music theory online : time signatures and meterlesson 4
Dr. Brian Blood





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Music and silence .. combine strongly because music is done with silence, and silence is full of music.
Marcel Marceau (1923- ) French mime

Time Signature and Meter :: Unusual Time Signatures and Hypermeasures :: Mensuration
Common Time & Alla Breve/Cut Time :: Changing Time Signatures :: The Whole Bar Rest :: Incomplete Bars :: Ametric Music


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Time Signature and Meter :: top

Key words:
time signature
meter
beat
pulse
simple time
simple meter
compound time
compound meter
divisive rhythm
1

Time Signature and Meter

Where we divide time into various units of measurement (hours, minutes, seconds), so we divide music into beats. You can think of the beat as the 'pulse' of the music. The association of music with 'dance' is central to much of Western music and demonstrates how responsive we are to repetitive rhythmic patterns. Dancers require that dance music be regular. It should neither speed up nor slow down. This is best achieved by imitating the dancers' steps in the rhythm of the musical line. The shape or pattern of the step sequences finds itself reflected in the pattern of strong and weak beats in the accompanying music. A march, for example, imitates the 'left-right' pattern of the marchers' steps - the meter comprises two beats; the first strong and the second weak. By convention, the first beat in a bar is usually the strongest.

BarPattern of Beats or MeterPattern over Four Bars
1 beat barStrong1: S | S | S | S |
2 beat barStrong Weak2: S W | S W | S W | S W |
3 beat barStrong Medium Weak3: S M W | S M W | S M W | S M W |
4 beat barStrong Weak Medium Weak4: S W M W | S W M W | S W M W | S W M W
6 beat barStrong Medium Weak Strong Medium Weak6: S M W S M W | S M W S M W | S M W S M W | S M W S M W

The regularity of the meter is imposed on the musical line by using a regular number of beats in each bar but we have to choose which note sign is going to be the beat.

The time signature is written as two numbers, one set above the other, usually placed immediately before the first note. The upper number tell us the number of beats in a bar. The lower number tells us which note sign is to represent the beat.

Some examples are explained below.

Time SignatureDescriptionBeat Time DurationExplanationBar Time Duration
2
1
two beats in the bar
the beat is a semibreve (whole note)
a bar contains 2 times 1/1 (semibreve=a whole note)
3
2
three beats in the bar
the beat is a minim (half note)
a bar contains 3 times 1/2 (minim=a half note)
4
4
four beats in the bar
the beat is a crotchet (quarter note)
a bar contains 4 times 1/4 (crotchet=a quarter note)
6
8
six beats in the bar
the beat is a quaver (eighth note)
a bar contains 6 times 1/8 (quaver=an eighth note)
11
16
eleven beats in the bar
the beat is a semiquaver (sixteenth note)
a bar contains 11 times 1/16 (semiquaver=a sixteenth note)

A bar may be made up of notes and/or rests. We give some examples below which demonstrate the use of notes and rests to complete bars. In each case the total number of beats in a bar reflects that expected from the time signature.

Lesson 15 discusses in detail how to distinguish simple time/simple meter and compound time/compound meter.

Click here to read about how we 'say' or 'vocalise' time signatures. When we write them as text, for example when writing about time signatures, time signatures are generally written with the top number separated from the bottom by a slash, like a fraction, e.g. 3/4.

The time signatures we have discussed above are examples of what in music is termed divisive rhythm, a rhythm in which a larger period of time is divided into smaller rhythmic units.

While time signatures usually have no particular connotation as time signatures, experience shows that certain signatures are associated with certain tempi and particular musical forms. We give a summary below.

