A Survey of Music Theory for the College Classroom: Diatonic Harmony

Cadences and Small-Scale Form

Foundations of Form

Form refers to the organization or overall plan of all the musical elements in a piece, including rhythm, melody, harmony, dynamics, texture, articulation, register, and timbre and how they work together. The study of form is vital to understanding and performing western art music at any level.

The three foundational techniques that create musical form include the following:

  • Repetition – Because music exists in time, repetition creates a sense of musical unity. Musical ideas gain significance to the hearer as they are repeated.  
  • Contrast – Contrast creates conflict, heightens interest, and enhances the effect of repetition. Most musical pieces include at least a little contrast.
  • Variation – Variation consists of taking a musical idea and making changes to it without completely obscuring its lineage. This combines the concepts of repetition and contrast and is the basis for the theme and variations form.

The Building Blocks of Form

The single note is the smallest division in music. Notes combine to make cells, which are referred to by some as figures, figurations, or submotives. Cells can derive from motives and can include arpeggios, scales, and other short collections of notes. Cells are often featured in transitional (or “traveling”) music used to connect larger sections and themes. Motives are short musical ideas that can be primarily melodic, harmonic, rhythmic or a combination of the three. The term motive is used flexibly by musicians, but generally refers to something less than a phrase in length. Motives are integral to the creation of phrases and larger forms in the Western music tradition.

Motives are melodically or rhythmically distinct and are usually delineated in some way within the music, either through rests, articulations, note length, repetition or in some other way. Motives can be a few notes in length or may be long enough to consist of several smaller cells that stretch over one or more measures. The motives in music with slow tempos usually contain few notes, while the motives in music with faster tempos usually contain more notes. Motives also contain smaller submotives which can themselvses be developed.

To have importance, motives must be restated (repeated) and developed. Motives can be developed by being sequentially repeated, transposed, subjected to intervallic expansion and contraction, retrograded, modified in rhythm and pitch, imitated, subjected to rhythmic augmentation and diminution, inverted, ornamented, and so forth. If the original rhythmic pattern is preserved, a motive can undergo a great deal of pitch alteration without losing its identity.

Beethoven’s Symphony No. 5 in c minor provides good ground on which to examine the concept of motive.

Cadences

At the heart of musical form is the cadence. Cadences are arrival and resting places that are like punctuation marks such as commas and periods in written language. While cadences are a combination of the musical elements in a piece, this study emphasizes the harmonic component of that mixture. The proper performance of individual phrases and their groupings (periods, phrase groups, etc.) constitute one of the pillars of basic musicianship.

The typical cadences found in western music are illustrated below. These examples include only the penultimate and ultimate chords found at the ends of phrases and are to be approached as the goals of a longer progression. We will encounter variants of these cadences during future semesters of music theory.

Perfect Authentic Cadence (PAC)

Perfect authentic cadences consist of a root position V(7) to I (i). The melodic motion will end on the tonic note in the soprano and is typically approached by either the leading tone or supertonic note. PACs can occur at any cadence point within a piece but are almost always found on the final chord.

PAC

Imperfect Authentic Cadence (IAC)

Imperfect authentic cadences are not as final sounding as PACs. IACs are subdivided into three types.

Root Position IAC

As with the PAC, root position imperfect authentic cadences consist of a root position V(7) to I (i).  In a root position IAC, however, the mediant or dominant note of the key is in the soprano in the tonic chord.

Root IAC

Inverted IAC

In an inverted IAC, one or both chords are inverted. 

Inverted IAC

Leading Tone IAC

In a leading tone IAC, the approach to I (i) is by a viio(7) chord. The viio triad is typically found in first inversion, while the viiØ7 and viio7 chords can be used in root position or in any inversion. The leading tone seventh chord is particularly useful because it includes in common three of the four notes of the dominant seventh chord for a given key.

Leading Tone IAC

Half Cadence (HC)

Half cadences end on V(7) chords and are most commonly encountered as the internal cadences in periods or as the cadences in independent phrases or phrase groups. The supertonic scale degree supported by the V chord is by far the most encountered melodic note in this cadence.

