traditional harmony

8/10/2019 Traditional Harmony

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http://www.waybuilder.net/sweethaven/Humanities/Music/TraditionalHarmony/ David L. Heiserman,Editor

Lesson 1: PRELIMINARY KNOWLEDGE AND SKILLSOverview1-1 Placement of Voices1-2 Voice Motion1-3 Figured Bass and AnalysisLesson 2: PRIMARY TRIADS IN ROOT POSITIONOverview2-1 Part Writing Primary Triads (Major)2-2 Part Writing Primary Triads (Minor)2-3 Repeated Triads2-4 CadencesLesson 3: PRIMARY TRIADS IN FIRST INVERSIONOverview3-1 Part Writing First Inversion Primary Triads3-2 First Inversion Progressions3-3 CadencesLesson 4: PRIMARY TRIADS IN SECOND INVERSION

Overview4-1 Types of Second Inversion TriadsLesson 5: THE DOMINANT SEVENTH CHORDOverview5-1 Part Writing the Dominant Seventh Chord to Tonic5-2 Part Writing the Subdominant Triad to the Dominant Seventh Chord5-3 Melodic Preparation of the Seventh of the Dominant Seventh ChordLESSON 6: SECONDARY TRIADS IN ISOLATIONOverview6-1 Secondary TriadsLESSON 7: THE LEADING TONE AND SUBTONIC TRIADSIntroduction

7-1 Overview7-2 Part Writing the Leading Tone Triad7-3 Subtonic TriadLESSON 8: RELATING CHORD SCALES TO TRIADS, EXTENDED CHORDS ANDALTEREDCHORDSIntroduction8-1 Overview8-2 Part Writing Supertonic TriadLESSON 9: THE SUBMEDIANT TRIADIntroduction9-1 Overview

9-2 Part Writing Submediant TriadLESSON 10: PRINCIPLES OF PROGRESSIONIntroduction10-1 Overview10-2 Root Movement10-3 Chord Groups10-4 Chord ProgressionLESSON 12: ALTERNATIVE PRINCIPLES OF TRIADIC VOICE LEADINGIntroduction


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12- 1 Voice Leading of Repeated Triads12- 2 Voice Leading of Triads with Root Movement by Fifth12- 3 Voice Leading of First Inversion Triads12- 4 CadencesLESSON 13: SECONDARY DOMINANT CHORDSIntroduction13-1 Structure and Analysis13-2 Dominant of the Dominant Chords13-3 Part Writing Secondary Dominant ChordsLESSON 14: LESS COMMON SECONDARY DOMINANT CHORDSIntroduction14-1 Less Common Secondary Dominant CordsLESSON 15: SECONDARY LEADING TONE CHORDSIntroduction15-1 Structure and Analysis15-2 Secondary Leading Tone ChordsLESSON 16: COMMON CHORD MODULATION

Introduction16-1 Relationship of Keys16-2 Four Step Process

Lesson 1: PRELIMINARY KNOWLEDGE AND SKILLS

In this lesson, you will learn voicing, ranges, doubling, spacing, open and close positions, types ofvoice motion, objectionable voice motion, figured bass, and analysis.

After completing this lesson, you will be able to: Name and identify the ranges of the four voices. Write voice doublings. Write correct voice spacing in open and close position. Identify voice motions. Identify crossed voices, overlapping voices, parallel voices, and hidden voices. Write figured bass and analysis.

1. Voice Names.a. The four voices in traditional four-part writing are soprano, alto, tenor, and bass. These are oftenabbreviated as SATB. The soprano is the highest voice and is notated in the treble clef staff with itsstems up. The alto is the second highest voice and is notated in the treble clef with its stems down.The tenor is the third highest voice and is notated in the bass clef with its stems up. The bass voice is

the lowest voice and is notated in bass clef with its stems down (Figure 1-1).


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Figure 1-1. SATB Notationb. When the soprano and alto or tenor and bass are in unison (sounding the same pitch), the stems goup and down on the same note head (Figure 1-2).

Figure 1-2. Stemming Shared Note HeadsNOTE: The soprano part is often called the melody. The alto and tenor parts are called the innervoices. The bass part is called the bass line.2. Voice RangesThe normal singing range for the soprano, tenor, and bass voices is an octave and a sixth (Major13th). The alto range is an octave and a fifth (Perfect 12th). Figure 1-3 shows the notes of each voicerange. Avoid using the extreme range (the highest or lowest note or two) of each voice unless dictatedby the voice leading.

Figure 1-3. SATB Ranges3. Voice DoublingIn four part writing, the three-note triad must have one of its tones duplicated. When the triad is in rootposition (bass voice has the root of the chord), the bass voice and one of the three upper voices willhave the same letter name note. This doubling can be at the unison or any octave relationship.Doubling does not change the harmonic structure of the chord, but it may alter its color and resonance(Figure 1-4).

Figure 1-4. Voice Doubling

SELF REVIEW EXERCISE 1-1Write the inner voices of each triad. Use one third and double the root. The alto voice should have a note higher than

the tenor voice (Figure 1-5). Stay within the voice ranges.


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Figure 1-5. Voice Doublings

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4. Voice Spacinga. The distance between the soprano and the alto voices must be a simple interval of an octave orless.b. The distance between the alto and tenor voices must also be a simple interval.c. The distance between the tenor and the bass voices can be either a simple or a compound interval.However, there are restrictions on certain simple intervals between the tenor and bass voices. Theserestrictions, called low interval limits, dictate how low some intervals may be voiced. The restrictedintervals are the minor sixth, the tritone, the third (Major or minor), and the second (Major or minor).There are no limits on the other intervals within the bass voice range (Figure 1-6).

Figure 1-6. Low Interval Limitsd. Figure 1-7 shows incorrect and correct voice spacing.

Figure 1-7. Incorrect and Correct Voice Spacing

SELF REVIEW EXERCISE 1-2Correct the improperly spaced voicing. Reposition the alto and tenor voices. Do not change the soprano voice (Figure

1-8).


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Figure 1-8. Correct Voice Spacing


NOTE: The term chord is often used when referring to a triad.5. Open and Close Positiona. Triads can be written in either open or close positions. In open position, the distance between thesoprano and the tenor is a ninth or more. In close position, the distance between the soprano and the

tenor is an octave or less (Figure 1-9).

Figure 1-9. Open and Close Position Triadsb. The bass voice is not considered in determining open or close position.

SELF REVIEW EXERCISE 1-3Rewrite the following triads in open position. Use one root, one third, and one fifth of each chord to complete the

exercise (Figure 1-10).


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Figure 1-10. Triads in Open Position


SELF REVIEW EXERCISE 1-4Rewrite the following triads in close position. Use one root, one third, and one fifth of each chord to complete the

exercise (Figure 1-11).

Figure 1-11. Triads in Close Position


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6. Voice MotionGood part writing depends on the smooth connection of the individual parts and their independence ofmotion. The term "motion" is used to describe the relative change in pitch of two or more voice parts.Voice motion is usually described in simple intervals. The four types of motion are similar, parallel,contrary, and oblique.a. Similar motion occurs when two voices move in the same direction but produce different numericalinterval names (Figure 1-12).

Figure 1-12. Similar Motionb. Parallel motion occurs when two voices move in the same direction and produce the same(numerical) interval name (third, sixth, etc.). Interval quality (perfect, Major, minor, augmented, ordiminished) is not considered in determining parallel motion. A Major third to a minor third is parallelmotion (Figure 1-13).

Figure 1-13. Parallel MotionNOTE: When voices move in the same direction, the motion can be called direct motion. Similar andparallel motions are direct motion.c. Contrary motion occurs when two voices move in opposite directions (Figure 1-14).

Figure 1-14. Contrary Motiond. Oblique motion occurs when one voice sustains or repeats while the other voice moves (Figure 1-15).


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Figure 1-15. Oblique MotionNOTE: When voices move in dissimilar directions, the motion can be called indirect motion. Contraryand oblique motions are indirect motion.

SELF REVIEW EXERCISE 1-5Write the type of voice motion in the corresponding blanks provided below the measures. On the second line write

whether the motion is direct or indirect. The first measure has been done for you (Figure 1-16).

Figure 1-16. Identify Voice Motion


7. Objectionable Voice Motion

a. Crossed Voices. Crossed voices occur when the soprano does NOT have the highest pitch, the altothe second highest, the tenor the third highest, or the bass the lowest pitch. Do not write crossedvoices (Figure 1-17).


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Figure 1-17. Crossed Voicesb. Overlapping Voices. Overlapping voices occur when two adjacent voices move in similar or parallelmotion and the lower voice ascends to a pitch above that just left by the upper voice. Overlappingvoices also occur when the upper voice descends to a pitch below that just left by the lower voice. Donot write overlapping voices (Figure 1-18).