Time signatureAssociated information
1
1
used very rarely: several times by Edward Elgar (1857-1934) in several of his studies and in Variation 7 (Troyte, Presto, C major) of his Variations on an Original Theme (later called 'Enigma'), Op. 36, and by Alexander Borodin (1833–1887) in the Scherzo of his Symphony No. 2 in B minor
2usually used instead of 2/2, the mark, as applied up to the mid-eighteenth century, is employed in music that is very slow and also in music that is extremely fast. Hotteterre, who points out that the marking is never found in Italian music, recommends the use of supplementary signs to distinguish the slow from the quick. For example, the markings alla cappella or alla breve indicate an exceeedingly fast 2-in-a-bar tempo
2
1
cut time or alla breve, used for marches, sometimes marked
2
2
cut time, alla breve or 'in 2', sometimes marked
used for marches and fast orchestral music, and frequently occurs in musical theatre
3an alternative to 3/4, usually signifying a quicker tempo although Hotteterre (1719) indicates that music in 3 might be very slow or sometimes very fast
3
2
also known as double triple or major triple, because its pulse should be twice as slow as that of ordinary triple time (i.e. 3/4), the meter is usually taken in three slow beats
4
2
alla breve, rare in music since 1600, although Brahms used it occasionally. Marpurg (writing in about 1755) informs us that "this metre is used only in counterpoint and fugues"
2
4
used for polkas or marches. About its use in pre-mid-eighteenth-century music, Choquel (1759) writes that the meter is used for music that is neither too slow nor too fast; in other words, the speed is generally moderato
3
4
used for waltzes, minuets and scherzi and country & western ballads. In pre-mid-eighteenth-century French music, 3/4 signifies music that is neither too fast nor too slow
occasionally published time signatures can be incorrect. The Beatles' Norwegian Wood is published with a 3/4 time signature, possibly the result of a mistake by an assistant editor in a publishing house. McCartney didn't read music, at least not then. But in fact it is phrased in 6/8, which would be the correct time signature
4
4
common time widely used in classical music; the usual time signature in rock, jazz, country, and bluegrass, and most modern pop or dance music. 4/4 was rarely used before the mid-eighteenth century, when the standard symbol for four beats in a bar was common time symbol. Hotteterre (1719) informs us that common time metre is suitable for Preludes or first movements of Sonatas, Allemandes, Adagios, Fugues, etc. but not Airs de Ballet
5
4
used for Dave Brubeck's Take Five and the original versions of the theme from Mission:Impossible 1. It is also used in classical music by Gustav Holst in Mars from The Planets; usually grouped as 3+2 or 2+3
6
4
in pre-mid-eighteenth-century French music, sometimes called 'the meter of six slow beats'. Although originally used in slow music (and seldom found in Italian music), it was used later for lively buoyant airs and particularly for Reprises in French baroque opera
7
4
used for numerous Genesis songs, Money by Pink Floyd (see also 7/8 below) and The Unsquare Dance by Dave Brubeck
9
4
in pre-mid-eighteenth-century French music, suitable for music with three slow beats in each bar, neither too slow nor too fast
12
4
Brossard (1703) writes that this meter "is suitable for tender, affectionate kinds of expression, and sometimes for lively and animated kinds". Other writers indicate that the meter is performed with four beats to the bar, but gravely, each beat having three crotchets (quarter notes) or the equivalent
2
8
as applied to pre-mid-eighteenth-century music, the marking 2/8 is usually to be thought of as a metre of one rapid beat, suitable for Tambourins and other pieces of like character
3
8
or minor triple, as applied to pre-mid-eighteenth-century music, generally very quick, twice as fast as music in 3/4
4
8
as applied to pre-mid-eighteenth-century music, although sometimes used in place of 2/4, the marking 4/8 is usually to be thought of as a metre of two rapid beats
6
8
used for light, double and triple jigs, fast waltzes or marches. In general, music in 6/8 is taken at a faster speed than music in 6/4 and is most commonly felt as two beats to the bar
7
8
the sheet music for Money by Pink Floyd shows a predominant time signature of 7/4 (simple septuple). David Gilmour, the guitarist, states it as being 7/8 on the documentary, The Making of The Dark Side of the Moon. Most rock music is in 4/4, or common time, and most of the exceptions are in 3/4 or a similar triple meter. During the guitar solo the song changes to 4/4, then returns to 7/4, then ends in 4/4 again. This was done because David Gilmour thought it would be too complicated to write the solo in seven beat form. Critics have commented that the change in dynamic (maintaining tempo but changing from seven beats to the bar to 8 beats making the song feel quicker) is one of the track's strengths
  • a distinction between 7/4 and 7/8 is discussed and demonstrated in this video
9
8
compound triple time, used today rarely although it occurs in Dukas' The Sorcerer's Apprentice and in traditional slip and hop jigs. It appeared in late seventeenth-century France as a meter that is to be taken half as fast again as its parallel 9/4, and was thought suitable particularly for gigues
12
8
common in blues and doo-wop, as well as some traditional single jigs or slides. In the eighteenth century the 12/8 metre was taken in 4, with three quavers (eighth notes) to each beat. In the opinion of Brossard (1755) this meter was used by the Italians for tender and affectionate feelings although it would then bear a marking such as adagio affettuoso without which the movement would be spirited and lively
3
16
a rare compound time (one sixteenth note triplet to the bar) which in the opinion of Brossard (1755) is suitable for extremely lively and exceedingly rapid music
6
16
a rare compound time (two sixteenth note triplets to the bar) used for extremely rapid pieces, what the Italians would describe as a prestissimo
9
16
a rare compound time (three sixteenth note triplets to the bar) for very fast music
12
16
suitable for extremely lively and rapid music which the Italians describe with the word prestissimo [Brossard (1755)]. Hotteterre (1719) suggests that one of the earliest to use this marking in France was Franįois Couperin
14
16
used by Philip Glass' Mad Rush
although, as we mention above, rock music uses a basic 4/4 beat (however accented or syncopated), math rock frequently uses compound time signatures (meters) such as 7/8, 11/8, or 13/8, or features constantly changing meters based on various groupings of 2 and 3. This rhythmic complexity, seen as "mathematical" in character by many listeners and critics, is what gives the genre its name

