Notation

The various forms of musical notation can be divided into 2 distinct categories. Nomenclatures use normal writing with letters, numbers or names for notes. Diagrams use pictorial or abstract symbols to represent notes. These categories can be further sub-divided. A nomenclature can show absolute pitch or relative pitch. A diagram can show absolute pitch or a method of fingering. The term notation is usually reserved for the former type of diagram while the latter type is called tablature. Ideally a system of writing music should be able to show note duration as well as absolute or relative pitch.

Letter Notation

This is an absolute pitch nomenclature.

Letters of the alphabet have often been used to stand for notes. One system has been more enduring than the rest. The first 7 letters of the European alphabet are used for the seven notes of a modal scale and are repeated at each octave. Different sizes and styles of lettering were used to indicate each octave. Also because of its modal roots there were two meanings for B requiring different script styles. The lower is now known as B-flat and the modern flat symbol comes from its original rounded style. The upper is B-natural and gave rise to the modern natural symbol. In Germany in Bach's time, a corruption of writing led to the letter H being used for B-natural, while B meant B-flat.

Although A was obviously originally the first note, C is now generally regarded as the starting point. Also superscript and subscript ticks or numbers are used instead of letter size and style to indicate which octave is intended. So C' is 1 octave higher than C and C" is 2 octaves higher while C, is one octave lower. This system specifies the position but not the duration of a note.

Hexachord & Tonic Sol-fa Notation

These are relative pitch nomenclatures.

In the first half of the eleventh century, Guido d'Arezzo developed a system of relative note pitches. He was a monk who taught other monks what to sing in church. Unlike the general population, monks were taught to read latin but not all learned to read music (though staff systems already existed). Guido chose the first syllables of the lines of a hymn that happened to start on consecutive notes. His hexachord system defined 6 relative notes: "ut re mi fa sol la". The original tune started on C, so the only semitone was in the middle (mi-fa). As the music moved out of range, the starting point for ut was moved to surround the next semitone. The seventh line of the hymn didn't actually use the seventh note added later. Also its name, "si", came from the initial letters of the words in the line rather than the first syllable.

Hexachord (plus 7th note) ut re mi fa sol la si

Hexachord shifted to sol ut re mi fa sol la

The tonic sol-fa system is derived directly from Guido's hexachord system and is still in use. The seventh note was included to complete the major scale and some renaming was done. The new names are more singable, having a uniform consonant plus vowel pattern. All consonants are different to allow abbreviation. The full names became: doh re mi fa soh la ti (though alternative spellings exist) and are abbreviated to d r m f s l t. The starting point or tonic is now only moved when the music modulates to a different key. Superscript and subscript ticks may be added to indicate octave register. Changed vowels on the names means sharp or flat notes. As well as bar-lines, punctuation (: and .) may be added to show rhythmic sub-divisions.

Latin Numeral & Name Notation

These are relative pitch nomenclatures used to define harmony rather than melody.

Starting from the first note of a scale, Roman numerals from I to VII are used for each note and the triad chord based on it. A small letter b or c follows a chord number to indicate first or second inversion (ie the bass note is not the numbered one). There are also names for the notes that describe their relationships.

Numerals I II III IV V VI VII

Explanation of Names subdom. submed. tonic mediant dominant

Staff Notation

This is a system of notation showing absolute pitch and duration that has evolved over time.

Staffs

The earliest form of staff (or stave) in the seventh century was a single horizontal line with note signs called "neums" written from left to right. Individual neums could be on "leger" lines above and below this. Then permanent parallel companion lines were added (sometimes in colour) to make note positions more obvious. Precise pitch was shown from the start but an imprecise indication of duration was added in the ninth and tenth centuries. The shape of note symbols and the number of lines and spaces varied a lot at first. A 4-line staff was very soon conventional for plainsong (the top line being C). The modern 5-line staff became conventional for nearly everything else in the seventeenth century. However, the original 1-line staff is still in use for untuned percussion.

