## 2. Pitch, Notes and the Octave

Pitch is how high or low a sound is, and Western music cuts it into twelve notes that repeat, under the same names, in every octave.

Source: https://musictheory.center/course/pitch-and-notes
Level: Beginner · Sound · 6 sections
Before this: Fundamentals of Music Theory

### Sound and Vibration

https://musictheory.center/course/pitch-and-notes#sound-and-vibration

> Play these two. Both come from the same thing vibrating — once slowly, once quickly. Which of them came from the faster vibration? Answer before you read on.

**Plays:** Sound one (A2) · Sound two (A4)

Drag the knob across the display. The wave drawn on it squeezes together as you move right and stretches apart as you move left, and the number underneath is how many times a second it repeats. This display is silent and so is the strip it draws: what you heard came from the chips above, and everything on this site that makes a sound sends it to the bar at the bottom of the screen.

| Sound | Vibrations per second | What you hear |
| --- | --- | --- |
| A2 | 110 Hz | Low — the open A string of a guitar |
| A4 | 440 Hz | Four times faster, and much higher — the A an orchestra tunes to |

**pitch**

**Definition.** Pitch is how high or low a sound is, and it is set by how fast the source vibrates: the faster the vibration, the higher the pitch.

Nothing else about the sound decides it. A string, a column of air, a drum skin, a loudspeaker cone — each of them moves back and forth, pushes the air around it into the same pattern, and your ear counts the pattern. Make the string shorter, tighter or thinner and it moves back and forth more times a second, and the sound you hear climbs.

That count has a unit. One hertz is one complete back-and-forth per second, and the two sounds above are 110 Hz and 440 Hz. You will not hear the number, and you never need to: the point of the unit is that a vague word like "higher" turns out to be a precise quantity, and that everything in the rest of this chapter follows from arithmetic on it.

Loudness is a separate matter and is easy to confuse with this one. A sound can get much louder without moving a hair up or down, because loudness is how far the source swings, not how often. Play either chip twice at different volumes on your own speakers and the pitch will not budge.

**Good to know**

- (Fact) Pitch and frequency run in the same direction, always and without exception. Of any two sounds, the one whose source vibrates more times a second is the higher of the two, whatever instrument made it and however loud it is.
- (Convention) The A above middle C is fixed at 440 Hz as the reference the rest of the tuning is built out from. That is an agreement rather than a property of the note: it was settled internationally in the twentieth century, many orchestras still tune slightly sharp of it at 442 or 443 Hz, and baroque ensembles commonly use 415 Hz instead.

**You already know this**

- Pitch, the first of the four elements — the clip where the only thing that changed was how high the sound was — https://musictheory.center/course/fundamentals#the-four-elements

**Where this goes**

- The distance between two pitches, counted and named — https://musictheory.center/course/intervals
- Loudness — how far the source swings rather than how fast — and the marks that ask a player for more of it or less — https://musictheory.center/course/orchestration

**In real music**

- Richard Strauss — “Also sprach Zarathustra” — the organ pedal note held under the first bar is about as slow a vibration as recorded music uses, and the trumpet call that rises over it is more than two octaves above — the two chips above, played by an orchestra
- Wolfgang Amadeus Mozart — “Queen of the Night Aria” — the staccato leaps near the end reach a note vibrating roughly four times faster than the bass line under it; listen for the four short stabs at the top of the phrase

**Lesson:** https://musictheory.center/lessons/musical-notes

**Try it on your instrument:** Find the lowest note your instrument can play and hold it, then find the highest and hold that. If it has strings, watch one while it sounds: on the low note you can often see it move.

**Check:** Two sounds, one after the other. Was the source of the second one vibrating faster or slower than the source of the first?

- Slower **(correct)** — Correct. The second sound was the lower of the two, and lower always means fewer vibrations a second: 220 Hz against the first sound's 440.
- Faster — Faster vibration raises the sound, and the second one dropped. Play the chip again and hum along with each note in turn — your own voice will have to relax downwards for the second.
- The same speed — Two sounds vibrating at the same speed are the same pitch and would be indistinguishable here. These two are a clear distance apart: the second is exactly half the speed of the first.

