and adds C sharp, once more on the seventh degree. Up a fifth to A adds G sharp; up a fifth to E adds D sharp. Every step up a fifth keeps the sharps it already had and adds exactly one. Go the other way instead — down a fifth from C, to F — and the formula needs a flat, B flat, for the mirror image of the same reason, and each further step down adds one more. Twelve steps of a fifth pass through all twelve notes and arrive back where they started, and the diagram below is that walk drawn as a ring rather than a line.

| Step | Key | Its seven notes | What the formula forced |
| --- | --- | --- | --- |
| Start here | [C Major](https://musictheory.center/scale/c-major) | C4 D4 E4 F4 G4 A4 B4 | Nothing |
| Up a fifth from C | [G Major](https://musictheory.center/scale/g-major) | G3 A3 B3 C4 D4 E4 F♯4 | One sharp: F♯4 |
| Up a fifth from G | [D Major](https://musictheory.center/scale/d-major) | D4 E4 F♯4 G4 A4 B4 C♯5 | Two sharps: F♯4 C♯5 |
| Up a fifth from D | [A Major](https://musictheory.center/scale/a-major) | A3 B3 C♯4 D4 E4 F♯4 G♯4 | Three sharps: F♯4 C♯4 G♯4 |
| Up a fifth from A | [E Major](https://musictheory.center/scale/e-major) | E4 F♯4 G♯4 A4 B4 C♯5 D♯5 | Four sharps: F♯4 C♯5 G♯4 D♯5 |
| Down a fifth from C | [F Major](https://musictheory.center/scale/f-major) | F3 G3 A3 B♭3 C4 D4 E4 | One flat: B♭3 |
| Down a fifth from F | [Bb Major](https://musictheory.center/scale/bflat-major) | B♭3 C4 D4 E♭4 F4 G4 A4 | Two flats: B♭3 E♭4 |
| Down a fifth from B flat | [Eb Major](https://musictheory.center/scale/eflat-major) | E♭4 F4 G4 A♭4 B♭4 C5 D5 | Three flats: B♭4 E♭4 A♭4 |

**circle of fifths**

**Definition.** The circle of fifths is the twelve keys arranged in order of rising fifths, so that every key stands between the two whose notes it shares all but one of.

Nothing about it has to be memorised, because it is a consequence rather than a diagram. Take any [major scale](https://musictheory.center/course/scales#the-major-scale), go up a perfect fifth, apply the formula from there, and six of the seven notes come with you: the fifth degree of the old scale becomes the [tonic](https://musictheory.center/course/scales#scale-degrees) of the new one, and only the note a [half step](https://musictheory.center/course/intervals#half-steps-and-whole-steps) below that new tonic has to be raised. One step, one new sharp, every time. Going down a fifth instead does the mirror image and adds one flat at a time. Do it twelve times and you have visited all twelve notes and returned to the start, which is what makes it a circle and not a list.

The two sides meet opposite C, at the point where six sharps and six flats describe the same sounds. That key is written F sharp major or G flat major depending on which direction you arrived from, and the choice is a matter of which is easier to read rather than anything the ear can settle. The same seam is why there are fifteen key signatures for twelve keys.

What the arrangement is good for is distance. Keys that sit next to each other share six of their seven notes, so a piece can slip between them almost without a seam; keys on opposite sides share only two, and moving between them is an event. That single measurement is behind most of what the circle gets used for: counting a signature, choosing a key to modulate to, and explaining why a progression that keeps falling by fifths sounds like it is going somewhere.

**Good to know**

- (Fact) Each step up a fifth adds exactly one sharp, because the only note that changes is the new scale’s seventh degree. The other six are the old scale’s notes read from a different starting point, and the seventh has to be raised to put a half step under the new tonic.
- (Convention) Sharps are added in the order F, C, G, D, A, E, B, and flats in the reverse order, B, E, A, D, G, C, F — the order the table in the previous section sets out. The order is not arbitrary — it is the circle itself — but writing the signs in it, at fixed heights on the staff, is a convention of Western notation that has been stable since the eighteenth century.
- (Fact) Twelve perfect fifths of seven half steps each span eighty-four half steps, which is exactly seven octaves, so the chain closes on the note it began with. It closes only because those fifths are the very slightly narrowed ones of equal temperament: twelve acoustically pure fifths overshoot seven octaves by about a quarter of a half step.