A single staff can be used for most instrument parts. Keyboard instruments, such as the piano, require a treble and bass staff pair. When two parts are shown on one staff, usually the higher has note tails pointing up and the lower has them pointing down. A score has all parts shown at once on a page with the staffs lined up under each other. A short score has parts compressed with more than one part per staff - eg SATB voices on a treble-bass pair. A full open score has every part on a separate staff.

Clefs & Pitch

With the extension of instrument ranges came the need for a clef to specify the pitch of the staff. The treble or G clef was used for higher note ranges, eg violin. The symbol started off as a letter G coiled around the line for G above middle C (the second from the bottom). The bass or F clef was used for lower note ranges, eg cello. The symbol started off as a letter F coiled around the line for F below middle C (the second from the top). The C clef is centred on the line for middle C. It is called an alto clef on the central line and a tenor clef on the second line from the top. The viola is one of the few instruments to routinely use the C-clef (either form). The tenor clef allows violin players to play the viola because open strings occupy the same positions.

Treble (G) Clef
	B	C	D	E	F	G	A	B	C	D	E	F	G	A	B

Alto (C) Clef
	C	D	E	F	G	A	B	C	D	E	F	G	A	B	C

Bass (F) Clef
	D	E	F	G	A	B	C	D	E	F	G	A	B	C	D

These notes on different staffs are all at the same pitch - middle C.

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Notes & Rests

The original note symbols, called neums, were block-shaped. This is because they were hand-drawn with calligraphic pens. The size of a neum gave some indication of its relative duration. A small neum was 1/3 or 1/2 of the next larger one - depending on the rhythm required. In plainsong, the duration and accentuation of notes was defined by the lyrics. Most early written music was religious as the general population couldn't even write their own language.

For some reason, larger note values were gradually abandoned and even smaller ones invented. Since durations are relative rather than absolute this did not imply a genuine increase in tempo. The "breve" (= brief) was once one of the shorter notes, being 1/3 or 1/2 of the "long". It is now the largest recognised and not in common use at all.

The vagueness in relative duration grew worse and was eventually dropped altogether. Each successively shorter note or rest became exactly half of the previous one. Triple rhythms were dealt with in two ways. A dot added to a note or rest means that it has half its duration again. So it is equivalent to three of the next smaller size. Alternatively, if triplets are a localised phenomenon in a piece, a line with the number 3 on it is drawn over or under the notes to group them. This notation has been extended downwards to duplets in what is otherwise triple time and upwards to quadruplets and the large note groups used by Chopin.

Note and rest durations are now counted as fractions of a semibreve (= half a breve):

Note & Rest Symbols 1 1/2 1/4 1/8 1/16

Dotted Notes & Triplets = while = 3/8 2/8

A note of any relative duration can be constructed by tying several notes together. A tie is a curved line that runs from one note to the next. The constituent notes should follow the pattern of the underlying rhythm (though there are a few exceptions). So a tie is required to hold a note over from one bar to the next. There is no point in tying rests together!

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To get from relative to absolute duration, a tempo signature was invented. This shows the number of a given note per minute. As it is a speed or frequency, it must be inverted to get the duration. For example: d=60 means 60 minims per minute. So 1 minim = 1/60 minute = 1 second.

Time Signatures & Bars

As rhythm became more precise and important, bar-lines were added. These divide the music into bars of equal duration (usually). The strongest beat or emphasis in the music is at the start of each bar. Lesser accented beats during the bar depend on the rhythmic pattern.

Despite its name, a time signature indicates rhythm not time. This is the pattern of strong and weaker beats. The earliest time-signatures indicated the rhythm type by a circle or arc. The full circle (symbol of perfection) meant triple time (because of the trinity in Catholic religion). A broken circle or arc (looking like a C) meant duple time - 4 beats or 2 beats with a vertical line added. The original circle symbol has been abandoned but its arcs are still in use. The C symbol has become equivalent to 4/4 (sometimes called common time) and the divided C to 2/2. Note that these are not supposed to be shown as fractions and do not mean the same thing.

