Music Theory III and IV Prince George's Community Collegeacademic.pgcc.edu/~njudy/files/McHose-2014Fall.pdf · Repeated Triads: First Principle ... fundamental bass of the preceding

Music Theory III and IVPrince George's Community College

Fall 2014 / Spring 2015

notes from

Contrapuntal Harmonic Technique of the 18th Centuryby

Allen Irvine McHose

Copyright 1947Out of print 1985

1985 Marcia L. NewlinWardRevised 1991 – Marcia L. NewlinWardRevised 2014 – Ned Judy

PGCC Music Theory - 2

Table of Contents

INTRODUCTION........................................3The Triad.................................................4Inversion..................................................5Harmonic Function..................................6Normal Progression...............................10Cadence................................................12Modulation.............................................14Chorale Style.........................................16Figured Bass.........................................17

CHAPTER ONE.......................................19Repeated Triads: First PrincipleTwo Triads with their Roots a Fifth Apart: First Principle

CHAPTER TWO.......................................21Repeated Triads: Second PrincipleTwo Triads with their Roots a Fifth Apart: Second Principle

CHAPTER THREE...................................23Two Triads with their Roots a Second Apart: First Principle

CHAPTER FOUR.....................................25Two Triads with their Roots a Third Apart: First PrincipleTwo Triads with their Roots a Third Apart: Chromatic Progression

CHAPTER FIVE.......................................28Two Triads with their Roots a Fifth Apart: Exception;The Triad with a Tripled Root as a Final Cadence

CHAPTER SIX.........................................30Two Triads with their Roots a Second or Third Apart (Exceptions)

CHAPTER SEVEN...................................33The Triad in First Inversion: Tonic, Subdominant, and Dominant Triads

CHAPTER EIGHT....................................36The Triad in First Inversion: Leading Tone,Supertonic, Submediant and Mediant Triads

CHAPTER NINE......................................40The Triad in Second Inversion

CHAPTER TEN........................................43NonHarmonic Tones: Introduction

CHAPTER ELEVEN.................................46The Passing Tone

CHAPTER TWELVE................................53The Suspension

CHAPTER THIRTEEN.............................59The Neighboring Tone: Passing Tone Suspension, Neighboring Tone in Combinations

CHAPTER FOURTEEN...........................62Other Nonharmonic Tones

CHAPTER FIFTEEN................................65Seventh Chords: Introduction

CHAPTER SIXTEEN................................69Dominant Seventh Chord

CHAPTER SEVENTEEN.........................77Supertonic Seventh Chord

CHAPTER EIGHTEEN.............................81Leading Tone Seventh Chord in Minor

CHAPTER NINETEEN.............................87Subdominant Seventh Chord in Major andMinor

CHAPTER TWENTY................................91Other Diatonic Seventh Chords

CHAPTER TWENTYONE.......................95Altered NonHarmonic Tones

CHAPTER TWENTYTWO......................98Altered Chords: Introduction

CHAPTER TWENTYTHREE.................100Altered Chords in Minor

CHAPTER TWENTYFOUR...................103Altered Chords in Major

CHAPTER TWENTYFIVE.....................105AugmentedSixth Chords

CHAPTER TWENTYSIX.......................107Modulation to Foreign Keys


INTRODUCTION

As a prerequisite to using and understanding this text, knowledge and training in the following subjects are necessary:

Major and minor key signatures

Major and minor scales (all forms)

Intervals

Major, Minor, Diminished, Augmented triads, and their inversions

Chorale Style texture (SATB) and basic part writing rules

Keyboard Skills, including the ability to play scales, triads and cadences

Sight singing and melodic dictation in major and minor keys

Harmonic dictation recognize at least I, IV, V in major and minor

This work has been made possible through the contributions of the music faculty and students of Prince George's Community College. Special thanks to Professor Mary Dumm for her guidance through this complex subject, and to Patricia Kyriss for preparing much of the text. All examples and diagrams were created using opensource software, including MuseScore.


The Triad

The triad is the most elementary sonority in tonal music. It consists of three tones, arranged in ascending thirds. The tone on which the triad is built is calledthe root. The other tones form intervals of a third and a fifth, above the root.

TRIAD NAME

A triad is named according to its root. The root in the example above is F, and so the chord is properly referred to as an F triad. The quality of the triad is also included in the triad's full name.

TRIAD QUALITY

Quality is determined by the combination of ascending thirds from which the triad is constructed. The various combinations of ascending major and minor thirds result in four triad qualities: major, minor, diminished and augmented.

major triad = M3 + m3 minor triad = m3 + M3

diminished triad = m3 + m3 augmented triad = M3 + M3

The relationship between the root and fifth is affected by the combination of ascending thirds. Major and minor triads both include the perfect fifth (P5). Diminished triads include the diminished fifth (d5), augmented triads include theaugmented fifth (A5).

diminished triad includes a d5 above the root.

augmented triad includes an A5 above the root


Inversion

The Theory of Inversion was introduced by Jean Philippe Rameau (1683 – 1764), who published his triate de l’harmonie (Treatise on Harmony) in Paris, in 1722. In this work, Rameau establishes chord inversion and the primacy of tonic, subdominant and dominant chords. This work is considered the cornerstone of modern harmonic theory.

With inversion, a triad can be arranged so that the root is not the lowest sounding tone. The 3rd or 5th can be the lowest sounding tone, but the quality remains the same.

The examples below show an F major triad, in both close and open structure.

Root Position – root is the lowest sounding tone.

close open

First Inversion 3rd is the lowest sounding tone.

close open

Second Inversion 5th is the lowest sounding tone.

close open

INVERSION AND QUALITY

Triads in any quality may be inverted. The examples above show a major triad,but minor, diminished, and augmented triads may also be inverted.

The triads which appear most often in root position are major and minor.

Diminished and augmented triads in root position are rare.


Harmonic Function

Rameau proposed that the major and minor keys were established through chord progression. He introduced the analytical concept of fundamental bass, in which a theoretical bass line is derived, consisting of only the roots of the chords. Rameau used this fundamental bass to analyze the distance between the roots of consecutive chords, and determine the harmonic progression. This technique preceded the use of Roman numerals in harmonic analysis.

The following example is an excerpt from a Bach chorale, with the fundamental bass line added below.

Was Gott tut, das ist wohlgetan J.S. Bach

When the fundamental bass (root of each chord) has been determined, the nextstep in Rameau's analysis is to study the relationship between each pair of consecutive notes, in order, as the composition progresses. Considering the interval of a fourth as the inversion of a fifth, the intervals appear in the fundamental bass of the preceding example in the following frequency:

Prime Fifth apart (or 4th) Second apart Third apart

1 11 2 1

Thus, the excerpt above includes one repeated chord, eleven progressions withthe roots of the chords a fifth apart, two progressions with the roots of the chords a second apart, and one progression with the roots of the chords a third apart. The prominence of root movement by fifth is obvious in this example.


While root movement by fifth was frequently used in the music of this period, composers did utilize other relationships. The following chorale is found in C. Heinrich Graun's Passion:

Der Tod Jesu (No. 11) C. H. Graun

Prime Fifth apart (or 4th) Second apart Third apart

2 7 9 4

In the example above, Graun has used more chord progressions with their rootsa second apart. When we continue with this type of analysis of the music of Bach, Graun, and their contemporaries, the following will be observed concerning root movement:

Prime Fifth apart Second apart Third apart

16% 52% 21% 11%

Root movement by fifth is the most frequentlyused progression of this period.

Rameau believed that major and minor keys are established by the fact that consecutive chords with their roots a fifth apart are in the majority. The major key is established by arranging three major triads so that their roots are a fifth apart.

In the example above, the C major triad is the chord of rest, also known as tonic. The other triads are active, and must progress to the chord of rest.

The triad with its root a perfect fifth above tonic is known as dominant.

The triad with its root a perfect fifth below tonic is known as subdominant.


The following Bach example illustrates a phrase using the tonic, dominant, and subdominant triads, in G major.

Lobt Gott, ihr Christen, allzugleich J.S. Bach

MINOR KEYS

Rameau also derived minor keys by arranging three minor triads having their respective roots a fifth apart.

DIATONIC TRIADS

Diatonic triads only contain tones that are found within the key signature. In minor keys, diatonic triads include tones found within any of the three forms of the minor scale. J.S. Bach and his contemporaries used all forms of minor in their compositions. Additionally, they frequently used a major triad as the last chord of a composition in a minor key. The resulting raised 3rd is known as a Picardy third. The diatonic tones in Bach's minor keys include the raised 6th and raised 7th, as well as the Picardy third..

Diatonic tones in f minor


ROMAN NUMERALS

Since the Classical Era, the use of Roman numerals has been the preferred method for identifying triad roots in musical analysis. Roman numerals reveal the functional relationship of the triads to the key.

ITonic

IISupertonic

IIIMediant

IVSubdominant

VDominant

VISubmediant

VIILeading

Tone

Lowercase Roman numerals can be used for minor triads. o and + symbols are included with diminished and augmented triads, respectively.

