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Musical Notation

A guitar player has several alternative notational systems available: tablature, chord symbols, chord boxes and various forms of shorthand. Each has its strengths, but also its weaknesses. The main weakness is that tablature and chord boxes are idiosyncratic to the guitar and require knowledge of how the guitar is constructed and tuned. Furthermore, tablature only specifies which frets and strings to play, it is difficult to notate rhythm, the relative duration of notes. Therefore, these alternative notational systems are at best memory aids.

Staff notation solves both these problems in one go. It is a self-contained notational system where you can notate pitch, duration, articulation, dynamics and many other aspects of music. It is also universal and has been relatively unchanged for hundreds of years: you can easily pick up one of Bach's original manuscripts and play from it, just as a musician in the year 2310 will likely (hopefully?) be able to play from your manuscript.

This article is to be considered as constantly under construction. Omissions are to be regarded as me not having got there yet.

The Staff

Lines

The most basic part of musical notation is the staff, which is a collection of five lines with four spaces in-between:

Blank musical staff

Notes are placed on any of the lines, or in any of the spaces, including on the edges of the staff:

Staff with notes

Notes are played from left to right; if two notes occupy the same vertical space they are to be played simultaneously. Lower notes are placed towards the bottom of the staff, higher notes towards the top.

If the staff isn't wide enough, temporary lines and spaces can be placed outside of the staff proper; these are called ledger lines:

Staff with ledger lines

Clefs

The relative pitches of notes are established by putting what's called a clef at the start of each staff. A clef fixes a certain pitch to the line where it is placed. There are three kinds of clefs:

G clef G clef
F clef F clef
C clef C clef

The G clef fixes the position of middle G, the F clef bass F and the C clef middle C. Clefs can be positioned on any line, but the common practice is to center the G clef on the second line (treble clef), the F clef on the fourth line (bass clef), and the C clef on either the third (alto clef) or fourth line (tenor clef):

Treble clef Treble clef
Bass clef Bass clef
Alto clef Alto clef
Tenor clef Tenor clef

Here are examples of middle C using the four clefs:

Middle C with four different clefs

Alternate clefs may appear at any time in written music, most often for longer passages that would be notated with too many ledger lines for easy reading.

In certain types of scores, most usually vocal music, clefs can be transposed, i.e. the notes sound an octave lower or higher than notated. Instead of writing 8va or 8vb throughout the entire piece, an 8 is added to the clef. If the 8 is added below the clef, the notes sound one octave below written, and vice versa.

Transposing instruments are never written with transposing clefs.

Pitch Standard

Staff notation is not tied to any particular temperament or tuning, nor are the notes, even those fixed by clefs, tied to any particular pitches. Therefore, it has been decreed by international standard (ISO 16:1975) that middle A, i.e. the A above middle C, should sound at 440 Hz.

The Notes

Notes and Beams

Notes take on various shapes depending on their relative duration. Notes fall in an exact 1:2 ratio to the next shorter and longer note values, so that a whole-note equals two half-notes equals four quarter-notes and so on.

Note values

I use American terminology (hopefully) consistently. In British parlance, note values have different names, stemming from mensural notation, the medieval precursor to traditional music notation:

AmericanBritish
Whole noteSemibreve
Half noteMinim
Quarter noteCrotchet
Eighth noteQuaver
Sixteenth noteSemiquaver
Thirty-second noteDemisemiquaver
Sixty-fourth noteHemidemisemiquaver

Stems point upwards on notes up to and including the second space, downwards from and including the third space. Notes on the center line can point either way:

Note stem orientation

Flags can be tied together as beams, with the majority determining the orientation:

Note beams

Ties and Dots

To lengthen a note, it can be tied to the next note, thereby adding their time values. This second note is not struck. The two tied half-notes in the following example are exactly equivalent to a whole-note:

Tied notes

Dotting a note is the same thing as tying it with a note of half its time value (1 + 1/2). This can be extended by double- (1 + 1/2 + 1/4) or even triple-dotting (1 + 1/2 + 1/4 + 1/8):

Dotted note and its equivalent Double-dotted note and its equivalent

There is no rule that says when one should use ties or dots, but a dotted note may not extend across a bar line, a tie must be used:

Syncopated 8th-note

Tuplets

Tuplets are divisions of a note that fall outside the normal 1:2 ratio. The most common variety of tuplet is the triplet, which has 2/3 the time value of a regular note. Hence, three triplets occupy the same space as two regular notes of the same value:

Quarter- and eighth-note triplets

Unflagged and -beamed notes use a bracket, whereas beamed notes simply put the number over the beam to indicate tuplets. In printed music, in long passages played solely with triplets, the number may be omitted after a measure or so.

Uneven tuplet numbers are considered to be played against the next smaller factor of 2. E.g. 5 notes are played against 4, 7 also against 4 but 9 against 8. Even numbers often mean lengthening of beats in triple or compound meters, which can alternately be expressed by ties or dots.

Rests

Rests are instructions not to play and follow the same basic principles of subdivision as notes. Note how the flags on the 1/8- through 1/64 rests correspond to those of the 1/8- through 1/64-notes:

Rest values

A whole-note rest can be used as a general one-measure rest (irrespective of time signature). Rests cannot be tied, but they can be dotted. They also cannot extend past the bar line, a new rest symbol is needed in that case.

