Semitone or half step
The smallest step on a piano, from one key to the very next.
Paused by your reduced-motion setting
Find Your PitchSeason 1Lesson 02
Musicians only use seven letters, so where do the other five notes come from?
By the end you'll find all twelve notes on a keyboard, tell a semitone from a tone by ear, know why one key has two names, and know what a cent is.
This lesson is about small steps in sound. Tap to turn it on: nothing plays until you press a play button.
TaviSeven letters on the way round. Is there a hidden note between every two letters?
MercCount the steps and find out.
Note—
Steps0· Hz × 2
Lesson 1's spiral of 37 beads from A2 to A5, three turns, every A on the same side. The five beads on each turn that have no letter of their own start dim with a question mark, and light once they are heard. With the keyboard, the arrow keys pick a note and Enter plays it.
Predict before you listen
Seven letters leave seven gaps on the way round. Does every gap hold one more note?
Choose an answer to unlock the play button.
Your guessTwelve steps, not fourteen. If every gap held a note, seven letters and seven more notes would make fourteen. There are twelve, so only five of the gaps hold one, and two hold none. Which two, and why? That's this lesson's story. (The letters run in order like the alphabet, so one note per gap was a fair guess.)
From Lesson 1: two questions, asked afresh
Recall from Lesson 1
Tap an answer one try each, then the reason
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Four words you'll meet before the first step
Semitone, tone, sharp and flat, cent
Tone or whole step
Two semitones.
Sharp sign and flat sign
One semitone up, and one semitone down.
Cent
A tiny unit for measuring the distance between notes. In the tuning MercuryPitch uses, a semitone is 100 cents.
Six steps, one object: a spiral, then a keyboard, then tiles, then a ruler
Twelve notes
Step 1 of 6
Fig. 1 The pitch spiral
Last note—
Steps0· Hz × 2
Drag to turn · tap a bead to hear it
A spiral of 37 beads from A2 to A5, three turns, every A on the same side. The five beads on each turn with no letter of their own start dim with a question mark and light once you hear them. Drag to turn it, or turn it a bead at a time with Turn left and Turn right; tap a bead to hear it. With the keyboard, the arrow keys pick a note, Enter or Space plays it, and Shift with Left or Right turns the spiral.
Fig. 3 The keyboard
Last note—
Unroll it, or tap a bead
Unrolled, every bead lands on a key: seven white keys and five black ones in every octave. Two keys played one after the other draw a bar between them, labelled with its number of semitones. Straightened, every key is the same width, one tile per semitone. With the keyboard, the arrow keys pick a key and Enter plays it.
A3 to G4
Fig. 4 The tile row
Thirteen equal tiles, A3 to A4, one per semitone. Lift out the five raises the five dark tiles: the seven letters then show five holes a tone wide, and two pairs, B and C, E and F, that touch, a semitone apart. With the keyboard, the arrow keys pick a tile and Enter plays it.
Fig. 5 One key, two names
The tile row with its names. Pick a white tile and press Sharp or Flat: an arrow steps one semitone up or down and writes the name it gives on the tile it lands on. A tile given two names gets one gold ring. With the keyboard, the arrow keys pick a tile and Enter plays it.
Answer the predict to unlock Sharp, Flat and the rare ones.Unlocked: pick a white tile, then press Sharp or Flat.
Fig. 6 The semitone ruler
Cents above A30
Frequency220.00Hz
Step 1 of 6
What's the very next note after A?
Start on A and step up to the very next note. You land on the bead between A and B. That step is a semitone, the smallest step a piano has, and the bead is a real note, one of the five with no letter of its own.
TryTap A3, then the bead after it, then B3.
NoticeTo your ear, the bead sits halfway between A and B, so A to B is two of these small steps.
Step 2 of 6
How many steps until we're back at A?
Keep taking semitone steps and count. From A3 you reach A4, one turn up the spiral, in twelve steps: seven letters, and five notes between them. In hertz each step is a little bigger than the last. To your ear, though, every step is the same size, so each one turns the spiral by the same amount. And twelve of them double the frequency, from 220 Hz to 440 Hz, which is exactly what an octave is.
TryPress Climb and watch the beads light. Then press Look down.
NoticeFrom above, one turn is a ring of twelve beads, evenly spaced like the hours on a clock.
Step 3 of 6
Isn't B to C the same step as C to D?
Unroll the spiral and every bead lands on a key: seven white keys and five black ones in every octave. Now look at B and C: there's no black key between them.
Predict
Which step is bigger, B to C or C to D, or are they the same?
Choose an answer to unlock the play buttons.
Your guess
C to D is the bigger step, two semitones; B to C is one. E to F is one too.
TryPress Straighten to draw every key the same width.
NoticeB and C touch, just like C and the black key above it.
