Wikipedia

Time signature

"Time (music)" redirects here. For other uses, seeHalf-time (music).

Atime signature(also known asmeter signature,[1]metre signature,[2]andmeasure signature)[3]is an indication inmusic notationthat specifies how manynote valuesof a particular type are contained in each measure (bar). The time signature indicates themeterof a musical movement at the bar level.

{ \key c \major \time 3/4 \relative c' { f a c } }
An example of a3
4time signature. The time signature indicates that there are threequarter notes(crotchets) permeasure(bar).

In a music score the time signature appears as two stacked numerals, such as4
4(spoken asfour–four time), or a time symbol, such ascommon time(spoken ascommon time). It immediately follows thekey signature(or if there is no key signature, theclefsymbol). A mid-score time signature, usually immediately following abarline,indicates a change ofmeter.

Most time signatures are eithersimple(the note values are grouped in pairs, like2
4,3
4,and4
4), orcompound(grouped in threes, like6
8,9
8,and12
8). Less common signatures indicatecomplex,mixed,additive,andirrational meters.

{ \override Score.SpacingSpanner.strict-note-spacing = ##t \set Score.proportionalNotationDuration = #(ly:make-moment 1/1) \key c \major \relative c' { \numericTimeSignature \time 4/4 s1 \defaultTimeSignature \time 4/4 s1 \numericTimeSignature \time 2/2 s1 \defaultTimeSignature \time 2/2 s1 \time 2/4 s2 \time 3/4 s2. \time 6/8 s2. } }
Basic time signatures:4
4,also known ascommon time(common time);2
2,alla breve,also known ascut timeorcut-common time(cut time);2
4;3
4;and6
8

Time signature notation

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Most time signatures consist of two numerals, one stacked above the other:

  • Thelowernumeral indicates the note value that the signature is counting. This number is always apower of 2(unless the time signature isirrational), usually 2, 4 or 8, but less often 16 is also used, usually in Baroque music. 2 corresponds to the half note (minim), 4 to the quarter note (crotchet), 8 to the eighth note (quaver), 16 to the sixteenth note (semiquaver).
  • Theuppernumeral indicates how many such note values constitute abar.

For instance,2
4means twoquarter-notes(crotchets) per bar, while4
8means foureighth-notes(quavers) per bar. The most common time signatures are2
4,3
4,and4
4.

Symbolic signatures

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"Common time" redirects here. For the short story, seeCommon Time.For the Field Music album, seeCommontime(album).For the time period, seeCommon Era.

By convention, two special symbols are sometimes used for4
4and2
2:

  • The symbolis sometimes used for4
    4    time, also calledcommon timeorimperfect time.
  • The symbolis sometimes used in place of2
    2    and is calledalla breveor, colloquially,cut timeorcut common time.

These symbols derive frommensural time signatures,described below.

Frequently used time signatures

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Simple versus compound

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Simple meters are those whose upper number is 2, 3, or 4, sometimes described asduple meter,triple meter,andquadruple meterrespectively.

Incompound meter,the note values specified by the bottom number are grouped into threes, and the upper number is a multiple of 3, such as 6, 9, or 12. The lower number is most commonly an 8 (an eighth-note or quaver): as in9
8or12
8.

Other upper numbers correspond toirregular meters.

Beat and subdivision

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Main article:Beat (music)

Musical passages commonly feature a recurring pulse, orbeat,usually in the range of 60–140 beats per minute. Depending on the tempo of the music, this beat may correspond to the note value specified by the time signature, or to a grouping of such note values. Most commonly, in simple time signatures, the beat is the same as the note value of the signature, but in compound signatures, the beat is usually adotted notevalue corresponding to three of the signature's note values. Either way, the next lower note value shorter than the beat is called thesubdivision.