Triads built on the major scale

I ii iii IV V vi viio

Major minor minor Major Major minor dim

Triads built on the natural (pure) minor scale

i iio III iv v VI VII

minor dim. Major minor minor Major Major

Triads built on the Harmonic Minor Scale (raised seventh)

i iio III+ iv V VI viio

minor dim. Aug. minor Major Major dim.

Triads build on the Melodic Minor Scale (raised sixth and seventh)

i ii III+ IV V vio viio

minor minor Aug. Major Major dim. dim.


Normal Progression

Allen I. McHose (1902 – 1986) was an American music theorist and professor at the Eastman School of Music. He developed a chord classification system describing the functional relationships and normal progression of chords.

Tonic Classification – Tonic (tonal center, key center, chord or resolution)The tonic chord may progress to any chord in its key.

First Classification Dominant & Leading ToneChords built on either the dominant or leading tone progress normally to tonic.

Second Classification – Supertonic & SubdominantChords which have their roots on the subdominant or the supertonic progress normally to chords of the first classification. Supertonic is a perfect fifth above dominant.

Third Classification Submediant & dissonant TonicChords which have their roots on the submediant, and dissonant chords which have their roots on the tonic, progress normally to chords of the second classification. Submediant is a perfect fifth above supertonic.

Fourth Classification – Mediant & dissonant DominantChords which have their roots on the mediant, and dissonant chords which have their roots on the dominant, progress normally to chords of the third classification. Mediant is a perfect fifth above submediant.

Fifth Classification – Subtonic & dissonant Leading ToneChords which have their roots on the subtonic in a minor key, or dissonant chords which have their roots on the leading tone, progress normally to chords of the fourth classification. Subtonic is a perfect fifth above mediant in a minor key. Leading Tone is a perfect fifth above mediant in a major key.


NORMAL PROGRESSION OF CHORDS

Normal Progression is the most frequently used progression in music composed during the 18th century. Normal progression moves through the classifications toward tonic. Tonic may move to any other chord in its key. The tonic chord may also be used between two chords which form a normal progression without disturbing their function. Other progressions are used as a contrast to Normal Progression.

Repetition of chords is next in frequency of use. Tonic is repeated most, followed by dominant, subdominant, and supertonic.

Elision is next in frequency, occurring when a chord progresses to a chord two classifications away, while still moving toward tonic (skipping a classification).

Examples: iii – IV (4th class. to 2nd class.)vi – V (3rd class. to 1st class.)

Retrogression occurs when chords (other than tonic) move away from tonic.

Examples: V – IV (1st class. to 2nd class.)V – vi (1st class. to 3rd class.)vi – iii (3rd class. to 4th class.)ii – vi (2nd class. to 3rd class.)


Cadence

A cadence is a chord progression that concludes a phrase. The degree of resolution depends on the final chord of the cadence, and how it is prepared.

Perfect Authentic Cadence (PAC)

• dominant chord to tonic chord• both chords must be in root position• tonic note is found in soprano of tonic chord

Imperfect Authentic Cadence (IAC)

• dominant chord to tonic chord OR leading tone to tonic chord'• either chord is inverted OR tonic not is not in soprano of tonic chord

Perfect Plagal Cadence (PPC)

• subdominant chord to tonic chord• both chords must be in root position• tonic note found in soprano of tonic chord

Imperfect Plagal Cadence (IPC)

• subdominant chord to tonic chord OR supertonic chord to tonic chord (rare)

Authentic Half Cadence (AHC)

• any chord to dominant chord

Plagal Half Cadence (PHC)

• any chord to subdominant• infrequent usage

Deceptive Cadence (Dec)

• dominant chord to chord other than tonic• often dominant chord to submedient chord• tonic note usually in soprano of the second chord

Phrygian Cadence (Phry, or PC)

• subdominant chord to dominant chord, in minor key• subdominant chord in first inversion



Modulation

Modulation is used to effect a change of key in a musical composition. The key change may be occur at the beginning of a phrase, or within a phrase, depending on the method.

Phrase Modulation – key change which occurs at the beginning of a phrase. This can also be referred to as Direct Modulation.

Ach wie nichtig J.S. Bach

Common Chord Modulation – key change occurs within a phrase, with one chord functioning in two keys at the same time. This chord is referred to as the Common Chord, or Pivot Chord.

Gott lebel noch J.S. Bach

Chromatic Modulation – key change that occurs within a phrase, and involves a chromatic chord progression.

Das eugeborne Kindelein J.S. Bach

The phrase above begins in Bb major and the chords progress normally to the dominant. At this point, a chromatic chord modulation introduces the Dmajor triad. This chord is not found in Bb major, but it is found in g minor.


Enharmonic Modulation – key change that occurs within a phrase through respelling. It involves much chromaticism, and appears in the Romantic Period.

Note: The German Augmented Sixth chord (Gr6) will be covered later in this text.

Foreign Modulation occurs when the tonic of the new key is not a diatonic triad of the original key.

CLOSELY RELATED KEYS AND DISTANT KEYS

Key signatures that differ by only one accidental are referred to as closely related keys, because they contain multiple common tones and chords. Distant keys have fewer common tones and chords. The Circle of Fifths can be utilized to determine closely related keys, both major and minor.

Closely Related Keys are adjacent to the original key on the Circle of Fifths.


Chorale Texture

Choral Texture includes four voices: soprano, alto, tenor and bass (SATB). When completing the exercises throughout this text, use “safe” pitch ranges, identified with open note heads, below. When necessary, use the extended voice ranges, identified by the closed note heads.

soprano alto tenor bass

The combined ranges create an overall choir pitch range of three octaves, centered around Middle C.

DOUBLING

Chorale Texture includes four voices, while triads contain only three tones, and so one of the triad tones must be doubled (sung in two voices). A study of J.S. Bach's doubling, in major and minor triads in root position, reveals that he most often doubled the root.

Major Triad Minor Triad

Root Third Fifth Exc.* Root Third Fifth Exc.*

88% 8% 3% 1% 84% 13% 2% 1%

*Exceptional triad structures include three roots and a third; two roots and two thirds.

OPEN AND CLOSE STRUCTURE

When the soprano and tenor voices are an octave or less apart, the triad is in close structure. If the soprano and tenor voices are more than an octave apart, the triad is in open structure. The bass part is not considered when determining chord structure.


Figured Bass

Figured Bass consists of symbols used below the bass part, which refer to intervals found above the bass. It is also known as ThoroughBass. The practice of using Figured Bass began in the late 16th century and extended through the 17th century. By the 18th century, musicians had worked out a universal system of symbols. Below are examples of figured bass symbols for root position chords.

1. The bass note without any symbol indicates the root position of a triad. The tones of the chord will be in relation to the key signature in which the bass is found.

2. The flat, sharp, or natural sign is used to obtain chord spellings which would otherwise be impossible within the key signature. When the accidental appearsalone, directly beneath the bass, the interval of a third, or tenth, above the bass is altered accordingly. Optionally, a number three with a diagonal slash throughit can be used to indicate that the tone a third above the bass is to be raised onehalf step.

3. These symbols are also used to indicate the lowering or raising of the note afifth (or twelfth) above the bass tone.


4. If the pitches of both the third and fifth above the bass are to be altered chromatically, two symbols are used, the lower symbol referring to the third and upper symbol to the fifth.

INVERSIONS OF TRIADS AND SEVENTH CHORDS

As described previously, when a bass tone is the root of a chord, no figured bass symbol is used (root position). When a bass tone is not the root of a triad, the inversion is indicated by the following figured bass symbols:

Root position 1st inversion 2nd inversion

Inversions of seventh chords are indicated by the following figured bass symbols.

Root position 1st inversion 2nd inversion 3rd inversion


CHAPTER ONE

Repeated Triads: First Principle

When a triad is repeated with a new position in the soprano, move the three upper voices in similar motion and retain the structure of the first triad.

Compare to Rule 1A in Ottman.

Two Triads with their Roots a Fifth Apart: First Principle

When one triad progresses to another which has its root a fifth (or its inversion a fourth) above or below the first, keep the common tone in the same voice and move the remaining voices stepwise to the next triad tones.


PARTWRITING EXERCISES

On the following page, provide inner voices, using these methods:

1. Every triad must have two roots, one third, and one fifth.2. Each exercise must be in either close or open structure.3. When a triad is repeated with a new soprano tone, use the first conventional method.4. When two triads have their roots a fifth apart, use the first conventional method.

A complete analysis should accompany each exercise, including the Roman numerals and cadence markings.


PARTWRITING EXERCISES. CHAPTER 1


CHAPTER TWO

Repeated Triads: Second Principle

The change from close to open structure or the reverse may take place when a chord is repeated.

Compare to Rule 1B in Ottman.

Two Triads with their Roots a Fifth Apart: Second Principle

(used when First Principle does not work.)

When one triad progresses to another which has its root a fifth above or below the first, the three upper voices move in similar motion to the next triad tones.

Compare to Rule 2B in Ottman.

PARTWRITING EXERCISES.

On the following page, provide inner voices, using these methods:

1. Every triad must have two roots, one third and one fifth.2. When a triad is repeated, the two conventional methods may be used.3. When two triads progress so that their roots are a fifth apart, use either the first or second conventional method of voice leading.4. The exercises may have open and close structure during the phrase.5. The largest lead any upper voice may have when there is a change of harmony is the leap of a third.6. The largest leap an upper voice may have when a triad is repeated is the leap of a sixth. It is preferable to have the leap of a sixth in the soprano.



