Upper Structure Triads and Polychord Voicings

Introduction

In this lesson, we'll be looking at a new harmonic voice technique of combining two simple chords to create a bigger and richer sound. These are known as polychords. We'll first learn the basic vocabulary of polychord voicings and then see how these are used in contemporary compositions. Polychords are also used in classical music, but are also known as "tall-chords" because of how they look on the staff. We'll learn how classical composers have been using polychords in their compositions. In Composers on Composing we'll be asking how they use form in composition.

So, let's get lesson 7 started!

Objectives

By the end of the lesson, you will be able to:

Extending the Limits: Exploring Upper Structure Triads

Lego Bricks

You've probably heard the expression "the whole is greater than the sum of its parts." In this topic we'll learn to create rich and vibrant chord voicings by combining pairs of familiar chords. The result will be hip, sophisticated sounding voicings that can be used for maximum effect!

Jazz Voicings:

Up until this point we have used tension substitution in four-way close voicings as a strategy for building chord voicings.

Cmaj7 in Four-Way Close Spacing, with and without Tension Substitution:

This topic will explore another approach to building chord voicings that include tensions: the polychord.

Polychord voicing of G75(9): B- over G:

Polychord voicings consist of a lower structure that contains only chord tones of the basic function and an upper structure triad or 7^th chord drawn from its chord scale. The upper structure contains at least one tension. Harmonic avoid notes are not included in either structure, for obvious reasons. Polychord construction offers the conceptual advantage of combining two easily understood objects to create something richer and more resonant. The example above depicts a polychord voicing of a G75(9) chord. The chord consists of the upper structure, a B- triad superimposed over the lower structure, a G7 chord. The lower structure consists of the essential chord tones of G7: 1, 3, and 7. The upper structure includes chord tones 5 and 7 and the tension 9. When voicing a polychord, the upper structure may be in any position (inversion) and may be close or open spaced. The upper structure and lower structure should have the distance of at least a 3^rd between them. When writing a chord symbol that reflects this voicing, it is customary to put the upper structure symbol above the lower structure, separated by a horizontal line.

Identifying Upper Structure Triads

The Tonic Chord

Let's create a polychord voicing for Imaj7 in the key of C. The lower structure will consist of the chord tones of Cmaj7—the complete chord, the essential notes: 1, 3, and 7 or 1, 3, and 6 (if we employ an upper structure that includes chord tone 7). Now we need to select a triad from the chord scale that contains at least one available tension and no harmonic avoid tones. This eliminates any triad that contains the avoid tone S4. So, D-, F, and Bº are not options.

Triads with Avoid Tones Eliminated:

Of those remaining, C and E- offer no tensions, but G contains T9. Its remaining tones are the 5^th and 7^th of the lower structure, so a G triad is a good choice for an upper structure triad in this situation.

Polychord Voicings of Cmaj7:

The upper structure triad can be positioned as desired. Omitting the 5^th from the lower structure makes the overall sonority of the voicing clearer and less dense. If one uses C6 as a lower structure, adding a G triad as the upper structure yields the chord: Cmaj7 (13, 9).

A- also seems a viable choice for an upper structure triad as it contains 13, but the fact that it contains the root of the lower structure makes it problematic. If its 3^rd is positioned anywhere other than a half step above the lower structure, it creates the interval of a minor 9^th with the 7^th of the chord:

As you'll recall from earlier chapters, this is generally deemed too dissonant to work on a tonic function chord.

All in all, the triad built on scale degree 5 of the Ionian chord scale is the best upper structure for a polychord that expresses Imaj7.

The IV chord

The Lydian chord scale offers a number of viable upper structures for the IV chord.

Triads of F Lydian:

The G triad includes all three available tensions 9, 11, and 13. The E- triad replicates chord tone 7 and adds T9 and T11, and the C triad adds the option of T9. E-7 and Cmaj7 are also available as upper structure 7^th chords. These are all voicings of Fmaj7, differing only in the amount of doubling and tensions:

Polychord Voicings for IVmaj7 in the Key C:

Of the possible upper structures, the triad built on scale degree 2 of Lydian is often the most effective, as it contains all three tensions from the Lydian scale.

Upper Structures for Minor 7 Chords

Upper Structures for II-7 Are Built on 5 and 7:

The Dorian chord scale has two triads that are applicable as upper structures. Discounting the triads that contain the harmonic avoid note S6 and those that only replicate chord tones, the triads built on scale degrees 5 (T9) and 7 (T9 and T11) are useful. The Aeolian scale also avoids the 6th degree, so the same triads (those built on 5 and 7) are the upper structures for VI-7.