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When numbered time-signatures were invented, the semibreve was already the largest common note. The top number is the number of beats per bar (not all being strong ones). The bottom number is the size of the beats (eg 4 means quarters of a semibreve = crotchets). Music theory insists that a time-signature is not a fraction. So there is no dividing line between top and bottom numbers (except for the central staff line of course). However, it is the fraction of a semibreve occupied by each bar. Note that a time-signature can be an improper fraction for very good reasons and must not be reduced!

Crotchets are the closest thing to a standard in time signatures. So the bottom number is often 4, but 2 (minims) and 8 (quavers) are also common. The top number is the total number of beats per bar but also indicates the type of rhythm. 2 means simple duple time such as for a march. 3 means simple triple time such as for a waltz. 4 means simple quadruple time and is probably the commonest rhythm. This is a sort of duple time with a strong 1st beat, a fairly strong 3rd beat and weaker 2nd and 4th beats. 6 means compound duple time triplets (the main beats being 2 dotted notes or triplets). Many dances use this rhythm. 9 means compound triple time (the main beats being 3 dotted notes or triplets) and is relatively rare. 12 means compound quadruple time (the main beats being 4 dotted notes or triplets) and is less rare than 9. Swing dances may be written as 4/4 with a sharp dotted sub-rhythm but they are actually played as the softer 12/8.

Simple

Compound

Other top numbers have no conventional meaning and are an affectation of modern composers. Of these, 5 probably means a triple plus a duple. In a further extension of the system, more than one time-signature can be specified at the start. This means that the music alternates between different types of bar - yet another affectation.

Accidentals & Key Signatures

The original system of lines and spaces was based on the old 7-note modes or scales. These use only the white keys of a keyboard. The black keys were added later to fill the gaps where notes were a tone apart. Rather than make up new names and change the staff, the new notes were named after their nearest neighbours. At first there was no staff notation required as performers knew when to adjust a note for artistic reasons.

Accidentals are symbols added to indicate that a note is raised or lowered in pitch from normal. On a staff, they are written immediately before the note to be affected and on approximately the same level as it. In naming a note, the accidental comes after the note's base name. A sharp () means one semitone higher and a flat () means one semitone lower. A natural sign () cancels out any previous modification to a note so that it is at normal pitch.

	D	D#	D	Db

With the invention of equalised semitones came the abandoning of modes and a proliferation of accidentals. Any of the 12 equally spaced notes could be the main note or key of a piece of music. Key signatures were invented to absorb many of these accidentals. At the start of each staff, a key signature shows those required to create the correct tone and semitone pattern. This significantly reduces the number appearing next to notes. However, some accidentals still occur (eg when modulating to a new key). These include two new ones if the original key has many sharps or flats. Double-sharps () and double-flats () alter notes by a whole tone (two semitones). NB: music for trombones and some other instruments is still conventionally written with just accidentals.

The possibility of multiple names for the same note (especially the 5 new ones) led to duplication of keys and key-signatures. Key-signatures indicate major keys. A minor key uses the key-signature of the related major key - ie one that gives the least accidentals. The related major key is found by the third note of the minor scale, eg for Am the 3rd note is C. It is probably significant that this relationship shows up in the pentatonic scale. The only triads that can be made from its 5 notes are a related major and minor pair, eg CEG and ACE.

The key-signature of C is nothing (no sharps or flats are required). Am has the same key-signature but the piece may contain G# accidentals. Going up in fifths: G/Em has F#, D/Bm has F# & C# and so on. Going down in fifths: F/Dm has Bb, Bb/Gm has Bb & Eb and so on. While F# and Gb are the same pitch, their key signatures are very different. Which key of enharmonic notes should be chosen depends on the likely modulations to other keys.

C / Am	G / Em	D / Bm	A / F#m	E / C#m	B / G#m	F# / D#m	C# / A#m
C / Am	F / Dm	Bb / Gm	Eb / Cm	Ab / Fm	Db / Bbm	Gb / Ebm	Cb / Abm

Accidentals are not additive, each one replaces the previous state of the note. In music without a key-signature (eg trombone parts), each note must have its own accidental. The effect of the accidental does not persist beyond that note. In music with a key-signature, the sharps or flats of the signature persist unless changed. They apply to all octaves on the staff not just the line or space shown. An accidental on a note within the music shows a deviation from the stated key. It applies to all notes on the same staff line or space until replaced by another accidental or cancelled by a bar-line. Only tied notes carry the effect of an accidental beyond a bar-line. An accidental does not affect notes at octaves above or below, though this is a common mistake to make.