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CHAPTER THREE

Two Triads with their Roots a Second Apart: First Principle

When a triad progresses to a triad which has its root a second above or below, the three upper parts move contrary to the bass (contrary motion).

If a triad progresses to a triad which has its root a step above or below, the progression is called a Foreign Progression

Compare to Rule 3 in Ottman.

PARTWRITING EXERCISES CHAPTER 3

The partwriting principle of this chapter, together with the principles learned in Chapters 1 and 2, makes it possible to use practically the entire triad harmonic equipment in major and minor keys. Complete the following exercises, and provide a complete harmonic analysis should accompany the solution.

1. Every triad must have two roots, one third, one fifth.2. If it is desired, the change from open to close partwriting may take place when the triad is repeated.3. All principles of partwriting explained previously will be utilized.



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CHAPTER FOUR

Two Triads with their Roots a Third Apart: First Principle

When one triad progresses to another which has its root a third above or below the first, keep the common tones in the same voices and move the remaining voice stepwise to the next triad tone. (There are 2 common tones. When two triads in a progression have two common tones, they are related triads.)


Two Triads with their Roots a Third Apart: Chromatic Progression

A chromatic progression, as distinguished from a diatonic progression, is one which has in the second chord a chromatic inflection of a note common to both chords.

E G# B

C E G

A voice moving from G to Gsharp results in a chromatic scale line. The chromatic inflection may raise or lower a halfstep, while maintaining the common letter name.

E G# B C E G c eb g

C E G Ab C Eb C E G

The chords involved appear in root position.

This progression often appears between phrases, or between the last chord of a section and the first chord of a new section.

This thirdRelationship is a distinguishing characteristic of the music of Richard Wagner (18131883), Johannes Brahms (18331897) and John Williams (b. 1932).


THE CONVENTIONAL CHROMATIC PROGRESSION

The chromatic inflection takes place in the same voice when the chords have the same root or a root a third above or below.

THE LESS CONVENTIONAL CHROMATIC PROGRESSION

The chromatic inflection sometimes takes place in another voice. This method creates a cross relation.



Analyze and partwrite the following exercises:Every triad must have two roots, one third, and one fifth.Use all methods of partwriting presented in this and proceeding chapters.

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CHAPTER FIVE

Two Triads with their Roots a Fifth Apart: Exception;

The Triad with a Tripled Root as a Final Cadence

Roots a Fifth Apart, Exception (Compare to Rule 2C in Ottman)

When one triad progresses to another which has its root a fifth above or below the first triad, keep the common tone in the same voice, move the third of the first triad to the third of the second triad, and move the remaining upper voice by step to the next triad tone.

Any change from close to open structure or the reverse was limited in earlier chapters to repetition of a chord (root movement by Prime). The above examples now show that this change may take place when two triads have theirroots a fifth apart. When this exception is used, it should be surrounded by conventional procedures.

This exception is prohibited in ii – V progressions, due to the leap of the augmented fourth.

Triad with a Tripled Root in the Cadence (Compare to Rule 2D in Ottman)

In Bach’s harmonization’s of chorales, 1% of the root positions of major triads and 1% of the root positions of minor triads are found with a tripled root. Of these triads, over 95% are found as the last chord in the authentic cadence. The movement of the soprano is supertonic to tonic.



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CHAPTER SIX

Two Triads with their Roots a Second or Third Apart (Exceptions)

Roots moving up a second, exception (Compare to Rule 5 in Ottman)

When one triad progresses to another which has its root a second above the first, move the third of the first triad in thirds or tenths with the bass, and move the remaining upper voices to the next chord tones contrary to the bass. The second triad in this progression will have one root, two thirds, and one fifth.

This exception may be used in the following situations:

a. To avoid the augmented second in the progression VVI in minor.b. To change from open to close structure or the reverse.c. In the deceptive cadence.

ROOT MOVEMENT BY THIRDException (Compare to Rule 5 in Ottman)

When a triad progresses down a third to another which has a doubled third:

a. Keep two common tones and the remaining upper voice will leap usually a fourth, rarely a fifth.

b. Do not keep the common tones; move the third of the first triad in thirds or tenths with the bass and the remaining voices contrary to the bass.


When a triad progresses up a third to another which has a doubled third:

a. Keep the 5th of the first triad and the 3rd of the second triad as a common tone, and the remaining upper voices will move contrary to the bass to the next chord tones. (In leaps of 4ths).

b. Keep the 5th of the first triad and the 3rd of the second triad as a common tone, move the 3rd of the first triad in thirds or tenths with the bass, and the remaining voice will move by step to the next chord tone.

The Progression From a Triad with Doubled Third, Exception

A triad with a doubled third may progress to another which has its root, above or below, a fifth, second, or third. The voices containing the doubled thirds maymove to the next chord in contrary, oblique, or similar motion. Bach preferred contrary and oblique to similar.

The following examples illustrate the three horizontal resolutions of two voices when doubling the third of a triad:



In solving the exercises below, remember to follow an exception with a convention.

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CHAPTER SEVEN

The Triad in First Inversion: Tonic, Subdominant, and Dominant Triads

The theory of inversion permits changes of the intervallic structure of a triad without destroying the triad's identity, or quality.

The fist inversion of a triad has the third in the bass.

The complete figuration written below the bass tone to indicate the first inversion of a triad is 6/3. Under normal conditions, the 3 is omitted.

When a flat, natural, or sharp sign is placed below the 6, the third above the bass tone is affected. In other words, the accidental represents the interval of athird above the bass.

The use of an inversion of a triad makes possible better voice leading in the bass. An inverted triad coming between the strong root positions of triads increases the musical interest of a composition.

The first inversions of major and minor triads may be found as early as the 13 th century. The principles of voice leading into and out of an inverted triad were definite by the end of the 16th century.

The doubled tone in the first inversion triad may be approached and left by contrary, oblique or similar motion.


METHOD OF DOUBLING

The following tables show the method of doubling in the first inversions of majorand minor triads in chorale harmonizations by Bach:

Doubling in the Major Triad

Soprano 66% Bass 19% Inner Voices 15%

Doubling in the Minor Triad

Soprano 55% Bass 33% Inner Voices 12%

Of all triads found in the first inversion in Bach’s chorales the tonic, the first classification dominant, and the second classification subdominant triads have the highest frequency.

Tonic 50%Dominant 30%Subdominant 20%

A triad in first inversion may be introduced in the bass by chromatic stepwise motion. When this happens, the bass line usually ascends. The triad in first inversion is usually a first classification dominant triad in a related key, however,a slightly different analysis will be discussed later, in connection with this use of a chromatic chord progression.

Uns ist ein Kindlein heut’ gebor’n (3rd phrase)



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CHAPTER EIGHT

The Triad in First Inversion: Leading Tone, Supertonic, Submediant andMediant Triads

The following table shows the remaining possible triads used in first inversion, in major and minor keys. The triads in the third row are extremely rare in first inversion, in the music of the 18th century.

FIRST SECOND THIRD FOURTHCLASSIFICATION CLASSIFICATION CLASSIFICATION CLASSIFICATION

Major key vii° ii vi iii

minor key vii° ii° VI III+

rare VII II (V of V) vi° III

FIRST CLASSIFICATIONLeading Tone diminished triad

Bach used the diminished triad on the leading tone in two ways:

1. as a contrapuntal chord between two positions of the tonic triad

2. as a first classification chord preceded by the second classification subdominant triad.

Doubling When a leading tone triad appears in first inversion, the third is the best tone to double, and the fifth is the next best tone to double.

Never double the root of a leading tone triad.

Unequal Similar Fifths

Bach does not hesitate to write a perfect fifth moving to a diminished fifth, or the reverse, when it occurs between two upper voices.


SECOND CLASSIFICATIONSupertonic Triad

A study of the compositions of Bach, shows that he prefers the first inversion of the supertonic seventh chord to that of the supertonic triad.

The supertonic triad in inversion gives the aural effect of the bass line using the subdominant in root position.

Doubling

When a supertonic triad appears in first inversion, the third is the best tone to double, the root may be doubled if it is in the soprano.

Do not double the fifth in major keys. (It causes parallel fifths).

Avoid doubling the fifth in the minor keys.

The root or third are found in the soprano and the fifth is rarely found in the soprano in minor keys.

As in the chart on page one of this chapter, the II (V of V) is rarely found in 1st inversion.

THIRD CLASSIFICATIONSubmediant Triad

In a major key, Bach occasionally used the first inversion of the submediant triad as common chord between two keys. The triad becomes a second classification supertonic triad in the new key. In all instances the third is doubled.

Goptt sei gelobet und gebenedeiet (4th phrase)

Use of the submediant as a major or diminished triad in minor keys in first inversion is practically nonexistent in the works of Bach.


FOURTH CLASSIFICATIONMediant Minor Triad in a Major Key

Use of this triad in first inversion by Bach is restricted to a few progressions. The triad is approached by either the dominant or the subdominant triad. In both instances retrogression occurs in the classification of chords. The triad is followed by either a subdominant or submediant triad before it progresses to thefirst classification chord.