### High and Low

https://musictheory.center/course/pitch-and-notes#high-and-low

> Play the first two. They are so alike that most people call them the same sound, and yet one of them is plainly higher. Then play the third, which climbs from one to the other. What is it that stayed the same?

**Plays:** The lower of the two (C3) · The higher of the two (C4) · Climbing from one to the other (C3 D3 E3 F3 G3 A3 B3 C4)

Thirty-six steps, from the C below middle C up to the B two octaves above it, laid out evenly and coloured from one end of the spectrum to the other. Drag across the strip to hear the climb — it plays through its own voice rather than through the bar at the bottom, so the chips above remain the thing the dock is holding. Nothing is bunched up at the low end and nothing is stretched at the high end: every step across the strip is the same size to the ear.

| Sound | Where it sits | Vibrations per second |
| --- | --- | --- |
| C3 | The nearest C below middle C | 131 Hz |
| C4 | Middle C, near the centre of a piano keyboard | 262 Hz |
| C5 | The nearest C above middle C | 523 Hz |

**register**

*also called*: range (when the whole span an instrument or a voice can reach is meant, rather than one part of it)

**Definition.** Register is the part of the low-to-high span a sound comes from — whether it sits near the bottom of an instrument's reach, near the top, or somewhere in the middle.

High and low is one single dimension, and that is worth saying plainly because pictures of music rarely show it that way. There is one road, it runs from slow vibrations to fast ones, and every sound anyone has ever made sits somewhere along it. The strip above is that road drawn out: drag along it and the sound climbs without ever leaving the line. The third chip drives along the same stretch but stops at each lettered rung — seven of them and the return, which is a [major scale](https://musictheory.center/course/scales#the-major-scale), and chapter 7 is about why those particular seven.

Two things follow. The first is that "higher" is never a matter of opinion — of any two sounds, one vibrates faster, and that one is higher. The second is the strange thing you just heard: travel far enough up the road and you arrive at a sound that seems to be the one you left, only higher. The two Cs in the chips above are not the same pitch, and nobody would mistake one for the other, and yet almost everybody calls them the same note.

That return is not an illusion and it is not a matter of taste. It happens at a fixed distance, it happens again and again all the way up, and it is the reason a keyboard with eighty-eight keys needs only seven letters. The next section is about what that distance is.

**Good to know**

- (Convention) Every note in this course carries a number: C4 is middle C, C3 is the C below it, C5 the C above. The number changes at C rather than at A, so B3 and C4 are neighbours. Without the number, "C" names eight different sounds on a piano and no reader can tell which one is meant.
- (Fact) Middle C vibrates about 262 times a second. The C an octave above it is about 523, and the C an octave below about 131 — each step up the ladder doubles the count rather than adding a fixed amount to it.
- (Tendency — unison singing in Western and popular repertoire, where the two voices are heard as doubling rather than harmonising) A melody is heard as the same melody when it is moved bodily up or down: a man and a woman singing "the same" tune together are usually an octave apart and neither of them thinks they are singing different notes.

**You already know this**

- Pitch as the speed of a vibration — the two sounds at 110 Hz and 440 Hz — https://musictheory.center/course/pitch-and-notes#sound-and-vibration

**Where this goes**

- Register as a choice: which instrument is given which part of the range — https://musictheory.center/course/orchestration

**In real music**

- Queen — “Bohemian Rhapsody” — the opening a cappella section stacks the same voice in several registers at once; the lowest and highest lines are singing the same few notes far apart
- Giacomo Puccini — “Nessun Dorma” — the final "vincerò" climbs to the top of the tenor register and stays there — the effort you hear is a singer working at the very end of his road

**Try it on your instrument:** Play the lowest C your instrument can reach, then every C above it in turn, up to the highest. Count how many you found. Then play one of them and sing it, and notice whether you sang the one you played or one of the others.

