music theory online : note groupingslesson 15
Dr. Brian Blood





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My sole inspiration is a telephone call from a producer.
Cole Porter (1893-1964) American composer

Simple & Compound Time/Meter :: Uneven/Asymmetrical Time/Meter :: Triplets :: Duplets :: Other-lets :: Grouping Notes and Rests
Time Signatures, How We 'Say' Them


Important: To see and hear our 'live' music examples you will need to install the free Scorch plug-in for PC and MAC systems.


Simple & Compound Time/Meter :: top

Key words:
simple time
simple meter
compound time
compound meter
1

Simple & Compound Time/Meter

We had a preliminary look at time signatures in lesson 4.

A great deal of music, particularly that from the Western musical tradition, has an underlying pulse or beat. Think of the beat as something 'you tap your foot to' when you are listening to a piece of music. Bar-lines and time signatures are used to make the underlying rhythm, the pattern of beats of differing weight (strong, medium, weak), clearer to the performer. So, for example, a bouree which has four beats in a bar starts on the last beat; the gavotte, also written with four beat in a bar, starts on the third beat. Neither of these, unclear where bar-lines are absent, would not be clearer with bar-lines written into the score.

Sometimes time signatures might mislead the performer and we have adopted a 'convention' about how different time signatures relate to particular underlying rhythmic structures. This is illustrated in the three scores below. Two of these are the same piece of music written in two different ways.

This score is in 'three'; we have marked the three beats with dotted bar-lines. The beat is a crotchet (quarter note) and the time signature tells us that there are three crotchets (quarter notes) in each bar. This is an example of simple time or tempo semplice (Italian); the main beat can be divided into two inner beats, in this case quavers (eighth notes).

This score is written in six but 'felt' in two; we have marked the pulse with dotted bar-lines. The beat is actually a dotted crotchet (dotted quarter note) but the beat is divided into three quavers (eighth notes). Therefore, each bar contains six quavers (eighth notes). This is an example of compound time or tempo composto (Italian); the main beat can be divided into three inner beats, in this case quavers (eighth notes).

The third score has a compound time signature. A performer would be confused - should the piece be in two or in three. If the piece is to be played 'three in a bar' then it should be notated in three, as it was in the first example.

We can list various time signatures as simple time signatures or compound time signatures.

Beats per BarSimple
Time Signature
BeatCompound
Time Signature
Beat
2
(duple)
2
2
minim (half note) 6
4
dotted minim (dotted half note)
2
4
crotchet (quarter note)6
8
dotted crotchet (dotted quarter note)
2
8
quaver (eighth note)6
16
dotted quaver (dotted eighth note)
3
(triple)
3
2
minim (half note) 9
4
dotted minim (dotted half note)
3
4
crotchet (quarter note) 9
8
dotted crotchet (dotted quarter note)
3
8
quaver (eighth note) 9
16
dotted quaver (dotted eighth note)
if a piece is so quick that the feeling is of one beat in a bar, then the triple meter (usually 3/2 or 3/8) is compound (i.e. may be divided into three)
4
(quadruple)
4
2
minim (half note)12
4
dotted minim (dotted half note)
4
4
crotchet (quarter note)12
8
dotted crotchet (dotted quarter note)
4
8
quaver (eighth note)12
16
dotted quaver (dotted eighth note)

Uneven/Asymmetrical Time/Meter :: top

Key words:
uneven time
asymmetrical time
1

Uneven/Asymmetrical Time/Meter

The formal distinction between simple and compound time or meter becomes blurred particularly in the folk music of central Europe and Asia Minor where the pattern of dances steps is complex. Time signatures in which the number of notes in the bar is odd (i.e. 5, 7, 9, 11, 13, 15, etc.) are common. The uneven numbers break down into shorter inner groups of either simple or compound rhythms. So 5 will break down into a group of 2 followed by a group of 3 or, alternatively, a group of 3 followed by a group of 2. This pattern may change from bar to bar. A good editor will note the inner groups clearly so that the performer can quickly ascertain how the internal rhythmic forms should be accented by placing strong beats at the beginning of each of the inner groupings. Jazz and folk-inspired classical music makes use of uneven time signatures and is the richer for it. Meters in which the number of notes in the bar in a multiple of 3 may be compound meters when they break down naturally into equal groups of 3 (e. g. 3 + 3 + 3 = 9). If however they do not break down into equal groups, then the meter is asymmetrical (e.g. 4 + 3 + 2 = 9). The terms complex meter and irregular meter are also applied in these situations.