One of our readers, Kenneth J. Nessing, posed an interesting question:

"Is there an advantage, or other reason for, writing a piece in 5/4 as opposed to 5/8?

There is a convention whether to notate the lower figure in a time signature as an 8 or a 4. Usually, a 4, as the lower figure in a time signature, indicates that the music is to be played more slowly than when the lower figure is an 8. The speed difference is not as great as that found in Ars Nova mensuration (with its modus, tempus and prolatio) and so we may regard this now as just a convention. So, a jig (which is a quick 3 in a bar) is usually written in 3/8, while a minuet (which is usually a slower 3 in a bar) is written in 3/4.

References:

Unusual Time Signatures and Hypermeasure :: top

Key words:
odd meter
hypermeasure
1

Unusual Time Signatures and Hypermeasure

The second movement of Tchaikovsky's Symphony No. 6 in B minor, Pathetique, begins like a typical waltz, except for the unusual feature of a five over four time signature broken into two plus three crotchet beats per bar.

Click Allegro con grazia to hear the opening of the second movement.

Charles Ives, in his 114 Songs published in 1922, employs a number of unusual time notations. In some cases, for example songs no 21, 27 and 30, he uses no time signature at all, while in song no. 6 he marks a time signature of four and a half over four. In song no. 37 there is no time signature or bar lines and the performer is directed to mark off the bars to suite his taste. These effects demonstrate how composers have always tried to bend formal notation to produce novel effects. Ives used this particular set of songs to explore notation, harmony and the relationship between the artist, the music and the listener.

Charles Ives : Postface to 114 Songs

(selections from "Postface To 114 Songs", Essays Before a Sonata, The Majority, and Other Writings)

. . . . Be that as it may, our theory has a name: it is, "the balance of values," or "the circle of sources" (in these days of chameleon-like efficiency every whim must be classified under a scientific-sounding name to save it from investigation). It stands something like this: that an interest in any art-activity from poetry to baseball is better, broadly speaking, if held as a part of life, or of a life, than if it sets itself up as a whole -- a condition verging, perhaps, toward a monopoly or, possibly, a kind of atrophy of the other important values, and hence reacting unfavorably upon itself. . . .

. . . To illustrate further (and to become more involved): if this interest, and everyone has it, is a component of the ordinary life, if it is free primarily to play the part of the, or a, reflex, subconscious-expression, or something of that sort, in relation to some fundamental share in the common work of the world, as things go, is it nearer to what nature intended it should be, than if, as suggested above, it sets itself up as a whole -- not a dominant value only, but a complete one? If a fiddler or poet does nothing all day long but enjoy the luxury and drudgery of fiddling or dreaming, with or without meals, does he or does he not, for this reason, have anything valuable to express? -- or is whatever he thinks he has to express less valuable than he thinks?

This is a question which each man must answer for himself. It depends, to a great extent, on what a man nails up on his dashboard as "valuable." Does not the sinking back into the soft state of mind (or possibly a non-state of mind) that may accept "art for art's sake" tend to shrink rather than toughen up the hitting muscles -- and incidentally those of the umpire or the grandstand, if there be one? To quote from a book that is not read, "Is not beauty in music too often confused with something which lets the ears lie back in an easy-chair? Many sounds that we are used to do not bother us, and for that reason are we not too easily inclined to call them beautiful?" . . .

Possibly the fondness for personal expression -- the kind in which self-indulgence dresses up and miscalls itself freedom -- may throw out a skin-deep arrangement, which is readily accepted at first as beautiful -- formulae that weaken rather than toughen the musical-muscles. If a composer's conception of his art, its functions and ideals, even if sincere, coincides to such an extent with these groove-colored permutations of tried-out progressions in expediency so that he can arrange them over and over again to his delight -- has he or has he not been drugged with an overdose of habit-forming sounds? . . . .

