Chapter 3 of the Outline of basic music theory – by Oscar van Dillen ©2011-2020

The beginner’s learning book can be found at Basic elements of music theory.

Overview of chapters:

Chapter 1: Introduction
Chapter 2: Sound and hearing
Chapter 3: Musical notation
Chapter 4: Basic building blocks of melody and harmony
Chapter 5: Consonance and dissonance
Chapter 6: Circle of fifths and transposition
Chapter 7: Concerning rhythm, melody, harmony and form
Chapter 8: Further study

## Introduction to notation

Music is a time-art; music consists of sound and silence, performed by musicians. In musical notation therefore, symbols for both sound and silence are employed, set to a reading basis representing the flow of time. Although an experienced musician is able to almost read music notation as one reads a book, the actual sound effect of a musical score can only be fully appreciated by hearing. Notation is basically an instruction for performance, and less so an actual representation of the sound produced.

When evaluating the abilities in reading language some people may turn out to have a from of dyslexia, likewise it is also possible when evaluating the abilities in reading sheet music, some people may turn out to have dysmusia, at least this is both a phenomenon and a term currently being proposed and investigated.1

## Notation of time and rhythm

### Symbols for notes and rests

To represent different durations of tones, different note symbols were developed. The normal ratio of durations is 1:2, each smaller, faster note being twice as fast, or: half as long, which amounts to the same result, as the larger one. The system begins with the whole note. The smaller values then are the half note, quarter note, eighth note, etc., always halving the previous value. Older terms for these note symbols are still in use in some countries, such as “quaver”, “semi-quaver” and “crotchet”, but I consider these to be both confusing and outdated, so I prefer to use the numerical values and names.

Nevertheless, a simple table comparing both systems of naming is given here:

 International numerical nomenclature Traditional nomenclature whole note (1) semibreve half note (1/2) minim quarter note (1/4) crotchet eighth note (1/8) quaver sixteenth note (1/16) semiquaver thirty-second note (1/32) demisemiquaver sixty-fourth note (1/64) hemidemisemiquaver one hundred and twenty-eighth note (1/128) quasihemidemisemiquaver

Below are the notation symbols for most of these values:

note values

A similar system of symbols with relative durations is used for musical silences, called pauses or rests.

rest values

The whole rest can be used for two purposes:

1. A true whole rest, with the exact value of a whole note;
2. A full bar rest, not literally corresponding to and therefore independent of time signature.

### Meter

Meter is a usually simple repeating cycle of rhythm originating from poetry. Rhythms are often linked to meters which are also used in poetry. In Europe, these can be traced back to the ancient Greek meters, some of which have a binary strucure:

• iamb ᴗ –
• trochee – ᴗ
• spondee – –
• pyrrhic ᴗ ᴗ

others are ternary:

• anapest ᴗ ᴗ –
• dactyl – ᴗ ᴗ
• amphibrach ᴗ – ᴗ

In Ottoman as well as in classical Arabic poetry2 on rhythm and meter, a related but more complex system of 16 different meters was used, which explains why the rhythms in the music linked to these traditions are also more complex than those that are common in the West.

Example of text and meter:3

example of meter in poetry

There is a strong link to language and poetry in most of the world’s musical traditions, and such naturally leads to the use of meter in music. Meter in music is commonly represented by time signatures in notation. With the use of a time signature, it becomes mandatory to visually divide the notes into groups separated by vertical lines. Such groups are called bars. Each bar within one time signature has the exact same duration, with no notes nor rests more nor less than its full duration.

Meter in music is represented by time signatures.

### Time signature and bar

A time signature consists of two numbers, one above the other, without a horizontal line between them (it is not a fraction). The upper number indicates the number of beats, the lower number represents the note value used for one beat. Although time signatures using the quarter or eighth notes as basis are more common, theoretically many more are possible, and indeed sometimes used.
The most common time signatures are two-four, three-four, four-four and six-eight. Eighth and smaller notes can now be grouped and visually linked together per beat. In grouping these smaller note-values thick horizontal lines, called beams, are employed. These are double beams in the case of sixteenth notes, triple beams with thirty-second notes, etc. It is also possible to thus beam together notes of different values, as long as the beamed groups are a clear representation of the beat-structure. Further details on beaming will be explained later in this outline.

With the use of time signatures, the notes become grouped in units called bars or measures, each group separated from the next by a vertical line, called the barline.

