A Survey of Music Theory for the College Classroom: Chromatic Harmony 1

A Survey of Music Theory for the College Classroom: Chromatic Harmony 1


A Survey of Music Theory for the College Classroom is a concise, practical, and readable text and workbook for use in the freshman and sophomore music theory curriculum. The text is divided into four parts which are linked by a table of contents, allowing for a seamless transition between them.

A Survey of Music Theory for the College Classroom: Fundamentals

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

A Survey of Music Theory for the College Classroom: Chromatic Harmony I

A Survey of Music Theory for the College Classroom: Chromatic Harmony II and 20th Century Music

Most chapters include PDFs of exercises and excerpts for analysis. I encourage the instructor to supplement the course materials through the analysis of lengthy excerpts or complete pieces of music, especially during the sophomore year. I also highly recommend the use of Rising Software’s Musition (theory) and Auralia (aural skills) software. The Musition and Auralia software package is robust, customizable, and can be used to reinforce most concepts covered in freshman and sophomore theory. I have also written a comprehensive set of exams as well as about 1100 objectives questions for use in Blackboard. Please email me at semmons@angelo.edu from a valid faculty email address if you would like to access these tests or Blackboard pools.

In addition to the extensive excerpts for analysis, the reader will note the prevalence given to part-writing, especially in the books Diatonic Harmony and Chromaticism I. In my experience, part-writing is the laboratory in which the student can learn many of the fundamentals of music theory. Additionally, I have found that students enjoy and even prize the time spent at the boards actively learning through part-writing and the completion of similar in class exercises.

The examples from the literature in the text and workbook were taken from the IMSLP that are public domain in the United States. I wrote all the part-writing and short examples in the text, all the exercises for the workbook, and a few pieces for analysis that demonstrate various techniques.

I dedicate this book to the late Dr. Edward Pearsall and the late Dr. Mary Jeanne van Appledorn. I studied Schenkerian analysis and 20th century theory with Ed during my doctorate at Texas Tech. Through these classes and as a member of my dissertation committee, he had a profound influence on my understanding of music and on my writing. Dr. Van was one of a kind. I studied composition and theory with her during my doctorate, and she was a master teacher of composition, the use of scales, and the music of Debussy. I have happy memories of sitting with her at the piano banging through my music or analyzing various 20th century works. She taught with great care and with humor. I shall always be in her debt.

Stephen D. Emmons, Ph.D.

Table of Contents

Secondary Dominants

Diatonic and Chromatic Harmony

In diatonic harmony, the notes found within a passage of music use only the notes that are found in the prevailing key. In major keys this is seven notes, while in minor keys it is nine notes because of the existence of harmonic and melodic minor variants. It is possible to use chromatic nonchord tones (nonessential chromaticism) within a passage that is otherwise completely diatonic, as displayed in the next example.

nonessential chromaticism

When notes outside a given key are used as chord tones within a harmonic progression it is called essential chromaticism. These altered chords or chromatic chords become ever more frequent throughout the Common Practice Period. 

The most used chromatic chords are secondary functions, which include secondary dominants and secondary leading tone chords. Secondary functions are used in tonicization, which involves treating a note or chord like a temporary tonic by approaching it with its dominant or leading tone chord. The main purposes of secondary functions are to intensify the harmonic drive to the next chord, to allow access to chromatic melodic and bass notes, and to provide aural relief from strict diatonic harmony.

Secondary Dominants

Diatonic dominant chords are almost always either major (V) or dominant seventh (V7) chords, which means that secondary dominants must also be either major or dominant seventh chords. All triads that serve a tonic function must be major (I) or minor (i) chords, which means that only major and minor diatonic triads within a given key can be tonicized by secondary dominants. Please refer to the illustrations showing the diatonic chords in major and minor keys in the Lead-Sheet Symbols and Roman Numerals chapter in this text. 

In the next example, a V/V is used in place of the ii chord in the motion to the HC.

examples of secondary dominants

Secondary functions, like most chromatically altered chords, are usually substituting for a more common diatonic chord. The V7/V chord, for example, is clearly substituting for the diatonic ii7 chord in the following harmonic progression, just as the V7/vi is substituting for the iii7 chord. 

secondary dominant substitutions

Spelling and Identifying Secondary Dominants

To spell secondary dominants, follow these simple steps.