Accidentals

Staff notation contains spaces for the natural notes: C, D, E, F, G, A and B. Enharmonic notes are notated with accidentals: flat, sharp, double-flat, double-sharp and cancelled with the natural sign, as shown below:

Accidentals

An accidental applies to all notes on that line or space until the next bar line, unless cancelled by a natural sign:

Accidentals and naturals

Key Signature

The relative keys of C major and A minor require no enharmonic notes, hence there are no sharps or flats on the staff. All other keys require the use of one or more sharps or flats; the following is a passage in E major:

E major written with accidentals

This can quite obviously get rather unwieldy. However, there is a way around it. You simply take all the required accidentals and put them at the start of each staff:

E major key signature

The two preceding examples are exactly equivalent—but which would you rather sight-read?

The collection of accidentals at the start of the staff is called the key signature. These accidentals apply throughout the piece unless temporarily cancelled by other accidentals:

F sharp and F natural in key signature for G major

In the preceding example, the first three notes are all F sharps, because the key signature applies to all occurrences of F and not just the line where it is placed. The second measure contains three F naturals—note how individual natural signs are required, because an accidental only applies to the one line/space.

Accidentals can occur in spite of a key signature, even on the spaces/lines that are affected by the key signature. These are called cautionary accidentals are can be used to clarify potentially ambiguous situations:

Cautionary accidental; F natural followed by F sharp in the next measure

Accidentals are not cumulative, which is why in the preceding example, the F sharp in the second measure is not an F double-sharp.

Temporary modulations to other keys are usually written with accidentals, but permanent or more wide-ranging modulations might be aided by a new key signature in the middle of the piece. In such cases, a double bar line is written, followed by the new key signature. If the new key signature contains fewer sharps or flats, natural signs are used to cancel the unneeded signs:

Cancellation of A major into A minor

Here are the key signatures for 15 major keys and their relative minor keys:

C major/A minor C major
A minor
F major/D minor F major
D minor
G major/E minor G major
E minor
B flat major/G minor B flat major
G minor
D major/B minor D major
B minor
E flat major/C minor E flat major
C minor
A major/F sharp minor A major
F sharp minor
A flat major/F minor A flat major
F minor
E major/C sharp minor E major
C sharp minor
D flat major/B flat minor D flat major
B flat minor
B major/G sharp minor B major
G sharp minor
G flat major/E flat minor G flat major
E flat minor
F sharp major/D sharp minor F sharp major
D sharp minor
C flat major/A flat minor C flat major
A flat minor
C sharp major/A sharp minor C sharp major
A sharp minor

The keys with seven accidentals in the key signature are seldom seen because they're enharmonically equivalent to other keys that use fewer accidentals. C sharp major (7 sharps) equals D flat major (5 flats) and C flat major (7 flats) equals B major (5 sharps). G flat and F sharp both use six accidentals, so there it's either way.

In other clefs, key signatures are written as follows, making sure that no accidental is placed on a ledger line:

Flat key signatures Sharp key signatures

Tempo and Time Signature

Time Signature

In music notation, measures (or bars) are indicated by vertical thin lines:

Bar lines

The length of each measure is indicated at the start of the piece by the time signature. The bottom number indicates which note value is the basic note value of the beat, the top number tells us how many such notes are to be played per measure.

2/4 time

In the above example, the time signature means that each measure must be filled out by notes equalling the value of two quarter notes (2/4 = 2 x 1/4).

4/4 time is also known as common time and is frequently simplified into the symbol C: [1]

Common time

2/2 time, or alla breve time, has a similar symbol with a strikethrough:

Alla breve time

Tempo

The absolute time values of notes are defined by setting the tempo. Traditionally, tempi are expressed using Italian words, e.g. Allegro (fast), Andante (slowish, lit. "walking"), Presto (really fast) or Adagio (really slowly).

The tempo can also be specified in more detail by stating the note value indicated in the time signature and how many such beats should occur per minute (BPM: beats per minute).

In compound triple meters, the beat is often felt on a higher note value, so in such meters, the metronome mark is specified using a dotted note of the next longer note value. For example, in 6/8, 9/8 and 12/8 time, the tempo is often set against a dotted quarter note.

Guidelines for Notating

In addition to the above, there are general guidelines for notating music. Unless a certain effect is sought, they can be summarized quite easily: no unnecessary complication. Music notation is supposed to be quick and easy to write and unambiguous to interpret, especially on the fly.

Spelling

Correct spelling is important. Notes have many names (35 names for 12 notes!) in order to make them fit in widely different contexts. A G might be notated as an F double-sharp as a leading-note in G sharp minor:

G sharp minor

An A might be renotated as a B double-flat in a diminished seventh chord resolving into an A flat triad:

D flat major

An F is notated as an E sharp as a leading-note in F sharp minor and major:

F sharp minor

Ties, Rests and Beams

Notes and rests should ideally not extend across beats (measure 1) unless the note picture becomes clearer by not tying (measure 2):

Off-beat ties

Beams should be used to group notes that belong to the same beat:

Grouped beams

Note Values

As the absolute durations of notes are determined by setting the tempo, it might be a relevant question why there are so many flavors of triple time: 3/2, 3/4, 3/8 and so on. Are these for different tempos?

Yes and no. In the old days, before the invention of the metronome, it was common practice to associate certain Italian tempo markings with certain note values as compared to the human heartbeat (60–80 bpm). Thus, in a slow tempo such as Adagio, one heartbeat might equal a quarter note, whereas it would equal a half note in a quicker tempo such as Allegro.

Nowadays, composers can set the tempo down to the last detail via electronic means. It is not necessary to associate certain base note values with certain tempi. The main principle of music notation can be a guiding principle: clarity. Fast passages in slow tempos can mean lots of flags and beams, which is why it can be important not to use too small base note values.

1. This comes from the late medieval preference for triple meters, due to the mystical connection with the Holy Trinity. Triple meters were indicated with full circles, "imperfect" meters such as duple meters with incomplete circles. [Go back]