**Check:** Three sounds in a row. Which of them came from the fastest vibration?

- The first — The first was the lowest of the three and therefore the slowest — about 131 vibrations a second. Low and slow are the same statement said twice.
- The second **(correct)** — Correct. The second sound was the highest of the three, so it was the fastest: about 523 vibrations a second, against 131 for the first and 262 for the third.
- The third — The third landed between the other two, which is exactly what it sounded like: about 262 vibrations a second, twice the first and half the second. All three are Cs, each one the same distance from the next — the distance the next section is about.

### The Octave

https://musictheory.center/course/pitch-and-notes#the-octave

> Play these two. The first sounds both together, the second one after the other. Before you read on, answer this about the first chip: how many things are sounding in it — one, or two?

**Plays:** Both at once (C4 C5) · One after the other (C4 C5)

Middle C and the C above it, sounded together. The upper one vibrates exactly twice as fast as the lower, and that two-to-one ratio is the whole of what this distance is. It is the only interval in music that people routinely hear as one sound rather than two.

| Note | Vibrations per second | Compared with middle C |
| --- | --- | --- |
| C2 | 65 Hz | A quarter of the speed — two octaves below |
| C3 | 131 Hz | Half the speed — one octave below |
| C4 | 262 Hz | Middle C |
| C5 | 523 Hz | Twice the speed — one octave above |
| C6 | 1047 Hz | Four times the speed — two octaves above |

**octave**

**Definition.** An octave is the distance between a note and the next note of the same name above or below it — the interval at which the frequency of a sound exactly doubles.

Doubling is the whole definition, and it is arithmetic rather than opinion. Middle C is about 262 vibrations a second; double that and you get 523, which is the C above. Double again for the C above that, halve for the C below. Nothing else in music is this simple, and nothing else is this universal: the doubling is why the two sounds fuse, because every vibration of the lower note is met by exactly two of the upper one, over and over, with no drift between them.

This is why a keyboard of eighty-eight keys needs only seven letters. The names run out after seven and then start again, because at the octave the ear has arrived back where it started: a fresh set of names would be describing a difference nobody hears. The number on the end of the name — the 4 in C4 — is the only thing that distinguishes one C from another.

Keep two facts side by side and the rest of the chapter follows. Notes an octave apart are not the same pitch, because one is clearly higher. They are the same note, because everything except [register](https://musictheory.center/course/orchestration#register-and-range) about them matches. Music theory takes the second of those seriously and builds everything on it.

**Good to know**

- (Fact) Doubling the frequency of a sound raises it by exactly one octave; halving it lowers it by exactly one. The ratio is 2:1, and it is the simplest ratio two different pitches can stand in, which is why the octave blends more completely than any other interval.
- (Convention) Western notation gives the two notes of an octave the same letter and tells them apart with a number — C3, C4, C5 — rather than inventing separate names. The word "octave" itself counts letters rather than steps: C up to C is eight letter names, C D E F G A B C.
- (Tendency — arranging in Western popular and orchestral music; chapter 18 takes it up in detail) Doubling a line at the octave is used to thicken it rather than to harmonise it: a bass guitar and a synth an octave apart, or a flute over a violin, are heard as one line with more body, not as two parts.

**You already know this**

- The climb from one C to the C above it, and the sound that seemed to come back — https://musictheory.center/course/pitch-and-notes#high-and-low
- Frequency in hertz — the number that is doing the doubling — https://musictheory.center/course/pitch-and-notes#sound-and-vibration

**Where this goes**

- The octave as the widest of the twelve simple intervals, and what inverting one does — https://musictheory.center/course/intervals

**In real music**

- Harold Arlen — “Somewhere Over the Rainbow” — the first two syllables, "Some-where", leap a full octave — the single most quoted example there is, and the reason the song opens so wide
- Nacio Herb Brown — “Singin' in the Rain” — the first two notes of the title line, "I'm sing-", jump an octave; the melody then walks back down through the gap it just made

**Try it on your instrument:** Play any note on your instrument, then find the nearest note above it with the same name and play them together. Do it from three different starting notes, and listen for the moment the two stop sounding like two things.

