Rhythm & Form on Music Theory Print

Binary form

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Structure#

A typical example of a piece in binary form has two large sections of roughly equal duration. The first will begin in a certain key, which will often, (but not always), modulate to a closely related key. Pieces in a major key will usually modulate to the dominant, (the fifth scale degree above the tonic). Pieces in a minor key will generally modulate to the relative major key, (the key of the third scale degree above the minor tonic), or to the dominant minor. A piece in minor may also stay in the original key at the end of the first section, closing with an imperfect cadence. The second section of the piece begins in the newly established key, where it remains for an indefinite period of time. After some harmonic activity, the piece will eventually modulate back to its original key before ending. More often than not, especially in 18th-century compositions, the A and B sections are separated by double bars with repeat signs, meaning both sections were to be repeated. Binary form is usually characterized as having the form AB, though since both sections repeat, a more accurate description would be AABB. Others, however, prefer to use the label AA′. This second designation points to the fact that there is no great change in character between the two sections. The rhythms and melodic material used will generally be closely related in each section, and if the piece is written for a musical ensemble, the instrumentation will generally be the same. This is in contrast to the use of verse-chorus form in popular music—the contrast between the two sections is primarily one of the keys used.

Fugue

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Etymology#

The English term fugue originated in the 16th century and is derived from the French word fugue or the Italian fuga. This in turn comes from the Latin fuga, which is itself related to both fugere (“to flee”) and fugare (“to chase”). Variants include fughetta (“a small fugue”) and fugato (a passage in fugal style within another work that is not a fugue).

Musical outline#

A fugue begins with the exposition and is written according to certain rules. The composer has more freedom once the exposition ends, though a logical key structure is usually followed. Further entries of the subject will occur throughout the fugue, repeating the accompanying material at the same time, and often accompanying key changes. The various entries may or may not be separated by episodes or occur in stretto. :: S = subject; A = answer; CS = countersubject; T = tonic; D = dominant Exposition A fugue begins with the exposition of its subject in one of the voices alone in the tonic key. After the statement of the subject, a second voice enters and states the subject with the subject transposed to another key (almost always the dominant or subdominant, with the latter being less common), which is known as the answer. To enable a natural harmonic progression, the answer may also be altered slightly (usually by changing one or a few notes near the beginning). When the answer is an exact transposition of the subject into the new key, the answer is classified as a real answer; alternatively, if the intervals of the subject are altered in any way, the answer is a tonal answer. During the answer, the voice in which the subject was previously heard accompanies with new material. If this new material is reused in later statements of the subject, it is called a countersubject; if this accompanying material is only heard once, it is simply referred to as free counterpoint. The countersubject is written in invertible counterpoint at the octave or fifteenth (two octaves). The distinction is made between the use of free counterpoint and regular countersubjects accompanying the fugue subject/answer, because in order for it to be heard accompanying the subject in more than one instance, the countersubject must be capable of sounding correctly when played above or below the subject, and must be conceived, therefore, in invertible (double) counterpoint. In tonal music, invertible contrapuntal lines must be written according to certain rules, because several intervallic combinations, while acceptable in one orientation, are not permissible when inverted. As an example, perfect fifths are contrapuntally acceptable, while the inversion of a perfect fifth results in a perfect fourth, which, unlike the perfect fifth, is considered a dissonance, requiring proper preparation and resolution. The countersubject, if sounding at the same time as the answer, is transposed to the pitch of the answer. Each voice then responds with its own subject or answer, and further countersubjects or free counterpoint may be heard. It is customary in the exposition to alternate entrances of the subject (S) with entrances of the answer (A). However, this order is occasionally varied. For example, the exposition from J.S. Bach’s The Well-Tempered Clavier Fugue No. 1 in C Major, BWV 846 uses a SAAS (subject-answer-answer-subject) exposition. A brief codetta is often heard connecting the various statements of the subject and answer, smoothly connecting each and often facilitating the modulation between the tonic and the key of the answer. The codetta, like other parts of the exposition, may be reused throughout the remainder of the fugue. The first answer must occur as soon after the initial statement of the subject as possible; therefore, the first codetta is often absent or very short. In the example shown above of J.S. Bach’s Fugue No. 16 in G minor, BWV 861, the first codetta is absent. The subject concludes on the quarter note (or crotchet) B of the third beat of the second bar, which harmonizes the opening G of the tonal answer. The later codettas may be considerably longer, and often serve to develop the material heard in the subject/answer and countersubject and possibly introduce ideas heard in the second countersubject or free counterpoint that follows. They may also be present to delay, and therefore heighten the impact of, the reentry of the subject in another voice. Finally, they may be modulatory passages to return the fugue to the tonic. The exposition usually concludes when all voices have given a statement of the subject or answer. In some fugues, especially those with an odd number of voices, the exposition will end with a redundant entry, or an extra presentation of the theme in a voice which has already entered. Furthermore, the entry of one of the voices may not be heard until considerably later. For example, in J.S. Bach’s Fugue in C minor for Organ, BWV 549, the subject entrance in the lowest voice (played by the organ pedals), is not heard until near the end of the fugue.