Any grouping of notes that is more complex than the time signature within it is notated represents a rhythm. Meter itself may be considered a rhythm, a simple rhythm, but rhythm is generally not a meter.

A longer sequence of rhythmical values may constitute a phrase.

### Binary time signatures

Binary time signatures are time signatures that have two (sub-)beats per beat, and can be recognized by the top number being 2, 3 and 4. Usually the lower number is 4, pointing to the 1/4 note (sometimes the 1/2 note occurs in older music). The following examples show how such time signatures can be used in their most simple form:

### Dots

Note that the last bar of a piece always ends with a double barline. Note also that a dot is used here to make a three-part note out of a two-part note: any dot adds 50% to its duration. A half note is the same as two quarter notes which is two beats. The dotted half note however equals three quarter notes, which in these time signatures equals three beats. Dots can be equally applied to notes and rests.

The following examples that also include rests show how these dots can be used for more complex rhythms:

### Ternary time signatures

Ternary time signatures are time signatures that have three (sub-)beats per beat, and can be recognized by the top number being 6, 9, 12; numbers of the multiplication table of 3, except 3 itself . (Though higher and lower valuses are possible, most often the lower number is 8, pointing to the 1/8 note; examples of these can be seen below:

Six-eight may be ternary per beat, it is in itself a binary time signature, as it has two beats per bar.

Note that with ternary beats, it is the dotted notes that represent a one-beat note!

### Ties

So far we have seen note-values which fit neatly into a time signature, and durations which are also corresponding to the basic structure. But not everything can be notated this way. Often it will be necessary to use more irregular divisions and durations. The use of ties allows for more flexibility in connecting notes. Two notes tied together become one value, and are performed as one tone.

Note how the second dot adds another 25%. The durations thus represented make sense only when notating sustained tones, such as of singers or wind instruments. For percussive music, such ties are normally not used, and this very same rhythm can be notated as below, with rests instead of ties:

The tie is notated from one note head to the next note head, it cannot tie several notes together with one symbol only. A tie cannot ever connect two different pitches, or tones, only two that are identical (but a slur can). The tie is therefore a rhythmical symbol.
Still, graphically the tie looks somewhat like a slur, but this is a sign to represent not the rhythmical, but the uninterrupted connection of various different tones being sung, played or bowed in one go. The difference is thus that ties are always used between just two notes representing exactly the same pitches or tones. The slur will be shown later, in the section on articulation.

As the relative silences of rests are identical, rests are never tied together!

### Tuplets

Finally, to complete the rhythmic possibilities of musical notation, what are called tuplets allow for even more subtle subdivisions, and even more variations per beat or beat-group become possible.

A tuplet is a temporary deviation from the theoretically normal division or subdivision within a time signature. Tuplets can be notated in various ways, with one number or a ratio (used especially for more unusual ratios). Depending on whether the group is connected, square brackets can be used to indicate exactly which are the notes and durations concerned. Tuplets always change from the time signature (sub)divisions to another regular (sub)division, which could also be represented by time signature changes. Tuplets are used for temporary changes in rhythm or when time signature changes would become too complicated for practical reading. The most common tuplet is the triplet, allowing for three against two notes.

Other examples are the quadruplet (four against three), or quintuplet (five against four or three). It is also possible to created nested tuplets: tuplets within tuplets. When writing such things, musicians often overlook simpler ways of writing the exact same rhythm. As notation is intended for practical use by performers, overcomplicated notation tends to create confusion and should be avoided. Besides, very complex ratios are hardly if ever performed mathematically exact, except by percussionists. The following slightly complex example contains the same rhythm thrice, notated in three different ways, ranging from simple to complex notation:

Of course, in these different examples, a slightly different counting and even tempo and feel are used. The indication of tempo in notation is generally important, especially when the sheet music is to be studied in situations without direct contact to the writer thereof.

### Basic tempo indication

Basic tempo indications are done with the one-beat note-value, an = sign and the number of beats per minute (also called bpm). The example above could then be notated in the following way, to produce three times the exact same rhythm, because of the tempo and counting adjustments notated:

Note that when changing the one-beat note, the equals sign = actually means becomes.

More on tempo indications can be found in the section on other notation symbols.