Figure 1-18. Overlapping VoicesNOTE: Measure 1 of Figure 1-18 also has a spacing error between the alto and tenor voices.

c. Parallel Voices.(1) Parallel perfect primes, perfect fifths, perfect octaves, and dissonant intervals (seconds, sevenths,augmented, and diminished) should be avoided. Do not write parallel primes, fifths, octaves, anddissonant intervals (Figure 1-19).

Figure 1-19. Objectionable Parallel VoicesNOTE: Parallel perfect fifths and parallel perfect octaves are usually called parallel fifths and paralleloctaves. Repeated notes are not considered parallel fifths or octaves.(2) A hidden fifth or octave occurs when two voices approach a fifth or an octave in similar motion. Ahidden fifth or octave is objectionable only when it occurs between the soprano and bass voice, andthe soprano is approached by a leap (Figure 1-20).


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Figure 1-20. Objectionable Hidden Fifth and Octave(3) Parallel fifths and octaves by contrary motion occur when two voices move by contrary motion fromone interval to the same interval. An octave to unison has the same effect. Do not write parallel fifthsor octaves by contrary motion (Figure 1-21).

Figure 1-21. Objectionable Parallels by Contrary Motion

SELF REVIEW EXERCISE 1-6Correct the crossed voices. Use only the exact pitch (octave) indicated to complete the exercise (Figure 1-22).


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Figure 1-22. Correct Crossed Voices


SELF REVIEW EXERCISE 1-7Draw a solid line to indicate the overlapping voices and draw a dotted line to indicate the overlapped voices in each

measure. Write the names of the voices overlapping and the notes that overlap. There may be more than oneoverlapping voice in each measure. The first one has been done for you (Figure 1-23).


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Figure 1-23. Identify Overlapping Voices


SELF REVIEW EXERCISE 1-8Draw a line to indicate the objectionable parallel motion in each measure. Label parallel fifths with a bracket and the

number 5 and parallel octaves with an 8. The first one has been done for you (Figure 1-24).


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Figure 1-24. Identify Objectionable Parallel Motion


SELF REVIEW EXERCISE 1-9Draw a line to indicate the objectionable hidden motion in each measure. Label hidden fifths with a 5 and hidden

octaves with an 8. The first one has been done for you (Figure 1-25).


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Figure 1-25. Identify Objectionable Hidden Motion


SELF REVIEW EXERCISE 1-10Draw brackets to indicate the parallel voices by contrary motion in each measure. Label parallel fifths by contrary

motion with a 5 and parallel octaves by contrary motion with an 8. The first measure has been done for you (Figure 1-26).


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Figure 1-26. Identify Parallel Voices by Contrary Motio

8. Figured BassFigured bass is a shorthand method of indicating harmonic accompaniment for a bass line. Arabicnumbers placed under the bass note designate the intervals (usually reduced to simple intervals)above the bass note. The figured bass does not indicate which voice (soprano, alto, or tenor) haswhich part (root, third, or fifth) of the chord. The intervals stay within the key signature unlesschromatically altered (lesson 2). Figured bass does not indicate open or close position (Figure 1-27).

Figure 1-27. Figured Bass Examples

SELF REVIEW EXERCISE 1-11Write the notes above the bass note that are indicated by the figured bass numbers. The first measure has been done

for you (Figure 1-28).


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Figure 1-28. Figured Bass


9. Roman Numeral Analysisa. Roman numerals written under the staff indicate chord analysis. They are not used below the bassnote except for analysis. The Roman numeral identifies the corresponding scale degree on which thetriad is built. Upper case numerals represent Major triads. Lower case numerals represent minortriads. Uppercase numerals with a plus sign (+) indicate an augmented triad. A lower case numeralwith a circle (o) indicates a diminished triad (Figure 1-29).

Figure 1-29. Quality of Triadsb. The root of the triad, not necessarily the bass note, is indicated by the Roman numerals whether thetriad is in root position or in an inversion (Figure 1-30).

Figure 1-30. Root in Relation to Bass NoteNOTE: Roman numeral analysis can be combined with figured bass to show a complete analysis(triad root, triad inversion).

SELF REVIEW EXERCISE 1-12Write the Roman numeral analysis below the bass clef staff. The exercise is in Major and minor keys (Figure 1-31).


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Figure 1-31. Roman Numeral Analysis

Lesson 2: PRIMARY TRIADS IN ROOT POSITION

In this lesson, you will learn about primary triads in root position. This lesson includes doubling, figuredbass, and basic principles for part writing root position primary triads in Major and minor.

After completing this lesson, you will: Identify root position triads. Write voice doublings. Write figured bass and analysis. Part write root position primary triads in Major and minor. Identify authentic, plagal, and half cadences.

1. Primary Triadsa. The primary triads are triads built on the tonic, subdominant, and dominant scale degrees. Theyestablish the tonal center (Figure 2-1).

Figure 2-1. Primary TriadsNOTE: The tonic, subdominant, and dominant scale degree notes (scale steps) are called primary ortonal notes. The supertonic chord is a secondary triad, but the supertonic scale degree can function asa primary note.


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b. The primary triads are built on the same scale degrees in both Major (I, IV, V) and minor (i, iv, V)keys (Figure 2-2).

Figure 2-2. Primary Triads in Major and MinorNOTE: In a minor key (harmonic minor), the dominant triad is Major. The third of the triad is raisedwith an accidental to create a leading tone.2. Root Position

A triad is in root position when the root of the triad is in the bass voice (Figure 2-3).

Figure 2-3. Root Position Triad3. Doubling of Root Position TriadsWhen a triad is in root position, the root of the chord (the bass note) is doubled. This doubled notemay be in any of the upper voices (Figure 2-4).

Figure 2-4. Root Position Doubling4. Figured Bass

a. The numerals , ,5, or 3 indicate a triad in root position.NOTE: The 3 represents the note an interval of a third above the bass note (the third of the triad). The5 represents the note the interval of a fifth above the bass note (the fifth of the triad). The 8 representsthe note that is the doubled root of the triad (Figure 2-5).


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Figure 2-5. Figured Bassb. Usually these numerals are omitted. A bass note with no numerals is understood to represent atriad in root position (Figure 2-6).

Figure 2-6. Root Position Figured BassNOTE: The figured bass is a complete figured bass when all upper voices are represented in the bassfiguring (including doublings). Essential figured bass is that numbering (or chromatic sign) which isneeded to represent the triad. Figure 2-5 is complete figured bass. Figure 2-6 is essential figured bass.c. Chromatic alterations are indicated by accidentals placed below the bass line.

d. The chromatic sign is the accidental (#, , or ) necessary to raise or lower the note being alteredwithin the key. It does not have to be a # to raise or a to lower.e. A chromatic sign used in the figured bass refers to the note a third above the bass if no numberaccompanies the chromatic sign (Figure 2-7).f. A slash through a number means to raise the note of that interval a half step (Figure 2-7).

Figure 2-7. Chromatic Alteration in Figured Bass5. Basic Principles for Part Writing Triadsa. Keep the common tone.b. Connect the remaining voices to the nearest available chord tones.First, look for half step movement.Next, look for whole step movement.Finally, connect any remaining intervals.c. Check your part writing for objectionable voice motion.


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2-5 CADENCES18. Authentic, Plagal, and Half Cadencesa. Authentic Cadence. The V to I or V to i chord progression at a phrase ending is called an authenticcadence. It is a perfect authentic cadence when both triads are in root position and the tonic scaledegree appears in the soprano of the tonic triad. Otherwise, it is called an imperfect authenticcadence. Authentic cadences create the feeling of full stop and are commonly found at final cadences(Figure 2-37).

Figure 2-37. Authentic Cadencesb. Plagal Cadence. The IV to I or iv to i chord progression at a phrase ending is called a plagalcadence. It is a perfect plagal cadence when both triads are in root position and the tonic scale degreeappears in the soprano voice of both triads. Otherwise, it is known as an imperfect plagal cadence.The plagal cadence, commonly called the Amen cadence, lacks the directional drive of the authenticcadence and provides a less final ending (Figure 2-38).

Figure 2-38. Plagal Cadencesc. Half Cadence. When any chord, regardless of inversion, moves to the V chord at a phrase ending, ahalf cadence occurs. A phrase that ends with a half cadence does not have a feeling of repose. Itcreates a feeling of suspense that is usually resolved in the next phrase with a final cadence (Figure 2-39).


