Accidentals
The black keys have no names of their own: they use the seven names with a sign added. Those signs are accidentals, which raise or lower a note without changing its name. Here you meet the five accidentals and learn how far each one reaches.
A surname does not change who someone is: Maria is still Maria, and the surname only says which Maria. Accidentals do the same for notes. They are signs that raise or lower a note by a semitone or a tone, and the note keeps its name; it only gains a qualifier. An F raised by a semitone is still an F, and is now called F sharp.
That is how the black keys of the piano get their names. They have none of their own; they use the usual seven names with an accidental.
Sharp and flat
A sharp (♯) raises a note by a semitone. A flat (♭) lowers a note by a semitone.
Here is F and, just to its right, the black key one semitone above: F♯. Now the other way, starting from B and going down a semitone:
The black key to the left of B is B♭.
Notice what follows. The black key between F and G is a semitone above F and, at the same time, a semitone below G. It can be called F♯ or G♭, depending on which note you start from. Two names for one sound is the subject of enharmonic equivalence, which has a topic of its own.
An accidental does not mean a black key
A sharp raises a note by a semitone, whatever key happens to be there. There is no black key between E and F, remember? So E♯, E sharp, lands on a white key: the same one as F.
In the same way, C♭, C flat, is the white key of B. These names look odd, but they do turn up in real music, and for a good reason: on the staff the note stays in the place of the name it has, E sharp on the line or space of E, and in some contexts that is what matters.
Double sharp and double flat
Sometimes a note has to be raised or lowered by two semitones, a whole tone, without changing its name. For that there is the double sharp (𝄪), which raises a tone, and the double flat (𝄫), which lowers a tone.
F𝄪, F double sharp, sounds on the key of G.
They are the least common of the five. Med also records triple sharps and flats, and notes that they are hardly ever used (Med 1996, ch. V).
The natural
The fifth accidental is the natural (♮). It cancels any of the other four and returns the note to its plain pitch. So it raises or lowers depending on what came before: after a flat, a natural raises; after a sharp, it lowers.
The first F has a sharp. The second, with the natural, is plain F again. Listen: the second F sounds a semitone lower than the first.
Written before, said after
We say "F sharp", with the name first and the accidental after. On paper it is the other way round: the accidental comes before the note, on the same line or in the same space. Blatter gives the simplest possible reason: a player needs to see the accidental before playing the note, not after (Blatter 2007, art. 2).
How far an accidental reaches
An accidental written in the course of the music does not apply only to the note it sits beside. It applies to every note of the same name and the same pitch until the end of the measure, the stretch between two vertical barlines.
In the first measure the second F has no sign at all, and still it is sharp: the first F's accidental still holds. After the barline it has lapsed, and the Fs in the second measure are plain. Lacerda sums up the rule: if the accidental should carry on into the next measure, it has to be written again (Lacerda 1966, ch. XVIII). The exception is a note tied across the barline, which carries its accidental with it.
There is a second limit: the accidental applies only to the note in that octave.
The sharp on the first F does not reach the F an octave higher. To raise that F as well, it needs a sharp of its own, as the third note has.
Key-signature accidentals
When a piece uses the same accidental all the way through, repeating the sign in every measure would be tiresome. So it can be written once, right after the clef, at the start of every staff. Accidentals written there make up the key signature.
With a sharp on the F line at the start, every F is sharp without a sign beside the note. And unlike an accidental in the course of the music, one in the key signature applies in every octave: the high F is sharp too. Since each key signature belongs to a key, it has a topic of its own.
The cautionary accidental
Sometimes the rule is satisfied and reading can still stumble. After a measure with F sharp, the F in the next measure is already plain by the rule, but the eye still remembers the sharp. In such cases a cautionary accidental is written: a natural that changes nothing and only warns. To draw even more attention to it, it can be put in parentheses. Lacerda also recommends the warning when an accidental appears at the start of a long measure and the note only comes back near its end (Lacerda 1966, ch. XVIII).
What comes next
With accidentals every key on the piano has a name, and several have more than one: that is the subject of enharmonic equivalence. Key signatures organise the fixed accidentals by key. And intervals, which measure the distance between two notes, depend on knowing exactly how many semitones each accidental adds or takes away.
References
- Blatter, Alfred. 2007. Revisiting music theory: a guide to the practice. New York: Routledge.Consulted: art. 2
- Lacerda, Osvaldo. 1966. Compêndio de teoria elementar da música. 3rd ed. São Paulo: Ricordi Brasileira.Consulted: ch. XVIII
- Med, Bohumil. 1996. Teoria da música. 4th ed. Brasília: Musimed.Consulted: ch. V