Enharmonics and double accidentals
Recognise notes that sound the same but are written differently, and read double sharps and double flats.
One key, two names
The black key between C and D is both C♯ (C raised a semitone) and D♭ (D lowered a semitone). One sound, two ways to write it. Such notes are called enharmonic: they sound the same but are spelled differently.
Which name to use depends on the context, not the sound: the key the music is in, or the interval being built.
Five black keys, each with two names: C♯ and D♭, D♯ and E♭, F♯ and G♭, G♯ and A♭, A♯ and B♭
C♯4 and D♭4, then F♯4 and G♭4: they sound alike
You have met this with intervals: a major third above A is C♯, not D♭. They sound the same, but a third spans three letters (A, B, C), so the note must be some kind of C.
Practice: Another name for C sharp
Enharmonics on the white keys
There are no black keys between E and F, or B and C. So E♯ is the key F, F♭ is the key E, B♯ is the key C and C♭ is the key B. These spellings are rare, but they occur in keys with many sharps or flats.
E, F, B, C: each of these white keys also has a name with an accidental
Practice: E sharp
Practice: Read notes with accidentals
Double sharps and double flats
A double sharp 𝄪 raises a note by two semitones, a whole tone. A double flat 𝄫 lowers it by a whole tone. F♯♯ sounds like G, and B♭♭ like A.
Double accidentals are needed for the same reason as enharmonic spellings: so that a note is called by the right letter in a key or an interval.
F♯♯4 sounds like G4, B♭♭4 like A4