IV. Form

36. Binary Form


36.1 Introduction

As discussed in Chapter 35, we may think of form in tonal Western art music as being hierarchically constructed. Notes may combine to form motives, motives may evolve and combine to form phrases, phrases may combine to form periods or double periods, and so on. In many cases, we can trace this combining of musical elements all the way to the highest level of the formal hierarchy: a complete composition.

In this and the following chapters, we will discuss several full-piece forms. As with such smaller forms as phrases and periods, which comprise only a fraction of a composition, we will see that there are numerous variations on each form having to do with the key plan (harmonic structure) and layout of various melodic content (thematic design). We will begin with binary form, one of the most common full-piece forms, particularly for shorter compositions.

36.2 Binary form overview

The following example shows a complete composition.

Example 36–1. Christian Petzold, Minuet in G major (from the Notebook for Anna Magdalena Bach, BWV Anh. 114).
  • example_36-1_0001
  • example_36-1_0002
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Note: Note that all of the labels identifying cadences in Example 36–1 indicate the type of cadence as well as the current key and the relation of that key to the home key. The first cadence, for example, is a half cadence in G major, the home key (I) whereas the cadence in m. 20 is a half cadence in D major, the dominant key (V).

We hear a motive in the first two bars of this piece. This motive is repeated in mm. 3–4, transposed and with a slightly different contour. The motive is truncated in the following measures and repeated three more times with an inverted contour as the phrase drives toward a half cadence in m. 8. To put it succinctly, these opening eight bars form a sentence. In mm. 9-16, we hear the sentence again but with the half cadence replaced by a PAC in the home key. Taken together, the two sentences found in mm. 1–16 form a parallel period.

After a repeat of mm. 1–16, we hear something new. This phrase begins in G major, but ends with a HC in the dominant key (D major) in m. 20. The move to the dominant is confirmed by a PAC in D major four bars later. These two phrases (mm. 17–24) constitute another period, although this time the phrases are contrasting and only four bars in length. The remaining measures present another contrasting period with the antecedent and consequent ending on a HC and PAC, respectively, both in the home key. After these two smaller periods repeat together as a unit, we have reached the conclusion of the piece.

The example below provides summarizing diagram of Example 36–1:

Example 36–2. Form diagram of Christian Petzold, Minuet in G major (from the Notebook for Anna Magdalena Bach, BWV Anh. 114).

example_36-2

Note: In diagrams such as the one shown above, we use capital letters (A, B, C, etc.) to label large-scale sections. When it becomes necessary to describe finer details, we will use lowercase letters (a, b, c, etc.) to label sub-sections. If a section or sub-section reappears later in a piece, it will be labeled with the same letter as the original. If a section or sub-section comes back in an altered but recognizable form, we will indicate that with one or more prime symbols (A′, A″, etc.). (Other texts use superscript numbers instead of prime symbols: A1, A2, etc.)

At the highest level, the piece shown in Example 36–1 is divided into two sections. This is made clear in several ways. The first sixteen bars form a cohesive unit—a period made of two eight-bar sentences. The next sixteen bars, on the other hand, are thematically contrasting and are therefore set off from that which comes before them. Furthermore, each of these sixteen bar spans is repeated independently from the other. Visually, this is made very clear on the score with the double bar lines and repeat symbols.

Pieces such as this are said to be in binary form—the prefix bi– specifying that there are two sections. The repeat pattern in Example 36–1 is standard: in a binary form the first and second sections are almost always repeated independently. Because of this, the two large-scale sections are sometimes called reprises and some theorists and teachers use the term two-reprise form instead of binary form.

Note: Students sometimes confuse periods and binary forms since both are comprised of two parts. The distinction between the two is one of scale. The term “period” refers to a short passage of music consisting of just two phrases (or four in the case of a double period). The term “binary,” on the other hand, is typically used to refer to the form of an entire composition, likely consisting of many more than two or four phrases. A piece in binary form can—and often will—contain one or more periods, but it would be nonsensical to say that a period contains one or more binary forms.

36.3 Harmonic structure

When discussing the harmonic structure of a binary form, we are concerned primarily with how each section ends relative to the home key. If a section ends conclusively—that is, with an authentic cadence—in the home key it is said to be tonally closed since it gives the listener a sense of harmonic closure. If a section ends with an inconclusive cadence—such as a half cadence—or if it ends in some key other than the home key, it is said to be tonally open since it leaves the listener with a sense of open-endedness. The A section of the piece shown in Example 36–1 is tonally closed because it concludes with a PAC in G major, the home key.