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Figure 2-39. Half Cadencesd. Plagal Half Cadence. When the I (i) chord moves to the IV (iv) chord at a phrase ending, a plagalhalf cadence occurs. As with a half cadence, the plagal half cadence creates a feeling of suspense.This is usually resolved in the next phrase with a final cadence (Figure 2-40).

Figure 2-40. Plagal Half Cadences

SELF REVIEW EXERCISE 2-7Part write and analyze the following progressions. Write the name of each cadence in the space provided (Figure 2-

41. Part A and Part B).

Figure 2-41. Part A. Root Position Progressions


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Figure 2-41. Part B. Root Position Progressions

6. Part Writing the I Chord to the V Chorda. The root of the triad is in the bass voice (Figure 2-8). The root of the dominant chord can be eitherup a perfect fifth or down a perfect fourth from the bass note of the tonic chord.


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Figure 2-8. Bass Noteb. One note in the tonic chord is also found in the dominant chord. This note is common to both triadsand is called the common tone. When connecting the tonic to the dominant chord, keep the commontone in the same voice (Figure 2-9).

Figure 2-9. Common Tonec. To achieve the smoothest part writing, move voices the smallest distance. Move the remaining twovoices down by step to the nearest chord tone. First, connect the half step movement and then thewhole step movement (Figure 2-10).

Figure 2-10. Descending Movement by Step

d. The scale pattern for connecting the I chord to the V chord (Figure 2-11).


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Figure 2-11. I to V Scale PatternNOTE: Remember that Arabic numbers indicate scale degrees not triad numbers.7. Part Writing the V to the I ChordThe scale pattern for connecting the V to the I is the reverse of the I to the V connection (Figure 2-12).

Figure 2-12. Connecting V to I

SELF REVIEW EXERCISE 2-1Part write the following I to V and V to I progressions (Figure 2-13).


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Figure 2-13. I to V and V to I Progressions


8. Part Writing the I to IV Chorda. The root of the triad is in the bass voice (Figure 2-14). The root of the subdominant chord can beeither a Perfect fourth up or a Perfect fifth down from the root of the tonic chord.


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Figure 2-14. Bass Noteb. Keep the common tone in the same voice (Figure 2-15).

Figure 2-15. Common Tonec. Move the remaining two voices up by step to the nearest chord tone. First, connect the half stepmovement, and then connect the whole step movement (Figure 2-16).

Figure 2-16. Ascending Movement by Step

d. Scale pattern for connecting the I chord to the IV chord (Figure 2-17).


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Figure 2-17. Connecting I to IV9. Part Writing the IV Chord to the I ChordThe scale pattern for connecting the IV to the I chord is the reverse of the I to IV chord connection(Figure 2-18).

Figure 2-18. Connecting IV to I

SELF REVIEW EXERCISE 2-2Part write the following I to IV and IV to I progressions (Figure 2-19. Part A and Part B).

Figure 2-19. Part A. I to IV and IV to I Progressions


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Figure 2-19. Part B. I to IV and IV to I Progressions


10 .Part Writing the IV Chord to the V Chorda. The root of the triad is the bass note (Figure 2-20). The root of the dominant chord is a Majorsecond above the root of the subdominant chord.

Figure 2-20. Bass Noteb. There is no common tone. Move the upper three voices down to the nearest chord tones in contrarymotion to the bass voice. First, connect the half step, next connect the whole step, and then connect

the minor third movement (Figure 2-21).


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Figure 2-21. Contrary Motion to Bassc. The scale pattern for connecting the IV chord to the V chord (Figure 2-22).

Figure 2-22. Connecting the IV to Vd. When connecting the IV to V, failure to move the upper voices contrary to the bass voice causesmotion problems of parallel fifths and octaves (Figure 2-23).

Figure 2-23. Objectionable Parallel Fifths and Octaves

SELF REVIEW EXERCISE 2-3Part write the following IV to V progressions (Figure 2-24).


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Figure 2-24. IV to V Progressions


11. Part Writing the V Chord to the IV ChordThe dominant chord is usually not connected to the subdominant chord. However, the dominant canprogress to the subdominant when it immediately goes back to the dominant chord. The upper threevoices move contrary to the bass voice (Figure 2-25).

Figure 2-25. Connecting V to IV to V

12. Part Writing the i Chord to the V Chord and V to i

Connecting tonic to dominant and dominant to tonic in minor is similar to connecting tonic to dominantand dominant to tonic in Major keys. The root is in the bass voice. Keep the common tone. Connectthe remaining two voices by half step to the nearest chord tones. Remember to raise the third of thedominant chord in minor (Figure 2-26).


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Figure 2-26. Connecting i to V and V to I

SELF REVIEW EXERCISE 2-4Part write the following i to V and V to i progressions (Figure 2-27. Part A and Part B).

Figure 2-27. Part A. i to V and V to i Progressions


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Figure 2-27. Part B. i to V and V to i Progressions


13. Part Writing the i Chord to the iv Chord and iv to i

Connecting tonic to subdominant and subdominant to tonic in minor is similar to connecting tonic tosubdominant and subdominant to tonic in Major. The root is in the bass voice. Keep the common tone.Connect the remaining two voices by step to the nearest chord tone. First, connect the half stepmovements, and then connect the whole step movement (Figure 2-28).


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Figure 2-28. Connecting i to iv and iv to i

SELF REVIEW EXERCISE 2-5Part write the following i to iv and iv to i progressions (Figure 2-29. Part A and Part B).

Figure 2-29. Part A. i to iv and iv to i Progressions

Figure 2-29. Part B. i to iv and iv to i Progressions


14. Part Writing the iv Chord to V Chord


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a. Connecting the subdominant to dominant in minor is similar to connecting subdominant to dominantin Major. The root is in the bass voice. Move the three upper voices down to the nearest chord tones incontrary motion to the bass voice. First, connect the two voices with half step movements, and thenconnect the minor third movement (Figure 2-30).

Figure 2-30. Connecting iv to Vb. When connecting the iv to V, avoid the melodic augmented second between the sixth scale degreeand the raised seventh scale degree. This interval should not appear in the same voice (Figure 2-31).

Figure 2-31. Melodic Augmented Secondc. Connect the upper three voices contrary to the bass to avoid the augmented second.

SELF REVIEW EXERCISE 2-6Part write the following iv to IV progressions (Figure 2-32).


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Figure 2-32. iv to V Progressions


15. Part Writing the V Chord to the iv ChordThe dominant chord is usually not connected to the subdominant chord in minor. However, thedominant can progress to the subdominant (minor) when it immediately goes back to the dominant.The upper three voices move contrary to the bass (Figure 2-33).

Figure 2-33. Connecting to V to iv to V

16. Picardy Third EndingThe final tonic chord of a composition in a minor key is occasionally made Major. The raised third ofthe triad is borrowed from the parallel Major and is known as the Picardy third. The Picardy thirdusually occurs when connecting the dominant to tonic chord at the final cadence (Figure 2-34).


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Figure 2-34. Picardy Third EndingNOTE: Use an upper case Roman numeral I for analysis when using the Picardy third because of theMajor quality of the tonic chord.

17. Any triad can follow itself

When triads repeat, you can reposition the voices within the chord.a. Move the upper three voices in similar motion up or down to another chord tone (Figure 2-35).Voices should not overlap.

Figure 2-35. Upper Voice Repositioningb. Reposition two of the upper voices so that the triad changes position from open to close or fromclose to open (Figure 2-36). The third voice has a common tone.

Figure 2-36. Changing Triad Positionc. The bass voice can either remain on the same pitch or jump an octave (Figures 2-35 and 2-36).NOTE: When repositioning a triad, you do not have the problem of hidden or parallel fifths or octaves.You still must make sure voices do not overlap, cross, or violate voice range and interval limits.


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Lesson 3: PRIMARY TRIADS IN FIRST INVERSION

In this lesson, you will learn the primary triads in first inversion. This lesson includes doubling, figuredbass, analysis, part writing procedures, and cadences.

After completing this lesson, you will: Identify first inversion primary triads. Write voice doublings. Write figured bass and analysis. Part write first inversion primary triads in Major and minor. Identify imperfect cadences.

1. First Inversion Triads.a. A triad is in first inversion when the third of the chord is in the bass voice. The fifth and the root arevoiced above the third (Figure 3-1).

Figure 3-1. First Inversion TriadNOTE: The root of the triad remains the root (scale degree upon which the triad is formed) regardless

of its position in the triad.b. First inversion triads allow for smooth voice leading of the bass voice and provide harmonic variety.2. Doubling of First Inversion Triads.a. When the primary triad is in first inversion, double the root or fifth of the chord (Figure 3-2). Theupper three voices will have one root and two fifths or two roots and one fifth.