The other typical appearance of the mediant triad in Bach is found in cadences. This incipient mediant is not really a mediant at all but a dominant. This occurs when the sixth above the bass moves to the fifth above the bass.

Doubling The third of the mediant triad is always doubled.

Mediant Triad in a Minor Key

The augmented mediant triad has a fairly high frequency in its first inversion. Use of this train is limited to certain typical progressions. The triad is preceded by a second classification chord (most often a subdominant triad) and then progresses to a submediant triad.

As in a major key, Bach used the augmented mediant triad in minor keys in the cadence formula. Still the incipent median actually is the resulting dominant.

Doubling The third of the chord is always doubled.


PARTWRITING EXERCISES CHAPTER 81.

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CHAPTER NINE

The Triad in Second Inversion

The second inversion of a triad has the fifth in the bass. The figured bass for the second inversion of a triad is 6

4

The fifth (bass) is always doubled.

The second inversion chord must always be prepared and resolved. The interval of the fourth is found between the bass and one of the upper voices. Due to the fact that the fourth was considered a dissonant interval from the 16 th

century until the beginning of the 20th century, this preparation and resolution is necessary.

Bach used the second inversion less often than one would expect. The following table shows the five second inversion chords and their use.

PreBach Bach

Accented Cadencial 6/4 Chord rare common

Stepwise 6/4 Chord common common

Passing 6/4 Chord rare quite common

Arpeggiated 6/4 Chord common less common

Pedal 6/4 Chord common rare

These five chords as shown are the only uses of second inversion.


SECOND INVERSION TRIADS

Accented Cadencial 6/4• must be accented• must occur at a cadence• 6 moves to 5, and 4 moves to 3• prepared by step from above or below• resolved by same tone

Stepwise 6/4

• does not have to be accented• does not have to occur at a cadence• prepared by step from above or below• resolved by same tone

Arpeggiated 6/4

• prepared by leap from same chord• resolved by leap to same chord, or to

same tone, or by step

Pedal 6/4

• prepared by same tone• resolved to same tone

Passing 6/4

• prepared by step• resolved by step, in opposite direction

of preparation



Label each second inversion chord by function name

1.

2.

3.

4.


CHAPTER TEN

NonHarmonic Tones: Introduction

Nonharmonic tones are notes which are not part of the chord, or implied harmony. They may also be referred to as nonchord tones, auxiliary tones, or embellishment tones.

A nonharmonic tone appears in a vertical sonority, but plays no part in the theory of inversion of that sonority.

A nonharmonic tone must always be prepared and resolved in the same voice in which it appears. The manner in which it is approached and resolved will determine its name.

THEORY OF NONHARMONIC TONES

A nonharmonic tone is related melodically to one of the members of the chord. Notice the potential nonharmonic tones that relate to each member of the Cmajor triad:

Along with the three tones of the triad, the nine potential nonharmonic tones comprise the entire chromatic scale.

Nonharmonic tones that appear in the key signature, or have the spelling of a scale tone, are called diatonic nonharmonic tones.

Nonharmonic tones with spellings foreign to the key signature are called chromatic nonharmonic tones (or altered nonharmonic tones) and will be studied in Theory IV.


CLASSIFICATION OF NONHARMONIC TONES

passing tone prepared by step and resolved by step in the same direction• Single, double, triple and quadruple• Unaccented and accented

suspension prepared by the same tone and resolved by step downwards.• Single and double• Occur on accented beat • Preparation must be at least the same rhythmic value as the suspension

neighboring tone prepared by step and resolved by step in opposite direction• Upper and lower • Single, double, triple, quadruple • Unaccented and accented

retardation prepared by the same tone and resolved by step upwards.• Special kind of suspension that is common in the Classical Period• Single and double

anticipation prepared by step and resolved by the same tone.• Found at the cadence in the soprano.• Anticipates the final tonic triad• Double – tenor and soprano.• Unaccented

appoggiatura prepared by leap and resolved by step, usually in opposite direction.• Common in the Classical Period.

escape tone prepared by step and resolved by leap, usually in opposite direction.• Found in the soprano near the cadence.

changing tone group prepared by step and resolved by step to same tone• Two nonharmonic tones, a third apart• Common in the Classical period. • Same as a turn. • Not found in Chorale style.

pedal point prepared and resolved by the same tone• Common in organ music in the Baroque period• Common in chorale music of the Romantic period• Not common in 18th century chorale style

free tone prepared and resolved by leap• Common in Classical and Romantic period


The following table illustrates the relative frequencies of nonharmonic tones. Comparing sixteenth century style with Bach’s style:

TYPE 16 TH CENTURY BACH

Passing tone very frequent very frequent

Suspension quite frequent quite frequent

Neighboring tone less frequent frequent(lower only) (upper and lower)

Anticipation not too frequent not too frequent

Escape tone not too frequent not too frequent(only in cambiata figure)

Appoggiature none rare in chorales

Changing tone none rare

Pedal point rare rare in chorales


CHAPTER ELEVEN

The Passing Tone

Passing tones appear in the choralestyle partwriting according to the following table:


UNACCENTED SINGLE PASSING TONE

The unaccented passing tone is the most frequent nonharmonic tone. It appears ascending or descending in any voice.

Mach's mit mir, Gott J. S. Bach

In the example above, the passing tones at 1, 2, 4 and 5 move to the next chordin similar motion with one or two other voices.

The passing tone at 3 moves in contrary motion to the remaining three voices.

The passing tone at 6 moves in oblique motion to the tenor, and in contrary motion to the remaining voices.

DEDUCTIONS

The melodic interval of a third formed by two harmonic tones in a progression oftwo chords is frequently filled in by a passing tone. An exception is found in the authentic cadence, or within the phrase when the three upper voices of the dominant triad progress downwards to the next chord tones of the tonic triad (second procedure). Passing tones between leading tone and dominant are rare in the chorales.

avoided preferred

Exercises: In the following exercises fill in the interval leap of a third in each voice:


ACCENTED SINGLE PASSING TONE

When the passing tone appears on a beat, it is called an accented passing tone. Descending accented passing tones are more frequent than ascending ones. They are often approached by an unaccented passing tone, producing two passing tones in a row, or consecutive passing tones. They most often occur in the bass.

Exercises: In the following exercises, insert several passing tones, including at least one accented passing tone. You will have to shift the rhythmic placement of the notes to fit in the accented passing tone.

UNACCENTED DOUBLE PASSING TONES

Unaccented double passing tones appear in similar motion ascending and descending, and in contrary motion. They are frequently, and any combinationof two voices may be employed. The percentage of ascending double passing tones is slightly higher than that of the descending type.

Erhalt' uns, Herr, bei deinem Wort J.S. Bach

About 84% progress in similar motion in thirds or sixths, about 16% are found to be in the contrary motion.


Exercises: In the following exercises use single and unaccented double passing tones:

ACCENTED DOUBLE PASSING TONES

Accented double passing tones are infrequent. They are appear in similar and contrary motion. Those found in similar motion are not common, and those found in contrary motion are extremely rare.

Nun lob', mein' Seel', den Derren J.S. Bach

In the example above, at 1 the accented double passing tones are in thirds, rising to the first inversion of the E7 chord.

Exercise: In the following exercise use single passing tones, and at least one unaccenteddouble passing tone:


TRIPLE PASSING TONES AND THE PASSING CHORD

Triple passing tones appear having two voices moving contrary to the third voice. In the following example, the triple passing tones at 1, along with the held tone, do not spell a chord (E – E – G – A).

O wir armen Sünder J.S. Bach

In the next example, the triple passing tones at 1, along with the held tone, spellseventh chord in second inversion. This chord does not function in the normal sense of chord classifications.

Schwing' dich auf zu deinem Gott J.S. Bach

A passing chord results if the vertical sonority formed by the three voices moving stepwise, along with the fourth remaining stationary voice, forms a chord that is nonfunctional.

Passing chords in the form of triple passing tones are more frequent than triple passing tones that do not spell a chord.

Passing chords may also result from combinations of passing tones and neighboring tones.


QUADRUPLE PASSING TONES

Quadruple passing tones are rare.

Ach Gott, wie manches Herzeleid J.S. Bach

UNCONVENTIONAL DOUBLING IN THE ROOT POSITION OF TRIADS INFLUENCED BY PASSING TONES

In the Bach Chorales, only 3% of the major triads in root position, and 2% of theminor triads, have the fifth doubled. Practically all triads with the doubled fifth are involved in progressions containing nonharmonic tones or other dissonances.

Christus, der uns selig macht J.S. Bach

Another unusual vertical structure of a triad appears in connection with the nonharmonic tones is composed of two roots and two thirds.

Triad with Two Roots and Two Thirds

Herzlich lieb hab' ich dich, o Herr J.S. Bach



For each of the following, provide alto and tenor voices. Identify the key and provide Roman numerals. Circle and label each passing tone.

1.

2.

3.


CHAPTER TWELVE

The Suspension

The suspension is prepared by the same tone and resolved by step downwards.