Metre (music)

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Metric structure#

The term metre is not very precisely defined. Stewart MacPherson preferred to speak of “time” and “rhythmic shape”, while Imogen Holst preferred “measured rhythm”. However, Justin London has written a book about musical metre, which “involves our initial perception as well as subsequent anticipation of a series of beats that we abstract from the rhythm surface of the music as it unfolds in time”. This “perception” and “abstraction” of rhythmic bar is the foundation of human instinctive musical participation, as when we divide a series of identical clock-ticks into “tick–tock–tick–tock”. “Rhythms of recurrence” arise from the interaction of two levels of motion, the faster providing the pulse and the slower organizing the beats into repetitive groups. In his book The Rhythms of Tonal Music, Joel Lester notes that, " o nce a metric hierarchy has been established, we, as listeners, will maintain that organization as long as minimal evidence is present". “Meter may be defined as a regular, recurring pattern of strong and weak beats. This recurring pattern of durations is identified at the beginning of a composition by a meter signature (time signature). … Although meter is generally indicated by time signatures, it is important to realize that meter is not simply a matter of notation”. A definition of musical metre requires the possibility of identifying a repeating pattern of accented pulses – a “pulse-group” – which corresponds to the foot in poetry. Frequently a pulse-group can be identified by taking the accented beat as the first pulse in the group and counting the pulses until the next accent. Frequently metres can be subdivided into a pattern of duples and triples. For example, a metre consists of three units of a pulse group, and a metre consists of two units of a pulse group. In turn, metric bars may comprise ‘metric groups’ - for example, a musical phrase or melody might consist of two bars x . The level of musical organisation implied by musical metre includes the most elementary levels of musical form. Metrical rhythm, measured rhythm, and free rhythm are general classes of rhythm and may be distinguished in all aspects of temporality: * Metrical rhythm, by far the most common class in Western music, is where each time value is a multiple or fraction of a fixed unit (beat, see paragraph below), and normal accents reoccur regularly, providing systematic grouping (bars, divisive rhythm). * Measured rhythm is where each time value is a multiple or fraction of a specified time unit but there are not regularly recurring accents (additive rhythm). * Free rhythm is where the time values are not based on any fixed unit; since the time values lack a fixed unit, regularly recurring accents are no longer a possibility. Some music, including chant, has freer rhythm, like the rhythm of prose compared to that of verse. Some music, such as some graphically scored works since the 1950s and non-European music such as Honkyoku repertoire for shakuhachi, may be considered ametric. The music term senza misura is Italian for “without metre”, meaning to play without a beat, using time (e.g. seconds elapsed on an ordinary clock) if necessary to determine how long it will take to play the bar. Metric structure includes metre, tempo, and all rhythmic aspects that produce temporal regularity or structure, against which the foreground details or durational patterns of any piece of music are projected. Metric levels may be distinguished: the beat level is the metric level at which pulses are heard as the basic time unit of the piece. Faster levels are division levels, and slower levels are multiple levels. A rhythmic unit is a durational pattern which occupies a period of time equivalent to a pulse or pulses on an underlying metric level.

Musical form

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Labeling#

To aid in the process of describing form, musicians have developed a simple system of labeling musical units with letters. In his textbook Listening to Music, professor Craig Wright writes: Some writers also use a prime label (such as B′, pronounced “B prime,” or B″, pronounced “B double prime”) to denote sections that are closely related, but vary slightly.