### Correct rhythmical notation

But back to basics now. As stated above, it is mandatory that the structures of the time signatures remain explicitly visible in notation. This means that connections through ties and vertical lines with shorter values must follow the beats: it is a rule that rhythmic notation must always show the beats, the natural accents pertaining to the structure of the time signature.

The first bar fails to show the third beat, which is the middle accent of the time signature. Such and similar notation is rather unpractical and will easily lead to mistakes in performance. The second bar shows all the beats and is technically correct. The third bar groups the beats evenly in two groups of two and is used very often in practice, especially in faster tempos, as more of the ‘feel’ of the bars as a whole is represented in this notation. It is therefore very important to write rhythm correctly, not only will incorrect notation lead to performance mistakes, but it also can cost valuable rehearsal time.

Ritten stough spelt inca rectly maykes reeding tuff…

So similar to reading text, the easier it is to grasp the music notated at first sight, the less misunderstandings will occur. The structures of the time signatures are therefore important to understand, so notation may follow them.

In all time signatures, the first beat is considered to be an accent. Every beat is accented more than its subdivision, so in 4/4 the first beat is stronger than the third, and both are stronger than beats two and four. In a longer series of off-beat notes, usually called syncopations, the beat-structure behind these faster notes should always be visible in notation, like the following example demonstrates:

A time signature adds a cycle, and hence a basic metric feel to a series of beats. Thus this series of twelve eighth-notes can become musically very different, depending on the time signature:

### Beaming

Note values smaller than 1/4 can be beamed together with the help of horizontal lines connecting the notestems; these replace the value-flags and by connections allow for more visible structuring of the rhythms intended.

When writing or typesetting music notation, great care has to be taken to make the beams that touch each stem point in the proper direction, which can be either left or right. The preferred direction follows from the rhythmical grouping, where each group or subgroup is made into a visible unit by means of the value flags from the first note onwards all pointing to the right (reading direction), whereas the last one to close the group points left, backwards, to indicated its belonging to the prior notes. Any note following a beam pointing left should be on a beat or subbeat.

A further refinement in beaming is possible to be able to visually group the rhythm notated by breaking beams under a common 1/8 beam, thus clearly showing the subdivision of each beat.

It is also possible to beam across staves, see below under directions of notestems.

### Odd time signatures

A time signature without regular division and subdivision is usually an odd time signature, consisting of a prime number of beats, e.g. 5, 7 or 11. These are usually also complex time-signatures, and the intended irregular subdivisions are also shown wherever possible in notation.

### Complex, or Compound, time signatures

Complex, or compound, time signatures consist of a compound of irregular divisions, such as a 9/8 divided in 2+2+2+3, which is a common Middle Eastern complex rhythm. In music where such are common, these are usually indicated with a simple 9/8 indication, as the irregular subdivisions are an integral part of the music style concerned.

When compound time signatures are not an integral part of the style musicians perform (such as having the example above performed by classically trained musicians), the subdivisions can better be notated more clearly with the intended subdivision indicated in the time signature itself.

### Notation of swing rhythm

“Swing” is a term used to denote Jazz interpretation of rhythmic notation, this means: in unequal eighth-notes. The sixteenth notes are not affected by this feel.

Today swing is usually notated in another font type, and indicated by adding (SWING) at the top left of the sheet music.

The 1/8 notes are approximately interpreted in triplets, with every upbeat accented.

### Exercises in rhythm

At the end of this Outline, exercises in rhythm are provided in the section Further study.

## Notation of pitch

### Staff and clef

A staff in notation normally consists of 5 parallel horizontal lines. The position of a notehead on a staff determines its pitch: a notehead can be notated either against or through lines.

Special notation, such as for percussion, can also employ staves consisting of a different number of lines, even only of 1 line (e.g. for bass drum or tamtam).

At the beginning of most staves a clef is employed to determine its exact usage and to determine the pitches notated.

A clef (originally from French, meaning: key) determines which pitches are notated on a staff.

#### Staff lines and ledger lines

The staff lines are numbered upwards, starting with the lowest line:

This numbering is used when describing notation orally, in spoken language, but can also occur in descriptive writing.