Upper Structures for VI-7 Are Built on 5 and 7:

Because of the placement of S2 and S6 in the Phrygian chord scale, III-7 has no possible upper structure chord.

The Phrygian Scale Yields No Upper Structures for III-7:

Upper Structures for the Dominant

By now, you should have a pretty clear idea of how the process for selecting upper structure chords works. Upper structures don't contain harmonic avoid tones and must contain at least one tension. For each situation, you should investigate the chord scale appropriate to the chord's function, using these principles to make your selection.

Since the Altered Dominant Scale presents all of the possible chromatic alterations for the V7 chord, it is rich with upper structure options for dominant function chords.

Upper Structure Triads from the Altered Dominant Scale:

The triad built on T9 also includes T13 and doubles the 3^rd (spelled enharmonically). The triad built on T9 also includes chord tones 5 and 7. The triad built on 5 includes chord tone 7 and T9. The triad built on T13 replicates the root and includes T9 and finally, the triad built on 7 replicates chord tone 3 and includes T9.

Polychord Voicings for G7 Altered:

Polychord Summary

Here's a summary of polychords:

Workshop: Upper Structure Triads

Download the attached PDF. Write the chord scale for each function and then work out its viable upper structure triads. Give a polychord symbol combining the lower structure and each upper structure. Identify the actual chord that each polychord voicing represents, giving tensions in parentheses. Check your answers against the answer key provided.

Download Upper Structure Triads workshop (PDF)

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This Over That: Building a Vocabulary of Polychords

If a + b = c and a + 2 = 3 then a = 1

Using letters to stand for numerical values can help us to understand mathematical principles. We have seen time and again in our work with theory how the application of numbers to pitches can help us to commute certain different relationships from key to key. In this topic we'll apply this principal to the task of acquiring a basic vocabulary of polychords that we can use for practical purposes.

In the last topic we introduced the idea of polychords (upper and lower structure) as a new way to construct voicings that include available tensions. We mined chord scales, looking for viable upper structure triads to use in their construction. The scales offer up numerous colorful options, but the process of scale mining is time consuming. In order to start you on the road to an understanding of the practical use of polychord voicings, it's probably best if we limit our choices to some of the most commonly used upper structure triads. This topic will deal with the idea of developing a basic practical vocabulary of polychords that expresses the most common harmonic functions—tonic, subdominant, dominant, secondary dominant, substitute dominant, and modal interchange. We'll use numerical relationships to commute those polychords from key to key.

Polychord Construction, Major 7 Chords

First off, let's review the process that we learned in the last topic and see where it leads in establishing a limited vocabulary. Let's mine C Ionian for the best polychord voicing that will express Cmaj7.

Maj7 Chord Summary

In summary, any maj7 chord may be voiced as a polychord with the formula Vmaj over R6 or Rmaj7. Maj7 chords that are best expressed with a Lydian chord scale (such as IVmaj7 and modal interchange chords that are maj7 in quality) will use the formula IImaj over Rmaj7.

Polychord Construction, Minor 7 Chords

The most common available tension for minor 7 chords is T9. The formula V- over R-7 will create a polychord that includes T9.

V- over R-7: Voicings of D-7, F-7, and C-7 with T9:

T11 and T9 can be incorporated into a min7 polychord with the formula VII over R-7.

VII over R-7: Voicings of C-7, G-7, and B-7 with T9 and T11:

These two formulas will cover almost every situation where a min7 chord is called for. III-7 with its Phrygian chord scale is somewhat problematic. As you'll recall from the last topic, the Phrygian chord scale has two avoid notes—S2 and S6 that eliminate the possibility of a good upper structure in the scale. There are two solutions to work around this issue. The first is just to replicate chord tones of III-7 in a polychord texture and the second is to treat the III-7 chord as the related II of V7/II and to use V- over R-7 with a T9 in the voicing. This is very common.

Likewise, the VII-75 chord has no really good polychord formula.The same goes for the min75 when used as a related II chord–just replicate the chord tones in the upper structure.

Minor 7 Chord Summary

In summary, any min7 chord may be voiced with an upper structure of V- or VII. If III-7 is to retain its functional integrity as a tonic chord there is no possible upper structure. The minor75 chord has no good upper structure from the Locrian chord scale.