Levels of organization#

The founding level of musical form can be divided into two parts: * The arrangement of the pulse into unaccented and accented beats, the cells of a measure that, when harmonized, may give rise to a motif or figure. * The further organization of such a measure, by repetition and variation, into a true musical phrase having a definite rhythm and duration that may be implied in melody and harmony, defined, for example, by a long final note and a breathing space. This phrase may be regarded as the fundamental unit of musical form: it may be broken down into measures of two or three beats, but its distinctive nature will then be lost. Even at this level, the importance of the principles of repetition and contrast, weak and strong, climax and repose, can be seen. Thus, form may be understood on three levels of organization which can be roughly designated as passage, piece, and cycle.

Ostinato

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European classical music#

Within the domain of European classical music traditions, Ostinati are used in 20th-century music to stabilize groups of pitches, as in Stravinsky’s The Rite of Spring Introduction and Augurs of Spring. The technique’s appeal to composers from Debussy to avant-garde composers until at least the 1970s “… lies in part in the need for unity created by the virtual abandonment of functional chord progressions to shape phrases and define tonality”. Similarly, in modal music, “… relentless, repetitive character help to establish and confirm the modal center”. Their popularity may also be justified by their ease as well as range of use, though, “… ostinato must be employed judiciously, as its overuse can quickly lead to monotony”.

Polyrhythm

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In western art music#

In some European art music, polyrhythm periodically contradicts the prevailing meter. For example, in Mozart’s opera Don Giovanni, two orchestras are heard playing together in different metres ( and ): They are later joined by a third band, playing in time. Polyrhythm is heard near the opening of Beethoven’s Symphony No. 3. (See also syncopation.) Chopin often explored the rhythmic possibilities inherent in the independence of a pianist’s two hands. A spectacular example may be found in his Étude, Op, 10 No. 10. Alan Walker comments that while this piece is straightforward for listeners, “From the player’s point of view, however, nothing is straightforward. Chopin has placed him inside a veritable hornets’ nest of cross-rhythms and syncopations. The melody first emerges from a background of triplets, then of duplets. Accents are changed without warning, shifting the balance of the phrase sideways, so to speak, together with the place of each note within it.” Polyrhythm is a particularly common feature of the music of Brahms. Writing about the Violin Sonata in G major, Op. 78, Jan Swafford (1997, p. 456) says “In the first movement Brahms plays elaborate games with the phrasing, switching the stresses of the meter back and forth between and , or superimposing both in violin and piano. These ideas gather at the climax at measure 235, with the layering of phrases making an effect that perhaps during the 19th century only Brahms could have conceived.” In “The Snow Is Dancing” from his Children’s Corner suite, Debussy introduces a melody “on a static, repeated B-flat, cast in triplet-division cross rhythms which offset this stratum independently of the sixteenth notes comprising the two dancing-snowflake lines below it.” “In this section great attention to the exactitude of rhythms is demanded by the polyrhythmic superposition of pedals, ostinato, and melody.”

Rhythm

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Anthropology#

Joseph Jordania recently suggested that the sense of rhythm was developed in the early stages of hominid evolution by the forces of natural selection. Plenty of animals walk rhythmically and hear the sounds of the heartbeat in the womb, but only humans have the ability to be engaged (entrained) in rhythmically coordinated vocalizations and other activities. According to Jordania, development of the sense of rhythm was central for the achievement of the specific neurological state of the battle trance, crucial for the development of the effective defense system of early hominids. Rhythmic war cry, rhythmic drumming by shamans, rhythmic drilling of the soldiers and contemporary professional combat forces listening to the heavy rhythmic rock music all use the ability of rhythm to unite human individuals into a shared collective identity where group members put the interests of the group above their individual interests and safety. Some types of parrots can know rhythm. Neurologist Oliver Sacks states that chimpanzees and other animals show no similar appreciation of rhythm yet posits that human affinity for rhythm is fundamental, so that a person’s sense of rhythm cannot be lost (e.g. by stroke). “There is not a single report of an animal being trained to tap, peck, or move in synchrony with an auditory beat”, Sacks write, “No doubt many pet lovers will dispute this notion, and indeed many animals, from the Lipizzaner horses of the Spanish Riding School of Vienna to performing circus animals appear to ‘dance’ to music. It is not clear whether they are doing so or are responding to subtle visual or tactile cues from the humans around them.” Human rhythmic arts are possibly to some extent rooted in courtship ritual. The establishment of a basic beat requires the perception of a regular sequence of distinct short-duration pulses and, as a subjective perception of loudness is relative to background noise levels, a pulse must decay to silence before the next occurs if it is to be really distinct. For this reason, the fast-transient sounds of percussion instruments lend themselves to the definition of rhythm. Musical cultures that rely upon such instruments may develop multi-layered polyrhythm and simultaneous rhythms in more than one time signature, called polymeter. Such are the cross-rhythms of Sub-Saharan Africa and the interlocking kotekan rhythms of the gamelan. For information on rhythm in Indian music see Tala (music). For other Asian approaches to rhythm see Rhythm in Persian music, Rhythm in Arabic music and Usul—Rhythm in Turkish music and Dumbek rhythms.