Notes outside the staff are notated with the help of (one or multiple) ledger lines. Ledger lines are small horizontal lines that act as a local extension of the staff at the position of the note, as can be seen in the next example, which shows all the steps in basic tones in a four octave scale:

#### Commonly used clefs

The following four clefs for notating pitch are still in use today, but many more historical clefs can be encountered in older sheet music4

• The G clef (sometimes also called violin- or treble clef) is used for most woodwind instruments, violin and the middle-high register in general. Middle C is notated on one ledger line below the staff.
• The F clef (also called bass clef) is used for low instruments, such as cello, double bass, bassoon and trombone, and the low register in general. Middle C is notated on one ledger line above the staff.
• The C clef can occur on the third or fourth line:
1. On the third line it is called alto clef and used for viola and alto-trombone exclusively.
2. On the fourth line it is called tenor clef and used for the middle-high register of low instruments, such as the cello, double bass and trombone.
3. In both cases, middle C is notated on the (middle) line where the clef is put.

### Directions of notestems and cross staff beaming

As seen in the basic forms of notes, those symbols with a notestem have two versions: one with the notestem upwards, one with the notestem downwards. The proper direction of the notestem depends on several circumstances:

1. The position of the single notehead (with 1/2 and 1/4 notes): only on the the third line of the staff one can choose freely, but should still sometimes take some care at producing a logical sequence of notes, depending on the grouping; noteheads below the third line have stems directing upwards, noteheads above the third line have stems directing downwards (bars 1 and 2)
2. When the average of the beamed group is neither above nor below the third line, one can freely choose in which direction the stems should point. (bar 3)
3. In more complex groups of notes connected with beams, the amount of “upwardness” of “downwardness” of all the noteheads is calculated per group; when on average below the third line, stems go up, and when on average above the third line, stems go down; (bars 4 and 5)

In staff systems performed by one player, it may be desirable to improve legibility by connecting rhythmic groups between registers in a single group beaming, connecting notes across staves. This is called cross staff beaming and is shown in the example below, containing piano notation.

The first bar is the best practical notation, as the path the eye needs to follow to read all the information, is more or less in the middle of the notation. In this first bar, the stem directions vary per register group, which for the piano player means: different for each of his hands. In the other two bars, a more extreme approach makes it harder to see the beams and the tones at a glance. In different situations, composers and publishers may need to choose between such options.

Note that all these bars also have partial beam breaks through the 32nd beam line, in the middle of the rhythmic figure, visually supporting the grouping. In the first bar, where there are different stem directions within a group, the third beam is therefore added to different sides (upper or lower).

### Basic tones

#### Definition of basic tones

There are 7 basic tones in most music, from which all other tones are derived by alteration. Together, these 7 basic tones make up a diatonic scale, for example a church mode. These basic tones occur in different nomenclatures.

Note that a tone represents a pitch, and is technically not identical to a note.

#### Systems for basic tones

There are various and different systems and nomenclatures for basically the same 7 basic tones.

The examples in the following sections make use of 3 different clefs.

##### Alphabetic nomenclature

In the international Western system, the following basic tones are used:

c, d, e, f, g, a, b

This alphabetic nomenclature normally denotes the following tones in notation:

##### German nomenclature

In the German nomenclature, the meaning of the letters is slightly deviant, as the b denotes an already altered tone in notation:

c, d, e, f, g, a, h

This special nomenclature allowed Johann Sebastian Bach to create a signature, with one note, to be read in 4 clefs, starting left then clockwise reading b-a-c-h, as is shown in the image on the right.

##### Latin nomenclature

Latin nomenclature is another widely used and originally Western system, based upon Latin solmisation:

do, re, mi, fa, sol, la, si

##### Relative Latin nomenclature

The latin nomenclature can also be used relatively, and ”do” can then mean any chromatic tone, for example:

Note that in these last transpositions, some basic tones are altered in the notation.

Alteration is treated in the next paragraph.

##### Indian nomenclature

In Indian nomenclature the following basic tones or swaras are used:

SA, RE, GA, MA, PA, DHA, NI

These can be represented in notation as well, in Indian notation:

S R G M P D N

##### Indian nomenclature transcribed

Transcribed to Western notation, SA is usually rendered as c, even though on different instruments SA can vary, so such transcriptions may need retranscription to a certain key if intended for practical performance.

There are two systems representing the lower and higher octaves, one using a dot above or below the tone, such as . The other system is more easy to use, typing on a computer keyboard, with apostrophes to the right when higher, such as S’ and to the left when in a lower octave, such as ‘S. I will use the latter:

### Alteration

#### Definition of alteration

Alteration in music is the changing of a basic tone, by raising or lowering it’s pitch with one or two semitones or other microtones; opening up possibilities of alteration is the first step in the direction of a chromatic system.