An analysis of 371 chorales* reveals that Bach used 1,661 suspensions of various types. According to these figures an average of over four suspensions for each chorale could be expected. In reality, there are 21 chorales without suspensions, 61 with one suspension, 56 with two, 43 with three and so on. There are a few chorales which contain as many as 19 suspensions. The longest chorale “herr Gott, dich loben wir”, which is really a combination of a number of chorales, contains 45 suspensions. The majority of chorales, however, have from one to four suspensions.

There are two kinds of suspensions, the single and the double. A little over 90%are single suspensions. These single suspensions are found throughout the phrase, but the double suspension is localized in the cadence formula.

* The Suspension in the Chorale Harmonizations by Bach, by Wayne Loren Dunlap, 1942.

SINGLE SUPSENSION

The single suspension may be found in any voice, but Bach had a definite preference. The following table shows the percentage frequency in each voice.

Soprano 2%

Alto 71%

Tenor 23%

Bass 4%

A suspension must be prepared and resolved, and so it involves three notes: the preparation note, the suspension note, and the resolution note.

The preparation note may be tied to the suspension note, or the suspension note may repeat the preparation note.


TYPES OF SINGLE SUSPENSIONS

Suspensions are named according to the intervals formed between the bass, and the suspension and resolution notes.

The 43 suspension is the most common single suspension. It is found most often in the Dominant chord. If it is used in a Plagal Cadence, it is found on the Tonic chord.

Wie schõn leuchtet der Morgenstern

The 98 suspension is the next most common single suspension. It is found most often in the Tonic chord.

Nun sich der Tag geendet hat

The 76 suspension is the next in frequency. It is most commonly found in the Leading Tone chord, which is always found in first inversion. The 6 in the 76 indicates first inversion.

Wenn mein Stündlein vorhanden ist


The 23 bass suspension is most commonly found on the Dominant Chord.

Es wird schier der letzte Tag

The 21 suspension is always found in the tenor, and is rare. While the 98 suspension may appear in any octave above the bass, the 21 suspension mustalways be a second above the bass, and thus must always be in the tenor.

Christ, der du bist der helle Tag

DEDUCTIONS

Every suspension demands a preparation note, a suspension note, and a resolution note.

The preparation note is a harmonic tone of the same pitch as the suspension note.

The suspension note is a dissonant tone.

The resolution note is a harmonic tone.

The suspension note descends either a half step or a whole step to the resolution note.

In the 43 and 76 suspensions the resolution note is rarely doubled in another voice.

In the 98 suspension the resolution note is doubled by the bass.

Under certain conditions parallel fifths may be avoided by use of a suspension.


The preparation note is usually twice as long, or equal to the length of the suspension note. The suspension note should not have a time value greater than that of the preparation note.

correct incorrect

Partwrite the following exercises, using passing tones and single suspensions:

1.

2.

3.


SINGLE SUSPENSION WITH CHANGE OF THE BASS TONE

Occasionally, when the suspended note resolves, the vertical structure may be a different inversion of the harmony or a new harmony. In both instances the normal resolution note is not disturbed. The 9 suspension with a change of bass is the most frequent, but this type of suspension may also occur on the 7, and rarely in the 4 (never when the single 4 suspension occurs in the dominant harmony).

The 9, 7, and 4 suspensions are treated in the same way as the 98, 76, and 43 suspensions. They have a preparation note, suspension note, and resolution note. The resolution, however, occurs as the bass moves either down a third, orup a third.

Für Freuden lasst uns springen

ORNAMENTAL SINGLE SUSPENSION

Occasionally, the suspension of the 4th and 9th are given a decorative melodic line at the time of resolution. The melodic ornament may contain stepwise motion, or leaps as large as a fifth. Most ornamental resolutions are located in either the dominant or tonic chords in the cadence. They may be found infrequently within the phrase in tonic or dominant harmonics. Sometimes passing tones may be found in another voice concurrent with the ornamental resolution of a suspension.


CHAIN SUSPENSION

A chain suspension consists of two or more suspensions in the same voice, in which the resolution of one suspension becomes the preparation of the next suspension. The 98 and 43 suspensions may be combined to form a chain suspension.

Komm, Gott Schöpfer, heiliger Geist

DOUBLE SUSPENSION

Double suspensions are infrequent. The majority appear in either the tonic or dominant harmonies. A few are found in the subdominant harmony. Although a double suspension may appear within a phrase, the greater majority are found at the cadence. The preparation note, suspension note, and resolution note will be found for each voice involved in the double suspension.

The 65 is the most common double suspension, the next is the 98. 43 76

Was mein Gott will, das g’scheh’

PARTWRITING EXERCISE CHAPTER 12


CHAPTER THIRTEEN

The Neighboring Tone: Passing Tone Suspension, Neighboring Tone inCombinations

The neighboring tone is next in the order of nonharmonic tone frequency. Single, double, and triple neighboring tones are found in the chorales.

Single neighboring tones are classified into two groups: lower neighboring tone (more frequent) and the upper neighboring tone. Accented neighboring tones are possible but they are rare.

The neighboring tone forms either a halfstep or wholestep relation to the harmonic tone, depending on its position in the diatonic scale.

The neighboring tone is found in all voices, least often in the soprano.

Schaut, ihr Sünder Auf, auf, mein Herz

DEDUCTIONS

Lower neighboring tones are most frequent.

The majority of neighboring tones are found in tonic harmony, next in dominant and subdominant, and lease of all in the remaining functions.

Occasionally the resolution tone of the neighboring tone is nonharmonic, due to a change of chord. Under these circumstances, the resolution tone usually has the characteristics of an accented passing tone.

Partwrite the following exercise, using passing tones, suspensions, and neighboring tones:


Double neighboring tones are less frequent than single. Upper double neighboring tones and contrary double neighboring tones are rare in comparison to the lower double neighboring tones.

The interval between two voices in which double neighboring tones appear is usually a third or a tenth. Double lower neighboring tones in similar motion usually form the interval of a third, or tenth. In contrary motion, they form other intervals, depending on the preceding notes.

O Haupt voll Blut und Wunden Ershienen ist der herrliche Tag

DEDUCTIONS

Lower double neighboring tones are the most frequent. The interval formed by the two voices in which lower double neighboring tones appear is usually a thirdor a tenth.

Contrary double neighboring tones are less frequent. The intervallic pattern created by two voices in which double neighboring tones appear in contrary motion, is as follows.

third – fifth – third

sixth – fourth – sixth

octave – sixth – octave

Upper double neighboring tones are rare. The interval formed by the two voicesin which upper double neighboring tones appear is most often a third, but a sixth is possible.

Partwrite the following exercises, using passing tones, suspensions, and neighboring tones:


There are a few examples of triple neighboring tones. The following examples illustrate Bach’s use of this type of nonharmonic device:

Valet will ich dir geben

Passing tones may occur in combination with neighboring tones, usually originating in the tonic harmony.

O Traurigkeit, o Herzeleid

Suspensions may be found in combination with neighboring tones. This device is most often found in dominant harmony in the cadence formula.

Wer Gott vertraut, hat wohl gebaut

In the following exercise, use neighboring and passing tones, and suspensions:


CHAPTER FOURTEEN

Other Nonharmonic Tones

ANTICIPATION

Single and double anticipations are among the least used nonharmonic tones. They are principally located in cadences.

Des heil'gen Geistes reiche Gnad'

Anticipations are usually found in the cadence, anticipating members of either the tonic harmony or the dominant harmony. Anticipations are frequently used in combination with passing tones or suspensions.

The single anticipation usually appears in the soprano. The double anticipation usually appears in the soprano and tenor.

ESCAPE TONE

Single and double escape tones are among the least used nonharmonic tones.They are found within the phrase, usually close to the cadence.

Hast du denn, Jesu, dein Angesicht

The single escape tone is found in the soprano and rarely in other voices. The majority of escape tones are found in tonic harmony.

The escape tone is always approached stepwise ascending from the harmonic tone, and it is resolved by leap, descending to the next harmonic tone.

Double escape tones are approached and resolved in the same manner as single escape tones, and form the interval of a third, and sometimes a sixth.


APPOGGIATURA

The appoggiatura is among the least used nonharmonc tones. Single appoggiatures are rare and double appoggiatures are practically nonexistent.

Jesu, nun sei gepreiset

The single appoggiatura may be found in any voice. It is found often on the beat and less often on the weak part of a beat.

The appoggiatura is approached from below by a leap of a third and resolved downwards by step.

Similar fifths and octaves are avoided with the use of the appoggiatura.

PEDAL POINT

Pedal point is not a characteristic device in chorales.

Verheih' uns Frieden gnädiglich

If the sustained tone is in an upper voice, it is an inverted pedal point.

Auf dich hoffen vir

Inverted pedal points may be the tonic, dominant, or median tones of the key. Iftwo tones are sustained, the device is called double pedal point.


CHORALE HARMONIZATIONS USING NONHARMONIC TONES

The method of approach to harmonization of the chorale remains unchanged. The student must first approach the harmonization as if he intended to use triads. After the framework is decided upon, the fourvoice solution may be worked into a contrapuntal harmonic style – an increased melodic interest in each voice line.