**Check:** The note you are about to hear vibrates about 262 times a second. Which note vibrates about 523 times a second — twice as fast?

- C5 **(correct)** — Correct. Doubling the frequency raises a sound by exactly one octave, so twice as fast as C4 is C5 — the same letter, the next number up. Nothing else about the note has changed.
- G4 — G4 is higher than C4, so the direction is right, but it is only about one and a half times as fast — a ratio of 3 to 2 rather than 2 to 1. That interval is a perfect fifth and you meet it in chapter 5.
- C3 — C3 is the right letter and the wrong direction. It vibrates at half the speed of C4, about 131 times a second, which puts it an octave below rather than above. Halving lowers; doubling raises.

### The Twelve Notes

https://musictheory.center/course/pitch-and-notes#the-twelve-notes

> Play this. It climbs from one sound to the one you would call the same, higher up, and it stops on every rung there is on the way. Count the rungs. Then play the second chip, which is the same ladder coming down.

**Plays:** Every rung from C to C (C4 C#4 D4 D#4 E4 F4 F#4 G4 G#4 A4 A#4 B4 C5) · The same rungs, coming down (C5 B4 Bb4 A4 Ab4 G4 Gb4 F4 E4 Eb4 D4 Db4 C4)

Twelve steps from middle C to the C above, and a thirteenth sound that is the first one again. Where the staff is showing, it draws the climb the way the first chip plays it, with sharps; either way the table below gives both spellings of every step, and the section after next says which to use when.

| Steps above middle C | Written with sharps | Written with flats |
| --- | --- | --- |
| 0 | C4 | C4 |
| 1 | C♯4 | D♭4 |
| 2 | D4 | D4 |
| 3 | D♯4 | E♭4 |
| 4 | E4 | E4 |
| 5 | F4 | F4 |
| 6 | F♯4 | G♭4 |
| 7 | G4 | G4 |
| 8 | G♯4 | A♭4 |
| 9 | A4 | A4 |
| 10 | A♯4 | B♭4 |
| 11 | B4 | B4 |
| 12 | C5 | C5 |

**chromatic scale**

**Definition.** The chromatic scale is all twelve notes of an octave played in order, one rung at a time, from any starting note to the same note an octave higher or lower.

Twelve is the number to remember out of this whole chapter. The octave is cut into twelve equal steps, those twelve are every pitch Western music uses, and everything above them — every [scale](https://musictheory.center/course/scales#what-a-scale-is), every chord, every [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) — is a decision about which of the twelve to use and which to leave alone. The thirteenth sound in the chip above is not a new note; it is the first one again, an octave up, and the pattern repeats from there in both directions for as far as any instrument goes.

Equal is meant precisely, and it is equal in the right way. Each step multiplies the frequency by the same amount, about 1.0595, rather than adding a fixed number of hertz to it, and twelve of those multiplications land exactly on double. That is why the strip in the section before this one has no bunching at one end: the steps are equal to the ear all the way up, even though the gap in hertz between two neighbouring high notes is many times the gap between two neighbouring low ones.

Seven of the twelve carry a letter of their own and the other five do not, which is the lopsided part and the part everyone trips over. The table gives both ways the nameless five are written — raised from the letter below, or lowered from the letter above. The widget above shows the same cut being made: drag through the first stage and the sound slides smoothly, then watch the dividing lines appear and the sound start landing on them.