Figure 3-2. First Inversion Doublingb. You will determine which note to double by the voice leading necessary to make the voices connectsmoothly.


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b. Connect the remaining voices to the nearest available chord tones.First, look for half step movement.Next, look for whole step movement.Finally, connect any remaining intervals.c. Check your part writing for objectionable voice motions and other mistakes.NOTE: In part writing root position triads, you followed specific scale patterns for each progression.However, when part writing first inversion triads, you must make choices that are not set patterns.Your choices are determined by the smoothest (generally the closest) voice leading.6. Apply the part writing procedure to a progression with a first inversion chord (Figure 3-9).

Figure 3-9. Progression with First Inversiona. First, keep the common tone. Place a C in the tenor voice (Figure 3-10).NOTE: The second chord is a C triad (I chord) in first inversion. The notes of the chord are C, E, andG. The fourth (doubled) note can be either a C or a G. The E (the third of the chord) is already presentin the bass voice. You should not use the E in any of the upper voices. The C is common to bothchords.

Figure 3-10. Common Toneb. Connect the half step movement. The only note of the triad left to voice before determining thedoubled note is the G. (The C and the E have already been voiced.) The G is not a half step fromeither the soprano A or the alto F (Figure 3-11). Go to the next step of the procedure.


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Figure 3-11. No Half Step Movementc. Connect the whole step movement. The G is a whole step from both the soprano A and the alto F.You can place the G in either the soprano or alto voice (Figure 3-12).

Figure 3-12. Choose Whole Step Movementd. The last voice (soprano or alto) can be either a C or a G. Remember, in first inversion triads you candouble either the root or the fifth of the chord.

(1) If you placed the G (from step c) in the soprano voice, you must decide which doubled note (the Gor C) is smoother voice leading for the alto voice. The G is a whole step from the previous alto note.The C is a fourth from the previous alto note. Therefore, the G is the better note to double (Figure 3-13). A skip of a fourth in an inner voice, when you have a closer voice to lead to, is poor part writing.

Figure 3-13. Alto Voice MovementNOTE: If the alto voice moves down to a C, the two inner voices are doubled. Remember, it is best todouble an inner voice with the soprano in first inversion triads when you have a choice (Figure 3-14).

Figure 3-14. Poor Voice Leading(2) If you placed the G (from step c) in the alto voice, you can place either a G or a C in the sopranovoice. The G produces smoother voice leading and is the best alternative at this time (Figure 3-15).


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However, the C produces a melody line (soprano) with a skip. (This can be important in keeping themelody line interesting for exercises in the next lessons.) Both movements are correct.

Figure 3-15. Soprano Voice Movemente. Check your part writing for mistakes.NOTE: Understanding how to part write first inversion triads is essential to basic part writing skillsbecause you must make decisions that are not set patterns. You must determine which note is the

best to use for each upper voice. When you part write root position triads (and second inversion triadsin Lesson Four), each voice follows a set pattern.7. Follow the procedure again.NOTE: Until you become proficient at part writing, you can, if you wish, spell the chord below the bassline. Place possible doublings in the spelling at the end (in parentheses). Cross off each letter (note)as it is voiced (Figure 3-16). (Cross off the third of the chord as you spell the chord because it isalready in the bass voice.)

Figure 3-16. First Inversion Progressiona. Keep the common tone. The common tone (G) is in the tenor voice (Figure 3-17). (Cross off theletter G below the staff.)


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Figure 3-17. Common Tone in Tenor Voiceb. Connect the half step movement. The D is not a half step from E or C. Therefore, there is no halfstep movement (Figure 3-18). Go to the next step.

Figure 3-18. Look for Half Step Movementc. Connect the whole step movement. The D is a whole step from either the soprano or alto note. TheD can be placed in either voice (Figure 3-19). (Cross off the letter D below the staff.)

Figure 3-19. Soprano or Alto Whole Step Movementd. The last voice (soprano or alto) can be either a G or a D.

(1) If you placed the D (step c) in the soprano voice, the best voice leading for the alto voice is a D(Figure 3-20).


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Figure 3-23. Change Upper Voices PositionsNOTE: When you have a choice between the soprano and an inner voice, you should normallymaintain the common tone in the inner voice and not in the soprano. Keep the inner voices as smoothas possible (Figure 3-24).

Figure 3-24. Choose Common Tone Voice9. Checking Your Part Writing.a. After you have completed your voice leading, study your work. Remember, the principle of partwriting is connecting the parts of one chord smoothly to the parts of the next chord (without errors).The smooth connection of voice movement is especially important for the inner voices. The melodycan (and should) have disjunct motion (skips) as well as conjunct motion (stepwise movement). Onoccasion, moving one voice by a small interval (for example, half step) will cause another voice tomove by a large interval (fourth). This may not be the best overall part writing if the fourth is an innervoice (Figure 3-25).

Figure 3-25. Large Movement Inner Voiceb. If the soprano had been an octave above the alto, the same part writing is better because thedisjunct motion can be in the soprano voice (Figure 3-26).


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Figure 3-26. Disjunct Motion Soprano Voicec. To avoid the large interval skip in the inner (alto) voice (Figure 3-25), move the root of the I chord upa whole step (to the D) instead of down a half step (Figure 3-27). You can then keep the common tonein the alto voice and skip a third in the soprano. This connection creates acceptable part writing for allparts.

Figure 3-27. Smooth Part Writing I6to VNOTE: The above progression has a hidden fifth between the tenor and bass. This hidden fifth isacceptable because it is between the bass and an inner voice. See Lesson 1, paragraph 7c(2).

SELF REVIEW EXERCISE 3-1Write the note in the second chord that is common to a note in the first chord. Analyze each chord (Figure 3-28).

Figure 3-28. Part Write Common Tones


SELF REVIEW EXERCISE 3-2Write the note in the second chord that is a half step from a note in the first chord. If no note is a half step movement,

leave the example blank. Analyze each chord (Figure 3-29).


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Figure 3-29. Part Write Half Steps


SELF REVIEW EXERCISE 3-3Write the note in the second chord that is a whole step from a note in the first chord. Analyze each chord (Figure 3-

30).

Figure 3-30. Part Write Whole Steps


SELF REVIEW EXERCISE 3-4Write the best note for the missing voice. Choose the best note of the chord to double. Analyze each chord (Figure 3-

31).

Figure 3-31. Part Write Missing Voices



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SELF REVIEW EXERCISE 3-5Complete the part writing of Self-Review Exercises 1,2, and 3 (Figures 3-28, 3-29, and 3-30).

Figure 3-28. Part Write Common Tones

Figure 3-29. Part Write Half Steps

Figure 3-30. Part Write Whole Steps

10. Tonic and Dominant Triads.a. Connecting the I6 and the V the i6and the V (Figure 3-32). The first inversion tonic chord is one ofthe most useful of the first inversion triads. It provides relief from the finality of the tonic chord in root

position when the tonic triad is written within the phrase.


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Figure 3-32. Connecting I6 and V i6 and VNOTE: The figured bass for the V in minor can also be written with a chromatic sign instead of . In Cminor, use a natural sign (Figure 3-33).

Figure 3-33. Chromatic Sign in the Figured Bassb. Connecting the I and the V6 the i and the V6(Figure 3-34). The dominant triad in the first inversionhas the leading tone in the bass voice. This creates a strong melodic significance to the bass line. Thebass voice usually resolves up a half step. The tonic chord in root position usually follows the firstinversion dominant triad.

Figure 3-34. Connecting I and V6 i and V6

NOTE: When the chromatically altered note is in the bass voice, no chromatic sign is placed in thefigured bass.c. Connecting the I6 to the V6 i6 to the V6 (Figure 3-35).NOTE: The V6does not resolve to the I6 because the bass note usually resolves up a half step.


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Figure 3-35. I6 to V6 i6to V6

SELF REVIEW EXERCISE 3-6Part write the following first inversion progressions (Figure 3-36. Part A, Part B, and Part C).

Figure 3-36. Part A. First Inversion Tonic and Dominant Progressions


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Figure 3-36. Part C. First Inversion Tonic and Dominant Progressions


11. Tonic and Subdominant Triads.a. Connecting the I6and the IV i6and the iv (Figure 3-37).

Figure 3-37. I6and IV i6and ivb. Connecting the I and the IV6 i and iv6 (Figure 3-38).


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Figure 3-38. I and IV6 i and iv6c. Connecting the I6and the IV6 i6and iv6 (Figure 3-39).

Figure 3-39. I6and IV6 i6and iv6

SELF REVIEW EXERCISE 3-7Part write the following tonic and subdominant first inversion progressions (Figure 3-40 Part A, Part B, and Part C).