References:

  • The Music of Charles Ives - including excerpts from the 114 Songs
  • The Music of Charles Ives - Exercises - showing examples of Ives' extraordinary ideas about tonality and rhythm

    Notation is but a means to an end. If the notation is formal nonsense then the composer's instructions will no longer have any meaning. Our task as performer is to discover the notion behind the notation. The time signature four and a half over four may be unusual but it is not nonsense. Using the information above, we realise that each bar will contain the equivalent of four crotchets plus one quaver.

    There is no reason why time signatures should not show more complicated groupings; for example, a group of four crotchets followed by a group of five quavers repeated over several bars might be notated 4/4 + 5/8. Rhythmic patterns like this, called odd meters, can be found in Balkan folk dance music. Time signatures compounded from smaller units, for example 4/4 next to 3/4, appear in music where the bars alternate, in this case with four and three crotchets in alternate bars.

    That a time signature might relate to groups made up of more than one bar has led to the concept of the hypermeasure, where the individual bars in a hypermeasure perform the same rhythmic role as individual notes in a single measure or bar. The example above, four over four plus three over four, is an example of a two-bar hypermeasure while a twelve-bar blues is an example of a twelve-bar hypermeasure.

  • Mensuration :: top

    Key words:
    mensuration
    modus
    tempus
    prolatio
    major
    minor
    1

    Mensuration

    Time signatures arose from mensuration, a system devised in the thirteenth century to govern rhythmic relationships in music. Relationships between the duration of different notes were defined as follows:

  • The relationship between the longa and the breve was called the modus;
  • The relationship between the breve and the semibreve, the tempus;
  • The relationship between the semibreve and the minim, the prolatio;

    These relationships could be either 3:1 (perfect, or in the case of modus or prolatio major) or 2:1 (imperfect, or in the case of modus or prolatio minor). By adjusting these relationships and mixing them amongst each other, many different divisions of time (just like modern time signatures) were constructed. The 'perfection of 3' comes from its association with the Holy Trinity.

    Reference:

  • Mensuration - An Introduction

  • Common Time & Alla Breve/Cut Time :: top

    Key words:
    common time
    modus
    tempus perfectum
    tempus imperfectum
    alla breve
    alla cappella time
    cut time
    1 Common Time & Alla Breve/Cut Time

    In earlier times it was common practice only to indicate the number of beats in a bar. Triple metre, e.g. 3/4, or tempus perfectum was represented by a circle (according to Pythagoras the sphere represents perfection), while tempus imperfectum, i.e. 4/4, was represented by a half circle in the form of a letter C. Duple metre, i.e. 2/2, was represented by a semicircle with a vertical line. The two latter symbols have remained in use even if they now appear in a somewhat stylised form. The half circle intersected by a vertical line can be used also for the time signature 2/1.

    The first symbol is called 'common time', representing four crotchet beats in a bar. This is illustrated in the first example below.

    The second symbol, similar to the first but crossed with a vertical line, is called alla breve (Italian, literally 'according to the breve'), alla cappella time or cut time. It usually represents two minim beats in a bar. This is illustrated in the second example.

    Again, bars can be made up of notes and/or rests.

    Reference:

  • Metrical Displacement and the Compound Measure in Eighteenth-Century Theory and Practice

    Cut time as used in dance music or jazz generally means that the music is played twice as fast as you would ordinarily expect, based on the notes. Where normally a crotchet would correspond to a beat, now the minim becomes the unit of counting. Merengue music is usually notated in cut-time; each of the "one - two" steps corresponds to a minim instead of a crotchet as might have been expected.

  • Changing Time Signatures :: top

    Key word:
    time signature
    1 Changing Time Signatures

    When the time signature of a piece remains unchanged it will only appear at the beginning of the first bar of the work. However, if the composer wants to change the time signature during the piece, this takes place at the beginning of the bar where the change is required, and the change remains in force until the end of the piece or until a further change is made. An example of this is given below.

    A number of readers have asked whether the tempo changes when the meter changes. In the example above, two bars (measures) of 2/4 followed by two bars (measures) of 3/4 and ending with one bar (measure) of 4/4, the duration of the crotchet (quarter note) remains the same through the five bar (measure) section unless there had been other markings to the contrary (for example, rall., accel., etc.).

    The Whole Bar Rest :: top

    Key word:
    whole bar rest
    multiple bar rest
    1 The Whole Bar Rest

    While, in general, every bar will contain the number of beats set by the time signature, in the form of notes, rests or both, there are occasions where a bar appears to have beats that do not add up to that given by the time signature.