**Good to know**

- (Fact) Twelve equal steps fill an octave exactly. Each step multiplies the frequency by the twelfth root of two — about 1.0595 — and twelve multiplications by that figure double it.
- (Convention) A rising chromatic run is normally written with sharps and a falling one with flats, which is why the two chips above are spelled differently. Both play identical sounds; the spelling follows the direction of travel.
- (Convention) Twelve is a choice, not a law of acoustics. Dividing the octave into twelve equal parts is the tuning nearly every Western instrument is built and tuned to, and it became standard only over the eighteenth and nineteenth centuries; other traditions divide the octave differently, and an unfretted string or a voice can sound everything in between.
- (Tendency — tonal Western music; chapters 7 and 8 name the seven and chapter 14 is about the visitors) A piece draws on seven of the twelve at a time and treats the other five as visitors, which is why a chromatic run sounds like a deliberate effect rather than like ordinary melody.

**You already know this**

- The octave, the distance this climb covers from end to end — https://musictheory.center/course/pitch-and-notes#the-octave
- The strip of evenly spaced steps you dragged across — these are those steps, one octave of them — https://musictheory.center/course/pitch-and-notes#high-and-low

**Where this goes**

- Half steps and whole steps: what one rung and two rungs are called — https://musictheory.center/course/intervals
- Choosing seven of the twelve, and why that choice is what a scale is — https://musictheory.center/course/scales

**In real music**

- Nikolai Rimsky-Korsakov — “Flight of the Bumblebee” — almost the entire piece is this ladder, run up and down at speed; the first four bars alone climb and fall through it twice
- The Beatles — “Michelle” — the line under "Michelle, ma belle" steps down one rung at a time and passes through notes that belong to no key in the song

**Try it on your instrument:** Start on any note on your instrument and play every note you can find going up, skipping none, until you reach the same note again. Count them. Then come back down the same way.

**Check:** You have just climbed from one note to the same note higher up, stopping on every rung. How many steps did the climb take?

- Seven — Seven is how many letter names there are, and how many white keys sit inside one octave of a keyboard. Five more notes live between them, and this climb stopped on all five.
- Eight — Eight is where the word "octave" comes from: C, D, E, F, G, A, B and C again is eight letters. But that count walks past the five notes that have no letter of their own, and this climb walked past nothing.
- Twelve **(correct)** — Correct. Twelve steps fill the octave, and the thirteenth sound is the note you started on, an octave higher. Those twelve are every pitch Western music has.

#### Why the steps are equal, and what it costs

Equal steps are a compromise, and knowing what was traded away explains a great deal of what you hear. The intervals the ear likes best are simple frequency ratios — 2:1 for the octave, 3:2 for a fifth, 5:4 for a third — and if you tune a keyboard so that those ratios are exact in one [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is), they come out badly wrong in a distant one. For centuries that was simply lived with: instruments were tuned for the keys a piece actually used, and remote keys sounded harsh on purpose.

Dividing the octave into twelve identical steps fixes every key at once by making all of them very slightly wrong. The octave stays pure, because twelve steps land exactly on the doubling. Everything else is detuned a little: an equal-tempered fifth is about two cents narrower than a pure 3:2, and an equal-tempered major third is about fourteen cents wider than a pure 5:4 — enough to hear as a slow beating on a held chord. Singers, string players and trombonists, who are not fixed to the twelve, quietly correct towards the pure ratios, which is why an unaccompanied choir can sound sweeter on a long chord than a piano ever does.

### Naming the Notes

https://musictheory.center/course/pitch-and-notes#naming-notes

> Play the ladder going up, then coming down. Now say out loud what you would call each note — letters, syllables, numbers, whatever comes to you. Whatever you used, a large part of the world uses something else for exactly the same sounds.

**Plays:** The ladder, going up (C4 D4 E4 F4 G4 A4 B4 C5) · The ladder, coming down (C5 B4 A4 G4 F4 E4 D4 C4)

Eight sounds and seven names: the eighth is the first one again, an octave higher. Both of the naming systems in the table below climb this same ladder, note for note, and disagree about nothing except what to call each one. These eight are the lettered notes only — the five without letters of their own are not on this ladder, which is why its steps are not all the same size.

| Letter | Solfège | The sound |
| --- | --- | --- |
| C | do | C4 |
| D | re | D4 |
| E | mi | E4 |
| F | fa | F4 |
| G | sol | G4 |
| A | la | A4 |
| B | si | B4 |
| C | do | C5 |

**note name**

*also called*: H for the note English calls B (in German-speaking countries, where a plain B means B flat and H means B natural)

**Definition.** A note name is the label a pitch class carries: one of seven letters, A to G, on its own or with a sharp or a flat attached — or, in France, Italy, Spain and Latin America, one of the seven solfège syllables from do to si, with the same signs available to it.