Other Symbols

There are many additional symbols above and below a staff and attached to notes. Some show unusual accentuation or decoration of individual notes. Phrase and breath marks group and separate notes. Section closes, repeat marks and other flow direction symbols show the structure of the music. There are notations for immediate or gradual changes in tempo, volume or pitch. A verbal description of how the music should be played may even be written on a staff (in any language).

Legato	Staccato	Staccatissimo	Marcato	Martellato	Tenuto	Fermata
Breath Mark	Down Bow	Up Bow	Mordent	Inverted Mordent	Turn	Inverted Turn

Coda		Bar Repeat		Segno		Section Repeats

Lute Notation

This is a tablature showing the position of fingers on the strings of the instrument.

It looks like a 6-line staff but each line represents a string rather than a note position. Both melody and accompanying harmony fit on the same diagram. Notes are shown as small letters written immediately above the lines from left to right. These letters indicate the fret position on the string not the name of a note to be played on that string. So 'a' is an open string, 'b' is the first fret, 'c' is the second and so on. Notes may have tails above the "staff" to indicate relative duration more precisely than just their order on the staff can. Bar-lines may be added.

Guitar Notations

The first type is a nomenclature that shows harmony.

Chords are named for their tonic note and any modifications to a basic triad. The first 7 letters of the alphabet give the basic note. Any sharp or flat change to this comes next. The letter m is added for a minor rather than a major triad. Any numbers show additional or replacement notes from the scale of the named key. The tonic is still number 1 but the numbers are modern not Roman. The number 7 always means the minor 7th unless maj7 is specified. The number 4 as in sus4 means the 4th note replaces the 3rd instead of being added. Another letter in brackets or after a forward slash means that this note is the base note of the chord instead of the expected tonic. Examples of chords are: G, Am, F#m, Bb, E7, Dm6, Csus4, Fmaj7, C/E.

The second type is a tablature that shows finger positions on frets.

Unlike lute tablature the strings are drawn vertically and each diagram is a separate entity. The diagrams are positioned over a staff showing the melody (usually vocal with lyrics). This is because the notation shows chords to be strummed as an accompanying harmony. Blobs indicate finger positions on the frets of the strings to be used as some may not be. Frets are counted from the top down. A hollow blob marks open strings. The string tunings are low to high from left to right: E A D G B E. Chord nomenclature should be combined with this tablature (the name being written above each diagram).

The third type is modern staff notation. This is used for classical guitar pieces that are similar to lute pieces. The guitar plays both melody and accompanying harmony. By convention, notes are shown an octave above their actual pitch.

Woodwind Notations

These are tablatures that show fingering with a picture of the holes of the instrument. They are used in self-help tutorials rather than in genuine music. Leaflets are sometimes included with an instrument - eg with ocarinas, flageolets or recorders. Basically, if an instrument is cheap, the purchaser is assumed not to want to pay for a teacher too.

Figured Bass

This is normal staff notation of a bass line with numbers (figures) written under each note. The numbers indicate the harmony to be constructed above the note. A keyboard or harp player would have to work out the missing notes of the chord. The top number indicates the interval of the top note from the given bottom one. Any number below this is the interval of the next to top note from the bottom one. Accidentals may be added (eg to change major into minor or vice versa). A line between successive figurings mean that one or more notes of the previous chord are held into the next.

5 over 3 or nothing at all means a normal triad in root position (tonic at the bottom). 6 over 3 or just 6 means the first inversion (median at the bottom). 6 over 4 means the second inversion (dominant at the bottom). 7 means the dominant 7th chord in root position. 6 over 5 is its first inversion, 4 over 3 is its second inversion and 4 over 2 means the extra note is at the bottom.