One of our readers offers as an illustration the song America from West Side Story by the American composer Leonard Bernstein, which is an excellent example of a tune in mixed time (or mixed meter), namely (6/8 + 3/4) where the value of the quaver (eighth-note) remains constant.

See America from West Side Story.

Triplets :: top

Key words:
irrational rhythm
triplet
1

Triplets

In music, the term irrational rhythm is usually applied to a rhythm in which an unusual number of beats is superimposed on the predominating tempo. More precisely, if n evenly-spaced beats are played in the time of m beats of the underlying tempo then the rhythm is irrational if neither of n and m is divisible by the other. The use of the term "irrational" in this context is quite different to the mathematical use of the term: indeed, rhythms of this sort are, in the mathematical sense, rational, as they are precisely defined by the ratio of beats played to beats in the underlying tempo.

One example is the triplet, used when in the context of a simple time signature one wants to subdivide a beat into three. The triplet notation lets you to do this.

To listen to this piece, called Triplets, press the play button displayed below.

Triplets

The triple notation has been shown in two ways - one, with the number 3 over the group of three quavers (eighth notes); the other, with a bracket as well as the number. The three quavers (eighth notes) are played in the time of two quavers (eighth notes), in other words the three quavers (eighth notes) divide a crotchet (quarter note) into three equal parts. We read the notation as meaning 'three notes in the time of two'. Any note can be divided in this way. For example, three crotchets (quarter notes) can be played in the time of a minim (half note). Any of the three notes can be a rest or can itself be combined with other notes or broken up into shorter notes.

Why not listen to two examples of the triplet rhythm used to great effect. The first is a ten bar extract from Albinoni's Concerto for Two Oboes and Strings.

Notice, in particular, when the triplet rhythm is being played against the quaver rhythm in another line in bars 4, 5 and 6.

Albinoni, Op.9 No. 6 - Finale (excerpt)

The second comes from The Dolmetsch Library, In Dulce Jubilo by J. S. Bach arranged for four recorders.

Here you will find notes tied into and between triplets, triplets containing rests and triplets with minims (half notes) as well as crotchets (quarter notes).

When notes with different time values appear within a triplet (for example, a crotchet (quarter note) and a quaver (eighth note) in place of three quavers (eighth notes)) the result is called a mixed-rhythm triplet.

In Dulce Jubilo - J.S. Bach arr. Dolmetsch

Duplets :: top

Key word:
duplet
1

Duplets

Where triplets are used in simple time to divide beats into three parts. duplets are used in compound time to divide beats into two parts. The notation is very similar except that the number 2 appears above the group which is shorthand for two notes in the time of three.

We give an example below.

Duplets

On the website Music Notation Questions Answered the following question is posed.

What is the correct note value of a dotted quaver (eighth note) duplet (two quavers (eighths) in the space of three quavers (eighths))?

The website experts comment:

"There is considerable controversy over the correct way to notate this duplet. The technically correct way is according to the same rule as other tuplets, which says that a note can only be shortened, never lengthened. This implies that, for instance, 3 notes in a crotchet (quarter) are quavers (eighths), but 5 in a crotchet (quarter) are semiquavers (16ths). This rule implies that 2 notes in a dotted crotchet (dotted quarter) are crotchets (quarters). This system is consistent, sensible, and is recommended by Stone, Roemer, and Rosenthal. However, common practice is to notate 2 in 3/8 as quavers (eighth notes). One possible explanation is that the player's eye is used to seeing a crotchet (quarter) divided into quavers (eighths), regardless of whether it has a dot. This method is recommended by Read and Ross. The most serious problem with this is that a given note value (say, a dotted minim (dotted half)) can be divided into 2 crochets (quarters) or 4 crotchets (quarters). This seems to be wrong by definition, not to mention confusing."

Other-lets :: top

Key word:
irregular divisons
1

Other-lets

The division of notes into smaller notes using triplets and duplets can be extended to irregular groups of even larger number, known collectively as tuplets or gruppo irregolare (Italian). Again there are 'notational' conventions for writing such grouping and these are listed below. As with triplets, the groupings can include rests and notes of different values (such groups are called mixed-rhythm tuplets). The 'convention' tells us the total time value of the group as written and as played.