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Figure 3-40. Part A. Tonic to Subdominant First Inversion Progressions


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Figure 3-40. Part B. Tonic to Subdominant First Inversion Progressions


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Figure 3-40. Part C. Tonic to Subdominant First Inversion Progressions


12. Subdominant and Dominant Triads.a. Connecting the IV6 and the V iv6 and the V (Figure 3-41).


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Figure 3-41. IV6 and V iv6 and Vb. Connecting the IV6 and the V6 (Figure 3-42).(1) The V6 does not usually resolve to the IV6 because the bass voice of the V6 should resolveupward by half step.(2) The V6 does not resolve to a iv6 (minor) and the iv6 does not resolve to V6 because anaugmented second would occur in the bass voice.

Figure 3-42. IV6 and V6NOTE: Be careful of parallel fifths in the IV6 to V6 progression. If the alto and tenor voices arereversed in Figure 3-42, parallel fifths occur.

SELF REVIEW EXERCISE 3-8Part write the following subdominant and dominant first inversion progressions (Figure 3-43).


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Figure 3-43. Subdominant and Dominant Progressions

Lesson 4: PRIMARY TRIADS IN SECOND INVERSION

In this lesson, you will learn the primary triads in second inversion. This lesson includes doubling,figured bass, part writing, analysis, and identification of types of second inversions.

After completing this lesson, you will: Identify second inversion chords. Write voice doublings. Write figured bass and analysis. Identify the four types of six-four chords. Part write second inversion primary triads.


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1. Second Inversion Triads.a. The triad is in second inversion when the fifth of the triad is the bass note. The root and third of thetriad are voiced above the fifth (Figure 4-1).

Figure 4-1. Second Inversion Triadb. Second inversion triads are harmonically unstable. They tend to function more as decorations orlinks between other chords rather than actual chords in the basic harmonic progression.2. Doubling of Second Inversion Triads.

Always double the fifth (bass note) of second inversion triads (Figure 4-2). The doubled note can be in

any other voice.

Figure 4-2. Second Inversion Doubling3. Figured Bass for Second Inversion Triads.

a. The numerals indicate a triad in second inversion (Figure 4-3).

Figure 4-3. Figured Bass Intervals

NOTE: The 4 represents the note the interval of a fourth above the bass note. That note a fourthabove the bass note is the root of the triad. The 6 represents the note the interval a sixth above thebass note. That note is the third of the triad.b. A second inversion triad can also be indicated by the numerals . The number 8 refers to the doubledbass note (Figure 4-4).


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Figure 4-4. Complete Figured BassNOTE: Two sets of numerals can occur under the same bass note. Using correct part writingprocedures, move the notes represented by the first set of numerals to the notes represented by thesecond set of numerals (Figure 4-5). Give each note one-half the rhythmic value of the bass note.

Figure 4-5. Two Sets of Bass Figuresc. Usually, only the appears under the bass note. The interval of the octave is understood because thebass note should always be doubled on a second inversion triad (Figure 4-6).

Figure 4-6. Second Inversion Figured BassNOTE: Second inversion triads are called six-four chords.4. Analysis of Second Inversion Triads.The Roman numeral indicates the scale degree upon which the chord is constructed (the root of thetriad). In a second inversion chord, the bass note is not the root of the chord. However, you candetermine the root of the chord from the bass note. Since the bass note is the fifth of the chord, theroot is the interval of a fifth below (or a fourth above the bass note). The number 4 identifies the root ofthe chord (Figure 4-7).


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Figure 4-7. Root Identification

Lesson 5: THE DOMINANT SEVENTH CHORD

In this lesson, you will learn the dominant seventh chord. This lesson includes doubling, root positionchords and inversions, figured bass, and part writing the dominant seventh chord.

After completing this lesson, you will: Identify the dominant seventh chord. Write doublings. Write root position and inversions. Write figured bass. Part write the dominant seventh chord.

1. Dominant Seventh Chords.a. The dominant seventh chord is a Major triad with the note an interval of a minor seventh above theroot of the triad added to the Major triad (Figure 5-1). The dominant seventh chord, a four-note chord,is built on scale step five.

Figure 5-1. Dominant Seventh Chord Structureb. In a minor key (harmonic minor), the dominant seventh chord is identical in structure to thedominant seventh chord in a Major key. They are both Major triads with a minor seventh interval fromroot to seventh (Major minor seventh chords) (Figure 5-2).

Figure 5-2. Minor Key Dominant Seventh ChordNOTE: The term dominant seventh is used to denote the structure of the seventh chord as well as the

scale degree location because the Major triad/minor seventh structure is only found on the dominantscale degree.2. Doubling of Dominant Seventh Chords.Since the dominant seventh is a four-note chord, there is no doubling of a note. All four notes of thedominant seventh chord are normally used in part writing. There is one exception discussed inparagraph 6b(1).3. Root Position and Inversions.


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written below the bass note. The third and fifth are understood and are included in the voicing eventhough they are not written in the figured bass (Figure 5-7).

Figure 5-7. V7Figured BassNOTE: In a minor key, you must notate the leading tone by using a chromatic sign (or a slash throughthe number 3) in the figured bass (figure 5-8).

Figure 5-8. Minor Key Leading Tone Notationb. First Inversion. The complete figured bass for the dominant seventh chord in first inversion is .Usually, only the is written under the bass note. The interval of a third (the fifth of the chord) isunderstood and is included in the voicing even though it is not written in the figured bass (Figure 5-9).

Figure 5-9. V Figured BassNOTE: In minor, the first inversion dominant seventh chord does not require a chromatic alteration in

the figured bass (Figure 5-10). The third of the dominant seventh (the leading tone) is the bass note.The accidental to create the leading tone is written on the staff. The figured bass for the first inversiondominant seventh chord in minor is identical to the first inversion dominant seventh chord in Major.


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Figure 5-10. Minor Key V Figured Bassc. Second Inversion. The complete figured bass for the dominant seventh chord in second inversion is

. Usually, only the is written under the bass note. The interval of a sixth (the third of the chord) isunderstood and is included in the voicing even though it is not written in the figured bass (Figure 5-11).

Figure 5-11. V Figured BassNOTE: In minor, the complete figured bass is required for the second inversion of the dominantseventh chord. It is needed to indicate the leading tone of the scale. The chromatic alteration can beshown by making a slash through the 6 or by placing a chromatic sign before the 6 (Figure 5-12).

Figure 5-12. Minor Key V Figured Bassd. Third Inversion. The complete figured bass for the dominant seventh chord in third inversion is .Usually, only the is written below the bass note. The interval of a sixth (the fifth of the chord) isunderstood and is included in the voicing even though it is not written in the figured bass (Figure 5-13).Sometimes only a 2 is notated as the figured bass for a third inversion dominant seventh chord.


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Figure 5-13. V Figured BassNOTE: In a minor key, the leading tone is notated by marking a slash through the 4 or by placing achromatic sign in front of the 4 (Figure 5-14).

Figure 5-14. Minor Key V Figured Bass5. Tritone Resolution.There is a tritone (abbreviated as TT) interval (diminished fifth or augmented fourth) between the thirdand the seventh of the dominant seventh chord. This interval requires specific movement in theresolution of the dominant seventh chord.a. Regular Resolution. The diminished fifth resolves to a Major third in a Major key or a minor third in aminor key. The augmented fourth resolves to a minor sixth in a Major key or a Major sixth in a minor

key (Figure 5-15).

Figure 5-15. Regular Tritone ResolutionNOTE: Regular resolution is the most common resolution of the tritone because it resolves theharmonically unstable, dissonant tritone interval to the stable, consonant interval of a third (or sixth).The regular resolution satisfies the melodic pull of the subdominant and the leading tone tendencytones (Figure 5-16).

Figure 5-16. Tendency Tonesb. Irregular Resolution. An irregular resolution of the tritone occurs when the seventh of the dominantseventh chord does not resolve downward to the third of the tonic chord but moves up by step to thefifth. The bass voice moves to the third of tonic chord. This occurs when the dominant seventh chordprogresses to the tonic chord in first inversion (Figure 5-17).


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Figure 5-17. Irregular Tritone Resolution

The dominant seventh chord normally resolves to the tonic chord.6. Root Position Dominant Seventh Chords.a. Connecting the V7chord to the I (complete V7).(1) The root of the tonic chord is the bass note (Figure 5-18).

Figure 5-18. Bass Note, V7 to I(2) Resolve the Tritone. Connect the third (leading tone scale degree) up a half step to the root of the

tonic triad. Then connect the seventh (subdominant scale degree) down a half step to the third of thetonic triad (Figure 5-19).

