In music, flat means lower in pitch. It may either be used generically, meaning any lowering of pitch, or refer to a particular size: lowering pitch by a chromatic semitone. A flat is the opposite of a sharp (♯) which raises pitch by the same amount that a flat lowers it.
The flat symbol (♭) is used in two ways: It is placed in key signatures to mark lines whose notes are flattened throughout that section of music; it may also be an "accidental" that precedes an individual note and indicates that the note should be lowered temporarily, until the following bar line.
Pitch change
The flat symbol is ♭ is a stylised lowercase ‘b’ , derived from Italian be molle for "soft B" and German blatt for "planar, dull". It indicates that the note to which it is applied is played one semitone lower, or in modern tuning exactly 100 cents.[1][2]
In traditional and modern microtonal temperaments the size of sharps or flats (chromatic semitones) is normally smaller than the size of the diatonic semitones found between E and F or B and C. In those tuning systems, the size of the shift made by the ♭ symbol usually conforms to the smaller-sized lowering of pitch;[a] however, for some tuning systems it may instead be replaced by a different symbol for raising and lowering pitch, depending on the author's preference and the intricacy of any microtuning involved.[b]
Starting with no sharps or flats (C major), adding the first flat (B♭) indicates F major; adding the next (E♭) indicates B♭ major, and so on, backwards through the circle of fifths.
Some keys (such as C♭ major with seven flats) may be written as an enharmonically equivalent key (B major with five sharps in this case). In rare cases, the flat keys may be extended further:
F♭ → B → E → A → D → G → C
requiring double flats in the key signature. These are called theoretical key signatures, based on the impracticality of their use, rather than the simpler, equivalent key in 12 TET. This principle applies similarly to the sharp keys.
Key signature example
The staff below shows a key signature with three flats (E♭ major or its relative minorC minor), followed by a note with a flat preceding it: The flat symbol placed on the note indicates that it is a D♭.
In 12 tone equal temperament( 12 TET )[c] lowering a note's pitch by a semitone results in a note that is enharmonically equivalent to the adjacent named note. In this system, B♭ and A♯ are considered to be equivalent. In most tuning systems, however, this is not the case.
As a temporary accidental
When used as a temporary accidental sign, the flat symbol is placed to the left of the note head.
Temporary accidentals apply to the note on which they are placed, and to all subsequent similar notes in the same measure and octave. In modern notation they do not apply to notes in other octaves, but this was not always the convention. To cancel an accidental signature later in the same measure and octave, another accidental such as a natural (♮) or a sharp (♯) may be used.
Related symbols
A double flat () lowers a note by two semitones, or a whole step.
A quarter-tone flat, half flat, or demiflat indicates the use of quarter tones; it may be marked with various symbols including a flat with a slash () or a reversed flat sign (). A three-quarter-tone flat, flat and a half or sesquiflat, is represented by a demiflat and a whole flat ().
The symbols -, ↓, , among others, represent comma flat or eighth-tone flat, or a quarter of a flat (not to be confused with the larger quarter tone).[d]
Although very rarely used, a triple flat () can sometimes be found.[3] It lowers a note three semitones, or a whole tone and a semitone.
The symbol of a quadruple flat,[e] or beyond, could be used but would be extremely rare in ordinary temperament.[4]
Historically, raising a double flat to a flat would be notated using a natural and flat sign (♮♭) or vice-versa (♭♮) instead of the conventional flat sign (♭). In modern notation the leading natural sign is often omitted.
To allow extended just intonation, composer Ben Johnston uses a flat as an accidental to indicate a note is lowered 70.6 cents.[5]
In environments where the symbol is not supported, or in specific text notation, a double flat is sometimes written as ♭♭, bb, etc. Likewise, a triple flat can also be written as ♭♭♭, etc.
Footnotes
^
For example: In quarter-comma meantone a flat always lowers a note's pitch by 76.05 cents ; in just intonation a flat normally lowers a note's pitch by 70.57 cents. Compare those to the somewhat excessive 100 cents used in 12 TET. In Pythagorean tuning the size of a flat is a whopping 113.7 cents. In well temperaments a flat is two or more different sizes, depending on the temperament and where the starting, unflattened note sits on the circle of fifths.
^ ab
For example, in 53 TET sharps and flats have two or three different sub-levels, and notation for flattening notes varies, but usually involves several different symbols; one of the sets of 53 TET flat symbols is ♭ (67.9 cents), (45.3 cents), and ↓ (22.6 cents), used both separately and in combinations.
^12 TET is the predominant system of tuning in Western music.
^
The size of the lowering of pitch by a "comma" varies, depending on the tuning system; it is normally 21 + 1 / 2 cents but can vary between 20–25 cents.[b]
^
A quadruple flat ( ) lowers a note by four semitones or two whole tones in standard tuning.
See also
Sharp (music) – Accidental raising the pitch of a note by one chromatic semitone (♯)
^Fonville, J. (Summer 1991). "Ben Johnston's extended just intonation – a guide for interpreters". Perspectives of New Music. 29 (2): 106–137. ... the 25 / 24 ratio is the sharp (♯) ratio ... this raises a note approximately 70.6 cents.(p 109)
MUSICAL SYMBOL DOUBLE FLAT 