  1. Find the note that is the root of the chord that will be tonicized.
  2. Go up a P5 to find the root of the secondary dominant.
  3. Build a major triad or dominant seventh chord on that root.

For example, write the V7/V in e minor.

spelling secondary dominants

Once you have learned to recognize and spell secondary dominants, it is easy to spot them within passages of music. When you find a chromatic chord within a passage of music and think that it might be a secondary dominant, use the following steps to analyze the chord.

  1. Check to see if the chord is a major triad or dominant seventh chord. If it is not, then the chord cannot be a secondary dominant. If it is a major triad or dominant seventh chord, go to step #2.
  2. Find the note that is a P5 below the root of the chord. If that note is the root of a diatonic major or minor chord within the key, then the chord is a secondary dominant.

For example, identify the following chord. Is this chord a major triad or dominant seventh chord? Yes, it is. Now go down a P5 to find the note being tonicized. Does the D serve as the root of a major or minor chord in B♭ major? Yes, it is the root of a mediant triad, which means this is a V/iii.

recognizing secondary dominants

The most common secondary dominant regardless of mode is the V(7)/V, followed by the V7/IV (major), V(7)/iv (minor), and V(7)/ii (major only) in that order of usage. In major keys, secondary dominants of the mediant scale degree are uncommon. In minor keys, however, the V(7)/III in minor keys is occasionally encountered, and this can be analyzed as either a VII(7) or as a secondary dominant as desired.

common secondary dominants

Deceptive cadences and progressions can be highlighted by using a first inversion V(7)/vi (VI) between the V and the vi (VI), which creates a chromatic bass line in major keys.

deceptive cadence with secondary dominants

The part-writing procedures for secondary dominants are the same as for regular V and V7 chords, so the rules regarding dominant seventh chord voice leading and the use of dominant seventh chords in circle of fifths progressions should be reviewed. Observe that sometimes secondary dominants resolve to a chord that also contains a seventh. If this happens, the leading tone in the secondary dominant can move down to become the seventh of next chord.

part-writing secondary dominants

Below is an example of secondary dominant seventh chords being used in a circle-of-fifths progression, with the altered chords substituting for the expected diatonic chords. As with the previous example, leading tones in the secondary dominant chords will resolve down by chromatic half step to form the seventh of the chord of resolution. Please review the other conventions regarding voice-leading in dominant seventh chords that are illustrated earlier in this text.

secondary dominants in a circle of fifths progression

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Secondary Leading Tone Chords


Secondary leading tone chords occur when diminished triads and seventh chords are used to tonicize a note/chord other than the given key’s tonic note/chord. The same principles apply to secondary leading tone chords as to secondary dominant chords, which is to say that any note/chord that can be tonicized by a V(7) can be tonicized by a viio(7).

The most used secondary leading tone chords in major and minor keys are the viio and the viio7. The viiØ7 is used less often but is occasionally seen tonicizing major chords, for example viiØ7/IV. The purpose of secondary leading tone chords is the same as secondary dominants, and together these chords provide the composer with a greatly enhanced harmonic palette. As with secondary dominants, secondary leading tone chords are substitutes for more common diatonic chords within the chart of harmonic progression. Additionally, secondary leading tone chords often pass through a cadential six-four on the way to the dominant chord. In the following example, the viio7/V is clearly substituting for the subdominant IV chord.

examples of secondary leading tone chords

Spelling and Identifying Secondary Leading Tone Chords

Because you now understand the construction and function of secondary dominant chords, learning to spell and recognize secondary leading tone chords is easy. If you want to spell a secondary leading tone chord, follow these simple steps.

  1. Find the note that is the root of the chord that will be tonicized.
  2. Go down a m2 to find the root of the secondary leading tone chord.
  3. Build a diminished triad, fully diminished seventh chord, or half-diminished seventh chord on that root.