Polychord Construction, Dominant 7 Chords

For Dominant 7 chords that are expressed by a Mixolydian chord scale, there are two upper structures: VI- and V-. VI- adds T13 and V- adds T9. These would be appropriate upper structures for V7 and V7/V in a major key.

VI- over R7 and V- over R7: Mixolydian Polychords:

These two formulas are also often heard in I7, IV7, and V7 voicings in the blues.

For secondary dominant chords that have a minor target chord: V7/III, V7/VI, and V7/II, the Mixolydian (9,9,13) scale is appropriate. II- over R7 creates a polychord that available tensions 9 and 13. (Please note that the 3 of the upper structure is spelled enharmonically.) Also, VImaj over R7 will create a polychord that includes T9 and T13.

II- over R7 and VImaj over R7: Mixo (9,9,13) Polychords:

There are two more important upper structures to mention for dominant function chords. The first is the altered dominant scale (see below).

The Altered Dominant Scale . . .

. . . offers Vmaj over R7 for a dom75(9) polychord.

Vmaj over R7: Altered Dominant Sound Polychord

The symmetric dominant scale offers many triadic possibilities . . .

. . . and is often represented by VImaj over R7, which yields the tension combination T9 and T13.

VImaj over R7: dom7(9,13):

These polychords are particularly effective for enhancing the expectation of resolution of the V7 chord to I.

Dominant 7 Chord Summary

Polychord Construction, Substitute Dominant Chords

Substitute dominants are expressed by the Lydian 7 chord scale. Like the Lydian chord scale, the optimal upper structure is IImaj. This upper structure will add all three available tensions 9, 11, and 13 to the lower structure. So, the polychord formula for subVs is IImaj over R7. Modal interchange chords that are also dom7 in quality—such as IV7 and VII7—will also use this formula!

IImaj over R7: Lydian 7 (9,11,13)

Investigating each of the chord scales for interesting upper structure chords is important work for composers. Finding just the right combination can help you to define your personal style. This system of polychord formulas leaves us with 12 possible combinations that will create viable voicings for the most common functions in major key, minor key, and blues tunes. So commit them to memory!

Final Summary of Polychord Formulas

Workshop: Polychords

For this workshop download the attached PDF and do the following:

• Give a polychord symbol for each of the formulas, using the given root

• Voice each upper structure over the given lower structure

• Identify each of the polychords with a standard chord symbol that includes tensions in parentheses

• Check your answers against the answer key provided

Download Polychords workshop (PDF)

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Building the Tower: Building Extended Chord Voicings with Upper Structure Triads

Lego Eiffel Tower

Now that we've had a chance to explore the concept of building polychord voicings, and to learn a basic vocabulary of polychords for practical purposes, it's time to put all of this great knowledge to use and to begin to realize chord progressions.

In this topic we'll work out polychord keyboard voicings for the tune "Triste" by the Brazilian composer Antonio Carlos Jobim.

Listen to the audio file as you follow the lead sheet. The piano part in the arrangement has been created using polychord voicing technique. We'll go through the process used to create this layer for the first half of the arrangement and then later you'll have the opportunity to work through the second half on your own as the workshop for this topic.

Lead Sheet for "Triste":

"Triste” Harmonic Analysis

As we investigate the lead sheet, the first thing that we need to do is to analyze the chord progression. Analysis is essential so that we know which chord scales we're working with. The chord scales will lead us to choose specific upper structures for our polychords, and those voicings will help us to define clearly the direction of the chord progression for those who listen to our arrangement. Here's a harmonic analysis for half of the tune, mm.1-16. Notice the pivot modulation that occurs from mm.12-13. The V7/III changes function to become the V7 in D major. The change of key is brief, as the tonic modal interchange chord I-7 becomes the related II in a sequence that will return to tonic in B Major on the downbeat of m. 17.

Harmonic Analysis of First 16 Bars:

Once we have analyzed the chord progression, let's take the time to identify the chord scales associated with each harmonic function.

Analysis and Chord Scales:

Download "Triste" Analysis and Chord Scales (PDF)

Polychord Formulas of "Triste"

Now that we have analyzed and thought about the chord scales, let's turn to our vocabulary of polychord formulas to help us to choose appropriate voicings.

Please be aware that the use of Roman numerals in these formulas is not for purposes of harmonic analysis but rather as shorthand to note the intervallic relationship between the root of the lower structure and the root of the upper structure triad. In these formulas, the Roman numerals do not relate to the key of the tune!

