TIME AND MUSIC

Some arts are expressed in space. For instance, painting is expressed in two-dimensional space, while sculpture and architecture are expressed in three-dimensional space. When we observe works of painting, sculpture or architecture, by approaching and looking at them, we can use as much or little of time as we want.

Music is different. Music is expressed in time and must be perceived in time. In this aspect, music is similar to poetry. Both poetry and music communicate thoughts and emotions between people. However, unlike poetry, music does not use words and therefore is much more abstract. It is often said that music is the most abstract of all art forms. Other forms of art are more representational because they quite often represent objects from real life (for instance, a sculpture of a man). The poet would say “music is love in search of words”. Instead of words, music uses sounds and these sounds take place in time. 

Measures

A measure (or a bar) is defined as everything written between the two adjacent vertical lines of a staff. The next figure shows the first eight measures from Bach’s Prelude No. 5 in D major, from Well-Tempered Clavier, book I.

Figure: The first eight measures from Bach's Prelude No. 5 in D major, from Well-Tempered Clavier, book I

Dividing a composition by measures simplifies the reading of music and makes it easier to find a position in it. In the figure, we can easily see that each of the three measures has the same total rhythmic value which is four quarter notes. Every measure must have its total rhythmic value in accordance with the time signature. Time signatures will be explained in the next chapter. For now, we can say that the symbol looking like letter C, positioned at the beginning of the score is the time signature. 

To further simplify finding the position in the score, measures can be numbered and measure numbers written in the score. Usually, measure numbers are written only for the leftmost measure in each staff, with the exception of the first measure. Accordingly, we see the measure numbers 3 and 6 in the figure. Usually, in multi-movement compositions, the measure numbers start from 1 at the beginning of each movement. In the text of this book, we shall use measure numbers when we refer to measures.

Vertical lines that delimit measures are called measure lines. Measure lines with special meaning do exist. The next figure shows the measure line that marks the end of a composition.  

Figure: The measure line that marks the end of a composition

The next figure shows the measure line that marks the end of a section and the beginning of the next one in a composition. Later, we shall learn about measure lines that are used to mark repetitions in compositions. 

Figure: The measure line that marks the end of a section and the beginning of the next one in a composition

Time signatures

We have already defined that every measure must have its total rhythmic value in accordance with the time signature. A time signature defines the total rhythmic value for the consecutive measures. The next figure shows a graphic symbol used for a time signature. In this example, the time signature indicates the total rhythmic value of three quarter notes in each measure. The upper number in a time signature indicates the number of notes and the lower number indicates their rhythmic value. The lower number 1 indicates the whole note, 2 indicates the half note, 4 indicates the quarter note, 8 indicates the eighth note etc. The symbol for time signature is placed at the beginning of a composition, after a clef and key signature.

Figure: A clef, key signature and time signature

In a text, we can write this time signature as 3/4. The most frequently used time signatures are: 4/4, 3/4, 2/4 and 2/2. The next figure shows the graphical symbol that is often used instead of 4/4. The symbol is called common time.  

Figure: The graphical symbol that is often used instead of 4/4 

The next figure shows the graphical symbol that is often used instead of 2/2. The symbol is called cut time.

Figure: The graphical symbol that is often used instead of 2/2 

The time signature can change in the middle of a composition and this is annotated by placing the new time signature in the score, at the beginning of the first measure that has the new total rhythmic value. 

Meters and beats

Music, like poetry, has a meter. The meter is a recurring pattern of more and less accented beats. The first pulse in a recurring pattern is more accented, while the others are less accented. A more accented beat is called a strong beat while a less accented beat is called a weak beat. The most often occurring meters in music are: double, triple and quadruple.

The double meter is the recurring pattern of two beats where the first one is strong and the second one is weak, that is: 

‒ ◡ ‒ ◡ ‒ ◡ …     (‒ denotes a strong beat and ◡ denotes a weak beat) 

Similarly, the triple meter is the recurring pattern of three beats where the first one is strong and the other two are weak: 

‒ ◡ ◡ ‒ ◡ ◡ ‒ ◡ ◡ … 

The quadruple meter is the recurring pattern of four pulses where the first one is strong and the other three are weak: 

‒ ◡ ◡ ◡ ‒ ◡ ◡ ◡ ‒ ◡ ◡ ◡ …  

It is assumed that notes starting on strong beats are played louder than notes starting on weak beats.