The two are parallel systems, not a system and its translation. Neither came from the other, both are complete, and a musician raised in one of them calls the notes by those names for life. Do is C, re is D, mi is E, fa is F, sol is G, la is A, si is B, and then do again an octave up. Every row of the table has a name in both columns, and no row has a name in only one.

The letters run A to G and then begin again, so the sequence is A B C D E F G A B C and so on around. The alphabet starting on A is a medieval inheritance — the scale it was assigned to is the one now called natural minor — but theory books almost always start counting from C instead, because the seven plain letters played from C spell a major scale with nothing added or taken away. That is why every example in this chapter starts on C rather than on A.

The names are labels and nothing more. A4 is 440 vibrations a second whether it is called A, la, or something neither of those traditions has heard of, and a piece does not become a different piece when it crosses a border. This page will show you the names your reading language uses; the sounds behind them do not change.

**Good to know**

- (Convention) Solfège syllables — do, re, mi, fa, sol, la, si — are the everyday names for the notes in France, Italy, Spain and Latin America, where do is always C and never moves. Letters A to G do exactly the same job in English- and German-speaking countries. Neither is a beginners' version of the other.
- (Convention) The same syllables are also used in much of the English-speaking world as **movable do**: do is whichever note the music is centred on at that moment, and the seventh syllable is "ti" rather than "si" so that every syllable begins with a different letter. Both practices are called solfège and they disagree about what "do" means, so it is worth asking which one someone is using before arguing about a note.
- (Convention) Seven letters and their sharps and flats cover every note on an eighty-eight-key piano, because the names start again at each octave. Only the octave number tells C3 from C4 from C5.

**You already know this**

- The twelve notes, seven of which carry a letter of their own — https://musictheory.center/course/pitch-and-notes#the-twelve-notes
- The octave, the distance after which every name comes back — https://musictheory.center/course/pitch-and-notes#the-octave

**Where this goes**

- Where each of these names sits on the staff, and how a clef decides — https://musictheory.center/course/notation
- Do re mi as the numbered degrees of a major scale, from any starting note — https://musictheory.center/course/scales

**In real music**

- Richard Rodgers — “Do-Re-Mi” — the canonical movable-do lesson set to music — each phrase starts one name further up the ladder above, and the seventh is "ti, a drink with jam and bread", not si; the film sings it in B flat, so do is B flat rather than C
- Lowell Mason — “Joy to the World” — the opening melody walks straight down all eight names of the ladder, from the do at the top to the do at the bottom, without skipping one

**Lesson:** https://musictheory.center/lessons/musical-notes

**Try it on your instrument:** Play the seven notes from C up to B on your instrument and name each one twice out loud: once with its letter, once with its syllable. Then start on G instead, where the letters run G A B C D E F — the same seven letters, just started from a different one — and do it again.

**Check:** A musician in Paris or Madrid tells you the tune begins on "sol". Which note do they mean?

- G **(correct)** — Correct. In fixed-do solfège the syllables are nailed to the letters and never move: do is C, re is D, mi is E, fa is F, sol is G. The note you just heard is that one.
- E — E is mi, the third syllable. Count up from do and you get do C, re D, mi E — so mi is the third of the seven names and sol is the fifth.
- A — A is la, the sixth syllable, one letter above sol. Close, and in the right part of the ladder, but one name too high.