Figure 5-19. Tritone Resolution, V7 to I(3) Connect the fifth down a whole step to the root of the tonic triad (Figure 5-20). You cannot drop thefifth of the dominant seventh chord to the fifth of the tonic triad. Parallel fifths between the tenor andbass will result. You must omit the fifth and triple the root of the tonic triad.


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Figure 5-20. Tripled Root(4) Scale pattern for connecting complete V7 to I (Figure 5-21).

Figure 5-21. Scale Pattern to Connect Complete V 7 to Ib. Connecting the V7chord to the I (Incomplete V7).(1) Instead of voicing the V7with a root, third, fifth, and a seventh, you can omit the fifth and double theroot in an upper voice (Figure 5-22). This is called an incomplete dominant seventh chord.

Figure 5-22. Incomplete Dominant Seventh Chord(2) The root of the tonic chord is the bass note (Figure 5-23).

Figure 5-23. Bass Note, V7 to I(3) The root of the dominant seventh chord (doubled in an upper voice) is a common tone with the fifthof the tonic chord. It remains in the same voice (Figure 5-24).


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Figure 5-24. Common Tone Incomplete V7

(4) Resolve the Tritone. Connect the third of the dominant seventh chord (leading tone scale degree)up a half step to the root of the tonic chord. Connect the seventh (subdominant scale degree) down ahalf step to the third of the tonic triad (Figure 5-25).

Figure 5-25. Tritone Resolution Incomplete V7

(5) Scale pattern for connecting an incomplete V 7 to I (Figure 5-26).

Figure 5-26. Scale Pattern to Connect Incomplete V 7to Complete INOTE: Remember, the complete dominant seventh chord resolves to an incomplete (tripled root) tonicchord. The incomplete dominant chord resolves to a complete tonic chord (Figure 5-27).

Figure 5-27. Complete and Incomplete V7

c. Connecting the V7 to the I6.


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(1) The third of the tonic chord is the bass note (Figure 5-28).

Figure 5-28. Bass Note, V7to I6(2) Resolve the Tritone. Connect the third (leading tone scale degree) up a half step to the root of thetonic triad. Connect the seventh (subdominant scale degree) up to the fifth of the tonic chord (Figure 5-29).

Figure 5-29. Tritone Resolution, V7to I6NOTE: This is the irregular resolution of the tritone. The parallel fifths that result are unequal fifths (adiminished fifth followed by a perfect fifth). The fifths are acceptable in this irregular resolution of thedominant seventh.(3) Connect the fifth of the dominant seventh chord down a whole step to the root of the tonic chord(Figure 5-30).

Figure 5-30. Connect the Fifth, V7to I6(4) Scale pattern for connecting the V7 to I6 (Figure 5-31).

Figure 5-31. Scale Pattern to Connect V7to I6


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d. Connecting the Cadential I to the V7 (Complete).(1) The fifth of the tonic six-four chord remains in the bass voice. It becomes the root of the dominantseventh chord (Figure 5-32).

Figure 5-32. Bass Note, I to V7

NOTE: Jumping the octave in the bass voice at a final cadence is common because it adds to thefeeling of finality.(2) Resolve the cadential six-four. Move the root of the tonic chord down a half step to the third of the

dominant seventh chord. Move the third of the tonic chord down to the fifth of the dominant seventhchord (Figure 5-33).

Figure 5-33. Resolve Cadential Six-fourNOTE: Moving scale step three to scale step two instead of to scale step four is necessary to resolvethe cadential six-four correctly.(3) Connect the fifth of the tonic chord down a whole step to the seventh of the dominant seventhchord (Figure 5-34).

Figure 5-34. Connect the Fifth, I to V7

NOTE: If the soprano and alto voices were reversed, parallel unequal fifths would occur. These areacceptable.(4) Scale pattern for connecting cadential I to complete V 7 (Figure 5-35).


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Figure 5-35. Scale Pattern to Connect Cadential I to Complete V 7

NOTE: The bass holds the common tone and the upper three voices descend by step (whole or half)in a I to complete V7 progression.

SELF REVIEW EXERCISE 5-1Analyze and part write the following root position dominant seventh chord progressions (Figure 5-36. Parts A, B).

Figure 5-36. Part A. V7to I Progressions


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Figure 5-36. Part B. V7to I Progressions


7. First Inversion Dominant Seventh Chordsa. Connecting the Vto the I.(1) The root of the tonic chord is the bass note (Figure 5-37).


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Figure 5-37. Bass Note, V to I(2) Keep the common tone (Figure 5-38).

Figure 5-38. Common Tone, V to I(3) Resolve the Tritone. Connect the seventh (subdominant scale degree) down a half step to the thirdof the tonic chord. The other note of the tritone is resolved in the bass voice (Figure 5-39).

Figure 5-39. Tritone Resolution, V to I(4) Connect the fifth down a whole step to the root of the tonic chord (Figure 5-40).

Figure 5-40. Connect the Fifth, V to I


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b. Scale pattern for connecting V to I (Figure 5-41).

Figure 5-41. Scale Pattern to Connect V to I

SELF REVIEW EXERCISE 5-2Analyze and part write the following first inversion dominant seventh chord progressions (Figure 5-42).

Figure 5-42. V Progressions


8. Second Inversion Dominant Seventh Chordsa. Connecting V to I.(1) The root of the tonic chord is the bass note (Figure 5-43).

Figure 5-43. Bass Note, V to INOTE: The V should function as a passing chord between the I and the I6.

(2) Keep the common tone (Figure 5-44).


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Figure 5-44. Common Tone, V to I(3) Resolve the Tritone. Connect the third of the dominant seventh chord (leading tone scale degree)up a half step to the root of the tonic chord. Connect the seventh (subdominant scale degree) down ahalf step to the third of the tonic triad (Figure 5-45).

Figure 5-45. Tritone Resolution, V to I(4) Scale pattern for connecting V to I (Figure 5-46).

Figure 5-46. Scale Pattern to Connect V to Ib. Connecting the V to the I6.(1) The third of the tonic chord is the bass note (Figure 5-47).

Figure 5-47. Bass Note, V to I6(2) Keep the common tone (Figure 5-48).


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Figure 5-48. Common Tone, V to I6(3) Resolve the Tritone. Connect the third of the dominant seventh chord (leading tone scale degree)up a half step to the root of the tonic triad. Then connect the seventh (subdominant scale degree) upto the fifth of the tonic triad (Figure 5-49).

Figure 5-49. Tritone Resolution, V to I6NOTE: This is an irregular resolution of the tritone and is acceptable in this progression.(4) Scale pattern for connecting V to I6 (Figure 5-50).

Figure 5-50. Scale Pattern to Connect V to I6

SELF REVIEW EXERCISE 5-3Analyze and part write the following second inversion dominant seventh chord progressions (Figure 5-51).


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9. Third Inversion Dominant Seventh Chordsa. Connecting the V chord to the I6.(1) The third of the tonic chord is the bass note (Figure 5-52).

Figure 5-52. Bass Note, V to I6(2) Keep the common tone in the same voice (Figure 5-53).


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Figure 5-53. Common Tone V to I6(3) Resolve the Tritone. Connect the third of the dominant seventh chord (leading tone scale degree)up a half step to the root of the tonic chord. The lower note of the tritone is resolved in the bass voice(Figure 5-54).

Figure 5-54. Tritone Resolution, V to I6(4) Connect the fifth of the dominant seventh down a whole step to the root of the tonic chord (Figure5-55).

Figure 5-55. Connect the Fifth, V to I6b. Scale pattern for the V to I6 (Figure 5-56).

Figure 5-56. Scale Pattern to Connect V to I6NOTE: The V only resolves to the I6.

SELF REVIEW EXERCISE 5-4


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Analyze and part write the following third inversion dominant seventh chord progressions (Figure 5-57).


10. Part Writing the Subdominant Triad to the Dominant Seventh Chord.a. Connect the IV to the V7.(1) The root of the chord is the bass note. The root of the dominant seventh chord is a Major secondabove the root of the subdominant chord (Figure 5-58).

Figure 5-58. Bass Note, IV to V7

(2) Keep the common tone in the same voice. This is the preparation of the seventh of the dominantseventh chord (Figure 5-59).

Figure 5-59. Common Tone, IV to V7

(3) Move the remaining two voices down to the nearest chord tone in contrary motion to the bass voice(Figure 5-60).


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Figure 5-60. Contrary Motion to BassNOTE: The V7 is incomplete when IV progresses to V7 in order to avoid parallel fifths.b. Connecting the IV6 to V7.(1) The root of the chord is the bass note (Figure 5-61).