Be sure that every nonharmonic tone that you insert or create follows the rules and does not create parallels. Nonharmonic tones tend to increase the melodic interest of the bass melody which must be solid before the nonharmonic tones are inserted. Many of the leaps of a third and fourth are filled inby passing tones.

Use the nonharmonic tones tastefully and stylistically, following the outlines in the previous chapters.

With the exception of the anticipation and the escape tone, DO NOT add nonharmonic tones to the soprano line.

PARTWRITING EXERCISE CHAPTER 14

Partwrite the following exercises using all the nonharmonic tones:

1.

2.


CHAPTER FIFTEEN

Seventh Chords: Introduction

A seventh chord is a fournote chord spelled in thirds. A seventh chord contains a triad plus a note that forms a seventh above the root. Seventh chords are classified as dissonant sonorities.

The identification of a seventh chord depends upon two factors: the tonal qualityof the triad, and the interval formed by the root and seventh. The name of the GB D F seventh chord is determined in the following manner:

First factor G B D major triad

Second factor G F minor seventh

G B D F is called a majorminor seventh chord.

Seventh chords used in compositions during the 18th and 19th centuries:

Structural name Common name

majorminor seventh seventh (dominant seventh)

minorminor seventh minor seventh

diminishedminor seventh halfdiminished seventh

majormajor seventh major seventh

diminisheddiminished seventh

diminished seventh

minormajor seventh minormajor seventh

augmentedmajor seventh augmentedmajor seventh


FIGURED BASS FOR THE SEVENTH CHORD

Figured bass for the root position of a seventh chord may be:

Figured bass for the first inversion may be:

Figured bass for the second inversion may be:

Figured bass for the third inversion may be:


THE PREPARED SEVENTH

The seventh of a chord is a chord tone, but it forms a dissonant relationship with the root. An examination of preBach examples of seventh chords shows that the seventh is usually preceded by a consonance and is resolved downward to a consonance. The dissonant seventh is preceded and followed by a consonance, much like a nonharmonic tone.

With this in mind, carefully observe the threenote melodic line of the voice which contains the seventh, in each of the following examples.

Melodic Figure Seventh Chord Figure

Suspension figure

Suspension figure

Neighboring tonefigure

Appoggiatura figure


In the Chorales by J. S. Bach, triads are more frequent than seventh chords.

Diatonic triads: 83.7%

Diatonic seventh chords: 14.8%

Altered triads and seventh chords: 1.5%

Inversions of seventh chords are more frequent than root position.

Root position: 26%

First inversion: 58.5%

Second inversion: 3%

Third inversion: 12.5%

Seventh chords appear in 1st and 2nd classifications, most of the time.

1st classification: 51% V7 39%vii°7 12.5% (most in minor)

2nd classification: 45.5% ii7 37%IV7 8.5%

3rd classification: 2.7% vi7 2.6% (most in major)I7 .4% (major only)

4th classification: .3% III 7 (major only)


CHAPTER SIXTEEN

Dominant Seventh Chord

The most frequent seventh chord is found in the first classification with its root on the dominant. The following table shows the type of chord and symbol used in major and minor keys.

Major Minor

V7 majorminor seventh V7

v7

majorminor seventh

minorminor seventh (infrequent)

ROOT POSITION

Suspension Figure 1) When the 7th of the V7 appears in the suspension

figure, the V7 is prepared by chords of the second classification, namely ii and IV.

2) In a major key, the 7th of the V7 chord descends one half step to its resolution tone.

3) In a minor key, the 7th of the V7 chord descends one whole step to its resolution tone.

4) The 7th the V7 chord may be ornamented in its resolution. Under all conditions of ornamentation, the dissonant 7th must be resolved.

5) The V7 chord may progress to either the tonic or submediant, within the phrase or at the cadence.

6) Occasionally a V7 complete may progress to an incomplete tonic.


Passing Tone Figure

1) When the 7th of the V7 is appears in the passing tone figure, the V7 is prepared by chords of the tonic and its inversions, or by the V triad in root position or first inversion, but not by chords of the second classification.

2) The 7th of the V7 chord descends by scale step to its resolution tone.

3) The 7th the V7 chord may be ornamented in its resolution.

4) The progressions, including the passing tone figure,are usually found in a cadence.

Appoggiatura Figure 1) When the 7th of the V7 appears in the appoggiature

figure, the V7 is preceded by the dominant triad.

2) The 7th of the V7 chord is usually approached from the 5th of the V triad. Occasionally the 3rd of the V triad may leap a fifth to the 7th of the V.


4) The 7th appears in the appoggiatura figure infrequently.

Neighboring Tone Figure

1) When the 7th of the V7 appears in the neighboring tone figure, the V7 is preceded by the vi chord (thirdclassification).



FIRST INVERSION

Suspension Figure

Was Gott tut, das ist wohlgetan

1) When the 7th of the V7 appears in the suspension figure, the V7 is prepared by chords of the second classification.

2) The 7th of the V7 chord descends to the resolution tone.

3) All four tones are present in the first inversion of the V7 chord.

4) The bass note of the first inversion of the V7 may be approached by step or leap.

5) The chord following the first inversion V7 is usually tonic. Sometimes the first inversion of the V7 may be followed by the root position of the V7.

Passing Tone Figure

Jesu, Jesu, du bist mein

1) The first inversion of the V7 is prepared by the tonic in first inversion or root position. Tonic has the 5th in the soprano, and V7 has the 7th in the soprano.

2) Special use of nonharmonic tones in the bass passing tones or suspensionsavoids unequal fifths between soprano and bass.

3) The leap from the bass note of the first inversion of tonic to the bass note of the first inversion V7 may be either a perfect fourth or a diminished fourth.

4) The V7 in first inversion may follow the V triad.



Jesu, deine tiefen Wunden

1) The first inversion of the V7 usually follows the root position of the tonic and progresses to the root position of the tonic.

2) The first inversion of the V7 may follow the first inversion of the tonic by leap in the bass, or by filledin leap.

Appoggiatura Figure

Was mein Gott will, das g'scheh'

1) When the V7 in first inversion occurs in the phrase, it follows the first inversion of the tonic and progresses to the tonic to root position. This progression is rare within the phrase.

2) The V7 in first inversion occurs occasionally at the beginning of a phrase, using the appoggiatura figure between the last chord of the preceding phraseand its resolution to the tonic. Cross frequently occurs in the voice leading in the progression to the V7.


SECOND INVERSION

The second inversion of the V7 is the least frequent position. This inversion of the chord is practically limited to the passing tone figure in Bach's chorales. Theneighboring tone, appoggiatura and suspension figures are rare.

The passing tone figure precedes and resolves the 7th in two ways: ascending and descending.

Passing Tone Figure

Descending Ascending

When the ascending passing tone figure is used, the 7th of the V7 rises to the dominant. A study of Bach's use of this figure will reveal that the 7th of the V7 does not resolve down in the conventional manner. Unequal fifths between two voices are frequent in this use of the V7.

1) The second inversion of the V7 may be used between the first inversion of the tonic and the root position of the tonic. Imperfect fifths may appear between upper voices.

2) The second inversion of the V7 may be used between the root position of the tonic and the first inversion of the tonic. The 7th of the V7 may ascend to the 5th of the tonic. Imperfect fifths may appear between upper voices.


THIRD INVERSION

Suspension Figure

Puer natus in Bethlehem

1) The third inversion of the V7 is prepared by chords of the second classification, namely ii and IV, and progresses to the first inversion of the tonic.

2) All four tones present in the third inversion.

3) The third inversion V7 chord may appear at the beginning of a phrase or within a phrase. It is rarely found as the final chord in a half cadence.

Passing Tone Figure

Wenn mein Stündlein vorhanden ist

1) The passing tone figure the V7 is less frequent than the suspension figure.

2) The third inversion V7 chord in a passing tone figure may appear at the beginning of a phrase or within a phrase.

3) When a chromatic passing tone figure is used, a modulation takes place.

4) Leaps in the voices leading occur when the chord is at the beginning of a phrase. Within the phrase the approach to the third inversion of the V7 is smooth in all voices.



Dir, dir, Jehovah, will ich singen

1) The third inversion V7 chord in a neighboring tone figure is rare.

2) The third inversion of theV7 both follows and progresses to the tonic in first inversion.

3) The progression is most useful within the phrase.

Appoggiatura Figure

Puer natus in Bethlehem

1) The third inversion V7 chord in a appoggiatura figure is rare.

2) The device is found between phrases and within a phrase.

a) between phrases a change of key takes place

b) within a phrase the third inversion of the V7 follows either the V or ii chord.

3) The third inversion of the V7 progresses to the tonic in first inversion.


CHAPTER SEVENTEEN

Supertonic Seventh Chord

The next most common seventh chord is found is the second classification with its root on the supertonic. The following table shows the type of chord and the symbol used in major and minor keys:

Major Minor

ii7 minorminor seventh ii°7

ii7

diminishedminor seventh

minorminor seventh (rare)

The 7th of the supertonic seventh chord usually appears in the suspension figure. It is found most often in first inversion, next in root position, occasionally in third inversion, and practically never in second inversion.

ROOT POSITION

Suspension Figure

Herr Christ, der ein'ge Gott'ssohn Du grosser Schmerzensmann

1) The ii7 chord may follow the vi or I chord, or occasionally the IV.