#### Symbols for alteration

In notation the following signs are used for this:

• Sharp, to raise the pitch by one semitone;
• Flat, to lower the pitch by one semitone;
• Double sharp, to raise the pitch by two semitones;
• Double flat, to lower the pitch by two semitones;
• Natural, to correct any of the previous alterations.

In the example below, all these alterations are notated on a b, with the enharmonic equivalents added after each note, but small:

#### Validity of alteration symbols

Sharps and flats notated at the clef (notated before the time signature!) are indications of a key signature; see the explanation on the circle of fifths. Sharps and flats as part of a key signature are valid for the whole staff and for all octaves, until revoked or changed into a new key signature.

Incidental sharps and flats can occur anywhere within a bar, and are valid for that bar only and only in the octave where they are placed. Often, so called cautionary accidentals are added to the following bar, to prevent mistakes. Cautionary accidentals can be
#a sharp, to remind one that a former flat or natural of a previous bar is no longer valid;
#a flat, to remind one that a former sharp or natural of a previous bar is no longer valid;
#a natural, to remind one that a former sharp or flat of a previous bar is no longer valid.

All this is summarized in the slightly complex example below:

This melody is composed in c minor. When notating music, choosing the right key is indeed very important, as “wrong notation” will confuse the reader, which is all too often also the future performer. The key is stated by the key signature, and although the key here is somewhat ambiguous due to the abundant use of alterations, this key is still confirmed by careful listening; and this impression could easily be reinforced by adding the proper harmonies to it. The key however is therefore not as apparent as it may seem from merely glancing at the key signature: for example there are five c‘s and just two e♭‘s, furthermore quite some extra alterations occur, plus it seems to first end in major, before reverting back to minor at last.5 When in doubt, the hearing takes priority over reading in determining “what key is it”. Now this example was composed to demonstrate how to read accidentals in practice, and so it contains a number of details which need special attention:

The bars in detail:

1. Immediately the 6th and 7th notes of the scale of c minor (natural minor being always taken as a key signature) are altered, to create a temporary minor melodic scale, the c# is notated correctly as such, and not to be confused with the d♭, which appears later: here it is a leading tone from c towards d;
2. The second tone, c, has a cautionary accidental added to it: a natural, reminding the reader that the validity of the sharp just before is cancelled by the new bar. Without the natural, this tone would still be c natural, but this fact could easily be overlooked during performance. The cautionary accidental placed before the a♭ is put in parentheses (this is a matter of taste for the engraver6), eliminating the likelihood of another a being erroneously performed here. Parenthesizing cautionary accidentals is merely another possible style, and normally the use of the two different styles of cautionary accidentals is avoided in one and the same bar (or even in one and the same piece of sheet music altogether); however, in this example this is done for obvious instructional reasons.
3. Two more incidental accidentals: d♭ and b natural; although not a single b♭ appears in the melody, it still belongs at the clef, as it is part of the correct key signature.
4. A most uncommon sight: the second, higher, d has no sign to make clear whether here also a d♭ was intended; a possible cautionary accidental has been omitted. Confusing passages like this will often lead to varying performances of the same sheet music. According to the strict rule however, the second d is natural, and should be performed as such. Hearing should confirm its logic (or not, as much modern music can be ambiguous in such matters).
5. This bar contains no cautionary accidentals, and the student should try to read it properly him- or herself, applying the rules which have been set out and explained before.

In some modern notation, flats and sharps are never valid beyond the note before which they are placed. In such notation often also bars and a time signature are missing (even though such music is not necessarily without rhythm), and sheet music like this should normally mention this out of the ordinary use of accidentals in a footnote or preface.

#### Microtone alteration

There is is no general standardization as to how to notate the finer-than-semitone intonations sometimes prescribed by composers or played by performers. In different books and scores, various alternatives have been used. In any case, notation does allow for precise quarter tone alteration and finer microtones such as shrutis and commas, as well as completely different tuning systems such as the Huygens-Fokker 31 tone system.7

Although for most systems of microtones there is no standardized notation, in the example below one of the possible notations for ascending and descending quarter tone scales is given:

### Exercises in melody

At the end of this Outline, exercises in melody are provided in the section Further study.