For example, write the viio/V in e minor.

spelling secondary leading tone chords

When you find a chromatic chord within a passage of music and think that it might be a secondary leading tone chord, use the following steps to analyze the chord.

  1. Check to see if the chord is a diminished triad, fully diminished seventh chord, or half-diminished seventh chord. If it is not, then the chord is not a secondary leading tone chord. If it is a diminished triad, fully diminished seventh chord, or half-diminished seventh chord, go to step #2.
  2. Find the note that is a m2 above the root of the chord. If that note is the root of a diatonic major or minor chord within the key, then the chord is a secondary leading tone chord.

For example, the following chord is a fully diminished seventh chord that tonicizes the mediant triad.

recognizing secondary leading tone chords

The part-writing procedures for secondary leading tone chords are essentially the same as for regular leading tone and leading tone seventh chords, and those rules should be reviewed.

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Modulation is the action of moving from one key or tonal center to another. Modulations can be between closely related keys (keys separated by at most one sharp or flat in their respective key signatures), or between distantly related keys (keys separated by more than one sharp of flat in their respective key signatures). Modulation to foreign keys occurs somewhat frequently in romantic music and certain 20th century musical styles. Modulations can also be quite brief, and some musicians may hear these as tonicizations rather than modulations. As with many things in music, modulations are at times open to interpretation and the dictates of individual musical taste.

Before we examine the diverse types of modulation, we should delve into the various key relationships. These can be summarized as follows:

  • Relative – A major mode key and a minor mode key that have in common the same key signature are called relative keys. An example of this is C major and a minor. Relative keys are also closely related.
  • Enharmonically Equivalent – Two keys that are both major mode or both minor mode that sound the same but are spelled differently are called enharmonically equivalent keys. Examples of these are C major and D major, and g minor and a minor. Moving between these is not considered modulation because the tonic notes are enharmonic.
  • Parallel – A major mode key and a minor mode key with the same tonic are called parallel keys. For example, the keys E major and e♭ minor. Changing from E major to e minor is considered a change of mode (a.k.a. mode mixture), and not a change of key because the tonic note does not change.
  • Closely Related – Two keys that are separated by no more than one sharp or flat in their respective key signatures are called closely related keys. It could be two major keys such as C major and F major, two minor keys such as d minor and g minor, or a major and minor key such as D major and e minor.
  • Foreign or distantly related – Two keys that are separated by more than one sharp or flat in their respective key signatures are called foreign keys. Examples include C major and D major, F major and F major, and C major and a minor. Modulations to remote, distantly related keys are more typical of the Romantic era than of earlier music.

Finding Closely Related Keys

To find the closely related keys to any given key, it is simple enough to think of the major and minor keys that are separated by no more than one sharp or flat in their respective key signatures. You can also use the following chart to find closely related keys.

Tonic key                                Subdominant key                   Dominant key

Relative major/minor              Relative major/minor              Relative major/minor

To identify the keys closely related to C major, we would fill out the chart in this manner:

C                      F                      G

a                      d                       e

To identify the keys closely related to b minor, we would fill out the chart in this manner:

b                      e (minor subdominant)        f (minor dominant)

D                     G                                         A

The most common modulations are between closely related keys. In major keys the most common modulation is from the tonic key to the dominant key, and in minor keys the most common modulations are from tonic to the mediant key (the relative major) or to the minor dominant key.

Common Chords

Before covering the types of modulation, the concept of common chords must be discussed. Common chords are chords that are shared by two keys. Keys that are closely related will share several chords in common, while keys that are distantly related will share few or no chords in common. In the following example, the chords shared by C major and its dominant G major are identified.

  • The C major triad is a I chord in the key C and a IV chord in the key of G.
  • The E minor triad is a iii chord in the key of C and a vi chord in the key of G.
  • The G major triad is a V chord in the key of C and a I chord in the key of G.
  • The A minor triad is a vi chord in the key of C and a ii chord in the key of G.