### Sharps, Flats and Enharmonics

https://musictheory.center/course/pitch-and-notes#sharps-flats-and-enharmonics

> Play all three. The first takes one small step upward, the second takes one small step downward, and they land in the same place. The third plays that landing place twice over, written two different ways. Listen for any difference at all between its two sounds.

**Plays:** C, then the step above it (C4 C#4) · D, then the step below it (D4 Db4) · Two spellings, one after the other (C#4 Db4)

Two note heads side by side, and one sound between them. The first sits on middle C with a sharp sign in front of it; the second sits on the D above with a flat sign in front of it. Different letters, different places on the staff — and the same key on a keyboard, the same fret on a guitar, the same 277 vibrations a second, reached from below in one spelling and from above in the other. The third chip above plays the two heads in order, and you will not hear the staff move.

- **Sharp** — ♯ raises the letter it is attached to by one rung
- **Flat** — ♭ lowers the letter it is attached to by one rung
- **Natural** — ♮ cancels a sharp or a flat and restores the plain letter

| The sound between two letters | Reached from below | Reached from above |
| --- | --- | --- |
| Between C and D | C♯4 | D♭4 |
| Between D and E | D♯4 | E♭4 |
| Between F and G | F♯4 | G♭4 |
| Between G and A | G♯4 | A♭4 |
| Between A and B | A♯4 | B♭4 |

**enharmonic equivalent**

**Definition.** Enharmonic equivalents are two written names for one and the same sound: C♯ and D♭ are the same key, the same fret and the same number of vibrations a second, spelled up from the letter below in one case and down from the letter above in the other.

The two signs do the work. A sharp sign ♯ raises the letter it is attached to by one rung of the twelve-rung ladder, and a flat sign ♭ lowers it by one. So the sound between C and D can be reached in two ways — push C up, or pull D down — and both journeys end on the same sound. A natural sign ♮ cancels either one and puts the letter back as it was.

Why keep two names for one sound? Because the seven letters are the skeleton, and music is written so that the skeleton stays legible. A piece uses seven of the twelve at a time, and those seven are spelled so that each letter appears exactly once: in the [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) of D the third note is written F♯ and never G♭, because G is already taken by the fourth note, and writing G♭ would put two Gs and no F in a seven-note row. The spelling says what a note is doing; the sound says nothing about it either way.

Notice also which pairs are missing from the table. There are five of them and not seven, because E and F are already only one rung apart, and so are B and C. That is the whole reason a keyboard has its black keys in groups of two and three instead of one between every pair of white ones.

**Good to know**

- (Fact) One rung is the smallest distance in the twelve-note system: there is nothing at all between a note and the note a sharp or a flat takes you to. Chapter 5 gives that distance its name, the [half step](https://musictheory.center/course/intervals#half-steps-and-whole-steps).
- (Convention) C♯ and D♭ name one sound, and they are still not interchangeable in writing. Which spelling is right depends on the key the music is in and on where the line is going next — a decision made for the reader, since the sound is identical either way.
- (Constraint — writing inside a [key signature](https://musictheory.center/course/keys-and-key-signatures#why-key-signatures-exist), which chapter 8 sets out in full) Each of the seven letters is used exactly once, so a note takes whichever sign keeps the letters running in order: F♯ in D major, never G♭.
- (Fact) On a piano or a fretted instrument the two spellings are physically the same note and cannot be played apart. On a violin, a trombone or in a choir they can be sounded very slightly differently, because the player is not tied to the twelve fixed steps.

**You already know this**

- The table of twelve, where both spellings already stood side by side — https://musictheory.center/course/pitch-and-notes#the-twelve-notes
- The seven letters, which are what a sharp or a flat is attached to — https://musictheory.center/course/pitch-and-notes#naming-notes

**Where this goes**

- Accidentals on the staff: where the sign is drawn, and how long it lasts — https://musictheory.center/course/notation
- Why a minor third above C is written E♭ and not D♯ — https://musictheory.center/course/intervals

**In real music**

- Ludwig van Beethoven — “Für Elise” — the famous opening alternates E with the note one rung below it, written D♯ — the same sound as E♭, spelled from below because of where the line is heading
- Dave Brubeck — “Take Five” — the tune is written on the flat side, so the same five nameless notes that a sharp-side piece would call F♯ and C♯ appear here as G♭ and D♭

**Try it on your instrument:** On your instrument, play C and then the note one rung above it, and say both of that note's names out loud. Then play D and the note one rung below it. Confirm with your hands that you arrived at the same place twice.