## Notation of intervals, chords and harmony

When notating simultaneous pitches, these are placed in exact vertical correspondence (one above the other), except with neighboring notes or smaller, as these will partially obliterate each other: these are placed diagonally or next to each other when identical. The placement of the notes is independent of the presence or absence of notestems, in the examples below the notestems are present for easier reference.

## Notation in scores

Multiple staves can be combined into a staff-system, normal use of a staff-system will assign one staff to each instrument. Square brackets are used to group a staff-system (or a part of it) together, curly brackets assign more than one staff to one instrumental part, as is e.g. customary in piano notation.

In a staff-system multiple staves are vertically synchronized like layers of simultaneous notation, the staves are connected at least at the beginning, but usually also at the end. Normally the bar lines are drawn through all the staves of a staff-system, but in case of a large score barlines between groups are not vertically connected.

As a rule, the staves of higher pitched instruments are put above those of the lower instruments. If this is done per group for all instruments of the classical orchestra, we call this the score-order of the staves.

The following orchestrated example is based upon the same music as the above, yet by its very orchestral sound implies a slower tempo. It also has a larger staff-system in which the instrument groups are visually linked by the use of square brackets on the left. The groups are also kept visually apart by the interrupted barlines between the groups:

In the above example there is still a lot missing: there are still no signs added to indicate tempo, dynamics, articulation or other special performance indications such as trills, mutes for the brass, stick type for timpani and so on.

In a score like this it is possible to notate several musical instruments on one staff, to save space. Note however, that in these cases the notestems of the parts point in different directions (one-staff polyphonic notation).

This score, set in normal score-order for the classical orchestra (top to bottom) is:

• Woodwind instruments (pic, 2fl, 2ob, 2cl, bcl, 2bsn, cbn)
• Brass Instruments (4 hn, 3tp, 3tbn, tb)
• Percussion (timp)
• Strings (vi1, vi2, vla, vc, cb)

Any additional solo-instrument would have to be added just above the first violin staff of the string section.

## Compact polyphonic notation

Notation of chords is a simple way of notating more than one simultaneous tone on a staff. Using this notation of connecting several noteheads to one notestem, has one limitation however: all tones must have the same timing and rhythm. In various cases it may be desirable to notate more than one melody on one and the same staff, with different timing and rhythm for each changing part. The example below was composed to demonstrate what a simple two-voice notation could look like: all tones belonging to a melody share the same direction of notestems.

More complex notation can be encountered using this compact polyphonic notation, especially in certain editions of the keyboard fugues of Johann Sebastian Bach, where often also rests are included in this type of notation.8

## Other notation symbols

### Tempo indications

An essential part of music, and therefore of notation, is the tempo. The very same music, performed in different tempi, can have vastly different effects and atmospheres. A proper choice of tempo is one of the main things any musician should be keenly aware of, and this choice is often dependent on the acoustic properties of the venue where a certain performance takes place as well.

There are many ways of notating tempo, all basic ways are indicated in the example below:

#### Classical tempo notation

Classical tempo notation is done in Italian terms, a short list of which is given here:

• Largo – Literally: broad, wide: very slow, one of the slowest tempo indications, only surpassed by the superlative term Larghissimo; another variation is the diminutive Larghetto, slightly less slow
• Lento – Literally: slow: generally slow, not further specified
• Grave – Literally: heavy: for serious music, with a procession-like tempo but much slower than Andante
• Adagio – Literally: gentle, quietly, carefully: medium slow
• Andante – Literally: going: slightly slow, like strolling rather than walking; the diminutive Andantino is slightly less slow, and generally lighter
• Moderato – Literally: moderate: moderate tempo, neither slow nor fast
• Allegro – Literally: merry, cheerful: generally fast, but not too fast; the diminutive Allegretto is lighter and less fast
• Vivace – Literally: lively: fast and lively
• Presto – Literally: prompt, immediate: very fast, the fastest tempo indication, only surpassed by the superlative term Prestissimo

Other Italian tempo-related terms which are relative to prior parts can also be encountered:

• Meno mosso – Literally: less motion: less fast than the passage before
• Istesso tempo – Literally: same tempo: same tempo as before, even though this may seem to not be the case
• Tempo primo – Literally: first tempo: revert to the tempo of the first section of the piece

#### Metronome numbers

analog metronome

Beethoven was one of the first composers to use a metronome. Metronomes until recently9 had a limited number of standard positions, a selection still often encountered in scores, ranging from 40-208 in steps of 3, 4, 6 or 8:

• 40 – 44 – 48 – 52 – 56 – 60 (indicated “Largo“)
• 60 – 63 – 66 (indicated “Larghetto“)
• 66 – 69 – 72 – 76 (indicated “Adagio“)
• 76 – 80 – 84 – 88 – 92 – 96 – 100 – 104 – 108 (indicated “Andante“)
• 108 – 112 – 116 – 120 (indicated “Moderato“)
• 120 – 126 – 132 – 138 – 144 – 152 – 160 – 168 (indicated “Allegro“)
• 168 – 176 – 184 – 192 – 200 (indicated “Presto“)
• 200 – 208 (indicated “Prestissimo“)

digital metronome

Today digital metronomes are in widespread use and allow for a stepwise choice of tempi in beats per minute, ranging from 40 – 208 in steps of 1.10

An interesting fact is that the tempo numbers correspond by and large to the number of beats per minute a living human heart can support: at lower and at higher heart rates humans normally do not survive.

##### Counting value changes

Counting value changes can be exactly notated by comparing note values, one should take care in reading and writing this, as the ”equals” sign = should be read as becomes: meaning in the example above, that the counting value of the quarter note is henceforward replaced by the dotted quarter note as counting value, while not changing counting tempo.

#### Jazz tempo notation

In jazz, tempi are generally loosely notated, and may greatly vary per performance; even one and the same piece can be recorded or performed at a wide variety of tempi. For reading notated Jazz, the following short list of commonly used terms is given here:

• (BALLAD) – “Jazz ballad“: slow, to very slow, generally with swing notation
• (MED) – “Medium tempo”: with swing notation
• (MED WALTZ) – “Medium waltz“: medium tempo waltz, in 3/4, usually with swing notation
• (BOSSA) – “Bossa Nova“: medium tempo with non-swing notation
• (MED UP LATIN) – “Medium up tempo, Latin feel“: with non swing notation
• (FAST 3) – “Fast in three“: fast 3/4 tempo
• (UP) – “Up tempo“: fast or very fast, with swing notation

### Dynamic indications

Dynamic indications are indications of the ”loudness”, or ”sound volume”, of the music to be performed.
The basic dynamic indications are usually printed in bold ”italics”, and are given in the example below:

These Italian terms are explained here:

• pp, pianissimo: very soft
• p, piano: soft
• mp, mezzo piano: medium soft
• mf, mezzo forte: medium loud
• f, forte: loud
• ff, fortissimo: very loud

In contemporary composed music, the fourfold indications pppp and ffff are quite common, and even up to a sixfold pppppp can be found with a composer like Morton Feldman. Nevertheless all these indications are quite relative and one should not be mistaken about the apparent precision they seem to imply. In practice, many more shades and differences than e.g. MIDI allows for (128 steps) are possible, but it makes no sense trying to notate such fine nuances. When for example a whole passage is indicated mf it will be only a computer to play all these notes at the same volume; all performers subtly vary the loudness of individual notes, this practice is a normal organic element of human music in all styles and from all ages.

Other terms are:

• fp, fortepiano: a loud beginning, then an immediately soft sustained tone; variations such as fpp or ffmp and the like are also possible
• sfz, sforzato or rf, rinforzato: reinforced tone, especially at the beginning, which is generally less an accent but more a quick though gradual temporal loudness growing into and leaving the beginning of a tone

Gradual and sudden transitions of dynamics are also possible, both can be seen in the example below:

• crescendo, or cresc.: getting louder gradually, it is also possible to indicate this by widening lines
• diminuendo, or dim. is the same as decrescendo or decresc.: getting gradually softer, it is also possible to indicate this by narrowing lines
• subito, or sub.: “suddenly” in Italian, indicating a sudden transition to another, often unexpected, sound volume; typically, in the example above ff comes unexpectedly after a diminuendo and an unexpected pp after a crescendo; the word subito not only clarifies this beyond doubt but more importantly a performer is more likely to not oversee this intended sudden dynamic transition

As a final remark to these indications being relative, let it be noted that for orchestral or big band use a mf for a trumpet more or less equals a f of a section of violins, (tenor or alto) saxophone or a french horn, and even a ff of a flute or solo violin, if measured in dB11. But all these dynamics depend not only on the timbre12 but also on the register of the note played; for example a single piccolo playing f in its highest register can always be heard, even with 10 trumpets playing ff at the same time.