Figure 5-61. Bass Note, IV6 to V7

(2) Keep the common tone (Figure 5-62).

Figure 5-62. Common Tone, IV6 to V7

(3) Move the remaining two voices by step to the nearest chord tone (Figure 5-63).

Figure 5-63. Step Movement, IV6 to V7

NOTE: The V7 is complete when IV6 progresses to V7.c. Connecting IV7 to the V .(1) The third of the chord is the bass note (Figure 5-64).


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Figure 5-68. Bass Note, IV to V(2) Move the remaining three voices by step to the nearest chord tones. First connect the half stepmovement, then the whole step movement, and finally the minor third movement (Figure 5-69).

Figure 5-69. Movement By Step, IV to V

LESSON 6: SECONDARY TRIADS IN ISOLATION

In this lesson you will learn the scale degrees used to build secondary triads, the quality of thesecondary triads, and commonly used secondary triads.

At the end of this lesson, you will be able to: Identify secondary triads, Identify quality of secondary triads, and Write Roman numeral analysis

Secondary chords (triads) are the supertonic, mediant, submediant, leading tone, and subtonic triads.Secondary triads are constructed on the second, third, sixth, and seventh scale degrees of the Majoror minor scale. Two triad qualities are possible for each secondary triad in minor because of thealtered sixth and seventh scale degrees of the minor scale. Secondary triads can create a rich andvaried harmony when they are used as substitute chords for primary triads.1. Supertonic Triad

a. The supertonic triad is built on the second scale degree. The supertonic triad is a minor triad whenbuilt on the Major scale (Figure 6-1). The harmonic analysis is ii.

Figure 6-1. Supertonic Triad on a Major Scaleb. The supertonic triad is a diminished triad when built on the harmonic, descending melodic, ornatural minor scale (Figure 6-2). The harmonic analysis is ii o.


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Figure 6-2. Supertonic Triad Built on a Harmonic Minor Scale

NOTE: Remember, in harmonic analysis, upper case Roman numerals represent Major triads. Lowercase numerals represent minor triads. An upper case numeral with a plus sign ( +) indicates anaugmented triad. A lower case numeral with a circle ( o) indicates a diminished triad.c. The supertonic triad is a minor triad when built on the ascending melodic minor scale (Figure 6-3). Itis identical to the supertonic triad in Major. The harmonic analysis is ii.

Figure 6-3. Supertonic Triad Built on the Ascending Melodic Minor Scale2. Mediant Triad.a. The mediant triad is built on the third scale degree. The mediant triad is a minor triad when built on

the Major scale (Figure 6-4). The harmonic analysis is iii.

Figure 6-4. Mediant Triad on a Major Scaleb. The mediant triad is a Major triad when built on the descending melodic or natural minor scale(Figure 6-5). The harmonic analysis is III.

Figure 6-5. Mediant Triad on a Natural Minor Scalec. The mediant triad is an augmented triad when built on the harmonic or ascending melodic minorscale (Figure 6-6). The harmonic analysis is III+.

Figure 6-6. Mediant Triad on a Harmonic Melodic Minor ScaleNOTE: The augmented mediant triad is rarely used.3. Submediant Triad.a. The submediant triad is built on the sixth scale degree. The submediant triad is a minor triad whenbuilt on the Major scale (Figure 6-7). The harmonic analysis is vi.

Figure 6-7. Submediant Triad on a Major Scaleb. The submediant triad is a Major triad when built on a harmonic, descending melodic, or naturalminor scale (Figure 6-8). The harmonic analysis is VI.


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Figure 6-8. Submediant Triad Built on a Harmonic, or Natural Minor Scalec. The submediant triad is a diminished triad when built on the ascending melodic minor scale (Figure

6-9). The harmonic analysis is vio

.

Figure 6-9. Submediant Triad Built on the Ascending Melodic Minor ScaleNOTE: The diminished submediant triad is rarely used.4. Leading Tone Triad.a. The leading tone triad is built on the seventh scale degree. The leading tone triad is a diminishedtriad when built on the Major scale (Figure 6-10). The harmonic analysis is vii o.

Figure 6-10. Leading Tone Triad on a Major Scaleb. The leading tone triad is a diminished triad when built on the harmonic or ascending melodic minorscale (Figure 6-11). The harmonic analysis is viio.

Figure 6-11. Leading Tone Triad on a Harmonic Minor Scale5. Subtonic Triad.

The subtonic triad is a Major triad. It is built on the natural minor and descending melodic minor scales(Figure 6-12). The Major subtonic triad is rarely used. The harmonic analysis is VII.

Figure 6-12. Subtonic Triad on a Natural Minor Scale

LESSON 7: THE LEADING TONE AND SUBTONIC TRIADS

In this lesson, you will learn substitutions, triad positions, doublings, uses, and part writing of theleading tone triad. You will also learn the use and function of the subtonic triad.

At the end of this lesson, you will be able to: Write voice doublings Part write first inversion leading tone triads as a neighboring chord Part write first inversion leading tone triad as a passing chord to/from I and I6. Part write the first inversion leading tone triad following the subdominant triad, and Part write the root position subtonic to first inversion subdominant and root position mediant triads.


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Both the leading tone and subtonic triads are built on the seventh scale degree. The root of the leadingtone triad, however, is a half step below the tonic. The root of the subtonic triad is a whole step belowthe tonic.

1. Leading Tone Triad.a. The diminished leading tone triad (viio) is found in both Major and minor keys (Figure 7-1).

Figure 7-1. Diminished Leading Tone TriadNOTE: Remember, the root of the subtonic triad is a whole step below the tonic.b. The leading tone triad is often called an incomplete dominant seventh with omitted root. The leadingtone triad is identical to the top three notes of the dominant seventh chord. The leading tone triad cansubstitute for the dominant seventh chord (Figure 7-2).

Figure 7-2. Common Tones, viio - V7

c. Unequal Fifths. The root and fifth of the leading tone triad in first inversion often ascend to the rootand fifth of the tonic chord. These fifths are NOT parallel perfect fifths. In the vii o6 triad, the intervalbetween the root (B) and the fifth (F) is a diminished fifth, not a perfect fifth. Unequal fifths are

acceptable (Figure 7-3).

Figure 7-3. Acceptable Unequal Fifths

NOTE: Remember, the triad is in first inversion when the third of the chord is the bass note. The fifthand the root are voiced above the third.2. Triad Positions.a. The leading tone triad is most frequently used in first inversion (Figure 7-4).

Figure 7-4. First Inversion Leading Tone Triad


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Figure 7-8. Doubled Root, viio6

SELF REVIEW EXERCISE 7-1Write the inner voices of each first inversion leading tone triad (Figure 7-9).

Figure 7-9. First Inversion Leading Tone Triad, viio6


4. Use of the Leading Tone Triada. The leading tone triad (viio6) serves largely as a passing or neighboring chord centered around thetonic triad.(1) The leading tone triad is used as a passing chord between the tonic triad and its first inversion. Thebass voice moves in stepwise motion (Figure 7-10).

Figure 7-10. viio6as a Passing Chord Between I and I6

NOTE: The viio6 is used as a substitute for the passing of the dominant triad.(2) The leading tone triad can also be used between the first inversion and root position tonic triad(Figure 7-11).

Figure 7-11. viio6as a Passing Chord Between I6and I(3) The leading tone triad is used as a neighboring chord between two like (root or first inversion) tonicchords (Figure 7-12).


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Figure 7-12. viio6as a Neighboring Chordb. The leading tone triad frequently occurs after the subdominant triad (IV) in place of the dominantchord when the soprano voice ascends (Figure 7-13).

Figure 7-13. Leading Tone Triad After Subdominant

SELF REVIEW EXERCISE 7-2Identify how the leading tone triad is used. Write in the space provided whether it is used as a passing chord,

neighboring chord, or as a substitute for the dominant (Figure 7-14).

Figure 7-14. Use of the Leading Tone Triad

5. Part Writing viio6 - Ia. Connect the two voices of the doubled note using oblique or contrary motion, if possible. Whenusing similar motion, avoid parallel fifths and octaves, move the remaining voices stepwise to thenearest chord tone (Figure 7-15).

Figure 7-15. viio6-Ib. The following is the scale pattern for connecting the vii o6chord to the I chord.


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NOTE:Although the leading tone triad functions and sounds like an incomplete dominant seventhchord, it does not resolve like a dominant seventh chord. The fifth of the vii o6(subdominant scaledegree) ascends to the fifth of the tonic chord. The seventh of the V7 chord (the same note as the fifthof the viio6) descends in a regular resolution (Figure 7-16).