Rondo

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Etymology#

The English word rondo comes from the Italian form of the French rondeau, which means “a little round”. Today the word rondo is widely used in the English language to refer to any musical work, vocal or instrumental, containing a principal theme which alternates with one or more contrasting themes. However, some English and German speaking composers have also adopted the term rondeau over the term rondo to refer to their compositions utilizing this form; particularly when writing in a French compositional style. In France, the word rondeau was first used in the Medieval and Renaissance periods to refer to the ‘forme fixe rondeau; a type of poetic and chanson form extant to France in the late 13th through 15th centuries. It originally developed as monophonic music (in the 13th century) and then as polyphonic music (in the 14th century). It disappeared from the repertoire by the beginning of the 16th century. Along with the formes fixes ballade and virelai, the forme fixe rondeau was limited to only vocal music due to its use within the specific context of French language poetry.

Sonata form

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Defining ‘sonata form’#

According to the Grove Dictionary of Music and Musicians, sonata form is “the most important principle of musical form, or formal type, from the Classical period well into the 20th century”. As a formal model it is usually best exemplified in the first movements of multi-movement works from this period, whether orchestral or chamber, and has, thus, been referred to frequently as “first-movement form” or “sonata-allegro form” (since the typical first movement in a three- or four-movement cycle will be in allegro tempo). However, as what Grove, following Charles Rosen, calls a “principle”—a typical approach to shaping a large piece of instrumental music—it can be seen to be active in a much greater variety of pieces and genres, from minuet to concerto to sonata-rondo. It also carries with it expressive and stylistic connotations: “sonata style”—for Donald Tovey and other theorists of his time—was characterized by drama, dynamism, and a “psychological” approach to theme and expression. Although the Italian term sonata often refers to a piece in sonata form, it is important to separate the two. As the title for a single-movement piece of instrumental music, sonata—the past participle of suonare, “to play an instrument “, as opposed to cantata, the past participle of cantare, “to sing”—covers many pieces from the Baroque and mid-18th century that are not “in sonata form”. Conversely, in the late 18th century or “Classical” period, the title “sonata” is typically given to a work composed of three or four movements. Nonetheless, this multi-movement sequence is not what is meant by sonata form, which refers to the structure of an individual movement. The definition of sonata form in terms of musical elements sits uneasily between two historical eras. Although the late 18th century witnessed the most exemplary achievements in the form, above all from Joseph Haydn and Wolfgang Amadeus Mozart, a compositional theory of the time did not use the term “sonata form”. Perhaps the most extensive contemporary description of the sonata-form type of movement may have been given by the theorist Heinrich Christoph Koch in 1793: like earlier German theorists and unlike many of the descriptions of the form we are used to today, he defined it in terms of the movement’s plan of modulation and principal cadences, without saying a great deal about the treatment of themes. Seen in this way, sonata form was closest to binary form, out of which it probably developed. The model of the form that is often taught currently tends to be more thematically differentiated. It was originally promulgated by Anton Reicha in Traité de haute composition musicale in 1826, by Adolf Bernhard Marx in Die Lehre von der musikalischen Komposition in 1845, and by Carl Czerny in 1848. Marx may be the originator of the term “sonata form”. This model was derived from the study and criticism of Beethoven’s piano sonatas.

Strophic form

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Etymology#

Strophe is derived from the Greek word (strophḗ, “turn”). It is the simplest and most durable of musical forms, extending a piece of music by repetition of a single formal section. This may be analyzed as “A A A…”. This additive method is the musical analogue of repeated stanzas in poetry or lyrics and, in fact, where the text repeats the same rhyme scheme from one stanza to the next, the song’s structure also often uses either the same or very similar material from one stanza to the next.