### Articulation

There is a wide variety of possible articulations, many of which can be notated. But as articulation depends not only on style but also on the musical instrument used, these articulations can greatly vary in practice. Even such basic articulations as staccato are very different in performance between for example a violin and a flute player, both classically trained. One should always check how certain players or types of players respond to certain articulation signs before prescribing these in a musical score.
Some examples of articulations are provided in the example below:

In different styles, there are different attitudes as well towards notated articulation. Jazz performers are used to choosing most if not all articulations themselves, often on the spot, as improvised, even when they are written out exactly in the sheet music; leading to a lively performance for sure, though perhaps not as a composer originally intended. In Jazz big bands one can expect more discipline as to the exact performance of notated articulation, especially with regard to slurs and short or accented notes. When working with classically trained musicians on the other hand, one needs to always provide at least a minimum of notated articulation, or none at all will be performed: in this tradition, players don’t usually add their own articulations and are not used to improvising even these, unless they are soloists and performing as such. Especially string players that perform in sections need to coordinate their bowing, and will always change bowing direction when notes are not slurred. For this reason, at least the slurring of groups of notes into phrases can be recommended for string orchestras, because in this case (and only in this particular case: with string groups) it is true that adding slurs is almost mandatory, as writing them will always lead to a better and more coordinated performance, almost even independent of how the slurs are placed.

When providing articulation however, one should take care not to overburden the sheet music with too many signs and symbols, as this may lead performers’ attention away from the more essential structural elements of the music, such as phrasing and breath, and so as not to provoke unnecessary mistakes.

### Score indications concerning form

#### Special barlines

An additional way to indicate form sections in music can sometimes be encountered by the use of double barlines, dashed barlines, or repetition signs (double dotted barlines). In the following image examples of these can be seen.

types of barlines

#### Rehearsal numbers

In longer scores so called “rehearsal numbers” -but these can also be letters- are used to easily refer to a passage for rehearsal purposes. Such indications mostly follow the form sections of the music, but this is not always the case. Rehearsal numbers are most practical when they can replace bar numbers, so e.g. “let’s play W” instead of “lets play… erm… bar … erm …. 1236…”.

More score indications concerning form can be found at the section traditional Italian score indications concerning form in the chapter Concerning rhythm, melody, harmony and form.

goto chapter 4  ► Basic building blocks of melody and harmony

## Footnotes

1. How the brain reads music: the evidence for musical dyslexia on PsyPost
2. Examples such complex meters and rhythms can be found on the page Darbuka patterns and on Maqam world
3. The Rime of the Ancient Mariner by Samuel Taylor Coleridge (original editions on Wikisource)
4. See the reference guide entry clef for a full overview..
5. The phenomenon of a major ending to what is basically a piece of music in minor is quite common though, and since the 17th century this is called the Picardian third, after the folk-music of the Picardie, a region in North-West France.
6. An engraver is the person responsible for the final look and layout of sheet music, a name still in use which refers to the centuries-long tradition of the engraving needed to produce the metal plates needed for printing.
7. Huygens Fokker Foundation website on theory of microtonal music
8. An example of a more complex compact polyphonic notation can be found in Bach’s first book of the Well-Tempered Klavier: the five-voice fugue in c# minor. The Petrucci Library (www.imslp.org) has a.o. this version; one should especially look at the ending.
9. A short history of the metronome: https://www.franzmfg.com/history.htm
10. German composer Karlheinz Stockhausen proposed and actually used a unique “equal tempered tempo system”. Comparing the doubling of the tempo to an octave, he divided this into twelve equal steps: 60 – 63.6 – 67.4 – 71.4 – 75.6 – 80.1 – 84.9 – 89.9 – 95.2 – 100.9 – 106.9 – 113.3 – 120 (from his article ”…Wie die Zeit vergeht…”, Die Reihe 3, Vienna 1957). This system in part closely resembles the older metronome tempi, yet the latter still has seven more steps in between: the older more differentiated system was never replaced.
11. dB is the scientific abbreviation of Decibel, referring to sound-pressure: the scientific unit for sound volume.
12. Timbre means sound color, usually referring to the specific character, independent of pitch, but strongly dependent on the musical instrument. Not only do all instruments have a different timbre in relation to each other, but each instrument can produce a certain range within its own sound.