**You already know this**

- The perfect fifth from Chapter 5, the single step this whole arrangement is made of — https://musictheory.center/course/intervals#the-twelve-intervals
- The major-scale formula from Chapter 7, applied here from each new starting note in turn — https://musictheory.center/course/scales#building-any-scale

**Where this goes**

- Modulation moves a piece into another key, and the circle is what says which keys are near enough to slip into — https://musictheory.center/course/advanced-harmony

**In real music**

- Joseph Kosma — “Autumn Leaves” — the first eight bars are two runs of chords falling by fifths, four chords each, one step around the circle per chord
- Jimi Hendrix — “Hey Joe” — the entire song is five chords rising by fifths and then dropping back, which is one arc of the circle played over and over

**Try it on your instrument:** Starting on C, play up a perfect fifth on your instrument, then a fifth from there, and keep going until you arrive back on a C. Say each note name aloud. Then go round again, and at each stop build the major scale from the note you landed on and find the one note that has just changed.

[Walk the circle yourself: tap any key for its signature, its notes and its neighbours](https://musictheory.center/tools/circle-of-fifths?k=C&lens=key)

**Check:** Four sharps take you as far as E major. Going up one more fifth from E lands on the key that has five. Which key is it?

- B major **(correct)** — Correct. A fifth above E is B, and B major keeps E major’s four sharps and adds one more on its own seventh degree, A sharp — five in all. It is the fifth stop clockwise from C.
- F major — F is a fifth below C, not above E: it is the first stop in the other direction, and it has one flat rather than five sharps. Count up from E instead — E, F, G, A, B — and you land on B.
- A major — A major is the key you passed through on the way to E, with three sharps. Going back to it would be a step anticlockwise; the question asked for the next one up, which adds a sharp rather than removing one.

### Relative and Parallel

https://musictheory.center/course/keys-and-key-signatures#relative-and-parallel

> Play both. Each clip is two climbs in a row. In the first, the two climbs use exactly the same seven notes and begin in different places. In the second, they begin in the same place and three of the notes have moved.

**Plays:** Same notes, different starting point (C4 D4 E4 F4 G4 A4 B4 C5 A3 B3) · Same starting point, different notes (C4 D4 E4 F4 G4 A4 B4 C5 Eb4 Ab4 Bb4)

Two ways a pair of keys can be close. In the first clip the second climb runs C major’s seven notes from A instead of C, so nothing is added or removed and only home has moved: those two keys are written with the same empty space after the clef. In the second clip the second climb keeps C as home and lowers the third, sixth and seventh degrees, so E becomes E flat, A becomes A flat and B becomes B flat: same home, three flats, a different colour. On the diagram below, each key on the outer ring sits directly outside the minor key that shares its signature.

| Major key | Relative minor | Signature | The signs, in order |
| --- | --- | --- | --- |
| [C Major](https://musictheory.center/scale/c-major) | [A Minor](https://musictheory.center/scale/a-minor) | Nothing | — |
| [G Major](https://musictheory.center/scale/g-major) | [E Minor](https://musictheory.center/scale/e-minor) | One sharp | F♯4 |
| [D Major](https://musictheory.center/scale/d-major) | [B Minor](https://musictheory.center/scale/b-minor) | Two sharps | F♯4 C♯4 |
| [A Major](https://musictheory.center/scale/a-major) | [F# Minor](https://musictheory.center/scale/fsharp-minor) | Three sharps | F♯4 C♯4 G♯4 |
| [E Major](https://musictheory.center/scale/e-major) | [C# Minor](https://musictheory.center/scale/csharp-minor) | Four sharps | F♯4 C♯4 G♯4 D♯4 |
| [F Major](https://musictheory.center/scale/f-major) | [D Minor](https://musictheory.center/scale/d-minor) | One flat | B♭4 |
| [Bb Major](https://musictheory.center/scale/bflat-major) | [G Minor](https://musictheory.center/scale/g-minor) | Two flats | B♭4 E♭4 |
| [Eb Major](https://musictheory.center/scale/eflat-major) | [C Minor](https://musictheory.center/scale/c-minor) | Three flats | B♭4 E♭4 A♭4 |

**relative key**

**Definition.** A relative key is the key that shares another key’s seven notes and its key signature while treating a different one of them as home: every major key has a relative minor whose tonic is three [half steps](https://musictheory.center/course/intervals#half-steps-and-whole-steps) below its own, and every minor key a relative major three half steps above.

A parallel key is the key that shares another key’s tonic and changes its notes instead. C major and C minor are parallel: both call C home, and the minor lowers the third, sixth and seventh [degrees](https://musictheory.center/course/scales#scale-degrees) a half step, so a piece that moves between them keeps its centre of gravity and changes its colour.