2) The ii7 may progress to V or sometimes to V7 or occasionally the vii° in firstinversion.

3) The ii7 appears in root position frequently, in major keys.

4) The seventh of the ii7 resolves in the same manner as the seventh of the V7.

5) The ii7 may appear at any point of the phrase.


Passing Tone Figure

In the example below, the ii7 is introduced through the first inversion of the ii. The passing tone figure is in the soprano. Notice that the resolution of the seventh is momentarily retarded to form the 6–5 melodic line over the dominant “G” in the bass.

Von Gott will ich nicht lassen

1) When the seventh of the ii7 appears in the passing tone figure, it is precededby the first inversion ii triad.

2) Small leaps may occur in the upper voiced between the ii and ii7, since the supertonc sonority is established by the first inversion of the triad.

3) The ii7 may be followed by the V triad or V7. The tonic triad in inversion may appear between the ii7 and the dominant harmonies.

Neighboring Tone and Appoggiatura Figures

There are no examples in Bach chorales of these melodic figures used in connection with the ii7 chord.


FIRST INVERSION

Suspension Figure

Jes Leiden, Pein und Tod

1) The ii7 in first inversion may follow IV in first inversion, vi, or I in root positionor inversion.

2) The ii7 in first inversion progresses normally to the V triad. Occasionally the Cadencial 6/4 chord precedes the V triad.

3) All chord tones are present in the first inversion of the ii7.

4) The progression ii7 V may occur during the time duration of one beat.

5) The ii7 in first inversion may appear at any point within the phrase. The majority, however, are found as part of a cadence.

Passing Tone, Neighboring Tone and Appoggiatura Figures

The ii7 in first inversion does not appear in these melodic figures.

SECOND INVERSION

The ii7 in second inversion does not appear in Bach chorales, as a functional chord.


THIRD INVERSION

Suspension Figure

Ach Gott, erhör' mein Seufzen

1) The third inversion of the ii7 follows the root position of the I chord.

2) The soprano, alto and tenor voices may descend or ascend, in similar motion, from the I triad to the third inversion of the ii7.

3) The third inversion of the ii7progresses to the V or V7, in first inversion.

4) This progress occurs most often at the beginning of a phrase.


The ii7 in third inversion is extremely rare, or does not appear in these melodic figures.


CHAPTER EIGHTEEN

Leading Tone Seventh Chord in Minor

Following the supertonic seventh chord in frequency is the leading tone seventhchord in minor. The vii°7 is a diminisheddiminished seventh chord. It may be used as a firstclassification chord, in the authentic cadence.

ROOT POSITION

Suspension Figure

Christ, der du bist der helle Tag

1) The vii°7 frequently follows the iv chord in root position or first inversion.

2) The vii°7 occasionally follows the ii7 in root position.

3) The root of the vii°7 may be approached in the bass by step or leap, including the leap of a diminished fifth, descending from the iv.

4) The upper voices progress smoothly.

Passing Tone Figure

Herlich tut mich verlangen

1) When the vii°7 appears in a passing tone figure in root position, a chromaticchord progression, or modulation is involved.

2) The 7th in the vii°7 usually appears in the tenor.



When appearing in a neighboring tone figure, the vii°7 is found in diatonic as well as chromatic progressions.

Gelobet seist du, Jesu Christ

Es ist das Heil uns kommen her

1) When the vii°7 appears in a neighboring tone figure root position, it usually follows the tonic in root position, and occasionally in first inversion.

2) The 7th in the vii°7 usually appears in the tenor, or alto, but not in the soprano.

Appoggiatura Figure

Du, o schönes Weltgebäude

1) The leap of the appoggiatura figure usually ascends, but occasionally descends to the 7th in the vii°7. The 7th descends to the resolution tone, in either case.

2) The vii°7 chord is usually preceded by a chromatically altered chord.


FIRST INVERSION

Ist Gott mein Schild und Helfersmann

Suspension Figure

1) The vii°7 in first inversion follows a secondclassification chord, usually the supertonic.

2) The vii°7 in first inversion progresses to the first inversion tonic triad.


1) The vii°7 in first inversion follows tonic (first inversion) or dominant.

2) The vii°7 in first inversion progresses to tonic in first inversion.

Passing Tone Figure

No examples found in the Bach chorales.

Appoggiatura Figure

1) The vii°7 in first inversion follows the vii° triad, or occasionally the tonic.

2) The vii°7 in first inversion progresses to the tonic in first inversion, or occasionally to the V7 in first inversion.

3) A passing tone often fills in the leap of the third in this melodic figure.


SECOND INVERSION

Ach Gott und Herr, wie gross und schwer

Suspension Figure

1) The vii°7 in second inversion follows secondclassification chords.

2) The vii°7 in second inversion progresses to tonic, in root position or first inversion.

Passing Tone Figure No examples found in the Bach chorales.


1) The vii°7 in second inversion follows tonic, in root position or inversion.

2) The vii°7 in second inversion progresses to tonic, in root position or first inversion.

Appoggiatura Figure

1) The vii°7 in second inversion follows tonic, in any inversion.

2) The vii°7 in second inversion progresses to tonic, in root position or first inversion


THIRD INVERSION

Wir Christenleut'

1) Third inversion of vii°7 is rare.

2) vii°7 in third inversion usually follows subdominiant in first inversion.

3) vii°7 in third inversion usually progresses to either V7 or tonic in first inversion.

4) The 7th may be appear as a suspension figure, or occasionally by the descending chromatic passing tone figure.


CHAPTER NINETEEN

Subdominant Seventh Chord in Major and Minor

The next prominent seventh chord is found in the second classification, on the subdominant in major and minor.

Major Minor

IV7 majormajor seventh iv7

IV7

minorminor seventh

majorminor seventh (first inversion)

ROOT POSITION

Suspension Figure

Vater unser im HJimmelreich

1) The IV7 follows tonic, or the thirdclassification submediant chord.

2) The IV7 progresses most often to the V triad, and sometime the V7.

3) The IV7 is most often found in the cadence formula.

4) The 7th of the chord is most often found in the soprano.

5) The IV7 is rarely incomplete.

6) The IV7 is found frequently on the second half of the beat.


Passing Tone Figure

Christins der uns elig macht

1) The IV7 follows IV triad in first inversion.

2) The IV7 progresses most often to the V triad, and sometime the V7.

3) The IV7 is most often found in the cadence formula.

Neighboring Tone and Appoggiatura Figures

These melodic figures are rare in Bach Chorales.

FIRST INVERSIONSuspension Figure

Herzlich tut mich verlangen

1) IV7 in first inversion follows the tonic, mediant, or mediant in first inversion.

2) IV7 in first inversion progresses to the V or V7, and sometimes to the vii°7 in root position.

3) iv7 (minor key) in first inversion progresses to the V in a phrygian cadence.

4) In most cases the, IV7 in first inversion is found on the first half of the beat.


These melodic figures are rare in Bach Chorales.


SECOND INVERSION

No examples of IV7 in second inversion are found in the Bach chorales.

THIRD INVERSION

Suspension Figure

1) The IV7 in third inversion follows first inversion tonic, or root position mediant.

2) The IV7 in third inversion is frequently a common chord in tow keys of a modulation.

3) The IV7 in third inversion appears near the beginning of a phrase or within the phrase.


No examples of IV7 in third inversion, with these melodic figures, are found in the Bach chorales.


CHAPTER TWENTY

Other Diatonic Seventh Chords

The other diatonic seventh chords include:

vii°7 in major First Classification

vi7 in major Third Classification

VI7 in minor Third Classification

I7 in major Third Classification

iii7 in major Fourth Classification

Leading Tone Seventh Chord in Major: The Root Position

The seventh chord built on the leading tone in a major key is a diminishedminor seventh chord (halfdiminished). The leading tone seventh chord in majoris much less frequent than in minor. The chord has a limited function in the chorales. It is found in the progression IV6 vii°7 I, and appears on the second half of the beat. It is controlled by the suspension figure.

Leading Tone Seventh Chord In Major: Inversions

Inversions of the vii°7 in major are rare.


Submediant Seventh Chord in Major and Minor: The Root Position

The submediant seventh chord, in major and minor keys, is found most often in root position. The following table shows the type chord and symbol used.

Major Minor

vi7 minorminor seventh VI7 majormajor seventh

vi°7 diminishedminor seventh

The vi7 in Major and the unaltered VI7 in Minor

O Ewigkeit, du Donnerwort

1) vi7 follows mediant (triads and seventh chords) or tonic triads.

2) vi7 progresses to the second classification (ii or IV), or first classification (V or vii° in first inversion).

3) The 7th of the vi7 appears in a suspension figure.

The vi°7 in Minor

Verleih, uns Frieden gnädiglich

1) vi°7 follows dominant, or mediant in first inversion.

2) vi°7 progresses to iv in the first inversion

3) The 7th of the vi°7 appears in a suspension figure.


Submediant Seventh chord in Major and Minor: Inversions

Examples of the submediant seventh chord are extremely rare. They usually appear as passing chords, and have no harmonic function.