In both of the examples below, the opening section is tonally closed:

Example 36–3 Franz Schubert, 38 Waltzes, Ländler and Ecossaises (D.145), Ländler No. 1 in Eb major.

example_36-3

Example 36–4. Maria Agata Szymanowska, 18 Danses de Différent Genre, Polonoise No. 2 in E minor.

example_36-4

Example 36–3 begins in Eb major and the first section ends conclusively with a PAC in the home key. The first section in Example 36–4 follows suit, beginning and ending conclusively in E minor. When a binary form begins with a tonally-closed first section, it is said to be a sectional binary. The word “sectional” indicates that since it is tonally closed, the opening section could exist as a standalone piece since the vast majority of tonal Western art music begins and ends in the same key.

Note: Notice that the very beginning of the second section of Example 36–4 seems to be in the key of G major, the relative of E minor. This has no bearing on our identification of this piece as a sectional binary. In determining whether or not a binary form is sectional, one is concerned with only the first section.

Now compare Example 36–3 and Example 36–4 to the following example:

Example 36–5. Ludwig van Beethoven, German Dance in C major (WoO 13, No. 10).

example_36-5

In this binary form, the first section is tonally open. It begins in C major and ends with a PAC, but the cadence in m. 8 is in a different key. When a binary form begins with a tonally-open first section it is said to be a continuous binary. In this case, the opening section modulates to the dominant key (G major).

Continuous binary forms are more common than sectional binary forms. An open-ended first section invites the listener to expect more music and the piece as a whole is more coherent. The modulation from C major to G major in Example 36–5 is typical: the vast majority of major-key continuous binaries modulate to the dominant.

Note: A half cadence is considered tonally open since it does not project a sense of harmonic closure. A binary form in which the opening section ends on a half cadence would therefore be considered continuous. The following piece provides an example:

Example 38–6. George Frideric Handel, Minuet in D major, (HWV A15.4).

example_36-6

When a continuous binary is set in a minor key, on the other hand, there are two common modulatory destinations. The opening section might modulate to the relative major, as in the following example:

Example 36–7. George Frideric Handel, Minuet in D minor, (HWV 462).

example_36-7

Here, the tonally-open first section begins in D minor and ends with a PAC in F major. The fact that D minor and F major have the same key signature allows for a very smooth transition into the new key.

The other common modulatory destination for the first section of a minor-key continuous binary is the minor dominant. Consider the following example:

Example 36–8. Johann Sebastian Bach, French Suite No. 1 in D minor (BWV 812), Menuet I.
  • example_36-8_0001
  • example_36-8_0002
  • example_36-8_0003
  • example_36-8_0004
  • example_36-8_0005

In this case, the opening section begins in D minor and ends with a PAC in A minor.

Note: There is a C# in m. 8, making a major triad out of what would otherwise be minor. This should not be interpreted as an indication of a modulation to the major dominant key. The major dominant of a minor key is not a closely-related key. (Consider the keys in question here: D minor has one flat in the key signature whereas A major has three sharps, a difference of four accidentals! A minor, on the other hand, shares six of its seven scale degrees with D minor.) Instead of hearing this as the tonic of a major key, the C# should be considered a Picardy third. The C§s in the preceding bars support this hearing.

You may have noticed that unlike all of the other examples shown above, the second large-scale section of Example 36–8 (mm. 9–24) is larger than the first large-scale section. Despite the number of evenly-divided examples shown in this chapter, binary forms with a longer second section are actually much more common.

You may have also noticed that the piece passes through F major (the relative major) on its way back to home key. Composers frequently include a small passage in a third key in the middle of a longer second section. This third key is not as structurally significant as the two keys heard before it. It is more of a stepping stone on the way back to the tonic than a foundational key area. The key scheme seen here—with a short passage in the relative major—is common for minor-key binaries that modulate to the minor dominant in the first section.