C and G major common chords

Types of modulation:

Common chord or pivot chord modulation (modulation typically occurring within a phrase)

Common chord modulations feature a common chord that serves as a pivot connecting two tonalities. The common chord (pivot chord) is usually a diatonic chord in both keys but is sometimes a secondary function in one or both keys. The common chord is often the ii or IV chord in the new key, which allows for quick tonicization of the new key. This chord often precedes the first dominant function chord in the new key, including cadential six-four chords. The new key is often confirmed by an authentic cadence shortly after the modulation occurs. It is possible for there to be more than one pivot chord, which creates a “grey area” in which one key smoothly transitions to another. The best way to identify the presence of a common chord is to find the first chord that makes little sense in the old key and go back one chord. If a common chord is present, it will usually be that chord.

common chord modulation

Mode mixture can be used to increase the palette of possible keys and chords, which simplifies modulation to some foreign keys. The following example is the same as that above, but now the modulation is to the remote key of g minor rather than the closely related key of G major. We will examine mode mixture in more detail in a future chapter.

common tone modulation with mode mixture

Chromatic modulation (within a phrase)

Chromatic modulation, also called modulation by chromatic inflection, is initiated by the chromatic shift of one or occasionally two pitches at the point of modulation. Chromatic modulation can be used to modulate to foreign keys, including those in a chromatic mediant relationship, as shown in the following example.

chromatic modulation

Sequential modulation (modulatory sequence) (within or between phrases)

Sequential modulation is achieved using a melodic and/or harmonic sequence in which a passage of music is simply stated in a new key, thus tonicizing a new pitch. Sequential modulations can involve as few as two chords or can be as long as an entire phrase. These modulations often follow the circle of fifths and may involve the use of secondary dominants. The following example is taken from measures 8-10 of the third movement of Mozart’s Piano Sonata in D major, K. 284. The theme modulates via a common chord modulation to the dominant in measure 5, and then returns to the tonic key in the third phrase via a sequential modulation. 

sequential modulation

Phrase or Sectional modulation (between phrases or sections)

In a phrase modulation, a new phrase or section simply begins in a new key. Phrase modulations can involve common chords, and the typical practice is for the cadential chord of the first phrase to be the common chord with the new key. This can be viewed as a phrase modulation that is “smoothed over” with the presence of a common chord. Phrase remodulations to the tonic are a common occurrence at the beginning of the second part in forms such as binary, rounded binary, and incipient ternary. Some musicians refer to phrase modulations as “direct modulations,” while other theorists reserve the term “direct modulation” for a modulation that occurs within a phrase that does not clearly fall into any other category of modulation.

phrase modulation

Common-tone (pivot-tone) modulation (within or between phrases)

Common-tone modulations can serve to bridge keys that are closely related or that are foreign, including those that stand in a chromatic mediant relationship. Common tone modulations typically feature a single tone that is common to two keys that is used as the pivot. These modulations can be quite dramatic in sound. The common tone is often highlighted by thinning the musical texture, thus making it a bridge or connection to the next key. 

Chromatic mediants are chords with roots a m3 or M3 apart, share one common tone, and that are both major triads or both minor triads. In seventh chords, the triads are both major or both minor. This is different from the diatonic mediant relationship, wherein the chord roots are a third apart within a given key.

diatonic and chromatic mediants

The following example illustrates a common tone modulation between keys that are in a chromatic mediant relationship.

modulation between chromatic mediants

Enharmonic modulation (typically within a phrase)

In an enharmonic modulation the common chord is reinterpreted enharmonically allowing it to function in the second key. The two types of chords used in enharmonic modulations are the Mm7, which can be interpreted as a dominant seventh (V7) and as a Ger+6 chord, and o7 chords, which have a large palette of keys to which they can progress. We will return to the topic of enharmonic modulation in the chapter titled Augmented Sixth Chords and Enharmonic Modulation.

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Binary and Ternary Form


As discussed earlier in this text, form refers to the organization or overall plan of all the musical elements in a piece, including rhythm, melody, dynamics, harmony, texture, articulation, register, and timbre and how they work together. We also found that there are three basic techniques that create musical form, including repetition, contrast, and variation. We now continue our examination of form by considering binary and ternary, two of the most significant structures in music.