The two relationships are worth keeping apart because they do opposite things. A move to the relative minor changes where home is without altering a single note or the signature, so it can happen inside a phrase and often goes unnoticed as a key change at all — it is why the same eight bars can sound major at the start of a verse and minor by the end of it. A move to the parallel minor keeps home exactly where it was and repaints everything around it, which is impossible to miss.

Finding either takes no memorisation. For the relative minor, count three half steps down from the major tonic — a minor third — and start the same notes there; for the relative major, count three up. For the parallel, keep the note and change the word, then lower the third, sixth and seventh: the signature moves three places anticlockwise around the circle, which is what turning C major into C minor and its empty signature into three flats amounts to.

**Good to know**

- (Fact) Relative keys share a key signature and differ only in tonic. C major and A minor are printed with the same empty space after the clef; nothing on the page distinguishes them, and only what the music leans on does.
- (Fact) Parallel keys share a tonic and differ in exactly three notes: the third, sixth and seventh degrees are each a half step lower in the minor. C major needs no signs and C minor needs three flats — E♭4, A♭4 and B♭4.
- (Convention) The distance to a relative minor is always a minor third down and the distance to a relative major always a minor third up. That is a consequence of the major and [natural minor](https://musictheory.center/course/scales#the-three-minors) patterns being rotations of one another, not a rule anyone chose; what is conventional is calling the pair "relative" rather than naming them by the rotation.

**You already know this**

- The natural minor from Chapter 7, the scale a minor key is built on — https://musictheory.center/course/scales#the-three-minors
- The minor third from Chapter 5, the exact distance between a major key and its relative minor — https://musictheory.center/course/intervals#number-and-quality

**Where this goes**

- Borrowing chords from the parallel key is the commonest way a major piece darkens without leaving home — https://musictheory.center/course/advanced-harmony

**In real music**

- Green Day — “Wake Me Up When September Ends” — the verse sits in G and the chorus drops into its relative minor without a single new note appearing
- The Beatles — “Blackbird” — the bridge moves between the major key and chords borrowed from the minor on the same home note — the parallel relationship, heard a chord at a time

**Try it on your instrument:** Play a major scale on your instrument. Then play the same seven notes starting from the sixth of them and ending there. Then play the major scale again with its third, sixth and seventh each lowered a half step. Name all three of the things you have just played.

[Compare C major with A minor, then with C minor, note by note](https://musictheory.center/tools/circle-of-fifths?k=C&lens=compare&vs=Am)

**Check:** Two climbs, one after the other. Do they share all seven notes and differ in where they begin, or do they begin on the same note and differ in three of their notes?

- Same notes, different home **(correct)** — Correct. The second climb ran C major’s seven notes from A, so not one note was added, removed or altered — only home moved, down three half steps. That is the relative minor, and the two keys are written with the same signature.
- Same home, different notes — A parallel pair keeps the starting note and changes three of the others: the second climb would have begun on C again and sounded E flat, A flat and B flat. This one began somewhere else entirely and never touched a flat.
- The same climb twice — The notes were the same, which is why this is worth a second listen, but the order was not: the second climb started three half steps lower and so put the small steps in different places. Listen to where each climb finishes and you will hear two different homes.

### Choosing a Key

https://musictheory.center/course/keys-and-key-signatures#choosing-a-key

> Play the first clip: six sounds at once, the six strings of a guitar with nothing held down. Then play the two climbs. One of them contains every one of those sounds; the other contains two. Which is which?

**Plays:** Six strings, nothing held down (E2 A2 D3 G3 B3 E4) · The first climb (D3 E3 F#3 G3 A3 B3 C#4 D4) · The second climb (Eb3 F3 G3 Ab3 Bb3 C4 D4 Eb4)

A guitar in standard tuning gives you E, A, D, G, B and E for nothing. The first climb is D major, whose seven notes include every one of those five letters, so a player in D can let open strings ring under almost anything. The second climb is E flat major, which shares only G and D with them, so nothing rings and every note has to be stopped by a finger. Below is the signature of B flat major, two flats — the key a trumpet or a clarinet reaches for by the same kind of reasoning, from the other side of the circle.