Step 4 of 6
So where do the other five come from?
Two semitones make a tone, or whole step, like C to D with the black key between them.
Now the opening question has its answer. Five pairs of neighbouring letters (A–B, C–D, D–E, F–G, G–A) are a tone apart, and each of those gaps holds one note. B–C and E–F are only a semitone apart, so there's no gap to fill. Seven letters plus five: twelve notes.
TryPress Lift out the five. Then play ten rounds of Semitone or tone? below.
NoticeA tone always skips over one key; a semitone never skips any.
Semitone or tone?
Ten rounds
Each round plays one step inside A3 to A4. Was it a semitone or a tone?
Keys 1 and 2 answer while you are in the game.
Step 5 of 6
Why does one key have two names?
The five need names, and they borrow them from their neighbours. A sharp (sharp sign) means one semitone up; a flat (flat sign) means one semitone down. So the key just above C is C sharp, and the key just below D is D flat: the same key, two names. Musicians call that enharmonic. Both are right: the music around it decides which one is written. MercuryPitch's pitch line shows the sharp names, typed with a hash sign, like C sharp 4.
TrySwitch the names to Both. Then tap F and press Flat.
NoticeOne semitone down from F lands on E, a white key too: F flat is another name for E.
Step 6 of 6
How big is a semitone, exactly?
We measure it in cents. In the tuning MercuryPitch uses, every semitone is a hundred cents wide, so the twelve semitones of an octave make 1,200 cents, and a tone is 200. MercuryPitch's Singing tab measures in cents too. Its Input monitor names the nearest note, and a bar shows how far above or below it you are, up to 50 cents either way. Fifty cents is halfway; past that, the next note is nearer.
TryDrag the marker slowly from A3 up to A sharp 3.
NoticeAt 50 cents the nearest note changes from A3 to A sharp 3, just as the Input monitor does.
Go deeper
- Why twelve equal steps exactly double the frequency. Each semitone multiplies the frequency by the same number, the twelfth root of 2, about 1.0595. Twelve of those multiply to exactly 2: an octave. So the gap in hertz grows as you go up (A3 to A sharp 3 is 13.08 Hz, A4 to A sharp 4 is 26.16 Hz), while every semitone is still 100 cents. Your ear hears multiplying, not adding (Lesson 1).
- Where the cent comes from. The cent comes from Alexander Ellis, who used it in 1885 to compare the scales of different musical cultures. One cent multiplies the frequency by about 1.000578.
- A second meaning. Singers also say a note is “sharp” when it's too high and “flat” when it's too low: the same directions, for a miss of any size.
Cadenza: your solo, and any octave counts
Sing it
Merc holds an A, slides up one semitone, and comes back. Tavi sings it an octave up.
Your turn: play Merc's slide, then do the same on a hum or an “ooh”, starting on Merc's A or the A an octave up, whichever is comfortable.
Keep it quiet and gentle, never push, and stop if anything feels uncomfortable.
Start the guide once you've heard Merc's slide. It counts you in, then a line sweeps along Merc's path: follow it up one row, a semitone, and back. Nothing listens here and nothing is scored. It's just for you.
A3 · 220 HzReady when you are
Ripresa: the theme comes back, from memory
Quick check
Tap an answer one try each, then the reason
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Coda: the closing bars
Three lines to keep
- Seven letters and five notes in the gaps: twelve notes, twelve equal semitones to the octave.
- A semitone is one key to the very next, white or black; a tone is two. B–C and E–F are semitones.
- One key can have two names, like C sharp and D flat. MercuryPitch measures in cents: 100 to a semitone, in the tuning it uses.
One-sentence challengeExplain to a friend, in one sentence, why there's no black key between B and C.
Practise in MercuryPitch
Ear Lab's Leap
In MercuryPitch's Ear Lab, Leap plays two notes, going up or down, and asks for the distance. There a semitone is called a minor 2nd (m2) and a tone a major 2nd (M2). Leap mixes in all twelve distances, so listen out for those two. For an easier first drill, Contour asks only whether the second note went up, down or stayed.
Practise it free: mercurypitch.com/ear-lab, then tap Leap.
Free play every control of the steps, on one stage
Last note—
Steps0· Hz × 2
Drag to turn · tap a bead to hear it
The whole object at once: the spiral, the keyboard it unrolls into, and the row of equal tiles. The buttons above switch between them. With the keyboard, the arrow keys pick a note and Enter plays it.
A3 to G4
Cents above A30
Frequency220.00Hz
The same lesson, as a film: 7:19, captions on
Watch the episode
Chapters tap to jump
Read the transcriptfrom the captions
Season 1, fourteen lessons and a trailer: theory and voice, alternating
The season, mapped
Each lesson's closing question opens the next. Pick a lesson to light up the path of lessons it builds on.