One-part Form

One-part forms are tonally closed – i.e., they begin and end in the tonic key – and are not divisible into smaller sections. All periods except for those with modulating consequents are one-part forms. Other musical units that do not satisfy the definition of period may nevertheless be one-part forms.

One-part forms may be divided into discrete phrases, but generally lack the contrasts of design typical of multi-part forms such as binary, ternary, rondo, and so forth. These forms lack conclusive cadences in the original key until the end and are absent any thematic restatements in the tonic key following contrasting phrases. A famous piece that is an excellent example of one-part form is J. S. Bach’s Prelude No. 1 in C from Well-tempered Clavier, Book I.

Binary Form

Binary form features a division into two main units of equal or unequal length, in which the second part will be longer than the first part. Binary forms usually contain similar material in each part, and so may be labeled as AA’ or AB. They often feature a “two-reprise” construction wherein each half is repeated, either by using a repeat sign or with the music written out again, and they close with an authentic cadence in the tonic key. Binary forms do not bring back complete phrases from Part 1 at any point within Part 2 in the tonic key, which is the primary difference between binary and rounded binary or incipient ternary forms. Binary forms may show some development of motives from Part 1 in Part 2.

Binary forms are classed as continuous or sectional. In a sectional binary form, Part 1 (A) ends with a tonic triad in the tonic key of the movement or piece, usually as part of an authentic cadence. In a continuous binary form, Part 1 (A) ends with anything other than the tonic I (i) chord in the tonic key of the piece. Examples of continuous endings for Part 1 include the half cadence in the tonic key as well as a perfect authentic cadence in a related key after a modulation has occurred. Indeed, modulations to the dominant are common in Part 1 in binary forms. Most binary forms exhibit this continuous or open tonal plan.

The following graph shows a typical binary form, but as with the other forms discussed in this chapter, various modifications and differences are common.

binary form chart

The Air from Handel’s Harmonious Blacksmith provides a clear example of binary form.

Handel excerpt

Rounded Binary Form

Rounded binary form is a hybrid structure that falls between binary and ternary forms. Some authors use the term “balanced binary” for this form, reserving the term “rounded binary” for what we will call “incipient ternary.” Rounded binary form features the return of the second phrase of Part 1 (the closing material of Part 1) in the tonic key at the end of Part 2. This return provides a satisfying ending and a “rounding off” of the form without upsetting the essential binary construction and without the stronger effect that a return of the first phrase of Part 1 would have. Most rounded binary forms feature an open (continuous) plan, with modulation to the dominant at the end of Part 1 (A), although closed (sectional) examples are sometimes encountered. Rounded binary forms close with an authentic cadence in the tonic key, and like binary form each half is often repeated in a two-reprise design.

The following graph illustrates a typical rounded binary form. Note the arrow indicating the return of the second phrase of Part 1 at the end of Part 2. A typical phrase label scheme for rounded binary is a b c b’.

rounded binary form chart

A fine example of a rounded binary form is the theme to the first movement of Mozart’s Piano Sonata K. 331Recall that we examined the first two phrases of this piece in chapter 8 because they include cadential six-four chords.

Mozart excerpt

Incipient Ternary Form

There is a grey area in the distinction between rounded binary and incipient ternary forms, and many musicians and authors prefer to see these structures as rounded binary. We will reserve the term incipient ternary for those instances in which the first phrase of Part 1 returns at the end of Part 2, which emphasizes the feeling of return to the beginning and therefore more closely approaches the principle of ternary construction. It should be noted that incipient ternary forms are not as common as are rounded binary forms, and it is more important to understand what is happening in the music rather than require absolute agreement on terminology.

The two halves of an incipient ternary will most probably be of the same length, making it like binary and rounded binary forms. As with binary and rounded binary forms, many incipient ternary forms feature an open (continuous) plan with modulation to the dominant during the second phrase of Part 1. The two phrases of Part 2 are occasionally independent phrases and thus will not form a period. Incipient ternary forms close with an authentic cadence in the tonic key. 