**Check:** Two sounds, one after the other. The first is written C♯ and the second is written D♭. Same sound, or different?

- The same sound **(correct)** — Correct, and nothing moved: one sound played twice. C♯ and D♭ are the same key, the same fret and the same 277 vibrations a second — two spellings of one note, which is what "enharmonic" means.
- The second is higher — A sharp raises and a flat lowers, so it is reasonable to expect the two to land apart. They do not. C raised one rung and D lowered one rung arrive at the same place, because there is exactly one rung between C and D.
- The second is lower — Nothing dropped. If you heard a fall, the spelling did it rather than the sound — play the chip again and count how many different pitches are in it. The answer is one.

### Key Takeaways

https://musictheory.center/course/pitch-and-notes#key-takeaways

- Pitch is how high or low a sound is, and it is set by how fast the source vibrates: faster vibration, higher pitch.
- Doubling the frequency of a sound raises it by exactly one octave, which is why a note and the note an octave above it share a name.
- Western music divides every octave into twelve equal steps, and those twelve notes, repeating in every octave, are all the pitches it uses.
- Seven of the twelve carry a letter of their own; the other five are written either as a sharp raised from the letter below or as a flat lowered from the letter above.
- Letters A to G and the solfège syllables do to si are two complete, parallel naming systems for the same seven notes, used in different parts of the world.
- Enharmonic equivalents such as C♯ and D♭ are one sound with two spellings, and which spelling is correct depends on the key rather than on the sound.

### Questions

**What is the difference between a note and a pitch?**

Pitch is how high or low a sound is, on a scale that runs smoothly from low to high. A note is one chosen point on that scale, given a name and usually a length. Every note has a pitch; not every pitch is a note, because most of them fall between the twelve.

**Why are there only twelve notes in music?**

Because Western music divides the octave into twelve equal steps and uses only those. Twelve is a choice, not an acoustic law: other traditions divide the octave differently, and instruments without frets or keys can play everything in between. Twelve survived because it makes every [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is) usable on one fixed instrument.

**Is C♯ the same as D♭?**

In sound, yes: on a piano or a guitar they are the same key and the same fret, about 277 vibrations a second. In writing they are not interchangeable. The spelling is chosen so that each letter appears once in a [key](https://musictheory.center/course/keys-and-key-signatures#what-a-key-is), which is why D major has F♯ and never G♭.

**What is an octave?**

An octave is the distance between a note and the next note of the same name, higher or lower. The higher of the two vibrates exactly twice as fast. Middle C is about 262 vibrations a second and the C above it about 523, which is why the two blend into what sounds like one thicker note.

**Why does A equal 440 Hz?**

By agreement, not by nature. Orchestras needed one reference so that instruments built in different places would match, and A above middle C at 440 Hz was standardised internationally in the twentieth century. Many orchestras still tune to 442 or 443, and baroque ensembles often use 415.

**Why do the letters start at A but music theory starts at C?**

The letters were assigned to a medieval scale that began on A, the one we now call [natural minor](https://musictheory.center/course/scales#the-three-minors). Modern theory starts on C because the seven plain letters, played from C, spell a [major scale](https://musictheory.center/course/scales#the-major-scale) with no sharps or flats — the simplest thing to point at on a keyboard.

### Other languages

- https://musictheory.center/course/pitch-and-notes/llms.txt
- https://musictheory.center/fr/cours/hauteur-et-notes/llms.txt
- https://musictheory.center/es/curso/altura-y-notas/llms.txt