| Instrument family | Keys that sit well | Why |
| --- | --- | --- |
| Guitar and bass | E, A, D, G and their relative minors | Five of the six open strings are the home notes of those keys, so the lowest note of a chord can be an open string and left to ring. The strings themselves are tuned in fourths, with one major third between the third string and the second |
| Violin, viola, cello | G, D, A, C and E | The open strings are tuned in fifths through those notes, and an open string is both louder and exactly in tune |
| Trumpet, clarinet, saxophone, horn | B flat, E flat, A flat, F | Each instrument is built around a fundamental that is not C, so its easiest fingerings and its written scales fall in flat keys |
| Voice | Whichever key puts the tune inside the singer’s range | A song is moved until its highest and lowest notes are comfortable, and no other consideration outranks that |
| Piano, harp and most software | All of them, near enough equally | Every key is the same distance pattern under the hand, and a sequencer moves a part to any of them with one command |

**choosing a key**

**Definition.** Choosing a key is deciding which pitch a piece’s home note will sit at, and the decision is made on practical grounds: the range of the voices and instruments that will play it, and which notes those instruments produce most easily.

[Range](https://musictheory.center/course/orchestration#register-and-range) comes first. A [melody](https://musictheory.center/course/melody#what-makes-a-melody) has a highest note and a lowest note, and the key is what sets where those land. A song that strains a singer at the top is moved down until it does not, and the key it ends up in is whatever that move produced — which is why the same song appears in different keys on different recordings by different singers.

After range comes what an instrument gives away free. A guitar and a violin both have open strings, which sound louder, need no finger and are perfectly in tune, so music written for them gravitates towards the keys that contain those notes: E, A, D and G for guitar; G, D, A and E for violin. Brass and wind instruments pull the other way. A trumpet, a clarinet and a tenor saxophone are each built around a fundamental note that is not C, and their simplest fingerings and cleanest tone fall in the flat keys, which is why band and jazz repertoire lives in B flat, E flat and F.

None of which is the same as a key having a character. The idea that D major is triumphant or E flat major heroic is a real tradition with a real origin, but that origin is the tuning systems in use before the nineteenth century, not the keys themselves — and the difference it names has not existed on a modern piano for two hundred years.

**Good to know**

- (Tendency — Western popular, folk, orchestral and band repertoire, and the instruments named) Guitar, bass and orchestral string music tends to be written in E, A, D and G, and wind, brass and big-band music in B flat, E flat, A flat and F. In each case the keys named are the ones whose notes the instruments produce with the least work.
- (Convention) Key characteristics — D major as triumphant, E flat major as heroic, F minor as mournful — come from a tradition of writing about affect that runs from Charpentier in the 1690s through Mattheson and Schubart to nineteenth-century programme notes. It described something real at the time: under the unequal temperaments then in use, each key genuinely had its own pattern of slightly different intervals. Under equal temperament every major key is the same set of distances moved to another pitch, so what survives is register, instrument timbre and expectation.
- (Constraint — arranging or accompanying a sung melody) Move a song to fit a singer before you make any other decision about the key. Every other consideration — open strings, comfortable fingerings, a tidy signature — is worth having only in a key the voice can actually reach.

**You already know this**

- The major scale from Chapter 7, which is what tells you whether a key lands on the notes your instrument likes — https://musictheory.center/course/scales#the-major-scale
- The circle of fifths from earlier in this chapter, which counts the signs for any of these keys at a glance — https://musictheory.center/course/keys-and-key-signatures#the-circle-of-fifths

**Where this goes**

- Picking a key that suits every player at once is the first decision an arrangement makes — https://musictheory.center/course/orchestration

**In real music**

- The Beatles — “Blackbird” — the part is played in G with the open G string droning under the moving line, from the first bar of the intro onwards
- Billy Strayhorn — “Take the A Train” — the standard is played in C, which puts the B flat trumpet and tenor parts in D and the alto part in A — the reason big-band charts look like four different keys at once

**Try it on your instrument:** Find the notes your own instrument gives you for nothing: the open strings of a guitar or violin, the notes a wind instrument plays with the fewest fingers down, or the notes that sit easiest in your voice. Write them down, then work out which two or three major keys contain all of them.

**Check:** B flat major is written with two flats. Which two notes do they sit on?

- B flat and E flat **(correct)** — Correct. Flats arrive in the order B, E, A, D, G, C, F, so a signature of two flats is always B flat and E flat — and the climb you just heard is B flat, C, D, E flat, F, G, A.
- B flat and A flat — B flat is the first flat, but A flat is the third, and a key never skips one. A signature containing A flat has at least three flats in it, which would make the key E flat rather than B flat.
- E flat and A flat — These are the second and third flats, and both of them appear only after B flat has. A key whose signature leaves B flat out has no flats at all: skipping the first one is not something a signature can do.