On occasion a bar may seem like one singular beat. For example, a fast waltz, notated in3
4time, may be described as beingone in a bar.Conversely, at slow tempos, the beat might even be a smaller note value than the one enumerated by the time signature.[example needed]

Mathematically the time signatures of, e.g.,3
4and3
8are interchangeable. In a senseallsimple triple time signatures, such as3
8,3
4,3
2,etc.—and all compound duple times, such as6
8,6
16and so on, are equivalent. A piece in3
4can be easily rewritten in3
8,simply by halving the length of the notes.

Other time signature rewritings are possible: most commonly a simple time-signature with triplets translates into a compound meter.

The choice of time signature in these cases is largely a matter of tradition. Particular time signatures are traditionally associated with different music styles—it would seem strange to notate a conventionalrocksong in4
8or4
2,rather than4
4.

Examples

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In the examples below,bolddenotes the primary stress of the measure, anditalicsdenote a secondary stress. Syllables such as "and" are frequently used for pulsing in between numbers.

Simple:3
4is a simpletriple metertime signature that represents three quarter notes (crotchets), usually perceived as three beats. In this case the subdivision would be the eighth note (quaver). It is felt as

3
4:oneandtwoandthreeand...

Compound:Most often,6
8is felt as two beats, each being a dotted quarter note (crotchet), and each containing subdivisions of three eighth notes (quavers). It is felt as

6
8:onetwo threefourfive six... (or, if counting dotted-quarter beats,oneand atwoand a)

The table below shows the characteristics of the most frequently used time signatures.

Simple time signatures
Time signature Common uses Simple drum pattern Video representation
4
4or

(quadruple)

Common time:Widely used inclassical musicand most forms ofpopular music.Most common time signature inrock,blues,country,funk,andpop.[4]
2
2or

(duple)

Alla breve,cut time:Used formarchesand fast orchestral music.
2
4

(duple)

Used forpolkas,galops,marches,and many styles ofLatin music(includingbolero,cumbia,andmerengue).
3
4

(triple)

Used forwaltzes,minuets,scherzi,polonaises,mazurkas,country & western ballads, R&B, and some pop
3
8

(triple)

Also used for the above but usually suggests higher tempo or shorterhypermeter.Sometimes preferred for certain folk dances such ascachucha
Compound time signatures
Time signature Common uses Simple drum pattern Video representation
6
8

(duple)

Doublejigs,jotas,zortzikos,polkas,sega,salegy,tarantella,marches,barcarolles,loures,and some rock music.Anapestic tetrameterpoetry also fits into6
8time when said aloud.
9
8

(triple)

Compound triple time:Used inslip jigs;otherwise occurring rarely ( "The Ride of the Valkyries",Tchaikovsky'sFourth Symphony,and the final movement ofJ.S. Bach'sViolin Concerto in A minor (BWV 1041)are familiar examples.Debussy's "Clair de lune"and the opening bars ofPrélude à l'après-midi d'un fauneare also in9
8)
12
8

(quadruple)

Also common in slowerblues(where it is called ashuffle) anddoo-wop;also used more recently in rock music. Can also be heard in some jigs like "The Irish Washerwoman".This is also the time signature of the second movement ofBeethoven'sPastoral Symphony.

Tempo giusto

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Main article:Tempo giusto

While changing the bottom number and keeping the top number fixed only formally changes notation, without changing meaning –3
8,3
4,3
2,and3
1are all three beats to a meter, just noted with eighth notes, quarter notes, half notes, or whole notes – these conventionally imply different performance and different tempi. Conventionally, larger numbers in the bottom correspond to faster tempi and smaller numbers correspond to slower tempi. This convention is known astempo giusto,and means that the tempo of each note remains in a narrower, "normal" range. For illustration, a quarter note might correspond to 60–120 bpm, a half note to 30–60 bpm, a whole note to 15–30 bpm, and an eighth note to 120–240 bpm; these are not strict, but show an example of "normal" ranges.

This convention dates to theBaroqueera, when tempo changes were indicated by changing time signature during the piece, rather than by using a single time signature and changing tempo marking.[5]For example, while3
8,3
4,3
2,and3
1have the same beat pattern, they would conventionally be used for increasingly slow music. A 20th century example is "O Fortuna"(1935–1936) byCarl Orff,which begins slowly in3
1,and then speeds up and changes to3
2.