Based on our analysis of function, chord quality, and chord scale, we have chosen the following polychords to express the harmony.

Analysis with Projected Polychords:

In mm. 1-2 and 5-6, the tonic chord may be expressed as Vmaj over R6. This will give us a maj7(9,13) voicing. We can also use this same formula in m. 13, when Dmaj7 is the tonic chord for a measure or two. Vmaj over R6 is a good way to express the tonic I chord. It may also be used for any maj7 chord.

M. 3 is a modal interchange chord (VI) that is maj7 in quality. Here Lydian tensions are appropriate, so let's use IImaj over Rmaj7. This will give us a maj7(9,11,13) voicing. This voicing is appropriate for the IV chord (when not preceded by its dominant) and for all maj7 quality modal interchange chords.

For the subV in m. 4 we'll also use a IImaj as the upper structure over R7. This will give us a Dom7(9,11,13) voicing. The same polychord will be appropriate for the second half of m. 16! IImaj over R7 is the sound of the subV and modal interchange chords that Dom7 in quality. The D-75 chord in m. 7 has no available upper structure because of the Locrian chord scale, so we'll skip over that for now (the same is true for the A-75 chord in m. 10).

There are a number of different upper structures that we could use for the V/II in m. 8. Let's make a note that we'll use II- over R7 because it will give us diatonic T13 and add an optional T9 that will give us a strong expectation of resolution to the minor target: C-. This is true also of the secondary dominants V/VI in m. 10 and V/III in m. 12. For each of these secondary dominants we'll use the formula II- over R7.

In m. 14 the A7 chord is V7 in D. Its chord scale is Mixo, so let's use VI- over R7 for this voicing. The same voicing is appropriate for the G7 chord on beat 3 of m. 15. VI- over R7 gives us a Dom7(13) chord.

So what's left? From mm. 9-16 the remaining chords are all min7 in quality and have T9 as an available tension. Let's use V- over R-7 for each of these voicings. This will give us a min7(9) voicing each time.

Download "Triste" with Projected Polychord Voicings (PDF)

Now let's look at a version of the chart with chord symbols that show the polychord voicings.

"Triste" with Polychord Symbols:

Download "Triste" with Polychord Symbols (PDF)

Lower and Upper Structure Voiceleading of "Triste"

We're ready to get started voicing the chords! First put the lower structure in place, voice leading the guide tones as you would in a three-voice texture: roots in the bass, moving the guide tones according to their scale tone tendencies. If it is advantageous to move a voicing up so that the guide tones don't exceed low interval limits, break at the end of a phrase (see mm. 4-5).

"Triste" Lower Structure Voiceleading:

Download "Triste" Lower Structure Voiceleading (PDF)

This three-voice realization of the changes is enough to carry the chord progression, but when we add the upper structure triads we'll get richer, more exciting harmonic colors!

Upper Structure

As we voice the upper structure, we apply the same principles of smooth voice leading, creating as much step-wise motion or common-tone connection as possible. When voicing the treble for the min75 chords, we replicate the 3^rd and the 7^th and add the 5 missing from the lower structure. This will distribute the voices equally (3 + 3) between the treble and bass staves. As you listen to the audio clip, notice the rich ringing, bell-like sonority that each voicing has as a result of the polychord combination of lower and upper structure!

"Triste" Upper Structure Voice Leading:

Download "Triste" Upper Structure Voice Leading (PDF)

Adding the Piano Part of "Triste"

OK, now its time to add this piano part to the arrangement!

"Triste" Arrangement with Polychords:

Download "Triste" Arrangement with Polychords (PDF)

It's starting to sound pretty sweet! You may notice that the keyboard parts in straight whole-, half-, and quarter-note values don't sync up with the anticipations in the melody and the bass part. We need to activate the rhythm with a little syncopation so that all of the parts in the rhythm section are locked in together!

Like so:

"Triste" with Polychords Rhythmically Syncopated:

Download "Triste" with Polychords Rhythmically Syncopated (PDF)

We're sure you'll agree that the band sounds a lot better now that the piano player is playing inside the groove! Let's just make a couple more adjustments. First off, we'll remove the roots from all of the piano voicings, leaving just the guide tones in the left hand of the piano part. This will allow the bass part to come through more clearly. These notes in the piano part are redundant because the roots of each of the chords occur at all of the crucial moments in the bass line.