Figure 7-16. Resolving Subdominant Scale Degree6. Part Writing viio6-I6.a. Connect the two voices of the doubled note using oblique or contrary motion, if possible. Whenwriting consecutive first inversion triads, each triad must have a different doubling (Figure 7-17).

Figure 7-17. viio6- I6

b. The following is the scale pattern for connecting the vii o6chord to the I6 chord.

7. Part Writing I-viio6.a. Connect the fifth of the I chord to the fifth of the viio6. Connect the root of I to the root of viio6and thethird of I to the third of viio6. This results in doubled thirds in the vii o6 chord (Figure 7-18).


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Figure 7-18. I - viio6

b. The following is the scale pattern for connecting the I chord to the vii o6 chord.

8. Part Writing I6 - viio6.

a. Connect the fifth of the I chord to the fifth of the viio6

. Connect the doubled root of the I chordstepwise to the root and third of viio6 (Figure 7-19).

Figure 7-19. Connecting I6- viio6

b. The following is the scale pattern for connecting the I 6chord to the viio6 chord.

9. Part Writing IV - viio6.a. Keep the common tone. Connect the fifth of the IV chord to the third of the vii o6and connect the thirdof IV to the root of viio6 (Figure 7-20).

Figure 7-20. IV - viio6

b. The following is the scale pattern for connecting the IV chord to the vii o6 chord.


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NOTE: The progression IV - viio6 is used when the melody line ascends and the use of the dominantchord (IV-V) would cause parallel fifths and octaves (Figure 7-21).

Figure 7-21. viio6 to Avoid Parallel Motionc. When the root of the subdominant triad (IV) is in the soprano voice, the soprano note is held over(common tone) to become the fifth of the viio6 triad (Figure 7-22).

Figure 7-22. IV - viio6, Root in Sopranod. The following is the scale pattern for connecting the IV chord to the vii o6 chord.

10. When the fifth of the viio6 triad is in the soprano, it ascends to avoid doubling the third in the I6chord. Normally, it descends by step (Figure 7-23).

Figure 7-23. viio6, Fifth in SopranoThe following is the scale pattern for connecting the vii o6chord to the I6 chord.


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SELF REVIEW EXERCISE 7-3Part write the following tonic to leading tone progressions (Figure 7-24).

Figure 7-24. Part Writing Leading Tone Progressions

11. The subtonic triad is a Major triad (Figure 7-25). It is not frequently used.

Figure 7-25. Subtonic Triad12. The subtonic triad (VII) can be used to harmonize a melody that includes the subtonic tone. Thesubdominant chord normally follows the subtonic triad. This has the effect of a passing chord (Figure7-26).

Figure 7-26. VII as a Passing Chord13. The subtonic triad can also resolve to the III triad in root position. The lowered seventh scaledegree (root of the subtonic triad) functions as a dominant of the mediant (Figure 7-27).

Figure 7-27. VII as a Dominant Function

SELF REVIEW EXERCISE 7-4Write the missing voices for the following progressions (Figure 7-28).

Figure 2-28. Subtonic Triad Part Writing

LESSON 8: RELATING CHORD SCALES TO TRIADS, EXTENDED CHORDS AND ALTERED CHORDS


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The supertonic triad can substitute for the subdominant triad, both are similar in sound and function.The subdominant scale degree is the bass note when the supertonic triad is in first inversion.In this lesson, you will learn subdominant substitution for supertonic, triad positions, doublings, uses,and part writing of the supertonic triad.

At the end of this lesson, you will be able to: Write voice doublings Part write the root position supertonic triad after the tonic triad Part write the first inversion supertonic triad following the subdominant triad Part write the supertonic triad progressing to the dominant triad Part write the supertonic triad progressing to the tonic six-four chord Part write to the first inversion supertonic triad to the first inversion leading tone triad

1. Two common tones link the supertonic and the subdominant triads (Figure 8-1).

Figure 8-1. Common Tones, ii - IV2. Triad Positions.a. The supertonic triad is most frequently found in first inversion in both Major and minor keys (Figure8-2).

Figure 8-2. Supertonic Triad in First InversionNOTE: The supertonic triad is usually a diminished triad in a minor key.

b. The supertonic triad in root position is less common than first inversion however, it may be found inroot position during a harmonic sequence (Figure 8-3).

Figure 8-3. Supertonic Triad in a Harmonic Sequencec. Supertonic triads are not normally found in second inversions.3. Doubling.a. The third of the supertonic triad (subdominant scale degree) is normally doubled (Figure 8-4).


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Figure 8-4. Doubled Third, ii6NOTE: The doubled third is usually found in secondary triads when the third is a primary tone (thetonic, subdominant, or dominant scale degrees).b. The supertonic triad can occur in root position with the root of the triad doubled (Figure 8-5).

Figure 8-5. Doubled Root, iic. The fifth of the supertonic triad (submediant scale degree) is not normally doubled. In a minor key,the fifth of the supertonic triad is the altered sixth scale degree. Doubling the fifth makes resolutionawkward (Figure 8-6).

Figure 8-6. Doubled Fifth, ii6 or iio6

SELF REVIEW EXERCISE 8-1Write the missing voices in the following supertonic triads (Figure 8-7).

Figure 8-7. Part Writing Supertonic Triads, ii, iio

, ii6

, and iio6


4. Uses of the Supertonic Triada. Preparing the dominant. The supertonic triad is used to prepare the dominant triad (V), especially ata cadence. In minor, the instability of the diminished fifth drives it strongly toward the dominant (Figure8-8).


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Figure 8-8. Preparation of Dominant, ii6or iio6

b. Preceding the cadential six-four chord. The supertonic triad precedes the tonic six-four chord at acadence. The bass note leaps up a fourth. This is an exception to the rule that cadential six-fourchords are approached by step (Figure 8-9).

Figure 8-9. Cadential Six-fourc. The supertonic triad moves to the diminished leading tone triad as a substitute for the dominantseventh chord at other than final cadences (Figure 8-10).

Figure 8-10. Leading Tone Triadd. The supertonic triad is preceded by a subdominant triad (IV) or by a tonic triad (I) (Figure 8-11).

Figure 8-11. IV to ii or I to ii

5. Part Writing I - ii and i - iio.a. Move the three upper voices of the tonic triad to the nearest chord tone of the supertonic triad incontrary motion to the bass voice (Figure 8-12).


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Figure 8-12. Part writing I ii and i - iiob. The following is the scale pattern for connecting the I chord to the ii chord and the i chord to the iiochord.

NOTE: Failure to write contrary motion causes parallel fifths or octaves.

SELF REVIEW EXERCISE 8-2Part write the following tonic to supertonic progressions (Figure 8-13).

Figure 8-13. Part Writing I - ii and i - ii o


6. Part Writing IV-ii6

a. Hold the two common tones and move the other voices stepwise (Figure 8-14).

Figure 8-14. IV - ii6

b. The following is the scale pattern for connecting the IV chord to the ii6 chord.

SELF REVIEW EXERCISE 8-3Part write the following subdominant to supertonic progressions (Figure 8-15).


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Figure 8-15. Part Writing IV - ii6and iv - iio6


7. Part Writing ii - Va. When the melody moves by step, keep the common tone and move the other voices stepwise(Figure 8-16).

Figure 8-16. Stepwise Melody, ii - VThe following is the scale pattern for connecting the ii chord to the V chord.

b. When there is a leap in the melody, move the three upper voices in similar motion to the nearestchord tones of the dominant triad (Figure 8-17).

Figure 8-17. Leap in Melody, ii - VThe following is the scale pattern for connecting the ii chord to the V chord.

8. Part Writing ii6 - V and iio6 V.a. Connect the two voices, ii6 V, moving from the doubled note first, using contrary or obliquemotion, if possible. Next, connect the remaining voices to the nearest chord tone (Figure 8-18).


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b. The following is the scale pattern for connecting the ii chord to the I chord.

SELF REVIEW EXERCISE 8-5Part write the following supertonic to tonic six-four progressions (Figure 8-21).

Figure 8-21. Part Writing ii-I 64


10. Part Writing ii6- viio6

a. The supertonic triad in first inversion (ii 6) connects to the leading tone triad in first inversion (vii o6) withtwo common tones. The other voice moves in stepwise motion (Figure 8-22).

Figure 8-22. ii6- viio6

b. The following is the scale pattern for connecting the ii 6chord to the viio6 chord.

SELF REVIEW EXERCISE 8-6Part write the following supertonic to subtonic progressions (Figure 8-23).

Figure 8-23. Part Writing ii6 - viio6

traditional harmony

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