HC

Plagal Cadence (PC)

Plagal cadences consist of the IV (iv) to I (i) progression. Plagal cadences are final sounding cadences and are often used in conjunction with the “Amen” at the end of traditional hymns. Plagal cadences are on rare occasions substituted for authentic cadences in periods.

PC

Deceptive Cadence (DC)

The deceptive progression and the special part-writing conventions that accompany it were discussed earlier. Deceptive progressions and deceptive cadences occur when the melodic motion and harmonic motion disagree. The most common deceptive progression is the V – vi (VI), but the V – IV6 (iv6) can also be found in the interior portions of phrases. In a DC, the ear expects the supertonic to the tonic (or alternately the leading-tone to tonic) notes in the melody to be supported by the V – I (i) harmonic progression but is instead surprised by the submediant triad. The usual voice leading of the notes with the V- vi (VI) progression are as follows:

  • Supertonic to Tonic
  • Leading tone to Tonic
  • The other voice skips down a third.

deceptive cadence

Phrygian Half Cadence (PHC)

The Phrygian half cadence occurs only in minor mode and consists of the iv6 to V progression. It is named after the Phrygian mode, a scale that was used in the Medieval period that we will study later. This cadence is most common in the Baroque period and was little used in the Classical and Romantic periods. The part-writing can be a little tricky, so it is best to double the fifth of the iv6 chord and resolve as shown in this example.

Phrygian HC

Phrase Groupings

Phrase

The phrase is the shortest structural unit in music that ends with a cadence. Phrases are somewhat independent musical ideas that can range from about two measures in length up to several times that, depending on the meter, tempo, and style. Music of the 18th and 19th centuries is often constructed in four measure phrases. Phrases can be marked in form charts using brackets and lowercase letters, as illustrated in the following examples, and these can be combined into larger form charts that show the overall form of a movement or piece.

Phrases are labeled based on their melodic content. The first phrase in a piece is marked with a lowercase “a.” Phrases whose melodies begin similarly to the first “a” phrase but that end in a different key or end with a different cadence are called a’ (a prime). The first phrase that is different from the initial “a” phrase is labeled with a “b,” and this can logically be extended to b’ (b prime) and so forth. If we encounter another phrase that is similar to a and a’ (or b and b’) we can label it a” or b” (a double prime or b double prime), but for the sake of visual clarity it is our custom to label phrases with a “2” to indicate double prime (for ex., a2, b2).

Period

A period is comprised of two phrases in an antecedent-consequent (question-answer) relationship. The second phrase ends with a stronger cadence than does the first phrase, for example HC, PAC or IAC, PAC. Periods are parallel when the melodies of the component phrases begin with similar or identical material and are contrasting when they are not similar.

paralle and contrasting periods

An example of a parallel period comes from the first two phrases of Schubert’s Sonata in A Major D. 664. The first phrase, labeled a, concludes with an IAC in m. 4, and the second phrase, labeled a’, terminates with a PAC in m. 8.

Schubert excerpt

The following parallel period is from the opening measures of Schubert’s Sonata in E Major D. 157. This illustrates the concept of formal elision, which occurs when phrase endings and beginnings overlap. The HC in m. 5 serves as the jumping off point for phrase a’, which in turn ends with a PAC in m. 9. 

Schubert example

A contrasting period is seen at the beginning of the first movement of Haydn’s Sonatina in C, Hob. XVI:35. The first phrase (a) ends in m. 4 on a HC and the second phrase (b) terminates in m. 8 with a PAC. This contrasting period is immediately repeated with ornamentation, making it an example of a repeated contrasting period.