Making Final Adjustments to Polychord Voicings of “Triste”

Next, let's play around with the position of the upper structure triads a little bit. This will create a bit of counter melody to the flute part, particularly while the flute is holding a long note. And lastly, let's change up some of the upper structure triads on the minor and dominant chords for variety.You'll notice that we have used both V- and VII over R-7 in mm. 9 and 11. And in mm. 10 and 12, VI and V over R7 create more tension on the secondary dominant chords. In m. 14 the upper structure has been changed to Vmaj over R7, adding T9 to the voicing and in m. 15, V- over R7 for the G7 chord. This last voicing helps to support the flute melody! We've also added a guitar part to double the flute an octave lower and harmonize the melody occasionally. Give it a listen now!

Download "Triste" with Final Adjustments to Polychord Voicings (PDF)

Workshop: "Triste," Second Part Analysis

Now it's your turn!

Analyze the second half of Jobim's "Triste" (mm. 17-32). Use the process outlined in the Polychords topic to create a piano part using polychord voicings to complete the second half of the arrangement. Check your solutions against the PDFs of the full analysis and full score of the arrangement.

Download Triste Lead Sheet (PDF)

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Mountains Rising: The Contemporary Classical Concept of Extended Chords

Mountain Peaks

If we look back at the development of Western harmony from our twenty-first-century perspective, we can see a clear trend. The earliest written music used primarily perfect octaves, 5ths and 4ths in its harmonies. Next, major and minor thirds were added and major and minor chords became the standard harmonic foundation. Around 1600, 7^th chords started to become an accepted harmonic element. In the nineteenth century, composers began to incorporate 9^th, 11^th, and 13^th chords into their compositions. The harmonic development of Western music has mimicked the expansion of the harmonic series. As the harmonic series expands beyond the 13^th partial, the note names begin to repeat. However, since the notes in a natural harmonic series are not the same as those of a tempered scale, the intervals become smaller and smaller. So, perhaps the next development in Western music will be microtonal music. Some twentieth- and twenty-first-century composers have been experimenting with microtones in their music, but it has not gained broad public acceptance. The computer has made it relatively easy to create microtonal music, although most people's ears are unable to differentiate the subtle changes in pitch. And, the tempered 12 notes to the octave scale has become ingrained in our world musical culture, so microtonal music, many say, sounds out of tune.

Extended Chords in the Classical Period

Development of Western Harmony Compared to the Harmonic Series:

Beethoven's Symphony No. 3, The Eroica

Ludwig Van Beethoven

Towards the end of the classical period (1750-1825), composers began to use the 9^th as a chord tone. Beethoven (1770-1827), with his fiery music that featured huge dynamic contrasts, utilized the V7(9) chord to great benefit. The chord ramped up the tension and gave the release of tension an even bigger contrast. The example below is from his Symphony No. 3, The Eroica. Although the 9^th is resolved before moving to the next harmony, it is repeated many times, causing it to become an integral part of the chord. When using traditional Roman numerals for 9^th, 11^th, and 13^th chords, only the highest chord tone is indicated next to the Roman numeral. Therefore what would be indicated as a V7(9) in contemporary Roman numeral analysis is marked V9 in traditional analysis. This same principle is true for 11^th and 13^th chords as well.

Beethoven's Use of the 9th Chord in Symphony No. 3:

Extended Chords in the Romantic Period

Schumann's "Scheherazade"

In the Romantic period (1825-1900) composers sought richer and more evocative harmonies, with 9^th, 11^th, and 13^th chords beginning to be heard more often. But most often they were still treated as dissonances, and although held for longer durations and heard together, they usually resolved to their expected targets.

Robert Schumann and his wife Clara, who was also a fine composer and pianist.

Scheherazade

The next example is an excerpt from Robert Schumann's (1810-1856) "Scheherazade" from his Album für die Jugend, Op. 69, a compilation of 43 short works written for his daughters. The piece has a iv9 chord in which the 9^th (E) is treated as an integral part of the chord. The 9^th chord adds a mildly exotic flavor to this piece depicting Scheherazade, a queen and the storyteller of the famous Persian book of folk tales One Thousand and One Nights. The 9^th (E) of the D-7(9) chord dissolves into the E7 chord, becoming its root. As you can see from the classical-style Roman numeral analysis, although the 9^th chord also has a 7^th, the number 7 left out and only the highest chord member (9) is indicated. This practice is different than modern chord symbols and modern Roman numeral analysis in which all of the tensions are usually indicated.