The following graph exemplifies incipient ternary form. Note the arrow indicating the return of the first phrase of Part 1 at the end of Part 2, giving a feeling of return to the beginning associated with ternary form. A typical phrase label scheme for incipient ternary is a b c a’.

incipient ternary form chart

A good example of an incipient ternary form is the theme to the third movement of Mozart’s Piano Sonata K. 284We examined measures 8-10 of this piece in the chapter on modulation because they include a sequential modulation. The two phrases of Part 2 do not form a period and should be considered independent phrases.

Mozart excerpt 2

Ternary Form (ABA)

Ternary form is the most important formal design in Western music and is the basis for larger scale forms such as sonata form and the rondo. Ternary form features a division into three main units of equal or unequal length, with the first and third parts being clearly related. The second or middle part generally features tonal, thematic, textural, or developmental contrast that sets it apart from the outer sections. ABA’ occurs when the restatement of A is modified from the original statement.

Ternary forms can be tonally closed (sectional), featuring an authentic cadence in the tonic key at the end of both Part 1 (A) and Part 3 (A or A’). Alternately, ternary forms can be open (continuous), with modulation to the dominant by the end of Part 1 (A). Parts 1 and 3 in a ternary form are usually of comparable length, and ternary forms close with an authentic cadence in the tonic key.

Part 2 (B) is ordinarily open in its tonal structure but is occasionally closed. Part 2 can be based on Part 1 (A), or it may involve new material. The main purpose of Part 2 is to provide contrast with the outer parts, which it does by using different melodic materials, textures, tonality, or some combination of these. Part 2 can be of similar length to the outer parts – a period or phrase group, for example – or it can be short, often consisting of a single independent phrase. More rarely, it can be longer than the outer parts.

The return of Part 1 is often not exact, but can be abbreviated, embellished, lengthened, or otherwise varied to create an A’.  The difference between ternary form and its hybrid cousins (rounded binary and incipient ternary) is the substantial return of all or most of Part 1 in ternary form.

Part 1 is very often repeated in ternary forms, and Parts 2 and 3 are also often repeated as a unit. This repetition scheme is called “two reprise” when both A and BA are repeated. These repeat signs have no bearing on the overall form of the piece.

Rounded binary and incipient ternary forms will approach and eventually become ternary form as the second section (or Part 2) loses its cohesion as a single unit and divides into two parts (Parts 2 and 3 or BA/BA’). This is emphasized through the strength of one or more of the following factors:

  • An increase in the length of literal return at Part 3 (A).
  • An increase in the contrasting qualities of Part 2 (B).
  • An increase in the expectation of return by using a retransition, grand pause, rests, or other similar devices at the end of Part 2 (B).
  • An increase in the divisiveness of the joint between Part 2 (B) and Part 3 (A) through full harmonic closure of Part 2.

This minimum number of phrases in a ternary form is usually five – with the two periods that form Parts 1 (A) and 3 (A or A’) flanking a single independent phrase that comprises Part 2 (B). Sometimes ternary forms can grow to seven and more phrases, with phrase groups, periods, three phrase periods, and double periods comprising one or more of the constituent parts.

The following graph shows a typical ternary form. Keep in mind this is one of many layouts possible for this most significant of forms.

ternary form chart

Tchaikovsky’s German Song is an example of a piece in sectional ternary form. Parts A, B, and A are all parallel periods in this piece.

Tchaikovsky excerpt

Links and Transitions

Small units such as phrases and periods are sometimes connected in some way to one another to keep rhythmic, harmonic, and melodic motion active following cadences. The most common way of connecting phrases is to use an anacrusis, as Haydn does in measure 14 of his String Quartet Op. 74, No. 3: II Largo Assai, as shown in the next example. The first violin plays a connecting flourish of sixteenth and thirty-second notes that propels the music into measure 15 and the new phrase. Such links between phrases and periods are usually quite short, sometimes only a beat or a few beats in duration, but at times can be extended to a measure or more.

example of link

Transitions and retransitions are sometimes used between larger sections in binary and ternary forms, as well as in larger forms. The two basic functions of transitions and retransitions are tonal/harmonic preparation and thematic preparation. Depending on the length of the piece, these transitions can be range from several measures in length to as little as a single chord. Transitions can occur in the place of a strong cadence at the end of a section and may consist of figuration or important motives. The result is what some musicians call “traveling music” that smoothly takes the ear from one section to another.