Complex time signatures

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See also:List of musical works in unusual time signatures,Quintuple meter,andSeptuple meter
"13/8" redirects here. For the date, seeAugust 13.
19
16Time Drum Beat
Problems playing this file? Seemedia help.

Signatures that do not fit the usual simple or compound categories are calledcomplex,asymmetric,irregular,unusual,orodd—though these are broad terms, and usually a more specific description is any meter which combines both simple and compound beats.[6][7]

Irregular meters are common in some non-Western music, and in ancient Greek music such as theDelphic Hymnsto Apollo, but the corresponding time signatures rarely appeared in formal written Western music until the 19th century. Early anomalous examples appeared in Spain between 1516 and 1520,[8]plus a small section in Handel's operaOrlando(1733).

The third movement ofFrédéric Chopin'sPiano Sonata No. 1(1828) is an early, but by no means the earliest, example of5
4time in solo piano music.Anton Reicha's Fugue No. 20 from hisThirty-six Fugues,published in 1803, is also for piano and is in5
8.Thewaltz-like second movement of Tchaikovsky'sPathétiqueSymphony(shown below), often described as a "limping waltz",[9]is a notable example of5
4time in orchestral music.

Examples from20th-century classical musicinclude:

In the Western popular music tradition, unusual time signatures occur as well, withprogressive rockin particular making frequent use of them. The use of shifting meters inThe Beatles' "Strawberry Fields Forever"and the use ofquintuple meterin their "Within You, Without You"are well-known examples,[10]as isRadiohead's "Paranoid Android"(includes7
8).[11]

Paul Desmond'sjazzcomposition "Take Five",in5
4time, was one of a number of irregular-meter compositions thatThe Dave Brubeck Quartetplayed. They played other compositions in11
4( "Eleven Four" ),7
4( "Unsquare Dance"), and9
8( "Blue Rondo à la Turk"), expressed as2+2+2+3
8."Blue Rondo à la Turk" is an example of a signature that, despite appearing merely compound triple, is actually more complex. Brubeck's title refers to the characteristicaksakmeter of the Turkishkarşılamadance.[12]

However, such time signatures are only unusual in most Western music. Traditionalmusic of the Balkansuses such meters extensively.Bulgarian dances,for example, include forms with 5, 7, 9, 11, 13, 15, 22, 25 and other numbers of beats per measure. These rhythms are notated asadditive rhythmsbased on simple units, usually 2, 3 and 4 beats, though the notation fails to describe themetric"time bending" taking place, orcompound meters.SeeAdditive metersbelow.

Some video samples are shown below.

5
4at 60bpm
7
4at 60 bpm
11
4at 60 bpm

Mixed meters

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While time signatures usually express a regular pattern of beat stresses continuing through a piece (or at least a section), sometimes composers change time signatures often enough to result in music with an extremely irregular rhythm. The time signature may switch so much that a piece may not be best described as being in one meter, but rather as having a switching mixed meter. In this case, the time signatures are an aid to the performers and notnecessarilyan indication of meter. The Promenade fromModest Mussorgsky'sPictures at an Exhibition(1874) is a good example. The opening measures are shown below:

Igor Stravinsky'sThe Rite of Spring(1913) is famous for its "savage" rhythms. Five measures from "Sacrificial Dance" are shown below:

In such cases, a convention that some composers follow (e.g.,Olivier Messiaen,in hisLa Nativité du SeigneurandQuatuor pour la fin du temps) is to simply omit the time signature.Charles Ives'sConcord Sonatahas measure bars for select passages, but the majority of the work is unbarred.

Some pieces have no time signature, as there is no discernible meter. This is sometimes known asfree time.Sometimes one is provided (usually4
4) so that the performer finds the piece easier to read, and simply has "free time" written as a direction. Sometimes the wordFREEis written downwards on the staff to indicate the piece is in free time.Erik Satiewrote many compositions that are ostensibly in free time but actually follow an unstated and unchanging simple time signature. Later composers used this device more effectively, writing music almost devoid of a discernibly regular pulse.

If two time signatures alternate repeatedly, sometimes the two signatures are placed together at the beginning of the piece or section, as shown below:

Detail of a score of Tchaikovsky'sString Quartet No. 2 in F major,showing a multiple time signature

Additive meters

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To indicate more complex patterns of stresses, such asadditive rhythms,more complex time signatures can be used. Additive meters have a pattern ofbeatsthat subdivide into smaller, irregular groups. Such meters are sometimes calledimperfect,in contrast toperfect meters,in which thebaris first divided into equal units.[13]

For example, the time signature3+2+3
8means that there are 8 quaver beats in the bar, divided as the first of a group of three eighth notes (quavers) that are stressed, then the first of a group of two, then first of a group of three again. The stress pattern is usually counted as

3+2+3
8:onetwo threeonetwoonetwo three...

This kind of time signature is commonly used to notate folk and non-Western types of music. In classical music,Béla BartókandOlivier Messiaenhave used such time signatures in their works. The first movement ofMaurice Ravel'sPiano Trio in A Minoris written in8
8,in which the beats are likewise subdivided into3+2+3to reflectBasquedance rhythms.

RomanianmusicologistConstantin Brăiloiuhad a special interest in compound time signatures, developed while studying thetraditional musicof certain regions in his country. While investigating the origins of such unusual meters, he learned that they were even more characteristic of the traditional music of neighboring peoples (e.g., theBulgarians). He suggested that such timings can be regarded as compounds of simple two-beat and three-beat meters, where an accent falls on every first beat, even though, for example inBulgarian music,beat lengths of 1, 2, 3, 4 are used in the metric description. In addition, when focused only on stressed beats, simple time signatures can count as beats in a slower, compound time. However, there are two different-length beats in this resulting compound time, a one half-again longer than the short beat (or conversely, the short beat is2⁄3the value of the long). This type of meter is calledaksak(the Turkish word for "limping" ),impeded,jolting,orshaking,and is described as anirregular bichronic rhythm.A certain amount of confusion for Western musicians is inevitable, since a measure they would likely regard as7
16,for example, is a three-beat measure inaksak,with one long and two short beats (with subdivisions of2+2+3,2+3+2,or3+2+2).[14]

Folk music may make use of metric time bends, so that the proportions of the performed metric beat time lengths differ from the exact proportions indicated by the metric. Depending on playing style of the same meter, the time bend can vary from non-existent to considerable; in the latter case, some musicologists may want to assign a different meter. For example, the Bulgarian tune "Eleno Mome"is written in one of three forms: (1)7 = 2+2+1+2,(2)13 = 4+4+2+3,or (3)12 = 3+4+2+3,but an actual performance (e.g., "Eleno Mome"[15][original research?]) may be closer to4+4+2+3.[clarification needed]The Macedonian3+2+2+3+2meter is even more complicated, with heavier time bends, and use of quadruples on the threes. The metric beat time proportions may vary with the speed that the tune is played. The SwedishBoda Polska(Polska from the parish Boda) has a typical elongated second beat.

In Western classical music, metric time bend is used in the performance of theViennese waltz.Most Western music uses metric ratios of 2:1, 3:1, or 4:1 (two-, three- or four-beat time signatures)—in other words, integer ratios that make all beats equal in time length. So, relative to that, 3:2 and 4:3 ratios correspond to very distinctive metric rhythm profiles. Complex accentuation occurs in Western music, but assyncopationrather than as part of the metric accentuation.[citation needed]

Brăiloiu borrowed a term fromTurkishmedieval music theory:aksak.Such compound time signatures fall under the "aksak rhythm" category that he introduced along with a couple more that should describe the rhythm figures in traditional music.[16]The term Brăiloiu revived had moderate success worldwide, but in Eastern Europe it is still frequently used. However, aksak rhythm figures occur not only in a few European countries, but on all continents, featuring various combinations of the two and three sequences. The longest are in Bulgaria. The shortest aksak rhythm figures follow the five-beat timing, comprising a two and a three (or three and two).

Some video samples are shown below.

3+2+3
8at 120bpm
The rhythm ofDave Brubeck's "Blue Rondo à la Turk":It consists of three measures of2+2+2+3followed by one measure of3+3+3and the cycle then repeats. Taking the smallest time unit as eighth notes, the arrows on the tempo dial show the tempi for ♪, ♩, ♩. and the measure beat. Starts slow, speeds up to usual tempo

A method to create meters of lengths of any length has been published in the Journal of Anaphoria Music Theory[17]and Xenharmonikon 16[18]using both those based on the Horograms ofErv Wilsonand Viggo Brun's algorithm written byKraig Grady.

Irrational meters

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Example of an irrational4
3time signature: here there are four (4) third notes (3) per measure. A "third note" would be one third of a whole note, and thus is a half-note triplet. The second measure of4
2presents the same notes, so the4
3time signature serves to indicate the precise speed relationship between the notes in the two measures.

Irrational time signatures (rarely, "non-dyadic time signatures" ) are used for so-calledirrational bar lengths,[19]that have adenominatorthat is not apower of two(1, 2, 4, 8, 16, 32, etc.). These are based on beats expressed in terms of fractions of full beats in the prevailing tempo—for example3
10or5
24.[19]For example, where4
4implies a bar construction of four quarter-parts of a whole note (i.e., four quarter notes),4
3implies a bar construction of four third-parts of it. These signatures are of utility only when juxtaposed with other signatures with varying denominators; a piece written entirely in4
3,say, could be more legibly written out in4
4.

The same example written using metric modulation instead of irrational time signatures. Three half notes in the first measure (making up a dotted whole note) are equal in duration to two half notes in the second (making up a whole note).
The same example written using a change in time signature.

According toBrian Ferneyhough,metric modulationis "a somewhat distant analogy" to his own use of "irrational time signatures" as a sort of rhythmic dissonance.[19]It is disputed whether the use of these signatures makes metric relationships clearer or more obscure to the musician; it is always possible to write a passage using non-irrational signatures by specifying a relationship between some note length in the previous bar and some other in the succeeding one. Sometimes, successive metric relationships between bars are so convoluted that the pure use of irrational signatures would quickly render the notation extremely hard to penetrate. Good examples, written entirely in conventional signatures with the aid of between-bar specified metric relationships, occur a number of times inJohn Adams' operaNixon in China(1987), where the sole use of irrational signatures would quickly produce massive numerators and denominators.[citation needed]

Historically, this device has been prefigured wherever composers wrotetuplets.For example, a2
4bar of 3 triplet quarter notes could be written as a bar of3
6.Henry Cowell's piano pieceFabric(1920) employs separate divisions of the bar (1 to 9) for the threecontrapuntalparts, using a scheme of shapednoteheadsto visually clarify the differences, but the pioneering of these signatures is largely due toBrian Ferneyhough,who says that he finds that "such 'irrational' measures serve as a useful buffer between local changes of event density and actual changes of basetempo".[19]Thomas Adèshas also used them extensively—for example inTraced Overhead(1996), the second movement of which contains, among more conventional meters, bars in such signatures as2
6,9
14and5
24.

A gradual process of diffusion into less rarefied musical circles seems underway.[citation needed]For example,John Pickard'sEden,commissioned for the 2005 finals of theNational Brass Band Championships of Great Britain,contains bars of3
10and7
12.[20]

Notationally, rather than using Cowell's elaborate series of notehead shapes, the same convention has been invoked as when normal tuplets are written; for example, one beat in4
5is written as a normal quarter note, four quarter notes complete the bar, but the whole bar lasts only4⁄5of a referencewhole note,and a beat1⁄5of one (or4⁄5of a normal quarter note). This is notated in exactly the same way that one would write if one were writing the first four quarter notes of five quintuplet quarter notes.

Some video samples are shown below.

These video samples show two time signatures combined to make apolymeter,since4
3,say, in isolation, is identical to4
4.

Polymeter4
4and4
3played together has three beats of4
3to four beats of4
4
Polymeter2
6and3
4played together has six beats of2
6to four beats of3
4
Polymeter2
5and2
3played together has five beats of2
5to three beats of2
3.The displayed numbers count the underlyingpolyrhythm,which is 5:3

Variants

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Some composers have used fractional beats: for example, the time signature2+1⁄2
4appears inCarlos Chávez's Piano Sonata No. 3 (1928) IV, m. 1. Both2+1⁄2
4and1+1⁄2
4appear in the fifth movement ofPercy Grainger'sLincolnshire Posy.

Example of Orff's time signatures (traditionally, these would be notated3
8and6
8respectively)

Music educatorCarl Orffproposed replacing the lower number of the time signature with an actual note image, as shown at right. This system eliminates the need for compound time signatures, which are confusing to beginners. While this notation has not been adopted by music publishers generally (except in Orff's own compositions), it is used extensively in music education textbooks. Similarly, American composersGeorge CrumbandJoseph Schwantner,among others, have used this system in many of their works.Émile Jaques-Dalcrozeproposed this in his 1920 collection,Le Rythme, la musique et l'éducation.[21]

Another possibility is to extend the barline where a time change is to take place above the top instrument's line in a score and to write the time signature there, and there only, saving the ink and effort that would have been spent writing it in each instrument's staff.Henryk Górecki'sBeatus Viris an example of this. Alternatively, music in a large score sometimes has time signatures written as very long, thin numbers covering the whole height of the score rather than replicating it on each staff; this is an aid to the conductor, who can see signature changes more easily.

Early music usage

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Mensural time signatures

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Main article:Mensural notation § Mensurations

In themensural notationof the 14th, 15th and 16th centuries there are nobarlines, and the four basicmensuration signsindicate the normal ratio ofdurationbetween differentnote values.Unlike modern notation, the subdivisions could be either 2:1 or 3:1. The relation between thebreveand thesemibrevewas calledtempus,and could be perfect (triple3:1 indicated by circle) or imperfect (duple2:1, with broken circle), while the relation between thesemibreveand theminimwas calledprolatioand could be major (3:1 orcompound,indicated by dot) or minor (2:1 orsimple meter).

Modern transcriptions often reduce note values 4:1, such that

  • corresponds to9
    8    meter;
  • corresponds to3
    4    meter;
  • corresponds to6
    8    meter;
  • corresponds to2
    4    meter.

N.B.: In mensural notation actual note values depend not only on the prevailing mensuration, but on rules forimperfection and alteration,with ambiguous cases using a dot of separation, similar in appearance but not always in effect to the moderndot of augmentation.

Proportions

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Main article:Mensural notation § Proportions and colorations
Proportion signs[22]
Proportion Notated values equivalent to Notated values
2or

2or

3

3

Besides showing the organization of beats withmusical meter,the mensuration signs discussed above have a second function, which is showing tempo relationships between one section to another, which modern notation can only specify withtupletsormetric modulations.This is a fraught subject, because the usage has varied with both time and place:Charles Hamm[23]was even able to establish a rough chronology of works based on three distinct usages of mensural signs over the career ofGuillaume Dufay(1397(?) – 1474). By the end of the sixteenth centuryThomas Morleywas able to satirize the confusion in an imagined dialogue:

it was a world to hear them wrangle, every one defending his own for the best. "What? You keep not time in your proportions." "You sing them false. What proportion is this?" "Sesquipaltry." "Nay, you sing you know not what; it would seem you came lately from a barber's shop where you had 'Gregory Walker' or aCurrantaplayed in the new Proportions by them lately found out, called 'Sesquiblinda' and 'Sesquihearkenafter'. "

Plaine and Easie Introduction to Practicall Musicke(1597)[24]

In general though, a slash or the numeral 2 shows a doubling of tempo, and paired numbers (either side by side or one atop another) show ratios instead of beats per measure over note value: in early music contexts4
3for example is unrelated to 'third-notes'.[25]

A few common signs are shown:[26]

  • tempus imperfectum diminutum,1:2 proportion (twice as fast);
  • tempus perfectum diminutum,1:2 proportion (twice as fast);
  • orproportio tripla,1:3 proportion (three times as fast, similar to triplets).

In particular, when the signwas encountered, thetactus(beat) changed from the usual whole note (semibreve) to the double whole note (breve), a circumstance calledalla breve.This term has been sustained to the present day, and though now it means the beat is ahalf note(minim), in contradiction to the literal meaning of the phrase, it still indicates that thetactushas changed from a short to a doubled value.

Certain composers delighted in creating mensuration canons, "puzzle"compositions that were intentionally difficult to decipher.[27]

Irregular bar

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Irregular bars are a change in time signature normally for only one bar. Such a bar is most often a bar of3
4,5
4or2
4in a4
4composition, or a bar of4
4in a3
4composition, or a bar of5
8in a6
8composition.

If a song is entirely in4
4a change to3
4will make the song feel like it has skipped a beat, the opposite is true for5
4where it feels like the song adds a beat. If a song changes to2
4is will make it feel like that bar is half as long as all the others[28][29]

Some popular examples include "Golden Brown"byThe Stranglers(4
4in a3
4composition), "I Love Rock 'n' Roll"originally byThe Arrows(7
4in a4
4composition), "Hey Ya!"byOutkast(2
4in a4
4composition), and "Wuthering Heights"byKate Bush(different kinds of irregular bars in a4
4composition).

See also

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  • Schaffel,a kind of swing in rock and techno music
  • Tala,meter in Indian music
  • Colotomy,a coinage by Jap Kunst to describe the metric structure of gamelan music.