9^th Chord in Schumann's "Scheherazade":

Mendelssohn's "Song Without Words"

The 11^th chord was not commonly used in classical music because the 11^th is the same note as the 4^th of a chord and was almost always treated as a suspension. As in contemporary music, when the 11^th is present, the 3^rd of a major chord is omitted. In the example below, Felix Mendelssohn (1809-1847), a child prodigy and prolific composer, in his "Song Without Words," includes an E7(9,11) chord. The 11^th is prepared like a suspension and is eventually resolved, but the sound is that of a 7,9,11 "tall chord." Felix's sister Fanny was also fine musician and composer of more than 450 pieces. She, like Mozart's sister Maria (Nannerl), and Clara Schumann, despite their wonderful talents, were denied careers as composers and musicians once they reached marriageable age, because they were women, and their music was not widely performed or disseminated.

Mendelssohn

Mendelssohn's "Song Without Words" Excerpt with an E7(9,11) Chord:

Strauss' "Blue Danube Waltz"

In lesson 6, Johann Strauss' "Blue Danube Waltz" was used as an example of unresolved 9^ths and 13^ths. Those notes could be thought of as integral parts of the chords rather than as melody notes. In that case the chords could be understood as 9^th chords and 13^th chords. Our modern ears probably hear them that way.

9^th and 13^th Chords in Strauss' "Blue Danube Waltz":

Extended Chords in the Impressionist Period

By the Impressionist period (1875-1925), composers were unambiguously writing music that featured 9^th, 11^th, and 13^th chords where the classical non-harmonic tones did not resolve and were clearly part of the chord. French composer Maurice Ravel (1875-1937), along with Claude Debussy, was one of the major composers of Impressionist music. Ravel was also a master orchestrator, and his orchestration of Modest Mussorgky's "Pictures at an Exhibition" still remains as one of Western classical music's major achievements.

Maurice Ravel

The following example is an excerpt of Ravel's "Rigaudon" from Le Tombeau de Couperin, an orchestra version of his suite for piano. The composition opens unambiguously with an 11^th and 13^th chord.

"Rigaudon" from Ravel's Le Tombeau de Couperin:

William Schuman’s "Three Score Set"

William Schuman

All of the examples we have studied up to this point have been examples of tonal harmony—that is, major and minor key harmony that is built around a tonic note and that can be understood in a key. In the twentieth century, composers began to experiment and write music that wasn't clearly in any one key. Some of this music still used tertian harmony—harmony based on chords built in thirds. American composer William Schuman's (1910-1992) "Three Score Set" utilizes chords built in thirds, but without a clear tonal center. Most of the chords in opening measures of "Three Score Set" are "tall chords"—triads with upper structures of various 9ths, 11ths, and 13ths. They can also be thought of as two triads acting independently. This example gives you a taste of mid-twentieth-century harmonic explorations and how composers pushed the limits of harmony built in thirds. As the common-practice classical music of the Baroque period through the Romantic period moves into the twentieth century, the harmonies break away from the traditional tonal practices and traditional Roman numeral analysis doesn't explain the music very well. When we fully enter this new musical world in Music Theory and Composition 4, we will no longer use Roman numeral analysis and we will utilize other ways to describe and analyze the music. The music in "Three Score Set" is no longer tonal in the traditional sense, so no Roman numerals are used for analysis.

An Excerpt from William Schuman's "Three Score Set":

Workshop: Classical Analysis

This workshop is in two parts:

1. Analyze the following excerpt, putting chord symbols and contemporary Roman numerals above the staff and classical style Roman numerals below the staff. You will see that the traditional Roman numerals no longer provide as much information as do the contemporary Roman numerals.

Download Classical Analysis Workshop (PDF)

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2. Add 9ths, 11ths, and 13ths to the progression given below to create a progression with "tall chords." Put chords symbols and contemporary Roman numerals above the staff and adjust the traditional Roman numerals below the staff to complete your analysis. Attach a copy of your score and sound file.

Download "Tall Chords" Practice (PDF)

There are many possible ways to complete this exercise. Below is one possible answer.

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Composers on Composing: Form's Influence on Composition

This week, in lesson 7, three more composers share their thoughts on composition.

The question posed to this week's composers is: How does form influence your composition?

Composers interviewed in Week 7:

Julius Williams—Contemporary classical music composer and conductor
Sheldon Mirowitz—Film and television composer
Susan Cattaneo—Songwriter and recording artist

Recap

In lesson 7 you have learned how to:

Next week we will be diving deeper into modulation by looking at Pivot, Direct, and Transitional Modulation techniques.