A very straightforward retransition is found in the third movement of Haydn’s Piano Sonata in D, No. 50, Hob XVI/37. This transition, which spans from measure 81-93, devolves into rapidly repeated dominant eighth notes which serve as the tonal preparation for the final repeat of the A section in this compound rondo form.

Haydn excerpt 3

Compound Ternary Form

Compound ternary (also called composite ternary) is created when each section of a ternary form further divides into a binary, rounded binary, incipient ternary, or ternary structure. This is an extremely flexible form and was common during the 18th and 19th centuries. Many arias, movements in piano sonatas, slow movements of symphonies, and minuets/scherzos are in compound ternary form. 

Compound ternary can include an exact repeat of Part 1 (Compound Ternary with Da Capo), and this layout is common in minuets and scherzos. The middle section is frequently called the “trio” and is often texturally lighter than are Parts 1 and 3. Trios usually feature modulation to a closely related key. Part 3 (A) is a literal repeat of Part I. Compound ternary forms are often found as the second or more commonly the third movement in a four-movement scheme. They usually feature decisive cadences that punctuate the three sections and are written without any transitions between sections. Occasionally first and second endings are used.

Shown next is the basic layout of compound ternary form. The optional Introduction, transitions, and optional codas/codettas are not marked. Each of the three parts (ABA) of compound ternary are usually tonally closed, with each part beginning and ending in the same key.

A                      B (trio)                         A

aba (or ab)      cdc (or cd, or c)           aba (or ab)

Tonic               Related key                 Tonic

Examples of compound ternary form for further study include the Minuet and Trio from Mozart’s Eine Kleine Nachtmusik, Franz Joseph Hadyn’s Piano Sonata in C, H ob. XVI/3 III: Menuetto and Trio, and Beethoven’s Minuet in G Major, WoO 10, presented as the next example. Both the Minuet and Trio are two-reprise incipient ternary forms.

Mozart excerpt 3

Mozart excerpt continued

Codas and Codettas

Codas and codettas reinforce the tonic key of a piece and have a strong cadential function. Codetta translates to “little tail” in Italian, whereas coda means “tail.” Codas are longer than codettas and are usually reserved for the end of a movement or piece, so the longer the movement or piece, the more likely a coda rather than codetta will be used. Codettas can be used to end larger sections within a piece, such as at the end of an exposition in sonata form. Codas and codettas are occasionally marked as such in the score, but most often are not.

Codas and codettas have significance beyond the simple reinforcement of a cadence, and codas can include references to earlier themes and will sometimes even feature further development of these themes. In compound ternary forms, codettas – if used – will more often be seen in Part I and Part III than in Part II, with the longest codettas occurring at the end of Part III.

An example of a codetta appears at the second ending in the final measures of Schumann’s Little Morning Wanderer, a piece from the Album for the Young, Op. 68. 

Schumann excerpt

A clear example of a coda is found at the end of the final movement Mozart’s Piano Sonata K. 331. This famous movement, entitled Rondo Alla Turca, combines elements of compound ternary and rondo forms and ends with a satisfying coda that begins in m. 96 at the second ending of the last refrain, as shown next.

Mozart ending of alla turca 1

Mozart ending of alla turca 2

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Borrowed and Neapolitan Chords

Borrowed Chords

The practice of borrowing chords from the minor mode and using them in the major mode is called mode mixture or modal borrowing. Modal borrowing greatly enhances the palette of harmonic colors available and blurs the line between major and minor keys. In the major mode we can borrow chords that include the \(\hat{3}\)\(\hat{6}\), and \(\hat{7}\) from the parallel minor key. The presence of these colorful chords in major keys can be refreshing, unexpected, and at times musically dramatic. 