The Tonic Seventh Chord in Major

The seventh chord built on the tonic in a major key is a majormajor seventh chord. Tonic harmony, when it is dissonant, has a strong tendency to progress to secondclassification chords. The I7 is a third classification chord.

Es is gewisslich an der Zeit

1) When the I7 in root position or inversion follows the V or V7, the 7th appears in a suspension figure.

2) When the I7 in root position or inversion follows the I (root position or first inversion), the 7th appears in a passing tone figure.

3) The I7 progresses to second classification chords. IV is more frequent then ii.

4) The incomplete I7 is rarely used.


The Mediant Seventh Chord in Major

In the fourth classification in a major key, occasionally a minor seventh chord appears on the median. In root position, the chord is usually incomplete, appearing with one root, two thirds, and one seventh.

Jesu, meiner Seelen Wonne

1) The mediant seventh in root position or in inversion is rare, and if found only in major keys.

2) This chord is found in a retrogression from either the first or second classifications.

3) The iii7 progresses normally to third classification (vi), or by elision to the second classification (IV).

4) The suspension figuration is the only one used.


CHAPTER TWENTYONE

Altered NonHarmonic Tones

A nonharmonic tone which has a spelling foreign to the diatonic scale, and which does not disturb the root relations with surrounding chords, is called an altered nonharmonic tone.

Such altered tones can be derived from the modes of the major scale. The following table shows each mode of the major scale, generated from the same tone, and the resulting chromatic alterations:

MODE SPELLING ALTERATIONS

1 2 3 4 5 6 7

Ionian C D E F G A B

Dorian C D E♭ F G A B♭ 2♭

Phrygian C D♭ E♭ F G A♭ B♭ 4♭

Lydian C D E F♯ G A B 1♯

Mixolydian C D E F G A B♭ 1♭

Aeolian C D E♭ F G A♭ B♭ 3♭

Locrian C D♭ E♭ F Gb A♭ B♭ 5♭

In comparing the modes with the major scale (Ionian), one finds that modes with the fewest alterations are the Lydian, with a raisedfour, and the Mixolydian, with a loweredseven. These are the most common chromatic alterations in major keys, in music of the 17th and 18th centuries.

Other alterations are less frequent, and include the loweredsix, loweredsecond, and the loweredthird in a major key. In minor keys, the raisedfour is the most common chromatic alteration. The raisedthree (at the final cadence) is less common, and the loweredtwo is rare.

BACH'S USAGE

More than one hundred altered nonharmonic tones appear in the 371 chorales.Most of the alterations occur in major keys. Three types of altered nonharmonic tones appear in a major keys: loweredseven, raisedfour, and loweredthree. In minor keys, Bach used only the raisedfour.

Altered nonharmonic tones are introduced and resolved most often diatonically, usually as passing tones, and infrequently as lower neighboring tones. They never appear as suspensions, escape tones, or appoggiaturas.


Modes of the C Major Scale


CHAPTER TWENTYTWO

Altered Chords: Introduction

An altered chord includes one or more tones that have been raised or lowered,and are not in the key. An altered chord may or may not retain the function of the basic diatonic chord from which it was derived, depending on the resulting chord quality.

When accidentals are repeated, and the alteration lasts throughout the phrase, this is indicative of a modulation.

When the altered chord retains root relationships with surrounding chords, and the chords progress normally within classifications, a modulation has not occurred.

BORROWED CHORDS

Some chromatic alterations result in chords that normally appear in the parallel key (minor or major). These chords are examples of borrowed chords.

For example, a “flat six” submediant (♭VI) in a major key is borrowed from the parallel minor.

Vater unser im Himmelreich

Borrowed chords retain the same harmonic functions as the chords they replace. The phrase, above, ends with a deceptive cadence, and the final chordis a borrowed submediant (V ♭VI).

Use of borrowed chords is also known as modal interchange, and chords can be borrowed from any modes, not only the parallel major and minor.


SECONDARY DOMINANT

A chord can be strengthened when it is preceded by a chord with a dominant relation (major triad or majorminor seventh, with the root a fifth above).

A chromatic alteration resulting in a dominant seventh quality (majorminor) is known as a secondary dominant.

The secondary dominant is structured to resolve to a chord that is not tonic. Thechord of resolution is temporarily “tonicized”.

For example, in a major key, when ii7 is altered to form a majorminor seventh, the resulting chord functions as a dominant of the V7 chord, or V7/V (five seven of five).

SECONDARY LEADING TONE

A chromatic alteration resulting in a diminished triad or seventh chord can function as a secondary leading tone. In a major key, modal interchange is often employed to form a fully diminished seventh chord (diminisheddiminishedseventh).


CHAPTER TWENTYTHREE

Altered Chords in Minor

The natural and raised six and seven scale degrees of the minor key are part ofthe diatonic minor system. In Bach's music, the only chromatic alterations foundin minor which produce altered chords are the loweredtwo and raisedfour scale degrees. The raisedfour is used in combination with the raisedsix (ascending melodic minor).

Altered Supertonic V/V and V7/V (secondary dominant)

Jesu, meine Freude

1) Usually appears in first inversion, with the altered tone in the bass.

2) The altered tone is never doubled.

3) The altered tone can be introduced in three ways: chromatic inflection; stepwise, usually from above; and by leap.

4) The altered tone ascends a halfstep to the dominant.


Altered Subdominant vii°7/V (secondary leading tone seventh)

Lebensfürst, Herr Jesu Christ

1) Usually appears in root position, with the altered tone in the bass.


3) The altered tone can be introduced in three ways: chromatic inflection, stepwise, usually from above; and by leap of a diminished fifth, most often in the bass.

4) The altered tone ascends a halfstep to the dominant. It rarely descends chromatically to the subdominant.

5) This chord may follow i, ii°, iv, iv and occasionally VI.


Altered Subdominant vii°/V (secondary leading tone triad)

Was mein Gott will, das g'scheh'

1) Usually appears in second inversion and is derived from the tonic.

2) Usually appears on the second half of a beat.

3) The bass voice leaps to the dominant.

4) Often included in a half cadence, preceding the dominant.

Neapolitansixth Chord

The chord built on the loweredsecond, found in first inversion, is commonly called the Neapolitansixth chord (N6). The Neapolitan chord is usually found in first inversion with the bass note doubled.

Ach Gott, von Himmel sieh' darein

The Neapolitansixth chord (N) can be resolved to any of the following chords:

Frequent Less Frequent

vii°7 second inversion

iv

vii°/V

V

i second inversion

iii first inversion


CHAPTER TWENTYFOUR

Altered Chords in Major

The mostfrequent altered chords in major are V7/ V and V7/ IV.

V7/ V

1) Usually appears in first inversion, with the altered tone in the bass.


3) The altered tone can be introduced in three ways: chromatic inflection, stepwise, usually from above; and by leap of a diminished fifth.

4) The altered tone ascends a halfstep to the dominant.

V7/ IV

1) Usually appears in root position, and sometime in first inversion.

2) The lowered seventh is usually approached from above by a whole step.

3) The lowered seventh descends a helfstep to the submediant.


Other frequentlyused altered chords.

V / VI V7/ VI

V / ii V7/ ii

vii°7/ ii vii° / ii

vii°/ V vii°7/ V


CHAPTER TWENTYFIVE

AugmentedSixth Chords

Thus far in this study of altered chords, the structure has been composed of major and minor thirds. Under certain circumstances raising or lowering scale steps produces chords containing a diminished third or its inversion, an augmented sixth.

The chords of the augmented sixth are found in major an minor keys, but are more frequent in minor.

There are three commonlyused chord structures containing the augmented sixth:

Italian Sixth French Sixth German Sixth

The augmented sixth interval resolves outward to an octave, which is usually the dominant of the key.

Italian Sixth French Sixth

German Sixth

The German Sixth is often followed by a secondinversion tonic chord, before resolving to the dominant. This is necessary for avoiding parallel fifths, because the German Sixth chord containsa perfect fifth.


CHAPTER TWENTYSIX

Modulation to Foreign Keys

Although modulation has been used in some of the examples in previous chapters of this book, it has been confined to the system of closely related keys.

Closely Related Keys

1) tonic of the new key is a diatonic triad in the original key

2) only one accidental difference in key signatures

Foreign Keys

1) tonic of the new key is not a diatonic triad of the original key

2) two or more accidentals difference in key signatures

Foreign Modulation

Harmonic movement to a foreign key is known as a foreign modulation.

Ach Gott und Herr, wie gross und schwer

B♭: I vii° I V V V7/ IV

A♭: V7/ V V7 I

The example above begins in key from B♭ major and modulates to A major. ♭This is a foreign modulation because the A major triad is not a diatonic triad in ♭the key of B♭ major. Additionally, B major has two flats, while A major has ♭ ♭four flats.


Modulation by Change of Mode

With the acceptance of equal temperament during the 18th century, composers gradually expanded the use of foreign modulation. Although every interval relationship between tonics might be possible, one outstanding relationship between tonics began to appear: change of mode.

The following diagram shows a system of closelyrelated keys to C major, and another system of closelyrelated keys in the parallel minor (c minor).

The two systems of closelyrelated keys appear foreign to one another, however, in the case of each key, the dominant chord is the same as in the parallel key. The following diagram illustrates this concept:

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