music theory iii and iv prince george's community...

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

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