#### Instruments that do not sound what they read

A trumpet in B flat reads a C and sounds the B flat below it. So does a tenor saxophone, an [octave](https://musictheory.center/course/pitch-and-notes#the-octave) further down; a clarinet in A sounds an A; an alto saxophone in E flat sounds the E flat below its written C; a French horn in F sounds the F. The player reads one note and the audience hears another, and the distance is fixed by the instrument.

The reason is historical and practical at once. Before valves, a brass instrument could only play the notes of one harmonic series, so players carried several instruments or several lengths of tubing and swapped between them. Writing every one of them as though its fundamental were C meant a player learned one set of fingerings and one set of written scales for the whole family, and only the part in front of them changed. Valves removed the need in the 1830s and the notation stayed, because by then every player in Europe had learned to read that way.

The consequence for a score is that a concert-pitch C major passage is written in D for the B flat instruments and in A for the E flat ones, each with its own signature, all on the same page. An arranger transposes each part by its instrument’s interval before printing it, which is a mechanical step — and the one place in ordinary musical life where getting a transposition wrong is immediately, publicly audible.

### Transposing

https://musictheory.center/course/keys-and-key-signatures#transposing

> Play all three. It is the same short tune each time, begun from a different note. Nothing inside it changes — the distance from each note to the next is identical in all three — and the only thing that moves is how high the whole thing sits.

**Plays:** The tune as written (C4 D4 E4 G4) · The tune higher (Eb4 F4 G4 Bb4) · The tune higher still (G4 A4 B4 D5)

The tune written out in C: up two steps, back to the first note, up to the fifth degree, and home. The table below is the same seven notes in three keys side by side. Read across any row and the pitch changes; read down any column and the pattern of degrees is identical, which is the whole of what transposing does.

| Note of the tune | Degree of the key | In C | In E flat | In G |
| --- | --- | --- | --- | --- |
| First | 1 | C4 | E♭4 | G4 |
| Second | 2 | D4 | F4 | A4 |
| Third | 3 | E4 | G4 | B4 |
| Fourth | 1 | C4 | E♭4 | G4 |
| Fifth | 5 | G4 | B♭4 | D5 |
| Sixth | 3 | E4 | G4 | B4 |
| Seventh | 1 | C4 | E♭4 | G4 |

**transposition**

**Definition.** Transposition is moving every note of a passage by the same interval, so that the distances inside it are untouched and only the pitch it sounds at changes.

The method is two steps. Measure the interval from the old tonic to the new one — C up to E flat is a minor third, C up to G a perfect fifth — and then move every note in the passage by that exact interval, accidentals included. Nothing is decided note by note: if one note moves a minor third, all of them do, or the tune is no longer the same tune.

Spelling is where transposing goes wrong on paper. Move the [letter names](https://musictheory.center/course/pitch-and-notes#naming-notes) by the same number of letters as the pitch moved, then take the accidentals from the new key’s signature: the third note of the tune above is the third letter of each key, E in C, G in E flat, B in G. Choosing spellings by sound alone — writing F sharp where the new key calls for G flat — gives a passage that plays correctly and reads wrongly, and a reader will stumble over it.

This is why a key is worth thinking of as a position rather than a set of notes. A singer asking for a song "a bit lower", a guitarist clamping a capo on the second fret, an arranger writing out a trumpet part, a producer dragging a MIDI clip up three semitones: all four are doing the same operation, and all four rely on the fact that the music itself survives it intact.

**Good to know**

- (Fact) Transposition preserves every interval inside a passage. Its melodic shape, its rhythm and its harmony come through unchanged; the only things that move are [absolute pitch](https://musictheory.center/course/ear-training#relative-and-absolute-pitch) and, with it, the register the passage sits in and the timbre of the instruments playing it.
- (Constraint — writing a transposed part out on a staff, rather than playing one by ear) Move the letter names by the same number of letters as the pitch moved, and let the new key’s signature decide the accidentals. Transposing by sound alone produces [enharmonic spellings](https://musictheory.center/course/pitch-and-notes#sharps-flats-and-enharmonics) that are correct to the ear and unreadable on the page.
- (Tendency — popular, folk and choral practice) A song is moved to suit whoever is singing it rather than kept in the key it was written in, so the same tune circulates in several keys at once and the "original" key is often just the one the first recording happened to use.