Simple and compound meters

Two types of meters exist: simple meters and compound meters.

In simple meters, the rhythmic value of beats is equal to the rhythmic value given by the time signature. For instance, the time signature 2/4 implies the simple double meter, 3/4 implies the simple triple meter and 4/4 implies the simple quadruple meter. In all these cases, the rhythmical value of beats is one quarter note, since this is the rhythmical value given by the time signature. 

In compound meters, the rhythmic value of beats is equal to the triple rhythmic value given by the time signature. For instance, the time signature 6/8 implies the compound double meter, 9/8 implies the compound triple meter and 12/8 implies the compound quadruple meter. In all these cases, the rhythmic value of beats is equal to three eight notes i.e. one dotted quarter note. 

The important thing to remember is that a time signature implies a meter i.e. strong and weak beats.

Although, in mathematics 3/4 is equal to 6/8, in music this is not a case because 3/4 is a triple meter while 6/8 is a double meter. The next figure illustrates the difference.

Figure: Difference between 3/4 and 6/8

More about beats

The first beat in a measure is called a downbeat and the last beat in a measure is called an upbeat (this terminology is related to movements of a conductor’s right hand which indicates beats).

In chapter Beams, we explained that notes can be beamed together for a better readability. When beams are used, the rule is that notes belonging to the same beat are beamed together i.e. beaming across beats is avoided. This can be easily seen in the figure in chapter Measures where the adjacent sixteenth notes that make a beat are beamed together (either four sixteenth notes or three sixteenth notes after the sixteenth rest). This way, we can at first glance break down each measure into beats. In this example, there are four beats in each measure.

For determining distances in space we use a ruler. A typical metric ruler has two levels of markings on it: centimeters which are further divided into millimeters. In a similar way, we can determine relative durations in music. We use measures which are further divided into beats. While each centimeter has ten millimeters, measures can have various numbers of beats. The time signature tells us how many beats are in one measure and the rhythmic value of a single beat. The next figure illustrates this.

Figure: Determining distances and relative durations

Anacrusis

Sometimes, a composition begins with what looks like an incomplete measure, followed with complete measures. Such an incompletely looking measure is called an anacrusis (or pickup). The total rhythmic vale of an anacrusis must be smaller than the total rhythmic vale of following measures which is defined by the time signature.

An anacrusis is used when a composition does not start on a strong beat. The following figure shows the beginning of Chopin’s Prelude No. 7 in A major where we see an anacrusis whose total rhythmic value is one quarter note, followed by measures whose total rhythmic value is three quarter notes (in accordance with the time signature). The figure also shows strong and weak beats.

  Figure: Chopin’s Prelude No. 7 in A major

When measures are numbered, an anacrusis is not numbered. That is, measure number 1 is assigned to the first complete measure.

Tempo

The rhythmic values of notes define only relative durations of notes, thus enabling us only to compare the durations. To determine the absolute durations of notes, a tempo must be known. 

A tempo defines how fast the music should be played i.e. how many rhythmic values should occur during a time interval. For instance, a tempo can be denoted as 120 quarter notes per one minute (i.e. 2 quarter notes per one second). This can be marked above a staff using the symbol called the tempo marker: 

Figure: A tempo marker

The term BPM, an acronym for beats per minute, is also used. In this case, we must also know the rhythmic value of one beat, which is defined by the time signature. In scores, a common practice is to use Italian words for annotating different aspects of music. In this and the following chapters, some of these words will be explained. Also, the translations from Italian into English will be given. The following Italian words are used often in tempo markers: 

• Grave = from 25 to 45 BPM, “grave” in English means “heavy”

• Lento = from 45 to 60 BPM, “lento” in English means “slow”

• Larghetto = from 60 to 66 BPM, “larghetto” in English means “rather broad”

• Adagio = from 66 to 76 BPM, “adagio” in English means “slowly”

• Andante = from 76 to 108 BPM, “andante” in English means “walking”

• Moderato = from 108 to 120 BPM, “moderato” in English means “moderate”

• Allegro = from 120 to 156 BPM, “allegro” in English means “cheerful”

• Vivace = from 156 to 176 BPM, “vivace” in English means “lively”

• Presto = from 176 to 200 BPM, “presto” in English means “quickly”

Let’s show how we can calculate the absolute duration from the relative duration when we know the tempo. For instance, if the tempo is 120 quarter notes per minute, the absolute duration of one quarter note is: 1 minute / 120 = 60 seconds / 120 = 1/2 seconds. Now, we can calculate the absolute duration of any rhythmical value. For instance, the absolute duration of a whole note is: 4 * 1/2 seconds = 2 seconds. 

A metronome is the device that produces a click at a regular interval and can be set to any BPM. Musicians can practice with metronome to improve their timing. However, in a expressive performance, not every note is aligned strictly with a steady pulse given by the metronome. 

A tempo can change during time. This can be indicated in a score by using a new tempo marker. Another possibility is to use one of the following expressions that indicate tempo changes. In scores for piano, tempo related expressions are usually written above the upper staff of the grand staff. 

“Ritardando” or the abbreviation “rit.” or “ritard.” indicates that the tempo should be gradually slowed down over time. “Ritardando” in English means “delaying”. “Accelerando” or the abbreviation “accel.” indicates that the tempo should be gradually sped up over time. “Accelerando” in English means “accelerating”. 

“Meno mosso” indicates the sudden change to a slower tempo while “più mosso” annotates the sudden change to a faster tempo. “Meno mosso” in English means “with less movement” while “più mosso” means “with more movement”. Alternatively, instead of “Meno mosso”, “Ritenuto” or “riten.” can be used. “Ritenuto” in English means “hold back”.  

“Doppio movimento” indicates the sudden change to the double tempo. “Doppio movimento” in English means “with double movement”. 

“A tempo” indicates that the tempo should change back to the base tempo (the tempo established by the last usage of a tempo marker). “A tempo” in English means “in tempo”.

"Tempo primo" indicates that the tempo should change back to the first tempo (the tempo established at the beginning of the composition or movement). "Tempo primo" in English means "first tempo".

“Tempo giusto” indicates that the tempo should be kept strict while “rubato” indicates free adjust of the tempo for expressive purposes. “Tempo giusto” In English means “with exact tempo” while “rubato” means “stolen”.

A fermata is marked with the “bird’s eye” symbol over a notehead or rest and indicates the temporary slowing of the tempo to increase the duration of the single note or rest. It often appears at the end of a section or movement. “Fermata” in English means “stop”.

Figure: A fermata

A metric modulation is a change of the tempo that is expressed relative to the current tempo. The metric modulation is marked as an equation that has different rhythmic values on the left and right sides of the equal sign. The duration of the rhythmic value on the left side in the old tempo is the same as the duration of the rhythmic value on the right side in the new tempo. Hence the equal sign. The next figure shows an example of metric modulation.

Figure: A metric modulation

In the figure, we see that the old tempo is 120 quarter notes per minute (as indicated with the tempo marker). Also, we see the metric modulation which specifies that a quarter note in the old tempo has the same duration as a dotted quarter note in the new tempo. A dotted quarter note is 3/8 and a quarter note is 1/4 = 2/8. In the same tempo, the ratio of their durations is 3/8 : 2/8 = 3 : 2 = 3/2. Thus, to achieve the same duration, the new tempo must be faster and equal to the old tempo multiplied by 3/2. That is, the new tempo is 120 * 3/2 = 180. The following figure shows how to rewrite the metric modulation from the previous figure using the tempo marker instead of the metric modulation.

Figure: The metric modulation from the previous figure, rewritten using the tempo marker

The aforementioned metric modulation can also be comprehended in the following way. Since the old tempo is 120 quarter notes per minute and the metric modulation equals the duration of a quarter note with the duration of a dotted quarter note, the new tempo is 120 dotted quarter notes per minute. This is illustrated in the following figure.

Figure: Another way to rewrite the aforementioned metric modulation

Breaking flow of time

The regular flow of time in music can be broken by the usage of a caesura. A caesura is marked with a pair of diagonal lines and indicates a short pause. Unlike a fermata, a caesura must be located to the right of a note or rest. The pause occurs after the normal execution of the note or rest. “Caesura” in English means “cutting”. A caesura cuts and breaks the regular flow of time in music.

Figure: A caesura