RhyThmic valueS of NOTES

The rhythmic value of a note indicates its duration. It can be a whole note, half note, quarter note, eighth note, sixteenth note… Each next rhythmic value is equal to half of a previous one and indicates a half shorter duration. Relations between durations of notes correspond to the relations between mathematical fractions. The duration of a whole note is equal to the duration of two half notes. The duration of a half note is equal to the duration of two quarter notes. The duration of a whole note is equal to the duration of four quarter notes… 

Until now, we used only one graphical symbol for notes: an unfilled notehead. This is the simplest possible graphical symbol for notes and is used only for notes that have the rhythmic value equal to the whole note. In general, the graphical symbol for a note can consist of a notehead, stem and flags. This is illustrated in the next figure. 

Figure: The graphical symbol for a note

The next figure shows the graphical symbols for notes that have different rhythmic values and also illustrates the relations between their durations. In the figure, the duration of the whole note is successively divided into two half notes, four quarter notes, eight eighth notes and so on. In the figure, we see that a notehead can be unfilled or filled, that an unfilled notehead can appear without or with a stem while a filled notehead must appear with a stem and that each flag shortens the duration of a note by half. Any number of flags can be used.

Figure: The rhythmic values of notes

It is important to notice that the rhythmic values of notes tell us only relative durations. That is, they enable us only to compare durations of notes. Later, we shall learn how to determine absolute durations of notes.

Ties

A tie is a curved line that ties (connects) two notes with the same pitch and indicates that they should be played as one note, whose pitch is same as the pitch of the tied notes and whose rhythmic value is the sum of the rhythmic values of the tied notes. The next figure shows two tied eighth notes that are equivalent to one quarter note.

Figure: Two tied eighth notes are equivalent to one quarter note

Dotted notes

A dotted note is a note with a dot next to it. The rhythmic value of a dotted note is equal to the rhythmic value of the note without dot, plus a half. The next figure shows a dotted quarter note and its rhythmic value which is equal to the rhythmic value of a quarter note plus the rhythmic value of an eighth note. 

Figure: A dotted quarter note

It is possible to use more than one dot. Each dot adds half the value of the previous dot to the rhythmic value of a note. The next figure shows a double dotted quarter note and its rhythmic value which is equal to the rhythmic value of a quarter note plus the rhythmic value of an eighth note plus the rhythmic value of a sixteenth note.

Figure: A double dotted quarter note

Beams

A beam is a line that connects consecutive notes to group them for easier reading. Only notes with flags (an eighth, sixteenth and shorter) can be beamed. The number of beams is equal to the number of flags. The next figure shows three notes written with and without beams. 

Figure: The same three notes written with and without beams

Tuplets

A tuplet is a modification of the rhythmic value of notes, which multiplies the rhythmic values of all the affected notes with a fraction number. The graphical representation of a tuplet contains a tuplet number and can also contain a bracket. Only when affected notes are not beamed together, a bracket is used, to improve the readability (this is shown in the next figure). 

A triplet is the most common tuplet. It multiplies the rhythmic values of the affected notes by 2/3. Thus, it shortens them in a way that three notes with the same rhythmic value will have total duration of only two of them. The next figure shows a triplet over three eighth notes, which makes their total rhythmic value equal to two eight notes i.e. one quarter note. The same triplet is shown when the notes are beamed together and when they are not. 

Figure: A triplet over three eighth notes, when they are beamed together and when they are not

The mathematical calculation for the total rhythmic value of a triplet over three eight notes is simple: 

( 1/8 + 1/8 + 1/8 ) * 2/3 = 3/8 * 2/3 = 2/8 = 1/4