Haydn example

Repeated Period

A repeated period happens when a period is immediately repeated, often with embellishments. This is not to be confused with a double period. Repeated periods can be parallel or contrasting. An example of a repeated parallel period occurs immediately after the slow introduction in the first movement of Haydn’s Symphony No. 102 in B.

repeated period

Independent Phrase

A phrase that does not combine with other phrases to form a period relationship or a phrase group is called an independent phrase. Independent phrases are sometimes present in small ternary forms where they form the middle section (Part 2 or Part B).

independent phrase

The third phrase of Purcell’s Minuet in a minor provides a clear example of an independent phrase. In this example, the first two phrases form a parallel period, and the overall form is ternary.

Repeated Phrase

A repeated phrase transpires when a single phrase is immediately repeated, either verbatim or with embellishments. The phrase labels and the cadences will be the same.

repeated phrase

In Chopin’s Nocturne, Op. 9 no. 1 in b minor, we find an example a repeated phrase with ornamentation. The first phrase terminates with an IAC on the down beat of m. 2, and the phrase is immediately repeated but with chromatic and melodic elaboration. Chopin utilizes the same technique a few measures later in mm. 8-12.

Chopin excerpt

Phrase Group

A phrase group consists of a series of phrases – at least two, but often more – in succession that belong together structurally but that do not constitute a period, three phrase period, or double period. The phrases in a phrase group range from being very similar to being highly independent of one another and may end in similar cadences or in a mixture of cadences. Phrase groups are often encountered in developmental sections, in transitional passages, or as the middle section (Part 2 or Part B) of a ternary form.

phrase group

This excerpt from Couperin’s Le Petit Rien illustrates the concept. The first phrase of the example finishes with an IAC in m. 20, and the second phrase ends with an HC in m. 24.

Couperin excerpt

Three Phrase Period

This structure occurs when three phrases unite to stand in a period relationship. When the cadences are progressively stronger (HC, IAC, PAC), the period will have one antecedent phrase and two consequent phrases. When two weak cadences are followed by a strong cadence (HC, HC, PAC), the period will have two antecedent phrases and one consequent phrase. The phrase labels will vary according to the similarity of the melodic materials.

three phrase period

The beginning of the first movement of Haydn’s Sonata No. 59 in E Major, Hob. XVI:49 provides an example of a three-phrase period with one antecedent phrase (a, which ends in a HC in m. 4 on a viio) and two consequent phrases (a' and b) which conclude with an inverted IAC in m. 8 and a PAC in m. 12.

Haydn excerpt

Double Period

A double period consists of four phrases in two pairs that unite to form a period relationship. The first three cadences will be relatively weak, and the last cadence will be decidedly stronger, for example HC, HC, HC, PAC. Parallel double periods have similar first and third phrases, while contrasting double periods feature dissimilar first and third phrases. Parallel double periods are common, while contrasting double periods are quite rare.

parallel double period

An example of a parallel double period comes from the opening measures of the first movement of Beethoven’s Piano Sonata Op. 26. Note that phrases two (b) and four (b’) are also similar, which is occasionally seen in these forms. This example follows the HC, HC, HC, PAC formula.

Beethoven example

Sentence

The sentence is typically an eight-measure long phrase that contains two four-measure components and a single cadence at the end, though other sentence lengths are possible. The first component of a sentence is called the presentation phrase and consists of a basic motive – often two measures in length – that is repeated or varied. The presentation phrase will not end with a clear cadence but does reinforce the tonic. The second component is called the continuation phrase and is less strict in construction. The main purpose of the continuation phrase is to drive toward a clear cadence. Continuation phrases may use sequential repetition, faster surface rhythm (smaller rhythmic values), quicker harmonic rhythm (rate of harmonic change), and melodic fragmentation to help propel the music toward a satisfying cadence.

Some period forms contain or are overlaid with the melodic structure of the sentence, which allows for varying analyses and interpretations.

sentence

The following example from the opening movement of Beethoven’s Piano Sonata in f minor, Op. 2 no. 1 is an example of a sentence that concludes in m. 8 with a half cadence. The basic motive is presented in mm. 1-2, repeated in mm. 3-4, and the continuation phrase propels to the cadence in m. 8.

Beethoven excerpt

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