References

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  1. ^Alexander R. Brinkman,Pascal Programming for Music Research(Chicago:University of Chicago Press,1990): 443, 450–63, 757, 759, 767.ISBN0226075079;Mary Elizabeth Clark and David Carr Glover,Piano Theory: Primer Level(Miami: Belwin Mills, 1967): 12; Steven M. Demorest,Building Choral Excellence: Teaching Sight-Singing in the Choral Rehearsal(Oxford and New York:Oxford University Press,2003): 66.ISBN0195165500;William Duckworth,A Creative Approach to Music Fundamentals,eleventh edition (Boston, MA: Schirmer Cengage Learning, 2013): 54, 59, 379.ISBN0840029993;Edwin Gordon,Tonal and Rhythm Patterns: An Objective Analysis: A Taxonomy of Tonal Patterns and Rhythm Patterns and Seminal Experimental Evidence of Their Difficulty and Growth Rate(Albany: SUNY Press, 1976): 36–37, 54–55, 57.ISBN0873953541;Demar Irvine, Reinhard G. Pauly, Mark A. Radice,Irvine’s Writing about Music,third edition (Portland, Oregon: Amadeus Press, 1999): 209–210.ISBN1574670492.
  2. ^Henry Cowelland David Nicholls,New Musical Resources,third edition (Cambridge and New York:Cambridge University Press,1996): 63.ISBN0521496519(cloth);ISBN0521499747(pbk); Cynthia M. Gessele, "Thiéme, Frédéric [Thieme, Friedrich]",The New Grove Dictionary of Music and Musicians,second edition, edited byStanley SadieandJohn Tyrrell(London: Macmillan Publishers, 2001); James L. Zychowicz,Mahler's Fourth Symphony(Oxford and New York: Oxford University Press, 2005): 82–83, 107.ISBN0195181654.
  3. ^Edwin Gordon,Rhythm: Contrasting the Implications of Audiation and Notation(Chicago: GIA Publications, 2000): 111.ISBN1579990983.
  4. ^Scott Schroedl,Play Drums Today! A Complete Guide to the Basics: Level One(Milwaukee: Hal Leonard Corporation, 2001), p. 42.ISBN0-634-02185-0.
  5. ^Dokter, Julia (2021).Tempo and Tactus in the German Baroque.University of Rochester Press. p.144.ISBN9781648250187.
  6. ^"musictheory.net".musictheory.net.Retrieved2023-08-02.
  7. ^"Odd Time Signatures: A Complete Guide | Hello Music Theory".hellomusictheory /.6 March 2020.Retrieved2022-02-20.
  8. ^Tim Emmons,Odd Meter Bass: Playing Odd Time Signatures Made Easy(Van Nuys: Alfred Publishing, 2008): 4.ISBN978-0-7390-4081-2."What is an 'odd meter'?...A complete definition would begin with the idea of music organized in repeating rhythmic groups of three, five, seven, nine, eleven, thirteen, fifteen, etc."
  9. ^"Tchaikovsky's Symphony No. 6 (Pathetique), Classical Classics, Peter Gutmann ".Classical Notes.Retrieved2012-04-20.
  10. ^Edward Macan,Rocking the Classics: English Progressive Rock and the Counterculture(New York: Oxford University Press, 1997): 48.ISBN978-0-19-509888-4.
  11. ^Radiohead (musical group).OK Computer,vocal score with guitar accompaniment and tablature (Essex, England: IMP International Music Publications; Miami, Florida: Warner Bros. Publications; Van Nuys, California: Alfred Music, 1997):[page needed].ISBN0-7579-9166-1.
  12. ^Manuel, Peter (1988).Popular Musics of the Non-Western World: An Introductory Survey(rev. ed.). Oxford University Press. p.131.ISBN9780195063349.
  13. ^Read, Gardner (1969).Music Notation: A Manual of Modern Practice.Boston: Allyn and Bacon, Inc.ISBN0800854535.[page needed]
  14. ^Constantin Brăiloiu,Le rythme Aksak,Revue de Musicologie33, nos. 99 and 100 (December 1951): 71–108. Citation on pp. 75–76.
  15. ^Audio: "Eleno Mome"fromThe Dances of the World's Peoples, Vol. 1: Dances of the Balkans and Near East,Smithsonian Folk Ways
  16. ^Gheorghe Oprea,Folclorul muzical românesc(Bucharest: Ed. Muzicala, 2002),[page needed]ISBN973-42-0304-5
  17. ^"The Journal of Anaphorian Music Theory".
  18. ^"Frog Peak Artist: John Chalmers".
  19. ^abcd"Brian Ferneyhough",The Ensemble Sospeso
  20. ^John Pickard: Eden, full score, Kirklees Music, 2005.
  21. ^Jaques-Dalcroze, Émile(1967).Rhythm, Music and Education.Translated by Harold F. Rubenstein. London: Dalcroze Society. p. 84, and Appendix, example 2.–Page 210in the French original
  22. ^Apel 1953,p. 150.
  23. ^C. Hamm:A Chronology of the Works of Guillaume Dufay based on a Study of Mensural Practice(Princeton, New Jersey, 1964)
  24. ^Thomas Morley:Plaine and Easie Introduction to Practicall Musicke(1597), quoted in the unsigned "Proportions" inNew GroveXV p. 307 (1980)
  25. ^Apel 1953,p. 189.
  26. ^Apel 1953,p. 148.
  27. ^Ernst Friedrich Richter,A Treatise on Canon and Fugue: Including the Study of Imitation,translated from third German edition by Arthur W. Foote (Boston: Oliver Ditson, 1888): 38. [ISBN unspecified].
  28. ^Songs That Skip a Beat,7 August 2019,retrieved2022-09-22
  29. ^Songs That Add a Beat,8 July 2019,retrieved2022-09-22

Sources

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