In continuous binaries that modulate to the relative major, you will sometimes see a brief modulation to the minor dominant in this same location. The following example illustrates:

Example 36–9. Johann Sebastian Bach, Suite in A minor (BWV 818), II. Courante.
  • example_36-9_0001
  • example_36-9_0002
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  • example_36-9_0004
  • example_36-9_0005

Likewise, major-key continuous binaries are often found passing through the relative minor on their way back to the home key:

Example 36–10. George Frideric Handel, Minuet in F major (HWV 520).

example_36-10

The following tables summarize the most commonly-encountered harmonic structures in continuous binary forms:

Example 36–11. Typical harmonic structure of major-key continuous binary forms.

example_36-11

Example 36–12. Typical harmonic structure of minor-key continuous binary forms.

a. modulation to relative major

example_36-12a

b. modulation to minor dominant

example_36-12b

Activity 36-1

Activity 36–1

Analyze each of the following binary forms and determine whether it is sectional or continuous.


Exercise 36–1a:

Question

Is the following binary form sectional or continuous?

Maria Agata Szymanowska, 6 Minuets, No. 4 in G minor.
  • activity_36-1a_0001
  • activity_36-1a_0002
  • activity_36-1a_0003
  • activity_36-1a_0004
  • activity_36-1a_0005
  • activity_36-1a_0006
Hint

Does the first section end conclusively in the home key?

Answer

This is a sectional binary form in G minor. The first section ends with a PAC in the home key.


Exercise 36–1b:

Question

Is the following binary form sectional or continuous?

George Frideric Handel, Minuet in G major, (HWV A15.2).
  • activity_36-1b_0001
  • activity_36-1b_0002
  • activity_36-1b_0003
  • activity_36-1b_0004
Hint

Does the first section end conclusively in the home key?

Answer

This is a continuous binary form. The first section ends with a PAC in the dominant key.


Exercise 36–1c:

Question

Is the following binary form sectional or continuous?

Joseph Haydn, Keyboard Sonata in G major (Hob.XVI:27), II. Trio.
  • activity_36-1c_0001
  • activity_36-1c_0002
  • activity_36-1c_0003
  • activity_36-1c_0004
  • activity_36-1c_0005
Hint

Does the first section end conclusively in the home key?

Answer

This is a continuous binary form. The first section ends with a PAC in the (minor) dominant key.


Exercise 36–1d:

Question

Is the following binary form sectional or continuous?

Johann Sebastian Bach, Cello Suite No. 3 in C major (BWV 1009), V. Bourrée I.
  • activity_36-1d_0001
  • activity_36-1d_0002
  • activity_36-1d_0003
  • activity_36-1d_0004
  • activity_36-1d_0005
  • activity_36-1d_0006
  • activity_36-1d_0007
Hint

Does the first section end conclusively in the home key?

Answer

This is a continuous binary form. The first section ends with an authentic cadence in the dominant key.

36.4 Thematic design

In addition to the harmonic structure, one must consider the melodic content—as well as its relationship to the underlying key plan—when analyzing a binary form. Here we are primarily concerned with the presence of any repeated material from the first large-scale section in the second large-scale section.

Consider the following example and take note of the important event that occurs in m. 17:

Example 36–13. Joseph Haydn, Partita in Bb major (Hob.XVI:2).
  • example_36-13_0001
  • example_36-13_0002
  • example_36-13_0003
  • example_36-13_0004
  • example_36-13_0005

In this continuous binary, the first large-scale section (mm. 1–12) is a modulating period—it begins in Bb minor and ends in the relative major (Db major). After the repeat we hear four bars of contrasting material. Then, in m. 17, the opening material comes back in the original key. When the opening material of a binary form reappears toward the end of the second section, we call it a rounded binary.

Notice that when the opening material comes back, the melody has been adjusted. Had the first section been copied note for note into the end of the second section, the piece would modulate again and would not end in the home key. Composers circumvent this by using one or more of a number of strategies. In this case, mm. 17–22 are identical to mm. 1–6. Then, mm. 23–28 simply take mm. 7–12 and transpose them up a sixth so that they stay in the home key.

A continuous rounded binary, then, has a two-part harmonic structure and a three-part thematic structure. The two parts of the harmonic structure correspond with the large-scale sections: the first section moves away from the tonic and the second section returns to the tonic. The first large-scale section also corresponds with the first part of the thematic structure. The second and third part—the contrasting material after the double barline and the return of the opening material—combine to form the second large-scale section.