    The most common difference occurs when a whole bar rest, identical to the semibreve rest (or whole-rest), is being used.

    The written time value is always 4 crotchets (or 4 quarter notes).

    However the played time value of a whole bar rest is set by the time signature.

    Thus, in 2/4, the whole bar rest has a played time value of 2 crotchets (or 2 quarter notes), while in 3/4, the whole bar rest has a played time value of 3 crotchets (or 3 quarter notes).

    This rest is illustrated below in four bars each with a different time signature.

    There is one exception to this usage: when the time signature is 4/2 the whole bar rest is the breve or double whole rest.

    Where there are a number of successive bars all marked in the score as whole bar rests and all bearing the same time signature they may be 'collected together' when printed in an individual part. We illustrate below a multiple bar rest lasting 21 bars.

    multiple bar rest

    Incomplete Bars :: top

    Key word:
    incomplete bar
    incomplete measure
    anacrusis
    1 Incomplete Bars

    A bar may not contain the expected number of beats when the first beat of a work is not a strong beat and so the first bar is incomplete. An opening that begins on a weak beat is called an anacrusis, a term derived from poetry. An example of a weak beat opening is given below.

    It is good practice to balance the incomplete bar at the beginning of the piece with a truncated or short bar at the end. The two bars taken together should have the same number of beats as an inner bar. However, this is no more than a 'convention' and nowadays it is often ignored.

    Time signatures are considered further in lesson 15.

    Ametric Music :: top

    Key word:
    ametric music
    1 Ametric Music

    One of the earliest needs for a methodical approach to musical notation arose from a desire to systematise religious chant. Guido d'Arezzo was not the first to notice that an oral tradition where the learning of musical lines passed from teacher to pupil, from choir director to choir member, would lead to the introduction of error and variation from the prescribed forms laid down in Rome, but he was one of the first to suggest how this might be overcome. The rhythmic detail in chant follows from the words and so a musical line with the words written above or below the notated line would suffice to guide the singer. There is no need to add bar lines to show a regular underlying pulse because chant, on the whole, does not have any formal regularity. In performance and conception the musical line is tied to the religious text and this is irregular.

    In early consort music, interesting musical effects were produced by placing parts together where the juxtaposition of rhythm in one line against a different rhythm in another made it impossible to bar both in any meaningful way. For the performer, the absence of barlines actually makes the individual part easier to play and produces a greater freedom in the interpretation of the musical line. In essence, the music is less 'vertical', less 'harmonic'; rather, it is more 'horizontal', more 'melodic'.

    In the twentieth century, composers looked again to ametric music as a way of freeing musical expression from the repetitive rhythmic patterns that the use of formal time signatures implies. Chant, which is generally unbarred, much of the consort music from the seventeenth century, and more modern compositions, where barring is irregular or absent and the music has no rhythmic regularity, is said to be ametric. Non-European folk traditions may also offer examples of ametric music, for example, honkyoku repertoire for the shakuhachi.

    During the 1930s, Messiaen took rhythmic ideas from India (deci tala), ancient Greece and the Orient and developed ametrical rhythm, describing it in a treatise published in 1944. The techniques he used included augmented or diminished rhythms, retrograde rhythms and polyrhythm, also called cross-rhythm.

    Michael Ball writes about Messiaen and about his approach to rhythm:

    "(As) teacher and lecturer at the Paris Conservatoire, he held classes in analysis, theory, aesthetics and rhythm but it wasn't until 1966 that he was officially appointed Professor of Composition. Many famous 'names' passed through these classes including Pierre Boulez, Karlheinz Stockhausen, Iannis Xenakis, Alexander Goehr and later George Benjamin for whom Messiaen had a particular fondness and admiration. Perhaps the one thing that rubbed off on all these composers was Messiaen's avoidance of regular metre, citing it as artificial, relating to marches and more popular music. Messiaen supported his argument by pointing out that in nature things are neither even nor regular. For example, the branches of a tree and the waves of the sea are not even patterns. However, what is 'true' is 'natural resonance', and this 'true' phenomenon is what his music is based on."

    For other examples of ametric music you might examine Gregorian chant, seventeenth-century consort music in facsimile (much was originally unbarred although some editions may include modern-day editorial barring) and, from the twentieth century, Ligeti's Atmosphčres (1961) or, from the end of the nineteenth century, Debussy's Prélude ā l'aprčs-midi d'un faune (written between 1892-1894).

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