Irregular Divisions in Simple Time
13 notes are written in the time of 2 of the same note.
example: 3 quavers (eighth notes) in the time of 2 quavers (eighth notes).
25, 6 and 7 notes are written in the time of 4 of the same note.
example: 5 quavers (eighth notes) in the time of 4 quavers (eighth notes).
39, 10, 11, 13 and 15 notes are written in the time of 8 of the same note.
example: 13 quavers (eighth notes) in the time of 8 quavers (eighth notes).
Irregular Divisions in Compound Time
12 notes are written in the time of 3 of the same note.
example: 2 quavers (eighth notes) in the time of 3 quavers (eighth notes).
24 notes are written in the time of 3 of the same note but also in the time of 3 beats of double the time value.
example: 4 quavers (eighth notes) in the time of 3 quavers (eighth notes); but sometimes 4 semiquavers (sixteenth notes) in the time of 3 quavers (eighth notes).

The irregular division of compound time is rare and notational 'conventions' are fluid. Simple time division is much more common and this has given time for composers and music publishers to establish and maintain a set of 'notational conventions'.

Grouping Notes and Rests :: top

Key words:
beatbeaming
1

Grouping Notes and Rests

It would be useful to set out the standard 'conventions' for notating music written in simple or compound time.

Simple Time
1Avoid or minimise ties.
2If the beat is a crotchet (quarter note):
beam quavers (eighth notes) through the whole of the bar in 2 or 3 crotchets (quarter notes) per bar;
if the signature is 4 crotchets (quarter notes) per bar, divide the beaming into two groups, separating the second beat from the third.
3If the beat is a crotchet (quarter note):
semiquavers (sixteenth notes) are beamed into crotchet (quarter note) groups;
demisemiquavers (thirty-second notes) are beamed into quaver (eighth note) groups.
4Keep rests to a minimum but make clear the rhythmic structure of the bar, just as with notes (see above).
5Beaming can continue over rests although this is best used only over a single beat.
Compound Time
1Avoid or minimise ties but try to preserve internal rhythmic structure by not using notation that misleads the eye. For example, in 6 the internal structure of the compound time signature is 2 not 3; in 12, 4 not 6.
2If the beat is a dotted crotchet (dotted quarter note):
beam quavers (eighth notes) through the whole of the bar in 1 dotted crotchet (dotted quarter note) per bar;
if the signature is 2, 3 or 4 dotted crotchets (dotted quarter note) per bar, divide the beaming into groups of dotted crotchets (dotted quarter notes).
3If the beat is a dotted crotchet (dotted quarter note):
semiquavers (sixteenth notes) are beamed into dotted crotchet (dotted quarter notes) groups;
demisemiquavers (thirty-second notes) are beamed into quaver (eighth notes) or dotted crotchet (dotted quarter notes) groups.
[our thanks to Mark Buckley for correcting an error in the text]
4Keep rests to a minimum but make clear the rhythmic structure of the bar, just as with notes (see above).
5A dotted crotchet rest (dotted quarter rest) can be shown as a crotchet rest (quarter rest) follow by a quaver rest (eighth rest) but should not be shown as a quaver rest (eighth rest) follow by a crotchet rest (quarter rest). A quaver note (eighth note) followed by two quaver rests (eighth rests) should be shown as such but two quaver rests (eighth rests) followed by a quaver note (eighth note) is best shown as a crochet rest (quarter rest) followed by a quaver note (eighth note).

How We 'Say' Time Signatures :: top

Key word:
saying key signatures
1

How We 'Say' Time Signatures

In England, we name time signatures as follows:

  • Three crotchets (quarter notes) in a bar (measure) is called "three-four" time - it is an example of simple triple time;
  • Four minims (half notes) in a bar (measure) is called "four-two" time - it is an example of simple quadruple time;
  • Six quavers (eighth notes) in a bar (measure) is called "six-eight" time - it is an example of compound duple time.

    In Italy, France and Spanish, a similar system is used also:

    • Three crotchets (quarter notes) in a bar (measure), written (3/4), is called tre quarti (Italian), trois quatre (French) or tres cuartos (Spanish)
    • Four crotchets (quarter notes) in a bar (measure), written (4/4), is called quattro quarti (Italian), quatre quatre (French) or cuatro cuartos (Spanish)
    • Six quavers (eighth notes) in a bar (measure), written (6/8), is called sei ottavi (Italian), six huit (French) or seis octavos (Spanish)

    Alternatively in Spanish, the time signatures may also be called tres por cuatro for (3/4), cuatro por cuatro for (4/4) and seis por ocho for (6/8).

    In Germany, 3/4 time is called 3/4-Takt, 4/4 time is 4/4-Takt, 6/8 time is 6/8-Takt, and so on.

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