The following example shows another continuous rounded binary:

Example 36–14. Elisabetta de Gambarini, Harpsichord Sonata in G major (Op. 1, No. 4), I. Tempo di Gavotta.
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In this case, we find the return of the opening material beginning in m. 25. Compare this moment to the beginning, measure by measure. The material heard in m. 25 corresponds with that of m. 1, but after that the two passages begin to diverge until mm. 30–32, which correspond with mm. 10–12, the conclusion of the first section. Unlike Example 36–13, we do not hear the entire opening section return. Even with this truncated and modified repetition, however, this is still considered a rounded binary. The most important criterion in identifying a rounded binary is whether or not the listener recognizes a return of the opening material in the original key.

The following diagram shows the harmonic and thematic structure of a rounded binary. Note that A′ (A prime) is used to designate the return of the opening material:

Example 36–15. Typical harmonic structure of rounded binary forms.

example_36-15

When the opening material does not return in the second section, a piece is said to be in simple binary form. Consider the following example:

Example 36–16. Wolfgang Amadeus Mozart, Minuet in C major (K.15f).

example_36-16

In this continuous binary form, the second section consists of entirely new material. There are similarities between the two sections, of course, but we never hear the opening measure return, let alone in the original key. This piece is, therefore, in continuous simple binary form.

In the following piece, we do hear the opening material come back, but not in the original key:

Example 36–17. George Frideric Handel, Passepied in A major (HWV 560).

example_36-17

Comparing the two sections of this continuous binary we can see a lot of similarities. The opening thematic material certainly returns with the pickup to m. 9, but since it is there written in a different key it does not qualify this piece as a rounded binary. Instead, like Example 36–16, this is a continuous simple binary.

The following table summarizes simple binary forms:

Example 36–18. Typical structure of simple binary forms.

a. Opening material returns in a different key:

example_36-18a

b. Opening material does not return at all:

example_36-18b

In the following example you will hear material from the first section come back toward the end of the second section, but this is not a rounded binary:

Example 36–19. Maria Agata Szymanowska, Polonaise in C major.
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In this sectional binary, we never hear the material from mm. 1–4 return in the second section. We do, however, hear the closing gesture from the first phrase (mm. 5–8) return to conclude the second section (mm. 13#). This does not qualify as a rounded binary since the opening measures do not come back. Instead, a piece is said to be a balanced binary when the two sections end with the same material.

Note that in Example 36–19 the closing phrase from the first section is repeated note for note at the end of the second section. In the case of a continuous binary, however, this repeated material will appear in a slightly altered form the second time around since the piece needs to end in the home key. The following piece provides an example:

Example 36–20. Ludwig van Beethoven, 6 Minuets (WoO 10), No. 6 in C major (Trio).

example_36-20

This continuous binary is in C major and modulates to G major in the first section. The material heard in mm. 5–8 returns in mm. 13–16, transposed and slightly altered so as to end in the home key. This, too, is a balanced binary.

Note: Some of the terminology here can become a little bit confusing. We used the word “balanced” in Chapter 35 as a synonym for “symmetrical,” referring to periods in which the two phrases were of equal length. Here the word refers to they way the two sections of a binary form conclude and has nothing to do with the length of the two sections.

Unfortunately, discussions of form tend to be rather inconsistent. The terminology you encounter in one book will often be noticeably different from the terminology found in another book. Much of this inconsistency may be attributed to the creative impulses of the composers themselves—many of whom strove for innovation over consistency—and to generations of music theorists who struggled to keep up! Your best course through this sometimes murky territory is to default to descriptions of the music as it appears instead of trying to force creative work into somewhat artificial categories.

Activity 36-2

Activity 36–2

Analyze each of the following binary forms and determine whether it is rounded, balanced, or simple.


Exercise 36–2a:

Question

Is the following binary form rounded, balanced, or simple?

Maria Agata Szymanowska, 6 Minuets, No. 4 in G minor.
  • activity_36-2a_0001
  • activity_36-2a_0002
  • activity_36-2a_0003
  • activity_36-2a_0004
  • activity_36-2a_0005
  • activity_36-2a_0006
Hint

Does any of the thematic material from the opening section come back at the end?

Answer

This is a balanced binary form. The second half of the first section (mm. 9–16) comes back at the end of the piece (mm. 25–32).


Exercise 36–2b:

Question

Is the following binary form rounded, balanced, or simple?

George Frideric Handel, Minuet in G major, (HWV A15.2).
  • activity_36-2b_0001
  • activity_36-2b_0002
  • activity_36-2b_0003
  • activity_36-2b_0004
Hint

Does any of the thematic material from the opening section come back at the end?

Answer

This is a simple binary form. None of the thematic material from the opening section comes back at the original pitch level in the second section.


Exercise 36–2c:

Question

Is the following binary form rounded, balanced, or simple?

Joseph Haydn, Keyboard Sonata in G major (Hob.XVI:27), II. Trio.
  • activity_36-2c_0001
  • activity_36-2c_0002
  • activity_36-2c_0003
  • activity_36-2c_0004
  • activity_36-2c_0005
Hint

Does any of the thematic material from the opening section come back at the end?

Answer

This is a rounded binary form. The entire first section (mm. 1–8) comes back at the end (mm. 18–24), recomposed so as to close the piece in the home key.


Exercise 36–2d:

Question

Is the following binary form rounded, balanced, or simple?

Johann Sebastian Bach, Cello Suite No. 3 in C major (BWV 1009), V. Bourrée I.
  • activity_36-2d_0001
  • activity_36-2d_0002
  • activity_36-2d_0003
  • activity_36-2d_0004
  • activity_36-2d_0005
  • activity_36-2d_0006
  • activity_36-2d_0007
Hint

Does any of the thematic material from the opening section come back at the end?

Answer

This is a simple binary form. None of the thematic material from the opening section comes back at the original pitch level in the second section.

36.5 Introductions and codas

Very frequently you will encounter small passages of music that do not participate in the main body of a form. Take the following piece, for example:

Example 36–21. Franz Schubert, 36 Originaltänze (D.365), No. 34 in F major.

example_36-21

As the double bar lines and repeat symbols make clear, this piece is in binary form. The first section, however, does not start right at the beginning. Instead, this piece begins with an introduction, a small segment of music designed to establish the key, meter, tempo, etc., preparing the listener for the beginning of the first main section. The presence of an introduction does not affect the status of this piece as a binary form.

In the following example we find a similar passage, this time at the end of the piece:

Example 36–22. Maria Agata Szymanowska, 18 Danses de Différent Genre, Waltz in F major.
  • example_36-22_0001
  • example_36-22_0002
  • example_36-22_0003
  • example_36-22_0004
  • example_36-22_0005
  • example_36-22_0006

In this sectional binary, the second large-scale section ends conclusively in m. 33. The two bars after the double barline re-articulate the cadence that closes the piece. A small passage such as this, which echoes the closing cadence, is known as a coda. Like the introductory measures seen in Example 36–21, the coda has no bearing on the status of this piece as a binary form.

36.6 Summary

Many composers, performers and listeners conceive of form in tonal Western art music as being hierarchical in nature. Small elements combine to form larger and larger elements all the way up to the highest level: a complete composition. Phrases, for example, can combine in various configurations to create large-scale sections of a piece. When a piece divides into two large scale sections it is said to be in binary form.

With regards to harmonic structure of a binary form, we are concerned primarily with whether or not the first section ends conclusively in the home key. If the first section is tonally closed, it is a sectional binary; if the first section is tonally open, it is a continuous binary. Of these two types of binary forms, the latter is the more common. If a continuous binary is in a major key, it will very likely modulate to the dominant; if it is in minor it will most likely modulate to either the minor dominant or the relative major. Some continuous binaries—particularly those with a longer second section—may also pass through a third key area on their way back to the home key.

When considering the thematic design of a binary form, we are primarily concerned with whether or not the opening material from the first large-scale section reappears in the second. If the opening material returns in the original key somewhere toward the end of the second section, the piece is said to be a rounded binary. If the opening material does not reappear in the second section—or if it reappears but in the wrong key—the piece is said to be a simple binary. If the closing material from the first section is also used to close the second section, the piece is said to be a balanced binary (even if this music is transposed or altered in some other way to end in the home key).

Finally, some pieces have short passages of music that do not participate in the main body of the form: an introduction if it is at the beginning and a coda if it is at the end. Generally speaking, such inclusions do not affect the form of the piece overall.

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