**You already know this**

- Half steps and whole steps from Chapter 5, the units the whole passage is moved by — https://musictheory.center/course/intervals#half-steps-and-whole-steps
- The circle of fifths from earlier in this chapter, which tells you the signature of whichever key you have just moved to — https://musictheory.center/course/keys-and-key-signatures#the-circle-of-fifths

**Where this goes**

- Playing one key’s seven notes from each of its degrees in turn gives the modes — https://musictheory.center/course/modes
- Numbering chords by degree rather than by letter is transposition applied to harmony — https://musictheory.center/course/diatonic-harmony

**In real music**

- Michael Jackson — “Man in the Mirror” — the final chorus lifts the whole arrangement up a half step, the same music at a new pitch
- Bon Jovi — “Livin’ on a Prayer” — the last chorus jumps up a minor third, which is the same distance the tune above moved from C to E flat

**Lesson:** https://musictheory.center/lessons/circle-of-fifths

**Try it on your instrument:** Play a four-note phrase on your instrument in C. Work out the distance from C up to E flat, move every note of the phrase by that distance and play it again. Then do the same from C up to G. Check at the end that the shape you hear is identical all three times.

[Transpose a chord chart from C to E♭ and watch every chord move by the same distance](https://musictheory.center/tools/chord-transposer?c=C+F+G+C&to=Eb)

**Check:** These three notes are C, E and G. Moved up by a whole step, what do they become?

- D, F sharp, A **(correct)** — Correct. Every note moves the same whole step: C to D, E to F sharp, G to A. F natural would be only a half step above E, so it has to be sharpened for the distances inside the chord to survive the move.
- D, F, A — The letters are right and one of the distances is not. E to F is a half step, so this version squeezes the gap between the first two notes and turns a bright chord into a dark one — a different chord, not the same one moved.
- D, G, A — D up to G spans four letters, not three — D, E, F, G — so the middle note lands where the fourth degree would be rather than the third. Move each letter on by exactly one instead: C to D, E to F, G to A.

### Key Takeaways

https://musictheory.center/course/keys-and-key-signatures#key-takeaways

- A key is the major or minor scale a piece treats as home, named after the note it keeps returning to.
- A key signature writes that scale’s sharps or flats once, after the clef, and applies them to every octave until the music says otherwise.
- The circle of fifths is what you get by applying the major-scale formula from each fifth in turn: every step up adds exactly one sharp, and every step down adds one flat.
- Neighbouring keys on the circle share six of their seven notes, which is why moving between them sounds smooth and moving across the circle does not.
- Relative keys share a signature and differ in which note is home; parallel keys share the home note and differ in three of their notes.
- Composers choose a key for range and for what an instrument plays most easily, not because the key has a character of its own.
- Transposing moves every note by the same interval, so the music survives intact and only its pitch level changes.

### Questions

**What does a key signature tell you?**

It tells you which letters are sharpened or flattened for the whole piece, in every [octave](https://musictheory.center/course/pitch-and-notes#the-octave), until a later sign cancels them. It also names the key down to a choice of two: one major key and its relative minor, which share the same signature and are told apart only by the music itself.

**How many key signatures are there?**

Fifteen: one with no sharps or flats, seven with one to seven sharps, and seven with one to seven flats. They cover only twelve different sounds, because three pairs are spelled two ways — B major and C flat major, F sharp and G flat, C sharp and D flat.

**What is the difference between relative and parallel minor?**

A relative minor shares its major key’s seven notes and its key signature, and starts three [half steps](https://musictheory.center/course/intervals#half-steps-and-whole-steps) lower: A minor to C major. A parallel minor shares the [tonic](https://musictheory.center/course/scales#scale-degrees) and changes three notes, lowering the third, sixth and seventh: C minor to C major, three flats against none.

**What is the circle of fifths for?**

It [shows at a glance how many sharps or flats any key has](https://musictheory.center/tools/circle-of-fifths), which keys are closest to the one you are in, and which minor key shares each signature. Composers use it to pick a key to move to; players use it to work out a signature without counting a scale out.

**How do I find the key of a piece?**

Start with the signature, which narrows it to two: a major key and its relative minor. Then look at the last bass note and the final chord, and at which of the two candidates the melody keeps returning to. The one the music settles on is the [tonic](https://musictheory.center/course/scales#scale-degrees). You can also [find the key from a chord chart](https://musictheory.center/tools/key-finder) directly.

### Other languages

- https://musictheory.center/course/keys-and-key-signatures/llms.txt
- https://musictheory.center/fr/cours/tonalites-et-armures/llms.txt
- https://musictheory.center/es/curso/tonalidades-y-armaduras/llms.txt