Borrowed chords function the same as the diatonic chords they replace. For example, the minor mode iv chord is a perfectly acceptable substitution for the usual IV chord in a major key. Some borrowed chords are much more common than others. For example, the viio7 is a commonly borrowed chord, while the v7 is not. The most used borrowed chords are those that involve the \(\hat{6}\)including the iio, iiØ7, iv(7) and viio7. This should not be surprising, since the supertonic, subdominant, and leading tone chords are the most prevalent harmonies after the tonic and dominant in both major and minor modes. 

Other commonly borrowed chords are the minor i chord and the VI(M7). The III(M7) and the VII are rather rare, which again makes sense because the mediant and subtonic triads and seventh chords are the least used diatonic chords in minor keys. 

Neapolitan Chord

The Neapolitan chord is built on the lowered second scale degre (\(\hat{2}\)) and is named after the “Neapolitan school” of 18th century opera composers based in Naples, Italy. The Neapolitan chord is almost always a major triad, and the symbol for it is simply N, or N6 when the chord is used in its typical first inversion. Note that some theorists use the alternative label II or the II6 for Neapolitan chords. Minor Neapolitan chords are exceptionally rare, and the lowercase letter n or n6 (orii and ii6) can be used on those occasions. The Neapolitan chord is normally used in minor keys and is most often in first inversion, hence the common designation Neapolitan sixth chord. It also occurs in the major mode, but this is not as frequent. It is occasionally found in root position and much less regularly in second inversion. It has the same function as the supertonic chord, but since it is a major triad, it has a remarkably different sound that adds drama to any progression.

The Neapolitan chord is normally used as a substitution for the supertonic triad, and so is often preceded by tonic, subdominant, and submediant functions, which in major keys can include borrowed chords. It is also possible to tonicize the Neapolitan chord with a secondary dominant or secondary leading tone chord.

The following chart shows all the possible borrowed and Neapolitan related chords in C major, except for the minor Neapolitan (n or n6). Not represented is the major tonic triad (I) that is often used as the final chord for minor mode pieces during the later Renaissance period and throughout the Baroque period. This usage is called the Picardy third, and it was thought to bring a more satisfying end to a minor mode piece than did the diatonic minor tonic triad. We do not think of the \(\hat{7}\) in harmonic minor nor the \(\hat{6}\) and \(\hat{7}\) in melodic minor as borrowed scale degrees, which means the major tonic triad is the only chord that can be borrowed from the parallel major key.

borrowed and Neapolitan chords chart

Part-Writing with Borrowed and Neapolitan Chords

Follow the usual part-writing procedures and rules established for diatonic triads and seventh chords. Remember that borrowed chords can be freely substituted for their diatonic equivalents in most musical textures. Consider the following example. Because of the extensive borrowing, most of this progression could be analyzed in c minor.

part writing borrowed and Neapolitan chords

Extra care must be taken when part-writing Neapolitan chords. 

  • Neapolitan chords are usually found in first inversion. In an SATB texture, double the third of the N6.
  • The N6 progresses directly to a V, to a V42, to a i64, or to a viio7/V(7) on the way to the tonic chord. 
  • The melodic objective of the \(\hat{2}\) is the leading tone. The \(\hat{2}\) can leap down to the leading tone in a \(\hat{2}\) – \(\hat{7}\) – \(\hat{1}\) pattern, or it can pass through the tonic in a \(\hat{2}\) – \(\hat{1}\) – \(\hat{7}\) – \(\hat{1}\) pattern, depending on the chord progression.
  • Care should be taken to avoid parallel fifths when progressing from an N6 to a i64. This can be done by using parallel fourths instead, as shown in the following example.

neapolitan chord part writing resolutions

Using Mode Mixture and Neapolitan Chords in Modulations

Modal borrowing and Neapolitan chords can be used in common chord modulations to foreign keys. Using borrowed chords in this manner unlocks all the closely related keys of the parallel minor. The closely related keys to C major include F, G, a, d, and e. By sliding into the parallel minor key of c minor, the closely related keys include f, g, E, A, and B. In the following progression, the foreign key of A is easily accessible by using the borrowed iv as a common chord.

mode mixture in modulations

Neapolitan chords can also be used as common chords in dramatic modulations to foreign keys, as the following example demonstrates.

neapolitan chords in modulation