Syncopation

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Types of syncopation#

Technically, “syncopation occurs when a temporary displacement of the regular metrical accent occurs, causing the emphasis to shift from a strong accent to a weak accent”. “Syncopation is very simply, a deliberate disruption of the two- or three-beat stress pattern, most often by stressing an off-beat, or a note that is not on the beat.”

Suspension#

For the following example, there are two points of syncopation where the third beats are sustained from the second beats. In the same way, the first beat of the second bar is sustained from the fourth beat of the first bar. Though syncopation may be very complex, dense or complex-looking rhythms often contain no syncopation. The following rhythm, though dense, stresses the regular downbeats, 1 and 4 (in ): However, whether it is a placed rest or an accented note, any point in a piece of music that changes the listener’s sense of the downbeat is a point of syncopation because it shifts where the strong and weak accents are built.

Ternary form

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Simple ternary form#

In ternary form each section is self-contained both thematically as well as tonally (that is, each section contains distinct and complete themes), and ends with an authentic cadence. It usually also has a contrasting character; for example section A might be stiff and formal while the contrasting B section would be melodious and flowing.

Da capo aria#

Baroque opera arias and a considerable number of baroque sacred music arias was dominated by the Da capo aria which were in the ABA form. A frequent model of the form began with a long A section in a major key, a short B section in a relative minor key mildly developing the thematic material of the A section and then a repetition of the A section. By convention in the third section (the repeat of section A after section B) soloists may add some ornamentation or short improvised variations. In later classical music such changes may have been written into the score. In these cases the last section is sometimes labeled A’ or A1 to indicate that it is slightly different from the first A section.

Through-composed music

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Examples#

Musicologist James Webster defines through-composed music in the following manner: Many examples of this form can be found in Schubert’s lieder, in which the words of a poem are set to music, and each line is different. In his lied “Erlkönig”, in which the setting proceeds to a different musical arrangement for each new stanza and whenever the piece comes to each character, the character portrays its own voice register and tonality. Another example within instrumental music is Haydn’s ‘Farewell Symphony’.

Tuplet

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Terminology#

The modern term ’tuplet’ comes from a rebracketing of compound words like quintu(s)-(u)plet and sextu(s)-(u)plet, and from related mathematical terms such as “tuple”, “-uplet” and “-plet”, which are used to form terms denoting multiplets (Oxford English Dictionary, entries “multiplet”, “-plet, comb. form”, “-let, suffix”, and “-et, suffix 1 “). An alternative modern term, “irrational rhythm”, was originally borrowed from Greek prosody where it referred to “a syllable having a metrical value not corresponding to its actual time-value, or … a metrical foot containing such a syllable” (Oxford English Dictionary, entry “irrational”). The term would be incorrect if used in the mathematical sense (because the note-values are rational fractions) or in the more general sense of “unreasonable, utterly illogical, absurd”. Alternative terms found occasionally are “artificial division”, “abnormal divisions”, “irregular rhythm”, and “irregular rhythmic groupings”. The term “polyrhythm” (or “polymeter”), sometimes incorrectly used instead of “tuplets”, actually refers to the simultaneous use of opposing time signatures. Besides “triplet”, the terms “duplet”, “quadruplet”, “quintuplet”, “sextuplet”, “septuplet”, and “octuplet” are used frequently. The terms “nonuplet”, “decuplet”, “undecuplet”, “dodecuplet”, and “tredecuplet” had been suggested but up until 1925 had not caught on. By 1964 the terms “nonuplet” and “decuplet” were usual, while subdivisions by greater numbers were more commonly described as “group of eleven notes”, “group of twelve notes”, and so on.

Variation (music)

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Variation techniques#

Mozart’s Twelve Variations on “Ah vous dirai-je, Maman” (1785), a French folk song known in the English-speaking world as “Twinkle, Twinkle, Little Star”, exemplifies a number of common variation techniques. Here are the first eight bars of the theme:

Melodic variation#

Mozart’s first variation decorates and elaborates the plain melodic line:

Rhythmic variation#

The fifth variation breaks up the steady pulse and creates syncopated off-beats:

Harmonic variation#

The seventh variation introduces powerful new chords, which replace the simple harmonies originally implied by the theme with a prolongational series of descending fifths: