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DISCOVERING HARMONY WORKBOOK Comprehensive Lesson Plans and Supplementary Exercises for First Level Harmony

Donna Goodwin-Wilson

Cover Design:

Allison Goodwin-Wilson Used with permission from the artist

Copyright ÂŠ 2013, 2018 by Donna Goodwin-Wilson Email address: discoveringharmony506@gmail.com All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, without written permission from the author.

PREFACE Harmony students often greet the beginning of their studies with a certain anxiety, yet resignation. The purpose of this workbook is twofold: 1. to lead the student through the first experience of harmony to emerge with a strong and confident harmonic understanding and 2. to help the student develop an appreciation for how the knowledge of harmony will complement and enhance the musical learning experience. The workbook begins with 25 goals which present a systematic building of harmonic vocabulary. Each goal provides a planned lesson which leads the student through â&#x20AC;&#x153;doingâ&#x20AC;? to the discovery of how and why the chords behave as they do. At the end of each lesson Practice Exercises reinforce the new concept. Then, Cumulative Exercises are given as an extended review. Finally, through a series of Self-Checking questions, the student is encouraged to critically evaluate the work completed. After mastering the 25 goals, this harmonic knowledge is used in the final sections of the workbook: Chorale Style, Analysis and Melody Writing. Each topic begins with detailed examples which are followed by many appropriate exercises for practice. At the back of this workbook are the Discovering Harmony Reference Pages. They are a constant companion, to be consulted whenever a question or uncertainty arises. These pages effectively summarize this basic harmony course. It is my hope that for each student who journeys through this workbook, harmony will become purposeful, creative and even fun.

ACKNOWLEDGEMENTS I want to express my sincere appreciation to my family, friends and colleagues who supported and encouraged me throughout this project. Special thanks to my son, Geoff, for his technical expertise. He helped me over a gigantic hurdle when I was about to give up. Also, a heartfelt thanks to my daughter, Allison, for her creative abilities. She created the cover of the book and did the computer version of the circle of fifths. Finally, credit to all my harmony students over the years for teaching me what it means to really understand.

TABLE OF CONTENTS Goal #1:

Triad Identification in Major and Minor Keys……………………………….. 1

Goal #2:

Drill Quality and Spelling of Triads in all Keys……………………………... 5

Goal #3:

Spacing of Primary Triads in Chorale Style………………………………..... 7

Goal #4:

Basic Skeleton Progression in Four Parts……………………………………. 11

Goal #5:

Two Chords With Roots a Second Apart………………….............................

Goal #6:

Identify and Write Cadences…………………………………………………

Goal #7:

Revoicing Repeated Chords………………………………………………….

Goal #8:

First Inversion Triads………………………………………………………… 29

Goal #9:

Relationship Between Soprano and Bass Voices…………………………….

Goal #10: Resolve V Three Different Ways……………………………………………. 43 Goal #11: Resolve the Inversions of V …………………………………………………

Goal #12: Deceptive, Stationary and Rising Resolutions……………………………….

Goal #13: Uses of the vii Chord……………………………………………………….

Goal #14: Treatment and Usage of ii and ii …………………………………………… 67 Goal #15: Passing, Neighbour, Incomplete Neighbour, Appoggiatura…………………. 73 Goal #16: Cadential Chord…………………………………………………………….

Goal #17: Uses of the iii Chord…………………………………………………………

Goal #18: Echappée, Anticipation, Suspension, Pedal Point……………………………. 94 Goal #19: Passing, Auxiliary and Arpeggio Chords…………………………………..

109

Goal #20: Write a Sequence of Descending Fifths……………………………………...

121

Goal #21: Apply a Dominant to the Chord of V………………………………………...

126

Goal #22: Modulate From a Major Key to the Dominant Major Key…………………..

135

Goal #23: Writing Progressions in the Minor Key……………………………………… 138 Goal #24: Modulate From a Minor Key to Relative Major or Dominant Minor………..

149

Goal #25: Root/Quality Chord Symbols………………………………………………… 153 Chorale Style……………………………………………………………………………..

160

Harmonic Analysis……………………………………………………………………….

182

Structural Analysis……………………………………………………………………….

213

Ideas For Developing Melodic Material…………………………………………………. 243 16 Bar Melody in Rounded Binary Form………………………………………………... 250

REFERENCE PAGES Circle of Fifths………………………………………………………………………….... i Triads on Scale Degrees………………………………………………………………….. ii Triads on Scale Degrees – Summary…………………………………………………….. iii A Progression Chart to Build On………………………………………………………… iv Doubling………………………………………………………………………………….. v Special Progressions………………………………………………………………………. vi Cadences………………………………………………………………………………….. vii Non-Chord Notes…………………………………………………………………………. viii Chords…………………………………………………………………………………… x Suspensions……………………………………………………………………………….. xii Major Key Progression Chart…………………………………………………………….. xiii Minor Key Progression Chart…………………………………………………………….. xiv Modulation to the Dominant……………………………………………………………… xv Modulation to the Relative Major…………………….………………………………….. xvi Modulation to the Dominant Minor………………………………………………………. xvii Use of III and VII in the Minor Key …………………………………………………….. xviii Root/Quality Chord Symbols……………………………………………………………… xix Baroque Dances…………………………………………………………………………… xx Related Keys……………………………………………………………………………..... xxi Structural Analysis Forms…………………………………………………………………. xxii Melodic Development Ideas………………………………………………………………. xxiii Melody Writing Procedure………………………………………………………………… xxiv Melody Writing Checklist…………………………………………………………………. xxv Instructions for Building the Key Slide Rule

GOAL #1 _________________________________________________________________________________________________________ Review of triad identification in major and minor keys. REFERENCE PAGES i ii iii

Circle of 5ths Triads on Scale Degrees Triads on Scale Degrees - Summary

LESSON Write a C major scale in the treble clef in whole notes â&#x20AC;&#x201C; use lots of space. Build a triad on each scale degree.

Review triad qualities:

A major triad contains a major third and a perfect fifth. A minor triad contains a minor third and a perfect fifth. An augmented triad contains a major third and an augmented fifth. A diminished triad contains a minor third and a diminished fifth.

Identify each triad in the C major scale as major (+), minor (-), augmented (x) or diminished (o). Use Roman numerals to identify the scale degree upon which each triad is built. The Roman numeral should reflect the quality of the triad as follows: A major triad uses an upper case Roman numeral. (e.g. I) A minor triad uses a lower case Roman numeral. (e.g. ii) An augmented triad uses an upper case Roman numeral with an x superscript. A diminished triad uses a lower case Roman numeral with a o superscript. Now write the harmonic minor scale of c minor in the treble clef using accidentals, NOT a key signature.

Build a triad on each scale degree. Fully identify each triad with a Roman numeral that reflects its quality. 1

Now do the same for c natural minor.

In the natural minor scale check the triad on the seventh degree. When working in the minor key, the raised 7th of the harmonic minor is assumed. The seventh degree of the scale in c minor is assumed to be B . Therefore (major) would be B D F . But the

There are additional triads relating to the melodic minor scale which use the raised 6th. If the raised 6th is used iio becomes ii and iv becomes IV. (VI would become #vio, but this chord is never used).

Two ideas require emphasis: 1. In every major key the qualities of the triads will be the same. For example, in every major key the leading note triad is diminished. In all major keys the subdominant triad is major. The minor key is much more variable. In the harmonic minor the median triad is always augmented. However in the natural minor (no raised 7th), the median triad is always major. Use of the melodic minorâ&#x20AC;&#x2122;s raised 6th changes the qualities of some chords. 2. When writing any chord in any key at any time, it is important to be aware of the quality of the chord, and by extension, the spelling of the chord. For example, the chord of V in G major is a major triad so it would be spelled not DFA but rather DF A. This is not crucial in beginning harmony since most of the time the key signature takes care of things. But if correct spelling becomes a habit, it will be extremely helpful. The melodic minor options are a good example. It cannot be assumed that the supertonic triad in a minor key is iio; it could be ii. Spelling becomes even more important when modulation, diminished sevenths and chromatic harmony start to enhance things. The moral of the story is: Try to develop an awareness of the qualities of the chords being written.

PRACTICE EXERCISES First write out and fully label all the triads in the following major keys. Use accidentals rather than a key signature. On the next page write out and fully label all the triads in the given harmonic minor keys. Use accidentals rather than a key signature. On the second line of each minor key exercise, write the 3 additional triads provided by the natural minor and the 2 additional triads provided by the melodic minor. Again, use accidentals.

SELF-CHECKING 1. Is the 7th always raised in the harmonic minor triads? 2. Is correct labeling used for VII in the natural minor? 3. Are correct accidentals used in the minor key for ii and IV? (raised 6th) 4

GOAL #2

_________________________________________________________________________________________________________ Drill quality and spelling of all triads in all major and minor keys. REFERENCE PAGES i xxvi

Circle of 5ths Instructions for Building the Key Slide Rule

LESSON First, turn to page xxvi in the reference pages and use the templates and the instructions to build a â&#x20AC;&#x153;key slide ruleâ&#x20AC;?. Work through the following examples. The sliding section of the key slide rule gives the note names for chords. The chord notes are written in short columns to be read from the top down. 1. Spell vi in E + Slide the ruler until E at the top of a column lines up with major keys I. Look across the top (+keys) as far as vi. Below vi reads CEG(B). The (B) does not apply unless spelling some type of 7th chord. Check the key signature for E + using the circle of 5ths. Using the key signature of E +, vi would be spelled CE G which is a minor triad. 2. Spell IIIx in fSlide the ruler until F at the top of a column lines up with minor keys i. Look across the bottom (- keys) as far as IIIx. From the top down the column above IIIx reads ACE(G). Ignore the (G). Check the key signature for f- using the circle of 5ths. Apply the key signature of f harmonic minor and spell IIIx A CE . 3. Spell ii in eSlide the ruler until E at the top of a column lines up with minor keys i. Look across the bottom (- keys) as far as ii. From the top down the column above ii reads FAC(E). Ignore the (E). Check the key signature for e- using the circle of 5ths. Apply the key signature of e melodic minor and spell ii F AC . C is the raised 6th. 4. Spell VII in c Slide the ruler until C at the top of a column lines up with minor keys i. Look across the bottom (- keys) as far as VII. From the top down the column above VII reads BDF(A). Ignore the (A). Check the key signature for c - using the circle of 5ths. Apply the key signature of c natural minor and spell VII, B D F .

PRACTICE EXERCISES Here are several spelling exercises to try: (Cover the answers below; then use the answers to check for accuracy.) a. A+ IV

___________________

E+ iii

___________________

b. b- IV

___________________

e - iv

___________________

c. c- v

___________________

k. B+ vi

___________________

d. f - VI

___________________

c - IIIx

___________________

e. D

___________________

m. a- viio

___________________

f. F + viio

___________________

n. f- ii

___________________

g. a - iio

___________________

o. g - iv

___________________

h. g-

___________________

p. D+ ii

___________________

VII

a. D F A

i. G B D

b. E G B

j. A C E

c. G B D

k. G B D

d. D F A

l. E G B

e. A C E

m. G B D

f. E G B

n. G B D

g. B D F

o. C E G

h. F A C

p. E G B

GOAL#3

_________________________________________________________________________________________________________ Learn to space primary triads for four part chorale style writing. REFERENCE PAGES i v

Circle of 5ths Doubling

LESSON In the study of harmony, chords are written in four parts as for a choir of sopranos, altos, tenors and basses. The primary triads of the key are I, IV and V. All of these triads have only 3 notes, but the choir has 4 voices, so one of the notes of the triad will have to be doubled. The best note to double in these three triads is the root of the chord. At this point there are many rules about four part writing, but it is possible to develop an eye for good spacing without worrying too much about the rules. Here are some ideas: 1. Sopranos do not want to sing notes too high above the staff. (approximately A above as a limit) 2. Altos do not want to sing notes too far below the treble staff. (approximately G below as a limit) 3. Basses do not want to sing notes too far below the bass staff. (approximately F below as a limit) 4. Tenor parts often look very high but this voice probably uses more ledger lines than any other voice. It is not uncommon for tenors to sing G above the bass staff. 5. Spacing between voices is not much of a worry. It is best to aim for consistent spacing among the top three voices, not more than an octave between soprano and alto or alto and tenor. 6. Spacing between bass and tenor is often quite large â&#x20AC;&#x201C; a 10th or even more. This looks odd at first but is actually just fine. At first it is time consuming to constantly be checking that each voice is written within the correct vocal range. But it will quickly become more comfortable. Trust the eye to see consistent spacing. However, in case the eye suspects a problem, following are the vocal ranges for occasional checking.

Practical Vocal Ranges

Below write the chord of IV in D+ in 4 parts. Use half notes. Soprano and alto notes are written in the treble clef with the soprano stems going up and the alto stems going down. Tenor and bass notes are written in the bass clef with the tenor stems going up and the bass stems going down. Remember the root will need to be doubled because four notes are needed. The root will also have to be in the bass part because only root position chords are to be used at this time. The other notes can go in any order at all. Now write the same chord two more different ways.

Now write the V chord in B + with four different voicings.

Following are many different solutions for a four part D+ IV chord with annotations regarding the four voice arrangement.

a. excellent b. also great – very even spacing c. wrong – too much space between alto and soprano d. wrong – tenor note is actually higher than alto note – part crossing e. bass and tenor very close; tenor and alto too far apart f. fine – big space between bass and tenor is totally fine g. correct – not much room anywhere , but nonetheless, correct h. correct – two voices can share the same note, just give the note 2 stems; an alternative is shown with bass and tenor singing 2 different G’s i. wrong – too much space between alto and tenor

PRACTICE EXERCISES Write the following chords in four parts. Write each one in three different arrangements. Try to develop an eye for good spacing.

SELF CHECKING Try to answer â&#x20AC;&#x153;noâ&#x20AC;? to each of the following questions: 1. Are the soprano and alto or alto and tenor more than an octave apart? 2. Is there any part crossing? 3. Do any of the four part arrangements look suspicious to the eye? 10

GOAL #4

_________________________________________________________________________________________________________ Learn to write the basic skeleton progression of chords in four part chorale style. REFERENCE PAGES iv v

A Progression Chart to Build On Doubling

LESSON Harmony is about choosing chords to follow one after another in a progression which is logical to our ears. A given chord will “want” to move to some other chords, but not to just any chord. Chords moving in an illogical progression: a) will not sound good, and b) will often lead to other errors in the part writing. So here is the skeleton progression (see reference page iv): I - vi - IV - ii - V - I The trick is to be moving forward on this progression path. Any key can be defined by V and I, dominant and tonic. Tonic (I) can move logically to dominant (V) and back to tonic (I). In the case of I to V to I, vi and IV and ii have been missed. These three chords are referred to as predominant chords and some or none or all of them may be used in a good progression. The important thing is to move forward. So here are some examples of good progressions: I - vi - ii - V - I I - IV - V - I I - V - I I - IV - ii - V - I I - vi - IV - V - I

……………and many more!!

The final I can serve as the start of another progression, for example: I - vi - V - I - IV - ii - V - I _____________ _________________ …………and around and around it goes.

When moving from one chord to another, follow three steps: 1. Is there a leading note (LN) in the last chord written? If there is, it must rise to the tonic in the same voice in the next chord. NOTE:

This is an introduction to that very sensitive note, the leading note (LN), that is, the 7th degree of the scale. Play a major scale and stop after playing the LN. This sounds very incomplete. The ear wants to hear the LN move to the tonic. If the LN does not resolve to the tonic, it can create all kinds of other mistakes. So ALWAYS, step 1, resolve the LN to the tonic in the same voice in the next chord.

2. Are there any notes which are common between the last chord written and the new chord? If the answer is â&#x20AC;&#x2DC;yesâ&#x20AC;&#x2122;, then keep those common notes in the same voice. 3. Move any remaining notes as smoothly as possible. In short: LN, common notes, smooth. Here is an example of the full skeleton progression in C+. Notice that the root of every chord has been doubled and the root of every chord is in the bass voice, that is, all root position chords.

Now try another version in C+. Notice that the voicing of the starting I chord is different this time. Always follow the three steps when moving from one chord to the next: LN, common notes, smooth.

PRACTICE EXERCISES At this point it is good to practice various progressions in lots of different keys. Work through the following exercises. A good method for these exercises is: 1. 2. 3. 4. 5.

Draw the clefs and key signature. Write the Roman numerals well-spaced. Put in all the bass notes. (Use half notes and no bar lines.) Write a nicely spaced first chord. Move carefully from one chord to the next: LN, common notes, smooth.

Students often question: “Should I go up or down to the next bass note?” The bass line can be quite “leapy” especially when all the chords are in root position. There is no need to worry about this. Leap up or down, but do NOT leap a 7th when a 2nd would work instead. 1. F+ I - V - I - vi - ii - V - I 2. A+ I - IV - ii - V - I - V - I 3. E + I - vi - IV - ii - V - I 4. B+ I - V - I - IV - ii - V - I 5. D + I - vi - IV - ii - V - I - V - I 6. C+ I - vi - ii - V - I - IV - ii - V - I 7. G+ I - IV - ii - V - I 8. E+ I - vi - ii - V - I SELF CHECKING 1. 2. 3. 4.

Does the LN always rise in the same voice? Have common notes been kept in the same voice? Is the root of the chord always in the bass? Does the voiceleading in these progressions look smooth?

After completing these exercises, it should be apparent that the LN occurs in the V chord, but in no other chord. Furthermore, the LN is always the 3rd of the V chord. So the LN is the 7th degree of the scale, but the 3rd of the V chord. This is a very important and often confused idea. So take time now to clarify and distinguish this difference.

GOAL #5

_________________________________________________________________________________________________________ Learn to handle the movement of voices between two chords that have their roots a 2nd apart. REFERENCE PAGES iv v

A Progression Chart to Build On Doubling

LESSON There are a few progressions on the Skeleton Progression Chart that were not written during the last lesson: I - ii, IV - V, and vi - V. What do all of these progressions have in common? The roots of each pair of chords are a 2nd apart. Chords with roots a 2nd apart demand special attention. Write I - ii in F+ following the 3 steps â&#x20AC;&#x201C; LN, common notes, smooth.

There is no LN in I. There are no common notes between I and ii. The smoothest possible connection presents parallel octaves and parallel 5ths. These parallels are forbidden. The parallels can occur between any two voices. Look at the following two examples. Then mark the parallels in the I - ii progression written above.

Rather than ever having to search for these unwelcome parallel 5ths and 8ves, there is a simple solution for writing a progression where the roots are a 2nd apart. The top three voices must move in contrary motion to the bass. soprano alto tenor bass The principle is: When two chords have their roots a 2nd apart (and therefore have no common notes), move the top three voices in contrary motion to the bass voice to avoid undesirable parallel octaves and fifths. Use this principle to write the progression IV - V in G +. Follow the contrary motion principle and the results will be good.

One progression remains: vi - V. This one is slightly different but uses the same principle. In this case the roots are still a 2nd apart, but the bass is stepping down instead of up. Therefore the top 3 voices will move up instead of down. Use the contrary motion principle to write the progression vi - V in D+.

PRACTICE EXERCISES

CUMULATIVE EXERCISES Write the following progressions. Verify with the progression chart that each progression is a good one. 1.

G+

I - ii - V - I

B+

I - IV - V - I - vi - V - I

E+

I - vi - ii - V - I - IV - V - I

D+

I - ii - V - I - IV - V - I

A+

I - vi - IV - ii - V - I

B+

I - ii - V - I

C+

I - ii - V - I - vi - V - I

F+

I - IV - V - I - ii - V - I

SELF CHECKING 1. Whenever two chords have roots a 2nd apart, has the contrary motion principle been used? 2. Does the LN in every V chord rise to the tonic in the same voice?

GOAL #6

_________________________________________________________________________________________________________ Learn to identify and write different cadences. REFERENCE PAGES iv v vii

A Progression Chart to Build On Doubling Cadences

LESSON A cadence is a two-chord progression that marks the end of a phrase. Every musical phrase ends with a cadence, allowing the music to breathe. There are four types of cadences â&#x20AC;&#x201C; perfect (or authentic), imperfect (or half), plagal and deceptive (or interrupted). Perfect Cadence This cadence is dominant to tonic (V - I) and gives the strongest sense of key. This progression has already been written in past goals. Imperfect Cadence This cadence ends on the dominant and therefore has much less sense of finality. The possibilities are: I - V, ii - V, IV - V, and vi - V. Again, all of these progressions have been covered through the study of the skeleton progression. Plagal Cadence This cadential progression is not yet shown on the Progression Chart. It is a IV - I progression and is often an extension of a perfect cadence: V - I - IV - I. The plagal portion of this progression is often referred to as a plagal extension. This is the first addition to the Progression Chart to Build On (reference page iv). Gradually chords and progressions will be added to the columns of the chart until the finished product resembles reference page xiii, Major Key Progression Chart. In the final I column of the skeleton progression add I - IV - I, the plagal extension. Also add I - IV - I to the first I column where it can be used as an expansion of tonic harmony.

Write a perfect cadence with the plagal extension in B +.

Write the plagal progression as an expansion of tonic harmony in A +.

Deceptive Cadence This is a very effective cadence which tricks the listener. The expectation is that V will move to I. But instead of I, a vi is heard, and instead of the music ending, it moves on. The first thing to notice about this progression is that the roots of the two chords are a 2nd apart. This means that the two chords have no common notes and that the contrary motion principle should be used. The bass voice is stepping up, so the other three voices should move down.

Using the contrary motion principle, write V - vi in F+.

There is a problem that arises. The LN is one of the top three voices that is supposed to move down so that it is in contrary motion to the bass. But the LN must always rise. The dilemma is: Should the LN fall in contrary motion to the bass or should the LN rise as all good LN’s do?? The answer is that the LN must rise! Since two voices are now stepping up, it is even more important that the other two voices move in contrary motion to the bass. Correct, if necessary, the F+ deceptive cadence written above. Perhaps something still looks wrong. One of the voices is leaping quite far – not as smooth as usual. The solution here is to double the 3rd instead of the root of the vi chord. Think about this. The deceptive cadence gets its name because it deceives the ear. In this cadence, the vi is a substitute for I. In F+ the root of I is doubled – this is the tonic note F. If the 3rd of vi is doubled, the doubled note is again the tonic, F. As a substitute for I, vi doubles the tonic note (3rd of the chord). Now make a final correction to the F+ deceptive cadence written above. When vi follows V, double the 3rd of vi. Now write another deceptive cadence in E +. When doubling the 3rd of vi remember that the doubled 3rd is actually the tonic note of the key. This doubling makes sense because in a deceptive cadence vi is being used as a replacement for I.

Finally, add vi to the final I column of the progression chart to show the possibility of a deceptive cadence as a substitute for a perfect cadence. 20

In the chorales of J. S. Bach a cadence occurs at each fermata sign. The chorale phrases vary a great deal in length because the chorales are all settings for spiritual texts. They are prayers that have been set to music. Therefore the phrases are built to match the natural pauses in the text. Following are excerpts from several chorales with lines under each pair of cadence chords. On the lines identify the two chords and name the type of cadence. There will sometimes appear to be â&#x20AC;&#x153;extraâ&#x20AC;? notes. Try to choose the main notes which will form appropriate cadence chords.

PRACTICE EXERCISES Practice writing the following cadences: 1. Write perfect cadences with the plagal extension in C+, E + and G+. 2. Write imperfect cadences in A +, B+, F + and E+. Use all four imperfect possibilities. 3. Write I - IV - I in F +, E+ and B +. 4. Write a deceptive cadence in G +, F+ and C +.

CUMULATIVE EXERCISES Write the following progressions. Here is a reminder of a working procedure for each exercise: 1. Write the name of the key below the clefs and add the key signature. 2. Write in the Roman numerals. 3. Write in all the bass notes. 4. Complete the chords, one at a time, following the plan of LN, common notes, smooth. 1. B +

I - IV - V - I - IV - I

2. C+

I - IV - I - vi - ii - V - I

3. D +

I - IV - ii - V

4. E+

I - IV - V - vi

5. F+

I - ii - V - I - IV - V

6. G+

I - vi - V

7. A+

I - vi - V - I - IV - I

8. D+

I - vi - IV - ii - V - I - V

SELF CHECKING 1. Does the LN in the chord of V always resolve to the tonic in the same voice? 2. When the roots of two chords are a 2nd apart, is the contrary motion principle used? 3. In V - vi is the 3rd of vi (tonic of the key) doubled?

GOAL #7

_________________________________________________________________________________________________________ Learn to revoice a repeated chord to expand the harmony. REFERENCE PAGES iv v

A Progression Chart to Build On Doubling

LESSON When moving from one chord to the next the emphasis so far has been to follow the plan of LN, common notes and smooth voiceleading. Chords have never been repeated. If a chord is repeated, it can be done in one of two ways: 1. repeat the chord with the same voicing 2. revoice the chord when it is repeated If a chord is revoiced, the idea of creating smooth voiceleading must be abandoned to some degree. However, leaps between notes of the same chord are not a concern. In the examples below the sound of the I chord is heard and the rearrangement of the notes in the second I chord still produces the sound of I. It is not difficult for a singer to leap to another note of the same chord. Listen to these examples.

Write a V chord in D+ followed by the chord of V again, revoiced. Is there any problem with this part writing?

The problem is that the LN in the first V chord is not resolving. Again, because the chord has not changed, it is permissible to the ear that the LN be passed around from one voice to another as long as it resolves when the chord changes. The following passage shows three revoicings of V. Notice how the LN hops around but when the chord changes, the LN clearly resolves. The concept of revoicing the same chord and resolving notes as the chord changes is very important throughout the study of harmony.

Play and study the next example.

It is interesting how vi is revoiced. The first vi has a doubled 3rd because it comes after V. When vi is revoiced it has changed to the doubled root. When the second vi moves to V notice that the bass steps down and the three upper voices move in contrary motion to the bass. Also notice that the first vi chord uses a double stemmed A in the treble clef, meaning that both the soprano and the alto will sing the same note.

CUMULATIVE EXERCISES In the following exercises, when a chord is repeated, revoice it. 1. B +

I - IV - IV - V - vi - vi - ii - V - V - I

2. A+

I - I - ii - ii - V - vi - IV - IV - V - V - I

3. G+

I - ii - V - V - vi - IV - V - I

4. E +

I - IV - IV - I - ii - V - V - I

5. F+

I - vi - vi - IV - I - ii - V - I - I - IV - I

SELF CHECKING 1. When chords have roots a 2nd apart is the contrary motion principle used? 2. When following V does vi use a doubled 3rd? 3. When the V chord is revoiced, does the LN ultimately resolve when the chord changes?

GOAL#8

_________________________________________________________________________________________________________ Learn to write first inversion triads for all chords in the skeleton progression. REFERENCE PAGES iv v

A Progression Chart to Build On Doubling

LESSON Write a C+ triad in root position in the treble clef. Beside it write the same triad in first inversion and then in second inversion.

Put the Roman numeral I under each triad. Now, using Arabic numerals (1,2,3â&#x20AC;Ś.), write the numbers corresponding to the intervals above the bottom note of each triad in descending order beside the Roman numeral. The triads should look like this:

This is called figured bass and tells in which inversion a triad is written. Up to this point in the lessons only root position triads have been used. The is omitted for indicating root position. Now it is time to add first inversion to the chord vocabulary. The figures indicating a first inversion triad are , but the 3 is routinely omitted. So the indication is just the 6 after the Roman numeral. When writing first inversion triads, the 3rd of the triad goes in the bass voice and the other notes are arranged in any order among the other voices. Doubling in first inversion triads is often considered a not-so-pleasant task in memorization. But there is logic and understanding in doubling. The most stable notes in any key are the tonic, subdominant and dominant notes of the scale. These are good and safe notes to double.

Here are the correct doublings. Think in C+: I6 IV6 V6 ii6 vi6

double root C (tonic) or double 5th G (dominant) double root F (subdominant) or double fifth C (tonic) double root G (dominant) or double fifth D (supertonic) double third F (subdominant) double third C (tonic)

There are no surprises here except the fifth of V doubling the supertonic. All the other possible doublings involve the three most stable scale degrees, tonic, subdominant and dominant. Wherever a triad can be used in root position, it can also be used in first inversion, except at an important cadence, where both chords must be in root position. One more important idea about first inversion triads: The use of first inversion triads can definitely lead to a bass line with fewer leaps. This will become more important later on. Write the following progression in C+:

Check your work: LN rises? Common notes kept in same voice? IV to V contrary motion principle? vi6 doubles 3rd (tonic of the key)

Write the following progression in F+:

Notice the similarity between IV and ii6 in this progression. Each has the same bass note â&#x20AC;&#x201C; B . Each has the same doubled note: root of IV is B ; third of ii6 is B . The common note between the two chords is D. There is one remaining note: F in the IV chord and G in the ii6 chord. These two chords are in fact so similar that ii6 - V presents the same problem as IV - V. Remember roots a 2nd apart use the contrary motion principle. In this case the bass notes are a 2nd apart and the contrary motion principle will again assure that no parallel octaves or fifths occur. Now check your work: 3rd of ii6 is doubled? ii6 - V uses contrary motion principle? Does the progression IV6 - V present the same problem as IV - V ? Look at the following three examples:

In example a, the root of IV6 is doubled and the smoothest movement is three voices moving down and one voice moving up. There are no parallels. In example b, the fifth of IV6 is doubled and the smoothest movement produces parallel fifths. In example c, the fifth of IV6 is doubled and the parallels have been eliminated.

Despite the first inversion, the roots of IV and V are still a 2nd apart and parallels are a possibility. The contrary motion principle is not 100% possible so watch carefully for parallels. It is time to add the first inversion alternative to all root position chords on the progression chart by writing (6) beside each chord except I in the final tonic column and the plagal extension, both of which should always be root position at a phrase end. (Note that I - IV - I in the first tonic column can use the first inversion on any of the three chords.)

PRACTICE EXERCISES Write each chord two different ways with correct doubling.

CUMULATIVE EXERCISES For each exercise verify on the progression chart that each progression is indeed a good one. Also notice that sometimes the chords will be expanded either by repeating the chord (in these examples practice revoicing) or by changing the chord to a different inversion. 1. A +

I - IV6 - I - ii - V6 - I

2. E+

I - I6 - IV - IV6 - ii6 - V - V - I

3. B +

I - vi6 - ii - ii6 - V - I

4. D+

I6 - ii - V - I

5. F+

I - vi - IV6 - ii - V6 - I - IV - I

6. A+

I - IV - IV6 - V - I

7. G+

I - I - ii - ii6 - V - vi

8. C +

I6 - IV - IV - ii - ii - V - V6 - I

SELF CHECKING 1. 2. 3. 4. 5.

Is the doubling of each first inversion chord correct? Is the contrary motion principle used when two chords have roots a 2nd apart? If the contrary motion principle cannot be used 100%, has care been taken to avoid parallels? Is the LN in the chord of V or V6 always resolving? If a chord is repeated, has revoicing been used?

GOAL #9 _________________________________________________________________________________________________________ Explore the relationship between soprano and bass voices. Understand the need for phrases, and therefore cadences.

REFERENCE PAGES iv

A Progression Chart to Build On

LESSON Here are the basics of good part writing which have been covered so far: 1. Respect the tendencies of chords to move forward within the fundamental progression: I - vi - IV - ii - V - I 2. Move from chord to chord following the 3 step plan: LN rises, common notes, smooth 3. When two chords have roots a 2nd apart, move the top 3 voices in contrary motion to the bass. 4. Freely revoice a repeated chord. 5. Substitute first inversion triads for root position triads when appropriate. This last point leads to the discussion of a smoother bass line and subsequently the shape of the soprano line with respect to the bass. In D+, write a bass line for the following progression:

Consider this a phrase. Each phrase must end with a cadence. This phrase ends with a perfect cadence (V - I). The two chords which form the cadence are most often in root position and it is advisable to stick to root position at phrase ends for now. However, the rest of the phrase can venture into the world of inversions. One of the uses of inversions is to make a smoother bass line. In the bass line above, notice the up and down leaps throughout the phrase. On the whole, basses tend to sing more leaps than the other voices and they are fine with it. However, it is desirable that there be a little more shape within the bass voice line. Choose some inversions to give this bass phrase a smoother line. Keep in mind that root position chords can be replaced with first inversion chords, and that any chord can be expanded by

restating it in its first inversion (e.g. I - I6). Try to create two different and more “shapely” bass lines. The first one is an example:

The next step is to add a soprano line to the progression. As much as possible it is good to move the soprano in contrary motion to the bass line. There are five kinds of motion: 1. 2. 3. 4. 5.

similar motion – two parts moving in the same direction parallel motion – like similar, but with the same interval between the two parts all the time contrary motion – one part moves up and the other down oblique motion – one part stays on the same pitch while the other part moves up or down stasis – no motion

When adding the soprano, aim for contrary motion. So if the bass is moving downward, try to move the soprano upward. And if the bass is moving upward, try to move the soprano downward. Following is one solution to the example above:

Contrary motion is observed most of the time. But there are also instances of oblique motion and stasis. Contrary motion is not always possible, but it is good to strive for it, so that the outer two parts (soprano and bass) move in a sort of mirrored way. At this point, try playing the two parts together to hear the effect. Now take the other two bass lines that were created earlier and add a soprano line to them.

The final step in this work is to add the alto and tenor voices. It is good to try to leave the bass and soprano alone. If it becomes absolutely necessary to change a bass or soprano note there is nothing to stop this from happening. But the soprano/bass outline is important, so keep it if possible. This final step could lead to some decision-making or compromise. Information such as what chords â&#x20AC;&#x153;wantâ&#x20AC;? to do, what the most stable doubling notes are, the strength of the LN and so on, help contribute to strong and well-equipped decision-making.

Following is a list of possible compromises. Then pairs of compromises are given. Select the one that would be the best solution. After completing the exercise, read about each of the compromises. a. Let the LN fall b. Triple the root of I c. Do not keep the common note d. Make a leap of a 6th or more in one voice e. Double the 3rd of I6 or IV6 f. Leave out the 3rd of a chord to keep smooth g. Double the 3rd of V6 h. Double the root in ii6 i. Abandon the contrary motion principle j. Move backwards within the predominant area 1. a or b?

___________

6. c or f?

___________

2. c or d?

___________

7. e or g?

___________

3. g or h?

___________

8. h or i?

___________

4. a or i?

___________

9. d or g?

___________

5. d or h?

___________

10. a or j?

___________

a. There are a couple of situations where the LN can fall which will be discussed later. At this point the LN falling is NEVER a choice. b. At a final cadence tripling the root of I is always a safe option. But never use 3 roots and the 5th of the chord. Instead always include the 3rd. This is because the 3rd is the note that gives the chord its quality of major or minor. Without it, the chord sounds incomplete and empty.

no 3rd incorrect

no 5th correct

c. Common notes are fairly low on the compulsory list and can easily be compromised. d. If a large melodic leap becomes necessary there may be some other problem. However, if it occurs between two voicings of the same chord it is just fine (as discussed in goal #7). large melodic leap in soprano is fine

e. Bach, in his many chorales, often doubled the 3rd of I6 or IV6. No harm is done, though this doubling is less common than the doubling of root or 5th. f. Leaving out the 3rd is always a poor choice as discussed in b above.

g. The 3rd of V is NEVER doubled because it is the LN of the key. Two LNâ&#x20AC;&#x2122;s, both rising, would mean two tonics, and therefore, parallel octaves.

h. First choice doubling for ii6 is the 3rd, but doubling the root, as is done in root position ii, is also fine. i. The only time the contrary motion principle should be abandoned is when the LN has to rise. Sometimes a given part is already abandoning the contrary motion principle and if this is the case, it just becomes extra important to check for parallels and try to assure contrary motion in the other voices.

j. Among the chords of vi and IV and ii it is acceptable to move back and forth, but it is always best to move forward if possible. All these chords have the same function â&#x20AC;&#x201C; they lead to dominant harmony.

Here are the correct answers: 1. b 2. c 3. h 4. i 5. h 6. c 7. e 8. h 9. d 10. j

CUMULATIVE EXERCISES In the first two exercises, restrictions are in place because of the given notes. Restrictions force limitations which can be very helpful. But limitations can also force decision-making and compromise. Decide on a good progression and then add the alto and tenor parts. In the next two exercises the progression is given. First create a melody which moves in contrary motion to the bass part, perhaps not always, but most of the time. Try to create some melodic shape with a range of more than a 5th but less than an octave. The last exercise presents a different challenge. With the melody given, it is necessary to decide on a good progression and then create a bass line to generally mirror the melody using root and first inversion triads. In all these exercises, play the soprano and bass parts together before adding the two middle voices.

SELF CHECKING 1. Is there a good cadence using root position chords at the end of every phrase? 2. Have parallels been avoided whenever two chords have roots a second apart? 3. Do the bass and soprano voices generally move in contrary motion to one another? 4. Has correct doubling been used? (Remember that there are alternate doublings for some chords in first inversion.) 5. Are the progressions in each exercise strong?

GOAL #10

_________________________________________________________________________________________________________ Learn to resolve the dominant seventh chord three different ways. REFERENCE PAGES Key Slide Rule iv A Progression Chart to Build On v Doubling vi Special Progressions LESSON It is time to add V to the dominant column of the progression chart. The dominant seventh chord intensifies the V chord and makes it want to resolve to I or vi even MORE than it did without the seventh. First of all notice the need for the bracketed note name on the Key Slide Rule â&#x20AC;&#x201C; the bracketed note name is the 7th. Follow this example through as a guide to using the slide rule to spell dominant seventh chords. Remember to apply the key signature to the spelling. For example, for A +, slide the A under I. Under V( ) read E G B (D). The (D) is the 7th of V . To spell the chord correctly, apply the key signature of A +. So V of A + would be spelled E G B D . There are three interesting and important things to notice about any dominant seventh chord. 1. This chord contains a major triad (V) plus a minor 7th (E to D ). This is true for ALL dominant seventh chords. They are sometimes referred to as major-minor seventh chords for this reason.

2. The 7th (D ) is the 7th of the chord. The 3rd (G) is the 7th of the key of A +. The 3rd is called the LN and the 7th is called the 7th.

3. In every V chord, the distance between the LN and the 7th is a diminished 5th. Inverted, the 7th to the leading note is an augmented 4th. Both of these intervals are called tritones because they are three whole tones big. The diminished 5th and the augmented 4th are the same size. The tritone is the tension in the chord and it needs to be resolved.

Following is a practice chart for spelling and understanding the dominant seventh chord.

Key

Spelling of V7

7th

F+

B+ E+

F+

D+ A+

C+

G+

Tritone o5th

Tritone x4th

There are three ways to resolve the root position dominant seventh chord: 1. V7 complete to I incomplete 2. V7 incomplete to I complete 3. V complete to I complete Method #1: V complete to I incomplete Write a complete V7 chord in four parts in the key of D+. Four notes and 4 parts means no doubling! Follow the steps to resolve this chord to I.

a) root of the I chord goes in the bass b) LN (3rd of the chord) must rise by step in the same voice to the tonic c) 7th (of the chord) must fall by step in the same voice Now only the 5th of the I chord is needed, but placing it in the missing voice creates a not-toosmooth movement as well as parallel 5ths. Therefore, the most logical thing to do is triple the root of I. Now the voiceleading is very smooth. Find the tritone in the above progression and notice how it resolves. If it is a diminished 5th, it closes to a 3rd. If it is an augmented 4th, it opens to a 6th. Also notice that the tritone can be a compound interval. The two notes that form the tritone do not have to be in adjacent voices. Below are two more examples showing the tritone resolutions.

This completes Method #1, V7 - I. V is complete; all its notes are used. I is incomplete; the 5th of the chord is missing. The LN rises; the 7th falls. The augmented 4th between the 7th and the LN opens to a 6th, or the diminished 5th between the LN and the 7th closes to a 3rd. 45

Method #2: V7 incomplete to I complete This method involves an incomplete V7. One note must be left out. Which one? root – needed for the bass voice in root position 3rd – LN, part of the characteristic tritone 7th – part of the tritone – required to be a 7th chord in the first place 5th – no particular importance Leave out the 5th. And if one note is left out, then one of the remaining notes needs to be doubled. Which one? 3rd – LN; NEVER double this sensitive note; doubling will create parallels if both resolve as they should 7th – the most dissonant note in the chord; doubling will create parallels if both resolve as they should 5th – has been left out so not an option Root – strong and stable; doubling will work well Now write an incomplete V7 in F+ in 4 parts. Follow the steps to resolve this chord to I.

a) b) c) d)

root of the I chord must be in the bass voice LN must rise in the same voice 7th must fall by step in the same voice fill in the last note of the I chord

Below are two more examples of method #2 showing the resolution of the tritones.

This completes Method #2, V7 - I. V7 is incomplete; leave out the 5th. I is complete; all notes of the chord are present. The LN rises; the 7th falls. The augmented 4th between the 7th and the LN opens to a 6th, or the diminished 5th between the LN and the 7th closes to a 3rd. Method #3: V7 complete to I complete This method is somewhat â&#x20AC;&#x153;unconventionalâ&#x20AC;? because the LN FALLS! Because of the unusual behaviour of the LN in this progression, it must be hidden in an inside voice (that is, alto or tenor) where this unusual voiceleading is less obvious. Both chords are complete in this method. Begin by writing a complete V7 chord in A+ in four part harmony. Be sure the LN (3rd of the chord) is in either the alto voice or the tenor voice. Then follow the steps to resolve this chord to I.

a) b) c) d)

root of the I chord must be in the bass voice LN falls a 3rd in the same voice 7th falls by step in the same voice complete the I chord

Notice in this method, the tritone cannot resolve in the usual way because the LN is not rising. This completes Method #3, V7 - I. V7 is complete; all notes are present with the LN in either the tenor or alto. I is complete; all notes of the chord are present. The LN falls a 3rd; the 7th falls. The tritone cannot resolve in the usual way.

PRACTICE EXERCISES Now practice the three different resolutions in different keys. Use a variety of voicings for the V7 chord. Every time a V7 chord is written, the automatic reflex should be to deal with the LN and the 7th, the two notes that form the tritone, that the listener wants to hear resolved. Method #1: Complete/Incomplete Method #2: Incomplete/Complete Method #3: Complete/Complete

A+, D +, F+, B + D+, F +, B+, E + G+, C+, E+, A +

CUMULATIVE EXERCISES Write the following progressions in four part chorale style. Try to incorporate all three methods of resolving V7. 1. B +

I - vi - V - I - ii - V7 - I

2. E+

I - I6 - IV - I6 - vi - ii6 - V7 - I

3. F +

I - I - vi - vi6 - IV6 - ii - V7 - I

4. C+

I - V7 - I - ii - ii6 - V7 - I

5. D+

I - IV - IV - ii - ii - V - V6 - I - V7 - I

6. G +

I - vi - vi6 - ii - ii6 - V7 - I

7. A+

I - I6 - vi - IV - IV - V7 - I - IV - I

8. E +

I - vi - ii - V7 - I - ii6 - V7 - I

SELF CHECKING 1. 2. 3. 4. 5.

Does the LN of V7 always rise or fall a 3rd in an inner voice? Does the 7th of V7 always fall? When V7 is incomplete, is the 5th left out? When I is incomplete, are there three roots and a 3rd? When two chords have their roots a 2nd apart, is the contrary motion principle used?

GOAL #11

_________________________________________________________________________________________________________ Learn to resolve the inversions of V7. REFERENCE PAGES iv v

A Progression Chart to Build On Doubling

LESSON Start by stacking the dominant 7th of G+ neatly in the treble clef in root position. Then write out the series of inversions of this chord.

Under each inversion write the Roman numeral V. Then use Arabic numerals in descending order to represent the intervals between the bottom note and each of the notes above it. The system of showing numerals to indicate intervals above a bass note is called figured bass. Over time the convention became to leave out certain numerals. Here are the correct figures for each inversion. The numerals commonly left out are in parentheses. Check these with the written inversions above. V7 (5) (3) So:

V6 5 (3) V V V V

V(6) 4 3

V(6) 4 2

means root position dominant seventh chord. means first inversion dominant seventh chord. means second inversion dominant seventh chord. means third inversion dominant seventh chord.

Some students like to remember this by backwards counting: 7 6 5 4 3 2 - with an extra 4 thrown in before the 2.

The resolutions of the inversions of V are not difficult if the LN and 7th are treated with care. Write V in Bb+; then follow the steps to resolve it to I.

a) LN must rise (in the bass) b) 7th must fall by step in the same voice c) one voice has a common note d) last voice moves smoothly Write V in E+; then follow the steps to resolve it to I.

a) root of I is in the bass b) LN must rise c) 7th must fall d) common note

Write V in D+; then follow the steps to resolve it to I .

a) b) c) d)

LN must rise 7th must fall, which means that I must be in first inversion common note last voice moves smoothly

In 3rd inversion, the bass note of the dominant seventh chord will be the 7th of the chord. The 7th must fall by step, which necessarily means that I has to be in first inversion. For this reason V always resolves to I . It is not necessary to memorize this because it will automatically happen when the 7th falls as it should. For all the inversions of the dominant seventh chord: * the LN rises * the 7th falls These two notes have very strong tendencies in the chord. They form the tritone which must resolve as the ear expects. Now add V and all its inversions to the dominant column of the progression chart.

PRACTICE EXERCISES Practice writing these resolutions. Vary the voicing as much as possible. Write V - I in A+, D +, F+ and B + Write V - I in D+, G +, B+ and E + Write V - I in G+, C+, E+ and A +

CUMULATIVE EXERCISES In the first two exercises, the bass and chord progression are given. Try to write a soprano part which, for the most part, moves in contrary motion to the bass. Then add the alto and tenor. In the next two exercises, the soprano only is given. Choose a good progression and move the bass, whenever possible, in contrary motion to the soprano before adding the inner voices. Wherever there is a *, use an inversion of V7.

SELF CHECKING 1. 2. 3. 4. 5.

Does every inversion of V7 resolve its tritone? Do the outer two voices move in contrary motion to each other most of the time? Do chords with roots a 2nd apart use the contrary motion principle? If vi is beside V, is the 3rd of vi doubled? If V7 is in root position, is one of the three methods of resolution used?

GOAL #12

_________________________________________________________________________________________________________ Learn the following three progressions: 1. deceptive resolution of V7 2. stationary resolution of V7 (V7 - IV6) 3. rising resolution of V7 (V â&#x20AC;&#x201C; I6) REFERENCE PAGES iv v vi vii

A Progression Chart to Build On Doubling Special Progressions Cadences

LESSON 1. Deceptive Resolution of V7 This progression can be easily tested. On the next staff, try resolving V7 to vi in each of the three methods â&#x20AC;&#x201C; Complete V7; Incomplete V7; LN of V7 falling a 3rd. Work in D+.

Question: Can V7 resolve properly to vi? Answer: Complete V7 works nicely with a doubled 3rd in vi. When V7 is incomplete, one of the voices is not quite so smooth. The LN cannot fall a 3rd in an inner voice because the resulting note is not in the vi chord.

On the next staff, try resolving each of the inversions of V7 to vi.

Question: Can V resolve properly to vi? Answer: Yes, but vi must be in first inversion because the LN in the bass must rise. Again, the doubled 3rd in vi when it is beside V or V7 is the best choice. Question: Can V resolve properly to vi? Answer: Yes, this works with vi in root position (doubled root) or with vi in first inversion (doubled 3rd). vi6 provides a smoother bass line and is in keeping with vi using a doubled 3rd when it is beside V. Question: Can V resolve properly to vi? Answer: No, it cannot. The 7th in the bass must fall and the resulting note belongs to vi, BUT the vi would be in 2nd inversion. This is NOT an option. 2. Stationary Resolution V7 - IV6 This is a very specific progression involving only the root position of V7. Write the complete V7 chord in four parts in E+.

Let the LN rise. The 7th cannot fall because it would fall to a note which is not part of the IV chord. So the 7th remains a common note. It does not move; it is stationary. Now there is one missing note. Which is the better choice â&#x20AC;&#x201C; to double the root of IV or the 5th of IV ? The 5th provides the smoother movement. 56

Now add IV6 to the final I column on the progression chart. IV6 is a replacement for a deceptive vi which in turn is a replacement for I. Think in C+. The note doubled in the I chord is the root, C. The note doubled in the vi chord beside V is the 3rd, C. The note doubled in the IV6 chord in the stationary resolution is the 5th, C. In every case, the tonic note of the key is doubled, which gives stability to the cadence. Note: IV6 can only be chosen from the final column of the progression chart in this very specific situation â&#x20AC;&#x201C; from root position dominant seventh only. To make this clear on the chart draw an arrow from V7 to IV6. 3. Rising Resolution V - I6 Write a four part V in A+. Then write the bass note for the resolution chord, I .

Let the LN rise. Let the 7th fall. Notice when the 7th falls I6 has a doubled 3rd. The usual options for doubling in I6 are the root or the 5th. So to avoid the doubled 3rd, the 7th is allowed to rise. Now I6 has a doubled 5th. The Rising Resolution and the Stationary Resolution have a couple of similarities to help remember them. Both are named for the behaviour of the 7th in the V7 chord. In the stationary resolution, the 7th is stationary. In the rising resolution, the 7th rises. The second similarity is that the chord of resolution is in first inversion and uses a doubled 5th.

PRACTICE EXERCISES Practice writing these special progressions. 1. 2. 3. 4. 5.

V7 V V V7 V

vi in B + and E+ vi in A + and B+ vi in G+ and A+ IV6 in F+ and E + I6 in D+ and C +

CUMULATIVE EXERCISES Now it is time to try some longer exercises involving all the chords and special progressions learned so far. Following are some reminders about approaching a longer exercise: 1. Always name the key on the left hand side under the clefs and key signatures. 2. Choose chords based on the skeleton progression. 3. If the bass is given, the chord choice is limited to root position or first inversion involving the given note. 4. On the other hand, if the soprano part is given there are significantly more choices. Try not to list all the possibilities, but rather to choose a chord that would work well in the progression. It is all about the direction the chords â&#x20AC;&#x153;wantâ&#x20AC;? to move. 5. In choosing chords, always choose the cadence chords first. It could be helpful to work forward and backward and meet in the middle somewhere. 6. Keep in mind the possibility of the soprano and bass moving in contrary motion to each other. 7. In these exercises a square bracket indicates an opportunity to use a dominant 7th chord and resolve it.

SELF CHECKING 1. 2. 3. 4. 5. 6.

In the deceptive resolution of V7 is the 3rd of vi doubled? In the stationary resolution is the 7th of V7 kept as a common note? In the rising resolution is the 7th stepping up instead of down? In an expansion of dominant harmony, does the LN move around but finally resolve? Is the contrary motion principle used to avoid parallels in progressions with roots a 2nd apart? Do the soprano and bass parts generally move in contrary motion to each other?

GOAL #13

_________________________________________________________________________________________________________ Learn two uses of the chord vii : 1. dominant function chord 2. passing chord used in the expansion of I REFERENCE PAGES iv v vi

A Progression Chart to Build On Doubling Special Progressions

LESSON 1. Dominant Function

As an introduction to the chord of , write two triads in the treble clef in E +, V and . If all the notes of these two triads are combined into one chord, the resulting chord is V7.

For this reason is an excellent chord to use in place of V. However, it must be used as a first inversion chord, . All diminished triads contain a diminished 5th between the root and the th 5 . The note not involved in the diminished 5th (that is, the 3rd of the triad) must be in the bass and is also the note that must be doubled. Never double either of the notes that form the tritone. If can substitute for V, then it should be possible to write progressions in D+.

- I or

- I . Try these

Now check the above work. In - I, if the tritone is treated carefully, C rises and G should fall, as though it were the 7th of V7 (remember V + = V ). One voice will be leaping. If the root of I is tripled for smoothness, the result is parallel octaves. The roots of these 2 chords are a 2nd apart, the two chords have no common notes, and therefore lend themselves to parallelism. This is a problem. In - I , if the tritone is resolved, I ends up with a double root and a double 3rd. This is a problem. Here is a possible solution. Imagine that is actually V without the root. In the rising resolution of V to I the 7th is allowed to rise. Similarly in these two progressions involving , the 5th of (equivalent to the 7th of the dominant seventh chord) is allowed to rise. Now write the two progressions again in D+ using this solution.

It may appear that there are still parallels fifths between C G and D to A. On close examination it is clear that one fifth is diminished and one is perfect. In order to be parallel, both fifths must be perfect. There is another solution for to I . Recall that there is a resolution of V in which the LN, hidden in an inner part, can fall a 3rd. If, in to I , the LN (root of ) is in an inner voice and falls a 3rd, AND the 5th of (7th of V7) rises by step, then the progression works well. Now write to I using this solution.

These examples have shown acting as a dominant function chord. Evidently, the simple progression of to the tonic must be handled with care. Now add to the dominant column of the progression chart. The dominant column of the chart now includes several options. As in any column, it is possible to move around within the column. Within the dominant column some chords are more dissonant than others. Always choose to move from less dissonant chords to more dissonant chords. If this is not done, there will likely be an unresolved note. V is less dissonant than or any inversion of V . Therefore V should never come after one of these. Following are some examples.

2. Passing Chord in the Expansion of I (I -

- I)

This is a very specific progression with very specific voiceleading. The two progressions below can be added to the opening tonic column of the progression chart. I - I I - I Write each of these progressions in B + on the staff below. Follow these steps: a) Write the bass line (B , C, D or D, C, B ) b) Write the soprano line which is the reverse of the bass (D, C, B ) c) Remaining two voices step down and then back up again

There really is no other way to write this progression. A few things to notice are: 1. The LN resolves to tonic. 2. The other note of the tritone steps up rather than falling. This is not a concern because the function of in this progression is not dominant. The purpose of here is simply to connect the two I chords. 3. There appears to be parallel 5ths in this progression. However, one 5th is perfect and the other is diminished. This does not constitute parallel 5ths. In order to be parallel, both 5ths must be perfect. 4. The opportunity to use this progression is easy to see. Look for the stepwise motion, up or down, in the bass or soprano, involving the first 3 notes of the key.

PRACTICE EXERCISES Practice writing each of the following progressions. Choose four different keys for each progression. 1.

â&#x20AC;&#x201C;I

3. I -

- I

4. I -

- I

CUMULATIVE EXERCISES Now write the following progressions paying close attention to all the voiceleading requirements. Choose a variety of major keys. 1. I -

- I - IV - V - I

2. I -

- I - ii - V - IV

3. I -

- I - V - V - I

4. I - vi - IV 5. I - I - IV - ii 6. I - V - IV 7. I - ii 8. I -

- I - I -

- I - I - V - I - I (dominant use of

in this progression)

- V - IV - V - vi

SELF CHECKING 1. 2. 3. 4. 5.

Have parallels been avoided when resolving the dominant functioning ? Have stationary and rising resolutions of V been treated correctly? In the expansion of I with , is the mirror voiceleading between soprano and bass used? In the deceptive resolution of V or V , is the 3rd in vi doubled? If the LN and/or 7th (of V ) get passed around among the voices, do they ultimately resolve?

GOAL #14

_________________________________________________________________________________________________________ Learn the importance and usage of the chord of ii and its inversion ii .

REFERENCE PAGES iv v vi

A Progression Chart to Build On Doubling Special Progressions

LESSON The ii chord “wants” to proceed to V. The dominant note in C+ is G. The 5th note up from G is D which is the supertonic note and the note on which the ii chord is built. It is as though ii is a “dominant” of V. Thus the progression is a strong one. Write IV - ii - V in C+.

The ii chord can be intensified by adding a 7th to it, that is, D F A becomes D F A C (C would be the bracketed note on the Key Slide Rule). The 7th (C) is a tension note and needs to be resolved. Just like the 7th in V7, the 7th of ii7 should fall by step in the same voice.

Now rewrite the progression changing it to IV - ii7 - V.

This 7th chord is not a major/minor 7th chord like V7. It is a minor/minor 7th chord, that is, a D minor triad with a minor 7th. This type of 7th chord not only requires the 7th to fall by step, but also requires the 7th to be “prepared”. Prepared means that the 7th (C in this case) must be heard in the previous chord in the same voice. So the 7th of ii7 must be prepared and resolve downward by step all in the same voice. Check that this happened in the last written progression. What if the 7th is not present in the previous chord? Test each chord that can come before ii: IV – yes, C is present vi – yes, C is present I – yes, C is present ii – no, C is not present The chord of ii could come before ii7. In a case like this when the 7th cannot be prepared, it must be approached by step from above. This sounds more serious than it is. If the chords of ii and ii7 are side by side, they share 3 common notes and the fourth note will move exactly as it should, stepping down to the 7th. Now try writing in C+ I - ii - ii7 - V.

Like V7, ii7 can double its root and leave out the 5th when it is in root position. Try this out in G+ with the progression I - ii7 - V7.

Remember when moving from I to ii7 the roots are a 2nd apart so use the contrary motion principle. To avoid a big leap in one voice it works better to double the root of ii7 (A) and leave out the 5th (E). On the treble clef staff below, stack the chord of ii7 in G+. Then write the inversions. Write ii beneath each inversion and beside each ii write Arabic numerals representing the intervals above the bottom note, from largest to smallest.

Notice that the numbers are identical to those used for the inversions of V7. This will be true for any 7th chord. Again, conventionally some of the numbers are left out. ii7 ii6 ii(6) ii(6) (5) 5 4 4 (3) (3) 3 2 The inversions ii and ii are not used very much. On the other hand, ii is a somewhat famous pre-cadential chord. In his chorales, Bach commonly wrote ii - V - I, especially at an important cadence.

Give this progression a try in Bb+. Use a I chord before the ii to prepare the 7th.

Now check the progression for the following points: 1. I - ii uses contrary motion as much as possible 2. All notes of ii are present â&#x20AC;&#x201C; do not leave out the 5th in the inverted chord 3. 7th of ii is prepared 4. 7th of ii falls by step 5. LN and 7th of V resolve properly Finally, add ii and ii to the ii column of the progression chart.

PRACTICE EXERCISES Fill in the chart below. The first one is done as an example.

Key

7th of ii

Possible pre-ii chord

A+

I–AC E

IV – D F A

F+

vi – C E G

ii – C E G

F+

IV – E G B

I–A CE

CUMULATIVE EXERCISES Write these progressions involving ii and ii . Do not worry about soprano/bass mirroring. Just move as smoothly as possible. 1. E +

I - vi - vi - ii - ii - V - I

2. A+

I -

3. D+

I - I - V - I - IV - ii - V - IV

4. B +

I - V - I - ii -

- I - ii - V - vi

- V - I

SELF CHECKING 1. 2. 3. 4. 5.

Is the 7th of ii and/or ii always prepared in the same voice in the previous chord? Does the 7th of ii and/or ii always fall by step? Is the rising resolution of V treated correctly? Is the stationary resolution of V treated correctly? Does the idiom I - I use mirroring between the soprano and bass?

GOAL #15

_________________________________________________________________________________________________________ Learn to recognize and use in appropriate places the following non-chord notes: 1. accented and unaccented passing notes 2. accented and unaccented neighbour notes 3. incomplete neighbor notes (cambiatas) 4. appoggiaturas REFERENCE PAGES v vi viii

Doubling Special Progressions Non-chord Notes

LESSON The progressions so far have been chords moving from one to the next without any decoration. Now it is time to learn to decorate these chords with non-chord notes, that is, notes that do not belong to the chord. Following is a melody with chord symbols. Circle all the notes that do not belong to the indicated chords.

Each circled note shows a different type of non-chord note. Label each circle with the letter of the correct non-chord note from the list below. a) passing note – connects two chord notes that are a 3rd apart – can be ascending or descending b) appoggiatura – there is a leap (usually up) to the non-chord note (on the beat) and then a step down to a chord note (not on the beat) c) neighbor note – steps up or down from the chord note and then back to the chord note d) incomplete neighbor note or cambiata – like an appoggiatura except that the non-chord note is NOT accented (not on the beat) e) accented neighbor note – like a neighbor note but falls ON the beat f) accented passing note – like a passing note but it falls ON the beat The correct order for the answers to the circles is: a, e, f, c, b, d

In four part writing each voice can be considered a melodic line and non-chord notes can be added. Look at the next example to see two more considerations for non-chord notes.

1. Passing notes or neighbor notes can occur more than one at a time in two voices that are a 3rd or a 6th apart. For example, at number 1 on beat 2 of the first bar, the alto and bass each have passing notes that are a 3rd apart. There is another example at number 3. 2. At number 2, there are two passing notes in two different voices, one ascending, one descending. This is a good use of double passing notes provided the two passing notes form the interval of an octave. This is commonly done when two voices are exchanging notes. In this example the alto and bass are trading the notes A and C . Both passing notes are Bâ&#x20AC;&#x2122;s forming an octave between alto and bass. One final note: Avoid combining different types of non-chord notes. For example, do not use a passing note in one voice at the same time as a cambiata in a different voice. Combinations such as this might create a different chord which could alter the progression incorrectly.

PRACTICE EXERCISES J. S. Bachâ&#x20AC;&#x2122;s four part chorales are filled with examples of non-chord notes. Following are five excerpts from the chorales with all the non-chord notes removed. Add non-chord notes and then compare with the actual Bach versions given at the end of the exercises. Note: There are still more types of non-chord notes to learn, so Bach will likely have used some different ones. But hopefully some of the non-chords added in the exercises will match with Bachâ&#x20AC;&#x2122;s! Note: Every fermata indicates the end of a phrase. Never insert non-chord notes between the end of one phrase and the start of the next.

Bachâ&#x20AC;&#x2122;s versions:

CUMULATIVE EXERCISES 1. Fill in the alto and tenor parts. Then add some non-chord notes. Try to use at least three different kinds.

2. Choose a progression for the given bass part. Write the soprano line keeping contrary motion between the two parts when possible. Add alto and tenor parts. Finally, add a few non-chord notes for melodic interest in the voices.

E+ 3. Find a good progression for the given melody. Add the bass part and then the inner parts. Finally, add some appropriate non-chord notes.

SELF CHECKING 1. 2. 3. 4. 5. 6.

Is the LN always rising or falling a 3rd in an inside voice? Are all 7ths falling? (except in special progressions V - I and V - IV ) Is the 7th of ii always prepared or approached by step from above? Is melodic interest developed through the use of non-chord notes? Are two neighbor notes used together only if they are 3rds or 6ths apart? Are two passing notes used together only: a. in 3rds or 6ths? or b. moving in contrary motion and forming an octave?

GOAL #16

_________________________________________________________________________________________________________ Learn proper use and voiceleading for the cadential chord.

REFERENCE PAGES iv v

A Progression Chart to Build On Doubling Chords

LESSON The root word of “cadential” is “cadence” and that is where this new chord will be used – at a cadence. First of all, write the basic triad of I in B + in the treble clef. Follow this with the inversions of the triad. Beside the Roman numeral I below each inversion, write the figured bass numerals for each. Remember, these numerals represent the intervals above the bottom note of the inversion and occur in descending order.

In root position, the 5 and 3 are generally left out. In first inversion the 3 is usually left out and what remains is I . The second inversion of the triad is I , that is, the 5th of the chord would be in the bass voice. The cadential chord will involve a triad in second inversion. Next write a four part arrangement of the chord of V in B +, leaving room for a chord in front of it.

In front of the 3rd and the 5th of the V chord write an appoggiatura, that is the note a step above the chord note. The two appoggiaturas are part of a different chord BEFORE the V chord. To complete the new chord, keep the two Fâ&#x20AC;&#x2122;s exactly the same. The new chord that has been written is a I chord and it is in 2nd inversion. Label the I chord with I . Note: ALL 2nd inversion triads double their bass note which is the 5th of the chord. Note: chords are limited in number and have very specific uses. Not just any chord can be used in 2nd inversion. And not just any situation can properly use a chord. The I chord that has just been found is named a cadential chord. It comes only with V and is considered a chord that decorates V. The decoration specifically must be the downward stepping appoggiatura-like movement between the two chords (I and V). Because an appoggiatura, by definition, is always accented, the I part of this progression must be in a metrically stronger position than the V chord. Write I to V in A+. Here, three appoggiaturas step down to the notes of V .

Now write I to V in D +. This is another possibility for the cadential chord.

Write the following progression in G+.

Notice that the 7th of ii7 cannot resolve immediately. It does not move anywhere though until it can resolve properly. This goes for any sensitive note that needs to resolve. If it cannot resolve immediately, it is acceptable to remain as a common note in subsequent chords until it CAN resolve correctly. One more note regarding the notation for the cadential chord: Instead of writing I - V , the progression is sometimes shown as just a V7 chord, but extra figures show the actual movement of the voices. Remember: V7 is actually V . When the appoggiaturas are added, the figures look like this: V There are two benefits to this notation: 1. It reminds the writer to move all the voices stepwise. 2. It reflects the fact that the true purpose of the I chord is to decorate V. In conclusion, either notation is good: I

- V

I - V should only be notated as two chords. Now add this progression to the dominant column of the progression chart.

PRACTICE EXERCISES 1. Write I to V in C+, F + and D +. 2. Write V

in E+, G + and A+.

3. Write I to V in B+, F+ and A +.

CUMULATIVE EXERCISES Practice writing the cadential chord in the following progressions. Decide on a time signature and rhythm which will cause the I to fall in a metrically stronger position than the V. 1. B+

I - V - IV - ii - I - V - I

2. C+

I - IV -

3. D+

I - IV - ii - V

4. E +

I -

5. A +

I - I - V - I - V

- I - ii - ii - V

- I

- I - IV - I - V - vi - I

SELF CHECKING 1. 2. 3. 4. 5. 6.

Are all the I â&#x20AC;&#x2122;s in a stronger placement in the bar than the Vâ&#x20AC;&#x2122;s? Do the notes of I step down to the notes of V? Is the bass note of I always the doubled note? Check the voiceleading in all special progressions. When the roots of two chords are a 2nd apart, is the contrary motion principle used? When vi follows V, is the 3rd of vi doubled?

GOAL #17

_________________________________________________________________________________________________________ Learn two uses for the chord of iii: 1. tonic use: I - iii - IV OR I - iii - ii 2. dominant use: iii - V or V or V REFERENCE PAGES Key Slide Rule iv A Progression Chart to Build On v Doubling vi Special Progressions LESSON In the treble clef, write the root position triads in E + of I and iii and V.

Notice that iii shares two notes with I and also shares two notes with V. Because of this, iii can be used in the tonic column and in the dominant column of the progression chart. The uses of iii are limited and very specific. 1. Tonic Use of iii In the tonic column it has been noted that I can move to IV (and back to I). With iii, it is possible to â&#x20AC;&#x153;extendâ&#x20AC;? I before moving to IV as in the progression I - iii - IV. In D+ write the progression I - iii - IV by following the steps on the next page.

a) Put in the bass notes b) Move the soprano down by steps starting with the tonic c) Fill in the I chord d) Double the root of the iii chord e). In iii to IV use the contrary motion principle Two comments about good voiceleading might be: 1. The soprano moves in contrary motion to the bass. 2. In iii - IV, roots are a 2nd apart, there are no common notes, and therefore all upper voices move contrary to the bass to avoid parallel 5ths or 8ves. One question about voiceleading might be: Question: The soprano note in the iii chord is the LN of D+ and it is falling! Is this OK? Why or why not? Answer: The strong tendency of the LN to rise is directly related to its dominant function. All LNâ&#x20AC;&#x2122;s written so far have occurred only in chords found in the dominant column. Any key is defined by V - I. To take this statement one step further, any key is defined by the movement of LN to tonic. In the progression above, the LN does not have a dominant function. It is basically a passing note leading to the IV chord and therefore does not need to rise. The tonic use of iii is very specific: The three chords are always in root position. The soprano always moves tonic, LN, submediant. iii always doubles its root. iii - IV always uses the contrary motion principle. Recall the very strong similarity between the chords of IV and ii . Use the Key Slide Rule in D+ to verify that IV doubles the root (G) and ii doubles the 3rd (G). Also the note B is a common note between the two chords. Because of this similarity, IV in the progression I - iii - IV can be substituted with ii . Write I - iii - ii in E +.

Check carefully for parallels in this progression. The parallels are difficult to avoid. Try rewriting the progression changing the doubling of iii to a double 3rd instead of a double root AND using a larger leap in one of the voices. The soprano line cannot change; the bass line cannot change. Move the inner voices carefully. Now add to the opening tonic column of the progression chart: I - iii - IV (moves to ii or V or back to I) I - iii - ii (must move to dominant harmony) 87

2. Dominant Use of iii In the progression iii - V, the iii chord comes just before V and is used in first inversion so that its bass note is the same bass note as V. Write iii - V in A+.

What would be the best note to double in iii ? The 3rd, i.e. the bass note, so that the same note will be doubled in iii as in V. In this progression the purpose of iii is really just an expansion of V. All notes but one are common notes. Now write iii - V in B +.

What other progression is this reminiscent of? The progression I - V is very similar. The purpose of iii is just a decoration of V. Two notes are common and two are stepping down like appoggiaturas the same as in the cadential I chord. When iii is used before V, keep as many common notes as possible. The other voice(s) must step down. The iii must be in a metrically stronger position than the V, again mimicking the cadential I . Remember this is because the notes stepping down are appoggiaturas, which by definition are accented, so they must occur on a stronger beat than the V chord.

There is one more possibility. Write iii - V in C+.

Two voices have common notes; two voices are stepping down; iii is in the metrically stronger position. Now add iii - V, iii - V and iii - V to the dominant column of the progression chart.

PRACTICE EXERCISES Write the following progressions to practice the tonic and dominant uses of the chord of iii.

CUMULATIVE EXERCISES Note: When an exercise includes a special progression such as I - iii - IV and the soprano is not given, immediately sketch in the required soprano part. This is to avoid being caught in a very different range than what is needed. If the required voiceleading is sketched in at the start, it provides a guide for the melody leading up to it. Note: In some of the exercises there are circled notes. Consider these notes non-chord notes. In some of the exercises, non-chord notes are required to be added. Circle any non-chord notes that are added to the exercise.

SELF CHECKING 1. 2. 3. 4. 5. 6.

Does the soprano line in I - iii - IV step from the tonic down to LN and then submediant? Are all voices common notes or stepping down in the progression iii - V (or V or V )? In iii - V, is iii in a metrically stronger position than V? Is the contrary motion principle used when two chords have roots a 2nd apart? Do the soprano and bass parts move generally in contrary motion to one another? Is the 7th of ii or ii always prepared?

GOAL #18

_________________________________________________________________________________________________________ Learn the appropriate use of the following non-chord notes: 1. échappée 2. anticipation 3. suspension 4. pedal point REFERENCE PAGES iv v vi viii xii

A Progression Chart to Build On Doubling Special Progressions Non-Chord Notes Suspensions

LESSON In the following melody with chord symbols, circle all the notes that do not belong to the indicated chords.

There are two kinds of non-chord notes in this melody: 1. Escape notes or échappées can be used when two chord notes are a step apart, stepping down. The escape note steps up from the first chord note and then falls a third to the second chord note. UP a 2nd; DOWN a 3rd. 2. The anticipation is most often used at an important cadence. It is a presentation of the final note “ahead of its time”. There should be 3 non-chord notes circled in the example. The two sixteenth notes in the first bar are echappes. The G in the bar of V is an anticipation of the final tonic G in the I chord. 3. Suspensions require more careful study. A suspension has 3 parts: a) Preparation – the suspended note must first appear as a chord note in the previous chord in the same voice b) Suspension – this note occurs WITH the chord but does not belong to it c) Resolution – the suspended note steps down to a chord note, usually the chord note that it replaced in the chord. Generally the chord does not change as the suspension resolves. 94

Following are three examples of suspensions for study. Example 1

In this first example, the chord of V contains the suspension in the tenor voice. The note C does not belong to the V chord. The preparation is found in the I chord in the tenor. It is the same note, C, and does belong to the I chord. The resolution takes place while still on the V chord. The C steps down to the note of resolution, B. Notice that the note B was not otherwise present in the V chord. It is as if the suspended C took the place of the B momentarily. The notation for this suspension is V . Recall that V on its own is really V , but the convention is to leave out the 5 and 3. When the suspension is used, the 3 comes back but with a 4 before it. The distance between the bass note (G) and the suspended note (C) is a 4th. When the suspension resolves, that interval becomes a 3rd. Example 1, then, is called a 4-3 suspension. The 4-3 suspension works best on a root position chord.

Example 2

In example 2, the chord of V contains the suspension (D) in the soprano voice. D does not belong to the chord of V, so it is a non-chord note. The suspension is properly prepared because the suspended note, D, occurs in the same voice in the previous chord where it does belong to the chord of ii. The suspension steps down to the note of resolution while the other notes of V are held. Notice that the suspended D momentarily replaces the chord note C. There must not be any other C in the V6 chord, which makes it necessary to double the 5th instead of the root. In all suspensions, the note of resolution must NOT be sounding in the chord containing the suspension, except if the note of resolution is in the bass. The notation for this suspension is V . First inversion V chord would normally be written V , but now the 6th above the bass note has been temporarily replaced by the 7th above the bass note. When the suspension resolves, the 6th takes its proper place. Example 2 is called a 7-6 suspension. The 7-6 suspension works best on first inversion chords.

Example 3

Example 3 shows a common triple suspension. It would be found only at a very significant cadence ending an important section or movement. The numbers, as always, indicate intervals above the bass note. Two of the resolution notes (the B â&#x20AC;&#x2122;s) are sounding in the suspension chord, but this is acceptable because the B is in the bass of the I chord. This example also contains a rising suspension, 7-8. This is easy to understand since 7 is the LN which would never step down because of its overpowering need to rise to the tonic! Any one of the three suspensions in example 3 could be used alone, but they can also be used in combinations.

4. A pedal point is a very special type of non-chord note. It occurs as a long sustained note or, less obviously, a constantly repeated note, usually in the bass, while the harmonies change above it. If the tonic note is the long or repeated note, it is called a tonic pedal point. If the dominant note is the long or repeated note, it is called a dominant pedal point. Pedal points can occur on other scale degrees and in other voices, but these situations are much less frequent. The indication to identify a pedal point is ____________________________________ ____________________________________ The solid line continues for the length of the pedal point. To analyze the chords over a pedal point consider whether the pedal point note belongs to each chord or not. Each chord is identified with its root position notation because the sustained low pedal note changes the sound of the inversions. Look at the following example:

The excerpt, from the second movement of Mozartâ&#x20AC;&#x2122;s piano sonata K330, is in f minor, with the repeated note F in the left hand being the tonic pedal point. Could the ii chord in the first full bar be labeled a ii chord instead of just ii? The pedal note is the 7th of ii . The 7th of ii must fall and ultimately, the F does resolve downward. So, the ii could be labeled ii over this pedal point.

Analysis examples do not always show chord writing in four parts. Sometimes the notes must be considered in groups. Look at the following Clementi excerpt:

This is two part writing, not four part writing. The left hand is playing broken chords, but for analysis purposes the notes can be imagined as solid chords. The first bar left hand is a C major triad in the key of C major, which is the chord of I. In bar 3, the right hand solid would form vii (BDF). The left hand at bar 3 forms solid from the bottom CDF. The C is the pedal point. D and F belong to the vii chord.

PRACTICE EXERCISES 1. Here are a few more Bach chorale excerpts stripped of their non-chord notes. Try to find opportunities to add various non-chord notes to them. Try to include: passing notes accented passing notes neighbour notes accented neighbor notes suspensions

incomplete neighbor notes (cambiatas) appoggiaturas chapp es (escape notes) anticipations

Note: Every fermata indicates the end of a phrase. Never insert non-chord notes between the end of one phrase and the start of the next. Add non-chord notes and then compare with the actual Bach versions given at the end of the exercises.

Here are Bachâ&#x20AC;&#x2122;s versions:

100

101

2. For each excerpt below name the key and indicate the pedal point.

102

103

3. In these musical excerpts, the pedal point is shown. Analyze all the chords under the pedal point and name them. All circled notes are non-chord notes.

104

105

106

CUMULATIVE EXERCISES Fill in the alto and tenor parts. Then add some non-chord notes. Try to use at least three different kinds.

Choose a progression for the given bass part. Write the soprano line keeping contrary motion between the two parts when possible. Add a few non-chord notes for melodic interest in the voices.

107

Find a good progression for the given melody. Add the bass part and then the inner parts. Finally, add some appropriate non-chord notes.

SELF CHECKING 1. Is the LN always rising or falling a 3rd in an inside voice? 2. Does the 7th of V rise with a doubled 5th in I ? 3. Is the 7th of V stationary when it resolves to IV with a doubled 5th? 4. Is the 7th of ii always prepared or approached by step from above? 5. Is melodic interest developed through the use of non-chord notes? 6. Are all suspensions prepared in the same voice in the previous chord? 7. Is the resolution note of each suspension NOT sounding in the suspension chord except in the bass voice?

108

GOAL #19

_________________________________________________________________________________________________________ Learn correct use of the following three second inversion ( ) chords: 1. Passing 2. Auxiliary (or Neighbouring) 3. Arpeggio REFERENCE PAGES iv v x

A Progression Chart to Build On Doubling Chords

LESSON So far the only second inversion chord described for use has been I - V, also called V This is a very specific use of I with very specific voiceleading indicated by the Arabic numbers in the second method of notation. All useable chords are similarly specific and may never be used arbitrarily or outside of the progressions described in this goal. 1. Passing Chord This chord can occur in four ways, all of which are the same in voice movement. The four progressions are: a. I - V - I b. I - V - I c. IV - I - IV d. IV - I - IV The first two simply expand the chord of I. Write them in the tonic column of the progression chart. The other two expand the chord of IV and should be added to the IV column of the progression chart. The voiceleading in a passing situation is reminiscent of the progression I - vii the soprano mirrors the bass.

- I where

Write I - V - I in A+. Be sure the soprano sings the same notes as the bass but in reverse order. Also recall that ALL chords double their bass note, that is, the 5th of the chord. The rest of the notes will take care of themselves.

109

Check the voiceleading in the above work: a) bass moves A B C b) soprano mirrors with C B A c) one voice has a common note, E, all the way through d) last voice moves in a neighbouring note fashion â&#x20AC;&#x201C; A G A All four passing progressions work in exactly the same way. If a given voice shows the first three notes of the key in a row, it is an opportunity for I - V - I or the reverse. If the three notes in a row are the 4th, 5th and 6th notes of the key, it is an opportunity for the other passing , IV - I - IV , or the reverse. The passing progression is one of those situations where it is a good idea to sketch in the mirroring voice early on in the exercise to help gauge the range. Here is an example of what can happen if the chord voicings have been in the wrong range leading up to the chord.

110

Start by sketching in the mirrored notes.

Then begin in a suitable range to arrive in the correct place.

2. Auxiliary (or Neighbouring) Chord This type of chord is again used for extending a harmony. There are two specific uses for the auxiliary chord. a) I - IV - I is used to extend the tonic chord. It is commonly used to extend the I of a perfect cadence and is referred to as a plagal extension. This progression can therefore be added to both tonic columns on the progression chart.

111

Write I - IV - I in E+. Notice that the bass note is the same for all three chords.

Check the voiceleading: i) bass is common note all the way through ii) one other voice has a common note throughout iii) the other two voices move like auxiliary (or neighbour) notes Rewrite the above progression using long notes to replace the repeated common notes. This is commonly found with the Auxiliary progression. Now write in A + a full perfect cadence followed by the plagal extension. Use complete V to incomplete I in the perfect cadence.

What problem is encountered if the I of the perfect cadence is not complete? It is impossible to maintain the auxiliary note movement. So it is important that the I chord be complete for this progression to keep its smooth voiceleading. Rewrite the A + progression above using complete V to complete I. Remember that the LN will have to fall a 3rd in an inner voice for this progression to work. b) V - I - V is used to extend the dominant triad. Voice movement is the same as in the other auxiliary . An indication for use of the auxiliary progression would be a long or repeated tonic or dominant note in one of the voices. This progression should now be added to the dominant column of the progression chart.

112

3. Arpeggio Chord Notice that all chords so far have been built with the chords of I, IV or V. There will never be a chord built on any other degree of the scale. If ii or vi or iii or vii ever appear, something is wrong! The arpeggio can only be used with any one of the primary chords, that is, I, IV or V. An arpeggio chord should have a different inversion of the before and after it. For example, any of these progressions would be fine: I - I - I I - I - I I - I - I I - I - I These examples use the chord of I. The same can be done using the chord of IV or V. Try writing V - V - V as smoothly as possible in G+.

It is possible for the voices to jump around in the arpeggio progression. This is because all the notes are notes of the same chord. The greater movement could provide more melodic interest. Try this approach in writing IV - IV - IV in F+. Keep in mind the soprano moving in contrary motion to the bass.

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One idiomatic use of the arpeggio I is shown in the next example. Notice that only the bass is moving. This is a common idiom in short dance movements at an end-of-section cadence.

There is another option for the chord that follows the arpeggio chord. This chord can be one that involves a bass note a step up or down from the arpeggio bass note. It can be a root position or first inversion chord provided the progression still makes sense. Write IV - IV in D+.

The IV has a D in the bass. The possibilities for the next chord are IV, IV OR a chord involving E or C . An E bass note could be:

a) the chord of ii in root position, which is a good choice of chord following IV or b) vii , a dominant function chord, also a good choice after IV

The C bass note could be:

a) vii in root position, but diminished triads are not used in root position, so this is not a legitimate possibility or b) V in first inversion, a very acceptable progression

Choose one of the above possibilities to complete the progression. To add the arpeggio ’s to the progression chart, write ‘Arpeggio I ’ in the opening tonic column. Write ‘Arpeggio V ’ in the dominant column. Write ‘Arpeggio IV ’ in the subdominant column. In the final I column write ‘I - I - I (arpeggio )’.

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There are several clues which can indicate an opportunity for a particular chord. This chart gives the main indicators for each .

Name of

Indicators

Passing

stepping up or down in soprano or bass 1-2-3 or 3-2-1 4-5-6 or 6-5-4

Auxiliary

long tonic note long dominant note neighbouring note movement

Arpeggio

leaps between notes of the same chord leap in the bass voice followed by a step up or down

Cadential

end of a phrase, downward step from a note of the tonic chord to a note of the dominant chord (provided the tonic is in a metrically stronger position than the dominant chord)

PRACTICE EXERCISES 1. Practise writing passing chords in the following keys: B+ I - V - I C+ IV - I - IV F+ I - V - I E+ IV - I - IV 2. Practice writing auxiliary chords in the following keys: (Sometimes use long notes instead of repeated notes.) G+ I - IV - I D+ V - I - IV - I Ab+ V - I - V F#+ V - I - V - V - I

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3. Suggest a possible chord for each example. Give the key, the chord symbols and the name of the chord.

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CUMULATIVE EXERCISES The following exercises incorporate all chords and progressions studied so far. Reminders: 1. With progressions that use very particular voiceleading, sketch in the notes that have to be in a certain place so that you can shape the phrase toward them. 2. It often works well to work backwards for a short distance, and then from the beginning, to settle on a good progression. 3. Add a few non-chord notes to each exercise. 4. Any given notes that are circled are non-chord notes.

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SELF CHECKING 1. 2. 3. 4. 5. 6.

Is the 5th , that is the bass note, of every chord doubled? Do the soprano and bass mirror each other in the passing progression? Does the plagal extension always start with a complete I? Does the cadential always have stepping down movement in the moving voices? Does the I in the cadential occur in a metrically stronger position than the V? When stepping away from the arpeggio , does the chord after the make a good progression?

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GOAL # 20

_________________________________________________________________________________________________________ Learn to write a four part descending 5ths sequence. REFERENCE PAGES Any pages from i to xiii. LESSON On the following bass clef staff, write the key signature for F major and the note F.

Then write a 5th below F, which is B . Down another 5th gives E, but take E up an octave to avoid getting too low. Notice that the E is now up a 4th, the inversion of down a 5th. Continue alternating down a 5th and up a 4th until a return to the note F has taken place. Notice these are not necessarily perfect 5ths. All the notes belong to the key of F major. If triads were built on each of these notes in the key of F+, the progression would look like this: I - IV - vii - iii - vi - ii - V - I Rewrite the series of notes building triads on each note and labeling the chords.

Just glancing at this progression, a few problems leap out. 1. vii is in root position – usually not acceptable 2. iii is not in one of its two, and only two, different functions 3. the LN (E) is not rising – it is not even falling nicely – it is leaping! Despite all these apparent “downfalls”, this is a sound progression. More than that, it is wellloved and very acceptable to the ear. Because of the pattern, it is predictable and any “errors” are immediately forgiven by the ear. This type of progression is called a sequence. There are other different sequences, but this one is perhaps used most extensively.

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When this sequence is written in four part harmony, each voice must proceed in a pattern just as the bass voice has done. Here is one possibility:

Another â&#x20AC;&#x153;errorâ&#x20AC;? has crept in. In order to keep the pattern, the root of vii has to be doubled creating a doubled LN. This is not a problem. If there is a sequence, everything is good! There are lots of ways to make the sequence more interesting. Variants of the sequence are possible by using inversions of some of the chords. This does not change that the sequence is a descending 5ths sequence because the roots of the chords are still descending 5ths. There are two possibilities for using inversions and keeping the sequence: a) I - IV - vii - iii - vi - ii - V - I b) I - IV - vii - iii - vi - ii - V - I Note that there must be a pattern in the naming of the chords and in the movement of each voice. Choose one of the above possibilities and write the progression in four parts in E +.

Another way to add interest to the sequence is by using non-chord notes. Look at the following sequence. Circle all the non-chord notes. The alto contains a passing note in a repeated pattern. The soprano contains a 9-8 suspension on every other chord. The note of resolution of the suspension IS sounding in the chord containing the suspension, but it is in the bass voice which is acceptable.

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Now write a descending 5ths sequence in E+. Try to use an escape note and a passing note in the pattern.

Sequences are fun to work with and great to play and listen to.

PRACTICE EXERCISES Practise writing the descending 5ths sequence as indicated below. Try for some creativity! 1. I - IV - ………… in the keys of D + and A+ 2. I - IV - …………. in the keys of G+ and B + 3. I - IV - …………. In the keys of E+ and F+

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CUMULATIVE EXERCISES In all of the following exercises, the circled notes indicate non-chord notes. Circle any further non-chord notes that are written.

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SELF CHECKING 1. 2. 3. 4. 5. 6.

Is the LN handled carefully in all dominant function chords? Do 7ths of V and ii always fall? Do any special progressions follow the voiceleading requirements? Are sequences observed in every voice? Do the soprano and bass voices move in contrary motion to each other most of the time? Does each exercise end with a cadence?

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GOAL #21

_________________________________________________________________________________________________________ Learn to apply a dominant to the chord of V in three ways: a. V of V b. V of V c. vii of V Learn two alternate methods of notating the applied dominant: V/V - V OR V - I V V /V - V

V - I V

vii / V - V

vii

- I V

REFERENCE PAGES Key Slide Rule v Doubling vi Special Progressions xiii Major Key Progression Chart LESSON It is very clear that the chord of V wants to move to the chord of I. It is V - I that really defines a key. It is V - I that the ear needs to hear to confirm a sense of key. This new applied dominant is a dominant functioning chord which is not followed by I, but rather by V. This will sound like a quick visit to the key of the dominant. Take a closer look. Set the Key slide Rule for G+. V in G+ is DF A. If we apply a dominant to DF A, it is as if DF A, for a very short time, becomes a I. Move the key slide rule so that DF A is I. Now, V is AC E. So in G+ music, the listener can be oriented to G+ but then, for a brief two chords, hear V - I in D+ before returning to G+. Here are three ways the chord symbols for the applied dominant can be written in G+. AC E

DF A

V/V

V (D+)

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Below is the applied dominant in G+ translated into notes.

The V / V chord is dominant function. As the third type of labeling shows, the music is momentarily in D+. Therefore, V / V has a LN (C ) and it must resolve (to D). The next chord, V, is actually V in G+, so it also has a LN (F ) which must resolve (to G). An important thing to remember is that while the temporary key is at play, the key signature is still the home key, so an accidental will be necessary. In the above example, the temporary key is D+ which needs one more sharp so that V / V will require an accidental (C ). Start by using the Key Slide Rule to help spell the following applied dominants and name the temporary key. Be sure to include all accidentals in the spelling.

Home Key B

Chord

Spelling

V/V V/V

FAC

V/V F+

Temporary Key

V/V V/V

DF A

Notice three things: 1. The spelling of V / V always begins on the supertonic of the home key. 2. The LN of the temporary key always requires an accidental. The new LN is always the 3rd of the new V chord. 3. The accidental creates chromatic movement. This chromatic movement must occur in the same voice. 127

An applied dominant can also take the form of V / V. An applied dominant does not have to be in root position. The first inversion of V is fine and all inversions of V are also good. Just remember to think in the new key when resolving the applied dominant. Then switch back to thinking in the home key. Write the following progression in G+. Resolve V / V thinking in D+. Resolve the following V thinking in G+.

Try one more in B +. Consider the following points when writing the progression: 1. ii leaves out its 5th to make a smoother movement from I. 2. Always keep chromatic movement in the same voice. 3. V / V is also incomplete â&#x20AC;&#x201C; leave out the 5th so that the following V will be complete. 4. The resolution of the 7th of ii is delayed, but it remains a common note until it does resolve.

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Now try applying vii , which is another dominant function chord found in the dominant column of the Major Key Progression Chart. Write the following D+ progression. Again consider each of the points below when writing the progression. 1. There is no chromatic movement in this progression. 2. The temporary key is A+. 3. Resolve vii - I in A+. Be watchful for parallels because the roots of the two chords are a 2nd apart. 4. The I in A+ is in turn a V chord in D+.

One final situation for the applied dominant, is V / V moving to V . In C+ write V / V - V. Be sure that the second chord is complete. This can be done by writing an incomplete V / V, or a complete V7 / V with the leading note falling a 3rd in an inside voice.

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If the V (that is, I in G+, V in C+) became a V , the note F natural would need to be added. Keeping in mind that it is necessary to keep chromatic movement in the same voice, it seems that the best place for the F natural would be following the F in the first chord. Rewrite the progression using the F natural. This creates a V incomplete (without its 5th) which works well. BUT, the temporary LN (F ) is not rising! It is falling a chromatic semitone. This is a common voiceleading for the LN especially as harmony becomes more complex and more chromatic. This is a good time to stop and review situations where the LN does NOT rise. 1. V (complete) - I (complete) LN can fall a 3rd if hidden in an inside voice. 2. I - iii - IV Soprano line is tonic falling to LN falling to submediant. LN does not have a dominant function here. 3. LN falls a chromatic semitone in V of V . 4. Sequence of descending 5ths

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PRACTICE EXERCISES Now write in four parts the following exercises. Though there are three types of applied dominant labeling, only one is given in each exercise. Eventually one method will become most comfortable, but at the start it is important to understand all three. 1. Write and resolve each applied dominant.

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2. Fill in the chart. The first line is an example.

Key

Chord

Spelling

Temporary Key

New LN

Bass Note

C+

V /V

DF AC

G+

B+

vii /V FACE

V /V

C D

D+

EG BD

BDF G+

C+

3. Carefully write each progression with an appropriate time signature. a)

A+

I - V /V - V - I

D+

IV - V / V - V - vi

F+

ii - V - I - I V(C+)

D+

IV - V of V - IV (stationary resolution)

E+

ii - V of V - I

C+

ii - V of V - I

G+

I - V /V - V - I

B+

vii - I - vi V(F +)

E+

ii - vii

of V - I

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CUMULATIVE EXERCISES In these exercises remember that whenever an accidental is present, it probably indicates an opportunity for an applied dominant. Also take time to add some non-chord notes to each exercise.

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SELF CHECKING 1. 2. 3. 4.

Does the new leading note in each applied dominant resolve to its tonic? Has the necessary accidental always been added to the applied dominant? Is chromatic movement kept in the same voice? If the new dominant is applied to a 7th chord, is the new LN falling a chromatic semitone?

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GOAL #22

_________________________________________________________________________________________________________ Learn to modulate from a major key to the dominant major key. REFERENCE PAGES v vi vii viii x xii xiii xv

Doubling Special Progressions Cadences Non-Chord Notes Chords Suspensions Major Key Progression Chart Modulation to the Dominant

LESSON Modulation is the movement in a piece of music from one key to another. Most music does not stay in the same key throughout, and the modulation to the dominant key is very common. In the previous goal, the dominant key was visited very briefly by introducing an applied dominant. An applied dominant to a quick temporary tonic is called tonicization. This is not considered a modulation because it is only two chords long. A modulation to the dominant, on the other hand, would move to the dominant key and stay there for a longer time. To make a modulation to the dominant there are three conditions: 1. Establish the original key, that is, state some kind of dominant to tonic to define the key. 2. Pivot chord 3. Establish the new key, again by stating dominant to tonic to define the dominant key. Pivot Chord A pivot chord is a chord which exists as exactly the same chord (spelled identically) in both the tonic and dominant keys. For example: C+ home key I CEG G+ dominant key IV CEG I in C+ has the exact same spelling as IV in G+ so it is a good pivot chord. Another example: C+ home key ii DFA G+ dominant key V DF A These two chords do not match because F does not match F . This cannot be used as a pivot chord.

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In the treble clef in B + write out all the triads in the key with their Roman numeral symbols underneath. Use accidentals, NOT a key signature.

B + (home key) Now do the same for F+ which is the dominant key of B +.

F+ (dominant key) Match up triads that are the same and enter them in this chart. The first pair is already entered.

B+ I

F+ =

= = =

These are all possible pivot chords when modulating from B + to the dominant key, F+. The favourite Baroque pivot chord for modulating to the dominant is vi = ii. The pivot iii = vi is the least effective of the pivot chords in the chart. The pivot should make sense in the B + progression which precedes it AND in the F+ progression which follows. For example: Bb+ I - vi - ii - V - I - vi F+ ii - V - I - IV - I This shows the common symbol to indicate a pivot chord. In B +, the vi pivot follows nicely after I; in F+, the ii pivot leads nicely to V.

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Now write this progression modulating from B + to F+.

One very important thing to remember about modulation is that having moved to a new key, the original key signature is still in place. Therefore accidentals will be necessary. Check the above modulation for E when in the key of F+. PRACTICE AND CUMULATIVE EXERCISES All special progressions and good voiceleading can be practiced at the same time as modulation with pivot chords. Follow the directions and use the recommended reference pages as a review. Each question should be about four bars long with an appropriate time signature. 1. Modulate from A+ to E+. Include a rising resolution, a deceptive cadence and three nonchord notes. 2. Modulate from D + to A +. Include I - vii

- I , an arpeggio chord and an anticipation.

3. Modulate from G+ to D+. Include a passing chord (with IV), a stationary resolution, and an appoggiatura. 4. Modulate from E + to B +. Include I - iii - IV, a supertonic 7th chord in 1st inversion (ii ) and some neighbour notes. 5. Modulate from F+ to C+. Include a plagal extension, V complete to I complete and an chapp e. 6. Modulate from B+ to F +. Include iii - V, a cadential chord and a cambiata. 7. Modulate from G + to D +. Include an applied dominant, a suspension and some passing notes. SELF CHECKING 1. 2. 3. 4.

Is the home key (original key) established with dominant to tonic? Is the pivot chord spelled exactly the same in both keys? Is the new key (the dominant key) established with dominant to tonic? Are accidentals used in the new key to accommodate the change in the key signature? 137

GOAL #23

_________________________________________________________________________________________________________ Learn the similarities and differences of writing progressions in the minor key. REFERENCE PAGES ii v vi vii viii x xii xiv xviii

Triads on Scale Degrees Doubling Special Progressions Cadences Non-Chord Notes Chords Suspensions Minor Key Progression Chart Use of III and VII in the Minor Key

LESSON Begin by writing the ascending c harmonic minor scale in the treble clef using accidentals rather than a key signature.

Next build triads on each scale degree assuming the harmonic minor. Name each triad with a Roman numeral reflecting its quality. (Check by comparing Triads on Scale Degrees, page ii in the Reference Pages.) These are the chords used in the minor key. But there are also some alternatives. If the LN (B ) is not raised, some new chord qualities occur. III becomes III, V becomes v and vii becomes VII. The flat in front of the VII shows that the root of the chord has been lowered. (If VII was written without the , it would be spelled BD F .) Write the three new chords involving the lowered LN. (When the LN is lowered, it is called the subtonic.) Write them first without a key signature, then WITH a key signature.

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There are three more alternatives in the minor key that occur when the raised 6th from the melodic minor scale is used. ii becomes ii, iv becomes IV and VI becomes vi which is not used. Write these three new chords involving the raised 6th. Again, write these both without and with a key signature.

It is very important to remember to use the necessary accidental for the raised 7th in the minor key, unless an alternative chord involving the subtonic is intended. Most of the Minor Key Progression Chart is like the Major Key Progression Chart but with the harmonic minor chord qualities. However, sometimes the alternative chords are used. 1. Use of III and III The progression I - III - iv uses major III, not III . This makes sense because the LN is not necessary in the progression since there is no dominant function. On the other hand, in the dominant use (III ), the augmented chord is used, since the raised LN is essential in dominant harmony. 2. Use of v Minor v is used in the tonic column after i and then proceeds to a predominant chord. Again, there is no dominant function in this chord; it is just an expansion of the tonic area. 3. VII and III relationship Spell III in d minor Spell VII in d minor Spell I in F major Spell V in F major

___________ ___________ ___________ ___________

So, VII to III in d minor is the same as V to I in F major which is the relative major of d minor. It is like using an applied dominant V / III to III. Or it could be labeled V - I F+(III)

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It is logical that the voiceleading for VII to III must be as though writing V to I in the relative major key. Write VII to III in f minor. This progression should be treated as though it is V - I in A +.

4. Minor ii and major IV These two chords are used to avoid the melodic interval of an augmented 2nd. The harmonic minor scale contains an augmented 2nd between the 6th and 7th notes of the scale. If any voice in the four part writing has the 6th followed by the 7th (or reverse), the resulting augmented 2nd in that voice must be avoided. In the following example, ii is used instead of ii to change the augmented 2nd to a major 2nd.

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5. III moving to inversions (not root position) of V The Minor Key Progression Chart shows III in the tonic column and indicates that it can move to an inversion of V . Start by writing III in b minor and try moving to V .

Notice that A is in one voice in the III chord and A is in a different voice in the V chord. This is called a cross relation. A cross relation is to be avoided and is easy to avoid. Simply keep any chromatic movement in the same voice. In this case, if the A of III was in the bass, it would be III which is unheard of. Therefore, III simply cannot move to V . Now write III in b minor again and try moving to V . Then try moving to V .

In these two progressions, it is easy to keep A and A in the same voice. 6. VII moving to inversions (not root position) of V The tonic column of the Minor Key Progression Chart shows VII following I, and indicates that VII then can move to an inversion of V . Experiment with VII moving to inversions of V . First write VII in f minor and try to move to V .

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The bass shows the chromatic movement from E to E . This is good, except if VII has a doubled root. While one E moves chromatically, the other one is in cross relation. The only way to solve this problem is to double a different note in VII. In most major triads the root is doubled. A second choice is usually the 5th. So rewrite VII to V with the 5th of VII doubled. This works well. Now write VII again in f minor and try to move successfully to V .

This will never work with VII in root position because the E in the bass will always create a cross relation with E in a different voice. As a possible solution put VII in first inversion and try again. Still there is a cross relation if the root of VII was doubled. Try changing the doubling to a double 5th in VII. This is a fine solution.

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Lastly try to move from VII to V . From previous experience it is safe to guess that it will be best to use VII in first inversion with a doubled 5th.

Just a few more notes about the minor key: 1. The 7th chord on ii is a diminished triad plus a minor 7th. This chord quality is called halfdiminished, indicated as ii . Of course, if the 7th is added to minor ii, then it is labeled ii just as in the major key. 2. Assume the harmonic minor except where the alternative chords are used. This means remembering the accidental to indicate the raised LN in the harmonic minor scale. 3. The final tonic chord in minor exercises can be a major I chord. This is often indicated as I (the 3rd of the I chord is raised to change the quality to major). The final major I in a minor key is called a Tierce de Picardie. 4. ii , being a diminished triad, should only be used in first inversion. 5. There is a possibility of another melodic augmented interval, the augmented 4th, occurring. It must be avoided like the augmented 2nd. It usually appears around the LN, so be on the lookout for it.

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PRACTICE EXERCISES It is time to write some minor progressions to test out some of these intricacies of the minor key. Each progression is followed by some discussion about good voiceleading.

III - V : V - i:

roots are a 2nd apart so move all voices in contrary motion to the bass to avoid parallels like V - I in the relative major, B +; the A in VII is the LN of B + and must rise chromatic movement is F to F in the same voice rising resolution just like in major keys

ii : ii - V: v: V:

no root position of diminished triads like iv - V; use contrary motion principle uses B uses B

I - VII: VII - III:

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ii - V : I :

use raised 6th beside the LN to avoid the augmented 2nd D major triad needs accidental F

i - VII: VII - V :

roots a 2nd apart; watch for parallels keep chromatic movement in the same voice; double 5th of VII

i - III - iv: III - V: ii - III :

uses major III uses augmented III roots a 2nd apart; use contrary motion principle 145

ii : V - VI:

prepare and resolve 7th double the 3rd of VI in the deceptive cadence

IV - V : V - iv :

IV uses raised 6th beside the LN to avoid augmented 2nd stationary resolution as in the major key

146

CUMULATIVE EXERCISES Following are some exercises in minor keys. Remember that good voiceleading and good progressions are the same as in major keys. Watch for augmented 2nds (and 4ths) and cross relations. Remember the accidental for the raised 7th. Consult the reference pages as needed.

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SELF CHECKING 1. 2. 3. 4. 5. 6.

Do the Roman numerals reflect the correct chord quality? Is any chromatic movement kept in the same voice? Have melodic augmented 2nds and 4ths been avoided? Is ii used only in first inversion? Is VII to III treated as V to I in the relative major? Has the accidental to raise the LN been used, except in III, v and VII? 148

GOAL #24

_________________________________________________________________________________________________________ Learn appropriate pivot chords to modulate: a) from minor to relative major b) from minor to dominant minor REFERENCE PAGES v vi vii viii x xii xiii xiv xvi xvii

Doubling Special Progressions Cadences Non-Chord Notes Chords Suspensions Major Key Progression Chart Minor Key Progression Chart Modulation to the Relative Major Modulation to the Dominant Minor

LESSON In a major key, the typical modulation is to the dominant major key. In a minor key, the typical modulation is either to the relative major or to the dominant minor. In the treble clef write out and name the triads in the key of g harmonic minor. Include VII and III. Use accidentals, not a key signature.

Now do the same for B +, the relative major of g minor.

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Match up triads that are exactly the same in the above two keys and enter them in the chart below. gi

B+ =

= = = = =

These are all possible pivot chords when modulating from the minor to the relative major. It is easy to make this modulation since both keys have the same key signature. All the possible pivot chords are quite commonly used except ii = vii . A reminder of the three conditions for effective modulation: 1. Define the home key, that is, state some kind of dominant to tonic harmony in the starting key. 2. Pivot chord 3. Define the new key, again by stating dominant to tonic harmony in the new key. Now write out and name the triads in the treble clef for d harmonic minor, which is the dominant minor of g minor. Include III and VII and use accidentals rather than a key signature.

Find all the possible pivot chords between g minor and d minor (the dominant minor) and enter them in the chart below.

= =

All three are good pivots for modulation from a minor key to its dominant minor key. 150

PRACTICE EXERCISES Fill in the blanks. 1.

i in a minor = ___________ in C major.

III in b minor = I in _________________.

____________ in b minor = V in D major.

ii in A + = ____________ in f minor.

_________ in E major = VI in c minor.

VII in e minor = III in _________________.

_______ in e minor = i in b minor.

iv in f minor = ii in _______________.

V in _______________ = VII in f minor.

10. _______ in e minor = VI in b minor. 11. III in ___________ = I in F major. 12. ii in C major = iv in ____________________. 13. IV in G major = VI in _______________. 14. _______ in c minor = vi in E +. 15. VII in d minor = _________ in a minor.

CUMULATIVE EXERCISES IMPORTANT NOTE: It is necessary to emphasize the utmost importance of keeping track of the key! With the minor key comes the need for an accidental for the raised 7th note of the scale. With modulation comes even more accidentals to accommodate the changes of key. Always take time to check for appropriate accidentals. Again, modulation with pivot chords provides an excellent opportunity to practice all special progressions and good voiceleading, this time particularly in the minor key. Follow the directions and use the recommended reference pages as a review. Each question should be about four bars long with an appropriate time signature.

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1. Modulate from c minor to E +. Include the progression i - III - iv, a cadential chord, and a suspension. 2. Modulate from f minor to A+. Include the progression i - vii two different non-chord notes.

- i , a rising resolution, and

3. Modulate from e minor to b minor. Include ii , a neighbouring chord on V, and two appoggiaturas. 4. Modulate from f minor to c minor. Include the progression i - III - V , the progression III - V, and two different non-chord notes. 5. Modulate from c minor to E+. Include the progression i - VII - V , a stationary resolution and an anticipation. 6. Modulate from b minor to f minor. Include the progression VII - III, a plagal extension and two chapp es. SELF CHECKING 1. Is the home key (original key) established with dominant to tonic? 2. Is the pivot chord spelled exactly the same in both keys? 3. Is the new key established with dominant to tonic? 4. Are accidentals used in the new key to accommodate the change in the key signature? 5. Are accidentals used in minor keys to indicate the raised 7th? 6. Have melodic augmented 2nds and 4ths been avoided? 7. Have cross relations been avoided, particularly in progressions involving VII or III moving to an inversion of V ?

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GOAL #25

_________________________________________________________________________________________________________ Learn to notate root/quality chord symbols. REFERENCE PAGES xix

Root / Quality Chord Symbols

LESSON The chord symbols that use Roman numerals with figured bass numbers to show inversion are called functional chord symbols. Functional chord symbols tell the chord’s place within the key. There is another method of naming chords called root/quality chord symbols. In this method, chords are named according to the root of the chord and the quality of that chord (major, diminished etc). There is no reference to key. The root/quality method of naming chords is a very practical one. Guitar players read this notation, and given a tune with root/quality symbols, a lead sheet, an accompaniment can easily be improvised on the spot. Write out the triads for E + in the treble clef. Use accidentals, not a key signature. Name the chords with functional symbols.

A major triad is named by simply using a capital letter naming the root of the chord. For example, the root/quality chord symbol for an F+ triad would be simply “F”. A minor triad is named by using a capital letter naming the root of the chord plus the lower case letter “m”. For example, the root/quality chord symbol for a g minor triad would be “Gm”. An augmented triad is named with a capital letter for the root of the chord plus the letters “aug”. For example, the root/quality chord symbol for a C augmented triad would be “Caug”. A diminished triad is named with a capital letter for the root plus the letters “dim” or the symbol “o”. For example, the root/quality chord symbol for a D diminished triad would be “D dim” or “D ”. Now name the E + major triads above with their root/quality chord symbols.

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Next, write out the triads for f minor in the treble clef. Do not use a key signature and include all the alternative chords. ( III VII v ii IV I ) Name each triad with both kinds of symbols, functional and root/quality.

The 7th chords studied so far are V and ii in the major key and V and ii in the minor key. Write with accidentals in the treble clef in D+, V and ii . Write with accidentals in the treble clef in b minor, V and ii .

Every dominant 7th chord is made up of a major triad and a minor 7th. The root/quality system names these with a capital letter for the root with a “7” beside it. For example, the root/quality symbol for V of E+ would be “B7”. The chord ii is a minor 7th chord. Every minor 7th chord is made up of a minor triad and a minor 7th. The root/quality system names these with a capital letter for the root followed by an “m” and then a “7” beside it. For example, in the root/quality system, ii in the key of A + would be written “B m7”. The chord ii is called a half-diminished 7th chord. Every half-diminished 7th is made up of a diminished triad and a minor 7th. The root/quality system names these with a capital letter for the root followed by the symbol “ 7”. For example, in the root/quality system, ii in the key of c minor would be written “D 7”. Now name the chords written in D+ and b minor above, with their root/quality symbols. To indicate inversions in this new system, write the chord symbol followed by a slash and the name of the bass note. Here are some examples: 1. D7 (DF AC) in first inversion would be D7/F 2. Fm (FA C) in second inversion would be Fm/C 3. G 7 (GB D F) in third inversion would be G 7/F Note: Think of the cadential as two chords, I and V or V . In e minor, the root/quality symbols for these two chords are Em/B and B7.

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PRACTICE EXERCISES Following are some chord progressions written in functional symbols with the key given. Rewrite each progression with the appropriate root/quality symbols. 1. A +

__________________________________________________________ 2. g -

_______________________________________________________________ 3. B+

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____________________________________________________ Now try the reverse. Following are some chord progressions written in root/quality symbols with the key given. Rewrite each progression with the appropriate functional chord symbols. 4. c -

B /D

G 7/D

__________________________________________________________________ 5. D +

D /A

G /B

E m7

___________________________________________________________ 6. f -

A aug

C7/B

Fm/A

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CUMULATIVE EXERCISES In the following exercises, write each chord progression in both a) functional chord symbols and b) root/quality chord symbols Remember that an accidental is probably: a) the raised 7th in the minor key or b) an indication of moving to a new key or c) an indication of an applied dominant A new key can be visited in two ways: a) an applied dominant for a short visit or b) a pivot chord to remain in the new key for a longer time Any circled note can be considered a non-chord note. Add additional non-chords to the four part writing when each exercise is complete. 1. Use a pivot chord where marked. Also use a delayed 7th in a cadential progression.

2. Find opportunities to use:

VII - III, a neighbouring chord and an applied dominant.

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3. Use pivot chords where marked to modulate to the dominant minor and then back again. Also use a supertonic 7th chord and the progression III - V .

4. This exercise stays in c minor throughout. Try to include in the progression a passing chord, the stationary resolution of V and the chord III .

5. Pivot to the relative major where marked. Also use an arpeggio and a 4-3 suspension. In the last bar include an escape note and an anticipation.

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SELF CHECKING 1. 2. 3. 4. 5. 6. 7. 8.

When two chords have roots a 2nd apart, has the contrary motion principle been used? Is the correct voiceleading used for all special progressions? Has the accidental for the raised 7th in the minor key been used? Do the 7ths of the dominant 7th chord and the supertonic 7th chord fall by step? Is the 5th (bass note) of every chord doubled? In V - vi, is the 3rd of vi doubled? In the cadential chord, is the I in a metrically stronger position than the V? Does every exercise end with a legitimate cadence?

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CHORALE STYLE

_________________________________________________________________________________________________________ REFERENCE PAGES vii xiii xv

Cadences Major Key Progression Chart Modulation to the Dominant

Until now exercises have been relatively short and focused on the particular goal being studied. Now the exercises will be longer, in chorale style, using all the harmonic language studied. This section will include three chorales with only one voice given. For each chorale, a step by step working procedure is given describing how to complete the work in four parts. A chorale is a sacred hymn tune. J. S. Bach wrote hundreds of chorales. He was a church musician and the chorales were written to set sacred texts to music. Each phrase of a chorale ends with a fermata. These are pauses at logical points in the text. Every fermata must be a cadence point. So when given a chorale to harmonize, the very first step is to decide the cadence chords at every fermata. Chorales at this level will be restricted to major keys, so remember the typical modulation to the dominant. There could be one or more cadences in the dominant key. What would be an indicator that the key of the chorale has changed? 1. An accidental, which is the LN of the new key, will be a clue to check for modulation. The same accidental could also simply mean a quick applied dominant. So examine the music to see if it seems to stay in the new key or if that accidental just happens once and then disappears. 2. The leap of up a 4th or down a 5th in the bass voice is often a helpful sign of key. These intervals usually mark a perfect cadence. Conversely, up a 5th or down a 4th may indicate an imperfect cadence. In each of the next three chorales four steps will be discussed to guide the harmonization: Keys and Cadences Progression and Bass Line Alto and Tenor Parts Non-Chord Notes

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Bach Chorale No. 6, Christus, der ist mein Leben

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The key is F+, so set the Key Slide Rule to F. But always keep in mind the possibility of the dominant key, C+. The main cadence chords in C+ would be a G major triad (V) and a C+ triad (I). Also look for B , the new LN. 1. Look at the first cadence point, that is, the first fermata. This cadence could be perfect in F+. Bach would probably not let all the voices stand still on half notes, so perhaps two chords of the dominant could be used, for example V, then V . Put in the chord symbols and the bass notes as shown before proceeding to the next cadence point. The fermata is always indicated above the soprano voice AND below the bass voice. At the second fermata the cadence still seems to be F+, perfect. Add bass notes, chord symbols and fermata as shown. Because the half note occurs as the fermata note this time, it is best to have all four voices as half notes. In the third phrase, the beginning and ending notes are C. The D at the cadence belongs to the V chord in C+. There are no B â&#x20AC;&#x2122;s as a sure sign of C+, but there are also no B â&#x20AC;&#x2122;s, so a cadence in C+ is a strong possibility. Again, the half note D would likely include two chords or at least two inversions of the same chord. Bach commonly wrote the progression ii - V - I, which works well at this cadence. D is the root of ii and the 5th of V . Add the chord symbols and make a note of C+ under this cadence. The final cadence is surely perfect in F+. Complete this cadence in the same way the others were done. 2. The next step is to find a progression and bass line for each phrase. Rather than try to think of all the possible chords that could be used for a given melody note, think instead of what would make a logical progression and see if it works. Work from both ends of the phrase. For example, in the first phrase, what logically comes before the cadence chord V is ii or IV. The beginning chord will likely be I. Choose chords and inversions based on a good progression and a good bass line in relation to the soprano. Complete phrases 1 and 2, soprano and bass. At the beginning of phrase 3 is the time to start thinking about the modulation to C+. Modulations work best near the beginning of the phrase. Sometimes even the last chord of the previous phrase can act as the pivot to the new key. In this case, the last chord of phrase 2 , I in F+, could also be named IV in C+, thus being a great pivot chord. Another option would be the first note in phrase 3 could be V in F+ and also I in C+. Later in phrase 3 are other opportunities for pivot chords, but earlier on is better â&#x20AC;&#x201C; it allows more time for C+ to be well established. Place the pivot on the first note of phrase 3. Note that the pivot does not have to be in root position. Be sure to use B when writing in the key of C+. Fill in the rest of the progression and bass line. Notice the first three notes of phrase 3 in the soprano suggest two special progressions, I - vii - I or I - V - I. Though these are not the only possibilities for harmonization, it makes sense to use the opportunity. In phrase 4 it is necessary to pivot back to F+ and the sooner the better because there is a B coming up very soon. The first note of phrase 4 (A) could be harmonized IV in C+ which is also I in F+ and then everything is in order to finish up in F+. Complete the progression and bass line for phrases 3 and 4.

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3. The third step is to fill in the alto and tenor voices. All that has been decided so far with regard to the progression and the bass line, is not written in stone. If necessary, it can be adjusted as the parts are completed. Again, remember to use B when writing in the key of C+. 4. The last step is to add some non-chord notes. Passing notes and neighbouring notes are easy to add and very effective if they are moving in two voices in 3rds or 6ths. The chord notes can also be shifted to create accented passing or neighbouring notes. Suspensions were very popular with Bach. Recall that a 4-3 suspension works best on a root position chord. A 7-6 suspension works best on a first inversion chord. Other possible suspensions are 9-8 and 7-8. Now the chorale is done. Following is the Bach version. Undoubtedly, Bachâ&#x20AC;&#x2122;s realization of the chorale will be somewhat more sophisticated. But a comparison of the two can be a good learning experience.

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Bach Chorale No. 27, Es spricht der Unweisen Mund

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1. This chorale is in B +. The first cadence is written in because it is an applied dominant which has not been studied. The two chords of an applied dominant and its temporary tonic can always form a cadence. In this case the cadence sounds like V - I in E +. The rest of the cadences are either in B + or in the dominant key of F+. Phrase 2 cadence is the down a 5th interval which indicates a perfect cadence in B +. The half note will need to be dressed up by movement in the other voices. This is an excellent opportunity for the cadential because I and V have the same bass note. Write in the chord symbols. Phrase 3 cadence is also a descending 5th, this time indicating F+. Write in the chord symbols with a special indication that this is F+. Phrase 4 looks like another descending 5th, back in B +. But the last three bass notes of this phrase also look like the arpeggio I idiom. Bach would not likely use the arpeggio I here. In the chorales he usually changes chords on every quarter note. Therefore, the better cadence will be V - I in B + on the last two beats. Add chord symbols for this cadence. The final cadence would again do well with the cadential . Another option would be to use the chord of V and then revoice it for the second beat. A third option would be to use a suspension on the V and then resolve the suspension on the second beat. This option is shown in four parts on the working copy of the chorale. It shows an ornamental resolution of the 4-3 suspension. B resolves to A, which is followed by a lower neighbouring note and then back to the resolution note. This all occurs on V and it is common to slide in the 7th of V just before the final I chord. This is a cadential “formula” that is worth mastering. 2. Next a chord progression is needed. With the bass given, the options are not too many. Do one phrase at a time. Take note of the following hints for choosing chords: a) Phrase one includes B – C – D which lends itself easily to I - vii

- I or I - V - I .

b) Phrase 2 includes A to B which should be recognized as LN to tonic, meaning dominant chord to tonic chord. c) Phrase 3 contains the “LN” A but it is not rising, so it must NOT be the LN. This is an indicator that the key has changed. F+ is the new key and the first note of phrase 3 could be the pivot chord. I in B + is equal to IV in F+. d) The second note of phrase 3 could stay on IV (in F+), but always try to change chords over a barline. The note in question could be ii , but ii must move to V and the next chord cannot be V. That leaves V in F+ and the B is then the 7th of V, which falls as it should. e) Eighth notes usually mean one of the pair is a non-chord note. Decide which of the two will belong to the selected chord and be sure that the other one is a legitimate non-chord note. f) The start of phrase 4 sounds an E almost immediately, so a quick pivot back to B + is needed. The last note of phrase 3 could be I in F+ which is V in B +. This takes care of the modulation quickly. g) Bar 7 is a bit tricky. If the first beat is I and the second beat is I and the third beat is I, that is a lot of I, and not very “Bach-like”. Try changing chords on both of the first two eighth notes. On beat two consider the D as an accented passing note. Change chords again on both eighth notes of the fourth beat.

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With all the progressions in place, try for a soprano line that works well with the bass line. Donâ&#x20AC;&#x2122;t forget the soprano fermatas while working on this step. Also remember to use E in the key of F+. 3. With the outer voices complete, it is time to add middle voices making any necessary changes along the way. 4. Finally, add non-chord notes. Always double check for accidentals when the key has changed. Again, it will be interesting to compare to Bachâ&#x20AC;&#x2122;s version which follows.

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Bach Chorale No. 310, Machâ&#x20AC;&#x2122;s mit mir, Gott, nach deiner G tâ&#x20AC;&#x2122;

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This chorale is in E+. A logical modulation would be to the dominant key of B+. So watch for an added A as a signal for a possible applied dominant or modulation. 1. At the first fermata the implied cadence is imperfect in E+. Notice the leap down a 4th indicating a move from tonic to dominant. The second cadence comes after an A# has been introduced. The roots of the two cadence chords in the bass move down a 5th, indicating a move from dominant to tonic, a perfect cadence in B+. Notice the half note in the soprano with two notes in the bass. Most of the time Bach changes chords on every quarter note, so here the half note will be part of two different chords. Cadence three looks exactly like cadence one, imperfect in E+. And of course, the final cadence will be perfect in E+. Notice that the first beat of the last bar steps down to the note belonging to the V chord. This stepping down motion is an opportunity for a cadential chord. Recall that in a cadential progression, all the notes (except the common note(s)) step down to the notes of the V chord. 2. The second step is to decide on a progression. Here are a few suggestions: a) In the first full bar, the bass line suggests either one of the following two idioms: I - vii - I or I - V - I The clue is the bass line stepping up from the tonic. b) On the first two beats of bar 2, the bass rises a semitone (LN to tonic). Leading note to tonic always suggests dominant harmony to tonic harmony. The soprano note on the first beat is the 7th of V and it is falling as it should. c) Bar 3 requires a pivot to B+. The first time that A is heard, it should be harmonized by a dominant function chord in B+. There is no A in the bass part on beat one, so that must be in E+. Beat two in E+ could be V or vii . In B+ it would be iii (not likely) or I (not likely). So if beat 2 is harmonized dominant in E+, it must move to tonic on the first half of beat 3 and the second half of beat 3 is dominant in B+. Therefore, by a kind of process of elimination, the pivot chord must be the first half of beat 3 which is I in E+ equal to IV in B+. d) The descending E+ scale that starts in the soprano, bar 5 is a sure sign that B+ did not last long. The pickup to bar 5 is an E+ chord and can serve as the pivot back to E+. The pivot chord is IV in B+ equal to I in E+. e) Bar 5 contains the E+ descending scale in the soprano. In particular, the LN (D ) falling should bring the special progression I - iii - IV to mind. However, I does not work because of the C bass note. One explanation for this situation would be: Beat one looks like vi, not I. vi can substitute for I because there are two common notes between the two chords. If the 3rd of vi (E) is doubled, it is the same as doubling the root of I (E). So the progression vi - iii - IV is acceptable in place of I - iii - IV. f) At the final cadence with the cadential , try out Bachâ&#x20AC;&#x2122;s trick of delaying the 7th. The chord notation would look like this: V So instead of quarter notes, the 8-7 voice will be a dotted quarter note followed by an eighth note. 168

3. With the progression complete, the next step is to fill in any missing bass or soprano notes. Then add alto and tenor parts. Double check for the accidental (A ) in B+. 4. Finally, add some non-chord notes. A special note about the text in chorale style: If there are two syllables on the same pitch, there must be two notes of that same pitch written to accommodate the syllables. Conversely, if there is only one syllable, there cannot be a repeated note on that syllable. This will be easier to see in an example.

Incorrect – the bass needs two B’s to accommodate the two syllables.

Incorrect – the bass must have only one B written since there is only one syllable of text.

Now check the last chorale to see that repetition of notes fits the text. Then take a look at Bach’s version on the next page.

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CHORALE EXERCISES Following are several chorales in major keys. Remember the four step procedure for completing them in chorale style. 1. Decide on the cadence at each fermata. Identify key and chords. Add bass notes and fermatas where needed. 2. Create a good progression for each phrase. Fill in any necessary soprano and/or bass parts. 3. Add alto and tenor parts with good voiceleading. 4. Add some non-chord notes to develop the style.

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HARMONIC ANALYSIS

_________________________________________________________________________________________________________ REFERENCE PAGES xix

Root/Quality Chord Symbols

The study of harmony so far has included:       

the core progression special progressions voiceleading tendencies of chords tendencies of sensitive notes within chords various non-chord notes cadences

Now it is time to learn to recognize these harmonic building blocks in celebrated works of many of the world’s favourite composers. This analysis practice should also contribute in a very practical and valuable way to:  

the efficient learning of new pieces improved sight reading skills

Harmonic analysis exercises require the labeling of all chords with correct inversions. The second requirement is the circling and classification of all non-chord notes. It is important to realize that there will not always be four voices in the examples for analysis. But, the core progression of chords will always be apparent. NOTE: All exercises in this section should be analyzed using both functional and root/quality chord symbols. Functional chord symbols are traditionally written below the staff. Root quality chord symbols are usually found above the staff.

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1. Broken Chords This first example is a short Mozart excerpt.

The first thing to notice is that this is not four voice harmony. There appear to be only two voices, but three voices at bars 7 and 8. Therefore, in this kind of work it is often necessary to gather “horizontal” groups of notes together to form a “vertical” chord. The left hand groups of 16th notes can be gathered into triads. Imagine the triads as solid to name each chord and its inversion. In bar 7, beat 1 could be gathered into a C+ triad. But beat 2 implies two different chords, so for consistency of harmonic rhythm within the bar, I - I - I should be indicated. This also shows the idiom I I more accurately. With the chords in place, attention can now be given to the right hand melody. It is easy at this point to circle all the non-chord notes. When that is done, go back and classify them. A shorthand method is often used for this purpose. passing note accented passing note neighbour note accented neighbour note cambiata appoggiatura échappée suspension anticipation

pn acc pn nn acc nn camb app ech sus (or susp) ant

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The tiny notes in this excerpt must be included in the analysis. Sometimes in playing and learning, these small notes are collectively referred to as appoggiaturas, but a close look at each one shows different situations. For example, in bar 1 the tiny F is actually an accented passing note. However, the F in bar 7 is a suspension. The question of accented or not accented can be tricky. Use the time signature as guide. 2/4 time is 2 beats in a bar. A passing or neighbouring note at the beginning of beat 1 or beat 2 would be considered accented. Thus, the D in bar 1 is not accented. Here is another example for clarity. In 9/8 (compound time) there are 3 beats in a bar, so accented non-chord notes can occur on 1, 4 or 7 of the 9 eighth notes. Following are exercises for analysis using the idea of grouping notes of broken chords together. Notice that the broken chords can be in either hand. Analyze all the chords and non-chord notes in the following excerpts. Analyze using both functional symbols below each line of music and root/quality chord symbols above.

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2. Tempo Affects Harmonic Rhythm The next two excerpts have to do with tempo. When the tempo is very fast, the chords will change less frequently. When the tempo is very slow, the chords will change more frequently. The frequency of chord changes is referred to as harmonic rhythm. The next two examples show first a very fast tempo and then a very slow tempo along with suggestions for analysis of the music.

In bar 1, ALL the notes of the right hand belong to the D+ I chord. The left hand is all D with a bunch of C neighbour notes. The first C neighbour note is definitely not accented. But what about the second one? It falls on beat 2 which could indicate an accented neighbour note. But with this presto tempo the performer would probably feel one in a bar making all the neighbour notes feel unaccented. The whole bar can simply be labeled I. This first bar sets up an harmonic rhythm of one chord per bar. Moving to bar 2, the first beat looks like I and the second beat looks like V. This demonstrates how V is really all a V chord that is decorated by the I . The G in this bar, when it does not have the accidental written beside it, may distract the reader into thinking V (AC EG), but the G is indeed sharp throughout the bar, and is a neighbour note. When a non-chord note carries an accidental (that is, it is not a note in the key), it is referred to as a chromatic non-chord note, in this case a chromatic neighbour note. Another spot to notice is bar 4, E and G in the right hand. This seems to be a bar full of I except for these two notes. Notice that they are both present in the previous chord and they both step down to notes of the I chord. So they both fulfill the requirements of suspension, a 9-8 suspension and a 4-3 suspension at the same time. 186

At the other end of the tempo spectrum, the following excerpt has an Adagio marking. Many more chord changes can be expected.

The middle voice is all chord notes rocking back and forth and the bass quarter notes determine the inversions of the chords. So far the harmonic rhythm is two chords per bar. But in bar 3, the chords begin to change on every eighth note. The slow tempo gives lots of room for changes of harmony. At the end of bar 3 there is a D natural to be accounted for. Whenever an accidental is introduced, three possibilities should come to mind: a) a chromatic non-chord note b) an applied dominant, that is, a quick V - I in the dominant key c) a modulation for a longer visit to the dominant key In this case, the excerpt ends soon after the D natural so it may be a modulation to the dominant key of E + as the music continues on, or it could just be V /V - V for a quick V - I in E +. Either analysis would be correct. Following are exercises for analysis requiring consideration of harmonic rhythm relative to tempo.

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3. Chorale Style Some analysis questions are in chorale style. This type of analysis is probably most familiar, solved by vertical analysis of each chord. The chords usually change on every quarter note beat, but sometimes they change on the eighth note, and occasionally only on the half note.

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4. Various Score Types Some analysis questions are not simply piano scores. In some of the previous analysis exercises, a vocal part or a violin part have been included. But some analysis excerpts could be written in string quartet score or even in an open vocal score. In any of these cases, it is important to include ALL the notes in the analysis.

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5. Minor Key Analysis Some analysis will be in a minor key. Give extra attention to the chord qualities. An example follows:

The presence of E indicates the key of f minor rather than A +. The chords seem to change with each quarter note in the left hand. This makes the harmonic rhythm two chord changes per bar. Taking into account the chord qualities in the minor key, the first chord is i and it is followed by ii . The seventh chord on ii happens three times in this excerpt. The third time is in bar 5 in second inversion, a much less common inversion for this chord. An explanation might be that this inversion is used to maintain the bass line, a falling f natural minor scale. It is very important to include the notes of the vocal line in the chordal analysis. In bar 3 in the voice part the A does not belong to the chord of ii . However, the A is present in the previous chord and falls by step to the chord note G which makes it a 7-6 suspension. The voice part includes some passing notes in bars 4 and 5. Most of the passing notes are not accented, but the E on the second beat of bar 5 would be accented. Because of the moderately slow tempo, the middle C passing note in bar 5 might also be considered accented. 197

Bar 4 contains a strong E presence in the left hand. If this were an E , there would be an augmented 2nd between it and the following D . This E is not functioning as a leading note. It can be explained in one of two ways. First, it could be called a passing note between i and VI. Second, it could be considered as the 7th of the i chord, forming i on the second beat. Of special note in bar 6 in the piano part is the F, which is not a note of the V chord. This F creates a 4-3 suspension, prepared in the previous chord and falling by step to the E in the final chord. Following are more minor key examples for analysis.

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6. A Mixture of Analysis Exercises The next section of exercises contains all different kinds of excerpts using all the harmonic vocabulary learned in the goals of this workbook. When analyzing, keep in mind the following reminders: a) b) c) d) e)

Consider where chords â&#x20AC;&#x153;wantâ&#x20AC;? to move. Account for all the notes, that is, circle and label all non-chord notes. Consider tempo when deciding harmonic rhythm, that is, how often the chords change. Label minor key chords carefully. The qualities are different than major. Always analyze with both functional AND root/quality symbols.

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STRUCTURAL ANALYSIS

_________________________________________________________________________________________________________ REFERENCE PAGES vii xx xxi xxii

Cadences Baroque Dances Related Keys Structural Analysis Forms

In structural analysis there are three requirements: 1. Identify the form. 2. Mark the structural phrasing. 3. Identify cadences and key at the end of every phrase. Pieces for structural analysis will be short Baroque dances. There is a summary of the characteristics of Baroque Dances in the reference pages (page xx). FORMS There are four possible forms: 1. symmetrical binary 2. asymmetrical binary 3. rounded binary 4. ternary Binary forms, as their name implies, have two main sections, A and B. The two sections are easily delineated by repeat signs. Each of the two sections is repeated. In symmetrical binary, the A and B sections are of equal length. In asymmetrical binary, B is longer than A. In rounded binary, the B section contains a restatement of A, but not the whole of A because of the key situation. The key situation is this: In binary form, if the A section starts in a major key, it usually ends in the dominant key. If the A section starts in a minor key, it usually ends in the relative major key or the dominant minor key. Then the B section moves back to the home key. SO, in rounded binary, when A comes back, it must stay in the home key because the piece is going to end with this. The idea is that A comes back in the B section, BUT it is altered so that it remains in the home key. Ternary form is an ABA form which makes it look like rounded binary. However, in Ternary form, when A comes back it is the entire A just as it was the first time. In order for this to happen, the key situation must be different in ternary form. The first A must end in the home key, because it will actually be the end of the piece. The B section will be in the contrasting key (dominant major, relative major or dominant minor). Then comes a complete restatement of A either as a Da Capo al Fine or the A section written out again in full. For a synopsis of the four forms see page xxii of the Reference Pages. 213

STRUCTURAL PHRASING It is necessary to develop a “feel” for where the phrases end. Here are a few tips: 1. Common phrase length is four bars. 2. Tap out the rhythm – sometimes the rhythm has resting points to mark the phrase end. 3. When a piece begins with a pickup, every phrase within the piece will have the same length of pickup. 4. Look for rhythmic similarities at the starts of phrases. 5. Look for idioms such as: a) arpeggio idiom b) octave leap on the dominant note moving to tonic in the left hand c) cadential formula where the final note is the tonic

Note: Structural phrases are often marked with square brackets instead of the curved line. KEYS/CADENCES At the end of every phrase there will be a cadence which must be labeled with the chord symbols, type of cadence and key. Recall that typically in binary form, the A section modulates from major to the dominant major or from minor to the relative major or dominant minor. The B section then begins in the new key and modulates back to the home key. In ternary form the A section remains in the home key and the B section is in the contrasting key. These are the most significant modulations. However, in these short dance pieces the composer may decide to visit a greater variety of keys. The closely related keys are found on either side of the home key on the circle of 5ths. For example, if the home key is E+, then other closely related keys are A+ and B+. Also included would be all the minors for these three major keys, that is, f -, c - and g -. Take a different kind of look at this. Write out the triads for E+ in the treble clef using a key signature. Name these triads with root/quality symbols.

These symbols are in fact the names of the closely related keys to E+ with the exception of D (or D dim) which is not the name of a key! Another example: If the home key is f-, then closely related keys on either side of f- on the circle of 5ths are c- and b -. Also included would be all the major keys for these three minor keys, that is, E +, A + and D +. 214

To take a closer look, write out the triads for f natural minor in the treble clef using a key signature. Name these triads with root/quality symbols.

These symbols are in fact the names of the closely related keys to f- with the exception of G (or Gdim) which is not the name of a key. To summarize, a key picture for E+ looks like this: A+ f-

E+ c-

B+ g-

A key picture for f- looks like this: E+ c-

A+ f-

D+ b-

A piece may modulate easily from the home key to any of the other keys in its key picture. In structural analysis, all keys in the relevant key picture should be considered. For a review of possible cadence types see page vii in the Reference Pages. Following are some examples of short baroque dance forms with the structural analysis explained.

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1. Decide the form. A quick count of the bars shows A=B in length. The A theme never comes back within the B section. So the form is Symmetrical Binary. 2. Decide the key of the piece. Three sharps means A+ or f -. The ending note of melody is an A. The full final chord is an A+ chord in root position. A+ is clearly the home key. 3. Draw the key picture for A+. D+ A+ E+ bfcAll these keys are possible cadence keys. 4. Mark the structural phrasing with square brackets. There are clear indicators of phrase ends in this example. a) the rhythm stops on a dotted half note at phrase ends except in phrase 1(quarter note, half note, both on the note B) b) on the dotted half note at cadences 2 and 3 the left hand plays an arpeggio idiom c) the two A section phrases begin with the dotted eighth-sixteenth rhythm as a pickup d) the two B section phrases begin with two eighth notes as the pickup 5. Name each cadence with key, chords, and type of cadence. Often these short dance movements have only two parts, so only two notes to determine a chord. Chords named in this way are called implied chords. But in this Bourree there are usually three notes to help determine the chord. Cadence #1: The first phrase ends on an E chord. This E chord could be V in A+ or the music may have moved to E+. The lack of a D eliminates the E+ possibility. So this cadence must be imperfect in A+ ending on V. Now what comes before the V? The bass plays an octave leap on A with notes of the A chord in the other part. So the cadence is imperfect (I - V) in A+. Cadence #2: The final bar of the A section is an E chord. There is a D nearby, an indicator of E+. E+ is also the expected key for the ending of the A section. The leap of up a 4th in the lowest voice at this cadence indicates V - I, a perfect cadence. Cadence #3: The final chord this time is a D+ chord. D+ is one of the closely related keys. There is a G natural near this cadence which is another indicator of the key of D+. The bass leaps down an octave and up a 4th, indicating a perfect cadence in D+. Cadence #4: Here is the end of the piece, an extremely likely place for a perfect cadence in the home key. This cadence shows the very common cadence indicator and pattern: octave leap on the dominant note then moving to the tonic.

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1. Decide on the form. A quick bar count determines an asymmetrical piece. Is it just asymmetrical or is it rounded? Nowhere does the opening of A return, so the form will be asymmetrical binary. 2. Decide the key of the piece. With one flat in the key signature, the possibilities are F+ or d-. The final chord is a clear F+ triad, so the key will be F+. 3. Draw a key picture for F+. C+ F+ B+ adgCadences could occur in any of these keys. 4. Mark the structural phrasing with square brackets. In this piece the cadences are evident because of the bass pattern of octave leap down and then up a 4th to the tonic. This pattern will also be helpful in naming the cadences. 5. Name each cadence with key, chords and type of cadence. Cadence #1: The octave leap pattern defines F+ perfect. Cadence #2: The G octave leap with

C+ perfect.

Cadence #3: An E has been introduced and correspondingly the left hand pattern shows B +. Cadence #4: Back to C+ Cadence #5: Final cadence is in the home key, F+, and the left hand pattern has been constant throughout the piece. Here are a couple more observations about this piece: a) When first and second endings are involved, the phrasing and cadences for both endings must be shown. b) Each phrase in this dance seems to have a stopping point midway through the phrase. It would be possible to name cadences at these points, but two bars is simply not long enough for a phrase. Also these mid-phrase cadences are not as strong because they do not use root position for both chords of the cadence.

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1. Decide on the form. B looks much longer than A. Does A come back in the B section? If so, is it a complete and exact repetition of A? A does come back at the pickup to bar 17 but it changes part way through. So the form is rounded binary. 2. Decide the key of the piece. No sharps or flats in the key signature means C+ or a-. The final cadence jumps up a 4th from G to C implying a perfect cadence in C+. Also, the last two melody notes are leading note to tonic in C+. 3. Draw the key picture for C+.

F+ dAll these keys are possible cadence keys.

C+ a-

G+ e-

4. Mark the structural phrasing with square brackets. This Menuet begins with four sixteenth notes as a pickup to the first phrase. Guessing a four bar phrase means the second phrase would start with the same rhythm – four sixteenth notes. Phrase three after the repeat sign begins with the same pickup rhythm. Again count four bars and the same four-note pickup occurs. At this point comes the return of A and the two final phrases which are rhythmically identical to the first two phrases of the dance. 5. Name each cadence with key, chords and type of cadence. Cadence #1: In this piece there are usually 3 notes to determine each cadence chord. The last chord of phrase one is clearly a C+ I chord. What comes before I is most frequently V and in this case the notes G B _ F form a dominant 7th chord in first inversion. Cadence #2: The likely key to end the A section is the key of the dominant, G+. Phrase 2 has clearly introduced F ’s suggesting G+. The final bass notes of the section are octave D’s (V in G+) to octave G’s (I in G+). The octave D’s are harmonized with B stepping down to A in the upper voice. This is the motion of a cadential chord which should be included as part of the cadence since its function is to decorate V. The cadence should be marked V - I, perfect in G+. Cadence #3: Phrase 3 starts with B ’s and C ’s which seem to indicate d- , one of the keys in the key picture. But the end of the phrase arrives again on a C+ chord (I ). The previous chord is G B _ F, again the dominant 7th this time in 3rd inversion, V . Cadence #4: The bass part in this phrase is nothing but G. This prolonged G suggests a pedal point. There are no F ’s to make it a tonic pedal point in G+, so it must be a dominant pedal point in C+. The final bass G in the phrase shows the other two voices stepping down bringing the cadential chord to mind. So the final chord is V . This is considered only one chord, not two. The previous chord is also I . I on its own would not usually be a cadence chord. However, the entire last 2 bars of this phrase seem to be I . Therefore it would be safe to call the cadence imperfect in C+ with the two chords labeled I - V . Cadence #5: Same as cadence 1. Cadence #6: This is clearly perfect in the home key. But look at the chord before the V. It is I and everything is stepping down. This I should be included as part of the cadence because it is actually part of the V. The cadence should be marked V - I, perfect in C+.

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1. Decide on the form. The giveaway here is the D.C. al Fine at the end which takes the performer back to the beginning for an exact repeat of the A section. This is an obvious ternary form. 2. Decide the key of the piece. The key signature indicates C+ or a-. To check the ending remember that the end of the piece is the end of the A section, NOT the end of the B section. Section A ends with an arpeggio idiom on A suggesting a-. There are also frequent G â&#x20AC;&#x2122;s (the raised 7th of a-) in the A section. 3. Draw the key picture for a-

dF+ All these keys are possible cadence keys.

aC+

eG+

4. Mark the structural phrasing with square brackets. If the first phrase is four bars long, it ends with an arpeggio idiom in the left hand and a melodic cadential idiom in the right hand. The second phrase starts with a short melodic and rhythmic motivic sequence and ends after four bars at the Fine. The right hand comes to a stop at the end of the third phrase with the left hand continuing to connect to the fourth phrase. The final phrase of the B section ends at the Da Capo al Fine. 5. Name each cadence with key, chords and type of cadence. Cadence #1: The bass arpeggio idiom reinforces an E+ chord. This is the chord of V in asuggesting an imperfect cadence. The chord before V involves D and A (implying the chord of iv) or perhaps B and D (implying the chord of ii ). Either of these possibilities would be correct since both form an imperfect cadence. Cadence #2: Normally, the expectation at the end of the A section of a piece in a minor key, would be a cadence in the relative major or the dominant minor. But in a ternary form, the end of the A section is the end of the piece. This must be a perfect cadence in a-. Cadence #3: In ternary form, the B section is where the contrasting key is explored. During phrase 3 there are no longer any G â&#x20AC;&#x2122;s, nor are there any other accidentals. This suggests the key of the relative major, C+. The final bass note of the phrase is G which steps up in a scale-like manner landing on the tonic C at the start of phrase 4. The G would indicate a V chord in C+. The chord before the V really only contains an F. This could imply the chord of IV or the chord of ii . Either would be acceptable, forming an imperfect cadence in C+. Cadence #4: The bass at the end of phrase 4 leaps from G up a 4th to C, which is extended in the arpeggio idiom. This forms a perfect cadence in C+.

One example of each form has been presented with many suggestions of things to look for to help decide key, length of phrases and cadence chords. Now work through the structural analysis of each of the following simple dance movements. Be sure to indicate: a) Key (also draw the key picture) b) Form c) Capital letters showing the sections d) Structural phrases e) Key of each cadence f) Chords of each cadence g) Type of each cadence 223

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Da Capo al Fine

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IDEAS FOR DEVELOPING MELODIC MATERIAL

_________________________________________________________________________________________________________

REFERENCE PAGES xxiii

Melodic Development Ideas

How are melodies developed? Are they just continuously new material spinning out of the composerâ&#x20AC;&#x2122;s pen? Not really. A melody begins with a few bars of a good idea. Then that idea is developed in an unlimited number of creative ways. Following are six of those ways. For each method a four bar statement of an idea is given. This is followed by a four bar answer to the statement using a development idea. Often a slight change is necessary at the end of the answering phrase so that the last two notes of the melody are always either leading note to tonic (7-8) or supertonic to tonic (2-1). 1. Repetition

2. Up a 2nd

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3. Up a 5th (or down a 4th)

4. Rhythmic Variation

5. Inversion

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6. Similar Style

In these examples, the entire first four bars are subjected to the development idea. But these six melodic development techniques can be applied not only to a four bar phrase, but perhaps also to only a small motive of a melodic idea. The six ideas can also be used in combination with each other to help develop a melody. Here are a few more ideas commonly used for building melody, with a short example of each. Notice that each example ends with 7-8 or 2-1 of the home key. 1. A melody often outlines a chord.

2. A motive can be used in sequence, that is, up or down any interval within the octave.

3. Any rhythmic motive can be used again with new melody.

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4. Any melodic motive can be used again with a new rhythm.

Now here are some short repertoire excerpts. For each excerpt describe two ideas used to build the melody. The first two are done as examples.

1. Opening staccato eighth notes outline the F+ I chord. 2. Bars 3 and 4 are the same rhythmic and melodic pattern a 3rd apart (a motive in sequence).

1. The same rhythmic/melodic motive is used over and over again. 2. The last note of each motive builds an a minor arpeggio.

1. _______________________________________________________________________ 2. _______________________________________________________________________

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1. _______________________________________________________________________ 2. _______________________________________________________________________

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1. _______________________________________________________________________ 2. _______________________________________________________________________

1. _______________________________________________________________________ 2. _______________________________________________________________________ 248

16 BAR MELODY IN ROUNDED BINARY FORM

_________________________________________________________________________________________________________

REFERENCE PAGES xx xxiii xxiv xxv

Baroque Dances Melodic Development Ideas Melody Writing Procedure Melody Writing Checklist

The goal of this section is to learn to expand a given opening to make a four phrase rounded binary form in 18th century dance style. This section will demonstrate seven useful steps to completing a 16 bar dance form by way of two step by step examples. EXAMPLE NUMBER ONE 1. Layout The highly important first step is to lay out the bars and phrases complete with repeat signs. The given opening may or may not include a pickup. Following is an example layout. Remember from structural analysis that both the A and B sections are repeated. Notice that this step includes marking the four phrases with square brackets. At this point the key should also be decided and labeled. Study the example carefully. When the correct layout is done, it is much easier to work through the composition. Always take the time to ensure that this step has been done accurately.

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2. Type of Dance and Harmonic Rhythm The next step is to determine a workable harmonic rhythm. Recall that harmonic rhythm means the frequency of the chord changes. This is closely related to tempo. Try to identify the type of dance that is indicated by the opening. Refer to reference page xx to help with this decision. Faster music will have less frequent chord changes. Slower music will have more frequent chord changes. Studying the given opening will help decide the harmonic rhythm. Once this decision has been made, it does not mean that the harmonic rhythm must be rigidly adhered to. Consistency is quite important, but often chords change more frequently near a cadence. This is one of the reasons a performer feels inclined to slow down at cadences. 3. Cadences Cadences in a 16 bar binary composition (at this level) will all be in the home key. There will be no modulation. Cadences 2 and 4 should be perfect cadences with the ending melody notes being 7-8 (leading note â&#x20AC;&#x201C; tonic) or 2-1 (supertonic â&#x20AC;&#x201C; tonic). Cadences 1 and 3 can be less final, so imperfect or deceptive would be appropriate. The cadence chords should generally change over a barline. However, in 4/4 time without a pickup, cadence chords work just as well on beats 1 and 3 of the last bar of each phrase. In this example a moderate tempo in 3/4 time suggests a minuet. This dance is in the key of e minor. The Moderato tempo would perhaps dictate 2 chord changes per bar even though the melody notes could all fit into one chord per bar. The chord changes would be on beats 1 and 3, fairly consistently. If the cadence should move over the barline, then the first cadence would be from bar 3, beat 3 to bar 4, beat 1. Bar 4 would then contain only one chord. At this point it is time to put all the cadence chords in place. Notice in this example that cadences 1 and 3 are both imperfect, while cadences 2 and 4 must be perfect.

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scale passage descending 5 notes leap of a 5th 2nds in neighbour notes pattern quarter note only bars passing notes are always the second in a group of 2 eighth notes If the harmonic rhythm is changing on beats 1 and 3, then the first E in bar 2 must be an accented passing note.

5. Choose Implied Harmony In order to choose good melody notes, the underlying harmony must be sound. So in this step, combine knowledge of the harmonic rhythm from step 2 with knowledge of a good progression, and write in chords which will later guide the choice of melody. Here is another copy of the minuet, this time showing chord progressions in keeping with the chosen harmonic rhythm. There are many, many possibilities. This shows just one harmonic solution for each example. During this step it also makes sense to copy the opening again at the start of the last phrase. This makes the piece rounded binary. Take a look at the chosen chords of the Minuet. Each phrase follows a good progression. Phrase 3 is the most interesting phrase. It uses the descending 5ths sequence progression. The melody of this phrase will also need to be sequential.

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6. Write the Melody The next step is to write melody using the underlying harmony and the opening ideas defined in step 4. But first take a look at more ideas from the dance literature. The possibilities are really limitless. Observations of Melodic Techniques in Short Dance Pieces 1. New rhythm introduced at cadence 2, then used in a sequence at phrase 3.

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2. Phrase 2 begins with a repeated motive.

3. Phrase 2 contains a simple sequence.

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4. Phrase shaping built on a scale up or down.

5. Melodic and rhythmic motives in sequence.

Now continuing with step 6, the Minuet is shown with a completed melody. 258

a) In bar 7 there is a new rhythm introduced. The new rhythm is then developed in the sequence in phrase 3. b) The eighth note scale passage from the opening is used 3 more times. In bar 3 it is stepping down, but in bars 5 and 6 it is inverted. Notice that the inversion in bar 7 requires the use of the melodic minor scale to avoid an augmented 2nd interval. c) The accented passing note from bar 2 is used at cadences 2 and 4. Its use causes the harmonic rhythm to change on beats 1 and 2 rather than beats 1 and 3. These accented passing notes could also be considered cadential chords on V (V but with no 4 and 3 present). 259

Following is the final version of the Minuet with completed cadences. a) At cadence 1 the soprano part is moving, so a long bass note in bar 4 is fine. b) In bar 3, iv is used in first inversion to avoid octave Aâ&#x20AC;&#x2122;s on the 3rd beat. The first inversion gives much more of the sound of a minor chord. c) Cadences 2 and 4 are the more final cadences. Still there should be some movement in the bass part. The arpeggio i is a very common cadential idiom in this style. d) Cadence 3 has a long note in the soprano so the bass needs to move. The scale motive from the 1st bar works nicely here.

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EXAMPLE NUMBER TWO 1. Layout In this example the given opening includes a pickup. This means that every phrase, without exception, will begin with a pickup. Repeat signs will have to be very carefully placed and the bars ending the A and B sections will be incomplete. Remember to decide and label the key during this step. Study the example carefully.

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2. Type of Dance and Harmonic Rhythm The next step is to determine a workable harmonic rhythm. Recall that harmonic rhythm means the frequency of the chord changes. This is closely related to tempo. Try to identify the type of dance that is indicated by the opening. Refer to reference page xx to help with this decision. Faster music will have less frequent chord changes. Slower music will have more frequent chord changes. Studying the given opening will help decide the harmonic rhythm. Once this decision has been made, it does not mean that the harmonic rhythm must be rigidly adhered to. Consistency is quite important, but often chords change more frequently near a cadence. This is one of the reasons a performer feels inclined to slow down at cadences. 3. Cadences Cadences in a 16 bar binary composition (at this level) will all be in the home key. There will be no modulation. Cadences 2 and 4 should be perfect cadences with the ending melody notes being 7-8 (leading note â&#x20AC;&#x201C; tonic) or 2-1 (supertonic â&#x20AC;&#x201C; tonic). Cadences 1 and 3 can be less final, so imperfect or deceptive would be appropriate. The cadence chords should generally change over a barline. However, in 4/4 time without a pickup, cadence chords work just as well on beats 1 and 3 of the last bar of each phrase. This second example in G major is in cut time, a quick tempo with a quarter note (2 eighth notes) pickup, defining a Bourree. The harmonic rhythm could be 2 chord changes per bar, however, the opening bar is clearly an outline of the G major (I) triad, implying only 1 chord change per bar. Although the harmonic rhythm appears to be a single chord per bar, a more likely solution at the cadence points is shown. Bar 3 will contain 2 chords, the second one being the first chord of the cadence. The second chord of the cadence will be 3 beats long, leaving the 4th beat as the pickup for the next phrase. Again, cadences 1 and 3 are imperfect, and the necessary perfect cadences occur at the end of phrases 2 and 4.

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4. Analyze the Composition of the Given Opening The next step is to study the given melodic opening. This opening provides the building blocks to expand the melody to 16 bars. Observe as many motivic ideas as possible. The observations can be melodic or rhythmic. In the Bourree, the composition of the given opening contains: a) eighth notes pickup â&#x20AC;&#x201C; chord note plus passing note b) broken chord quarter notes c) octave leap 5. Choose Implied Harmony In order to choose good melody notes, the underlying harmony must be sound. So in this step, combine knowledge of the harmonic rhythm from step 2 with knowledge of a good progression, and write in chords which will later guide the choice of melody. Here is another copy of the Bourree, this time showing chord progressions in keeping with the chosen harmonic rhythm. There are many, many possibilities. This shows just one harmonic solution for each example. During this step it also makes sense to copy the opening again at the start of the last phrase. This makes the piece rounded binary. The third phrase of the Bourree is again sequential, but in a different way. The progression ii V - vi is shifted down a step to create I - IV - V. Again, the melody will need to reflect this harmonic move. Notice two more things: a) Phrase 3 ends with V which is a good idea because phrase 4 starts with I. b) The ending of phrase 2 matches the ending of phrase 4. These could match melodically as well as harmonically.

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6. Write the Melody The next step is to write melody using the underlying harmony and the opening ideas defined in step 4. a) There is certainly not much in the way of rhythm to work with here, so a dotted rhythm is introduced in bar 2 and used again in every phrase. b) The first 3 given notes are a useful motive. Bar 3 uses the motive in sequence. Bars 7 and 15 uses the motive inverted and in sequence. c) Phrase 3 presents a 2 bar tune which is then repeated down a 2nd in keeping with the harmonic chord sequence. d) Bars 13 and 14 = bars 1 and 2, and bars 15 and 16 = bars 7 and 8. This is a common formula in rounded binary.

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7. Add a Bass Part at the Cadences The final step is to write in a bass part at each cadence and name the type of cadence. When writing only 2 parts, the note stems should follow the middle line rule. The parts should use up stems for notes on or below the middle line, and down stems for notes on or above the middle line. This step also includes adding rests in the bass clef part. a) Cadences 2 and 4 use the very typical left hand arpeggio idiom. b) Cadence 1 has a special consideration. If only root position ii is used, both voices would have A’s on the 3rd beat and then both voices would have D’s on the 1st beat of the next bar. This would be considered parallel octaves. In addition, the harmony would sound very thin. If only 1st inversion ii is used, then the 4th beat of the bar would sound two C’s and they would move to two D’s again, parallel octaves. The solution is to choose ii followed by ii, then V. c) In bar 4, the V chord has a long soprano note, therefore the bass should move. The dotted rhythm from bar 2 works well and causes the V to become V on the 3rd beat of the bar. d) Cadence 3 works well as two root position chords (no parallel octave problems). The soprano part is moving, an inversion of the moving part in the first cadence.

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Now try completing the following openings to create 16-bar, 4-phrase, rounded binary compositions. Refer to the seven steps in the two detailed examples. After carefully laying out each of the 6 openings below, decide the type of dance and a possible harmonic rhythm. For example, in opening #3 the repeated G’s could suggest one chord per bar. But at a more moderate tempo (allegretto), chords could change on beats one and three. This is likely a minuet.

Type of Dance

Harmonic Rhythm

Minuet

2 chords/bar (beats 1 and 3)

#1 #2 #3 #4 #5 #6

After each melody is completed, use the Melody Writing Checklist, page xxv in the reference pages, to check for any errors. For a synopsis of melody writing work, see “Melody Writing Procedure”, page xxiv in the reference pages. Be sure to play all the completed examples to hear how convincing this melody work has been. Add left hand chords according to the functional chord symbols. If the chord symbols are difficult to interpret quickly, try converting them to root/quality chord symbols and then play.

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REFERENCE PAGES Discovering Harmony Summarized In Charts and Tables

CIRCLE OF FIFTHS

TRIADS ON SCALE DEGREES

SUMMARY

iii

A PROGRESSION CHART TO BUILD ON predominant tonic I

dominant

tonic

DOUBLING Major Key

Minor Key

Doubling Instructions

I, IV, V

i, iv, V

use all the notes or double root, no 5th

triple root if preceded by complete V

double root or 3rd

double 3rd if directly after V or V

double root if not following V or V

I , IV , V

i ,iv ,V

double 3rd

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double 3rd

chords

double 5th, that is, the bass note

iii

III

double root

double root or 5th

double root

iii

III

double 3rd

use all notes or double root, no 5th

SPECIAL PROGRESSIONS V and inversions

3rd (LN) rises and 7th falls

V - I

incomplete V (double root, no 5th); complete I

V - I

complete V ; incomplete I (triple root, no 5th)

V - I

both chords complete; LN(3rd of V ) falls a 3rd in alto or tenor

V - I

7th of V rises a step; I doubles the 5th; rising resolution

V - IV

V must be in root position; 7th of V is a common tone; double the 5th of IV ; stationary resolution

I - vii

- I

soprano moves opposite to bass (e.g. In C+, I - vii C-D-E in soprano matches with E-D-C in bass)

ii and ii

7th is prepared in the same voice in the previous chord; 7th falls by step; 7th may be approached by step from above

I - iii - IV

soprano line is falling 8-7-6 (notice LN is falling)

iii - V

same bass note; all voices step down or have common notes; resembles the cadential chord

- I

CADENCES V - I V - I

V - i V - i

Perfect (or Authentic) Perfect

I - V ii - V ii - V IV - V vi - V

i - V ii - V ii - V iv - V VI - V

Imperfect (or Half) Imperfect Imperfect Imperfect Imperfect

Note: Imperfect cadences never end with V . IV - I

iv - i

Plagal

V - vi V - vi

V - VI V - VI

Deceptive Deceptive

Note: In deceptive cadences, double the 3rd of vi (VI), and use the contrary motion principle, except the LN must rise.

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NON-CHORD NOTES Passing note

- up or down - between 2 chord notes a 3rd apart - two may occur harmonically in 3rds or 6ths - may use two in a row between tonic and dominant notes of the key

Neighbour note

- up or down a step from the chord note and then back to the same chord note - two may occur harmonically in 3rds or 6ths

Accented passing note

- passing note is in a metrically stronger position than the chord note - neighbour note is in a metrically stronger position than the chord note

Accented neighbour note

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Incomplete neighbour Appoggiatura

chapp e Anticipation

Suspension

- also called a cambiata - arrives by leap on a dissonance - leaves by step to the chord note - a cambiata which falls on the beat

- also called an escape tone - arrives by step on a dissonance - leaves by leaping down a 3rd to a chord note - arrives before its harmony on the weak part of a beat - is restated on the beat with the chord to which it belongs

- prepared as a chord note in the previous chord - suspension is the dissonance (non-chord note) in the next chord - resolves downward by step to the note it displaced (no chord change) - exception is a leading note suspension which resolves up

CHORDS (see examples on next page)

Cadential

common notation V looks like I â&#x20AC;&#x201C; V( ) notes of the act like appoggiaturas decorating V( )

Passing

I - V - I I - V - I IV - I - IV IV - I - IV soprano moves opposite to bass one inner voice is common notes other inner voice shows lower neighbour note movement

Neighbouring

I - IV - I V - I - V two voices move like upper neighbour notes

Arpeggio

built on I, IV or V preceded by another inversion of the same chord followed by: - another inversion of the same chord OR - a chord built on the bass note a step up or down from the bass note

SUSPENSIONS Preparation

suspension note sounded in the same voice as a chord tone in the previous harmony

Suspension

non-chord note; often tied over from previous chord

Resolution

suspension resolves by step (usually downward) to the note that it displaced

9 – 8 is usually supertonic to tonic 7 – 8 is usually LN to tonic 4 – 3 is very common over a root position chord 7 – 6 is very common over a first inversion chord a) The note of resolution must not be present in another voice against the suspension unless it is in the bass. b) Double and triple suspensions are fine provided their resolutions form a proper chord.

xii

MAJOR KEY PROGRESSION CHART

Tonic

Pre-dominant

I (I ) I( ) – IV( ) – I(

vi (vi )

Dominant

IV (IV )

ii (ii )

V (V

IV – I – IV

V (

I – iii – IV

IV – I – IV

vii

I – iii – ii6

Arpeggio IV

I – vii – I I – vii – I I–V –I I –V –I Arpeggio I

)

Tonic

)

V iii – V( ) iii – V V–I –V Arpeggio V

I (I ) vi IV I – IV – I I – IV – I I–I –I (arpeggio )

MINOR KEY PROGRESSION CHART Tonic i (i )

Pre-dominant VI (VI )

Dominant

iv (iv )

ii (ii )

V (V

i( ) – iv( ) – i( )

iv – i – iv

V (

i – III – iv(ii )

iv – i – iv

vii

i – III – V

Arpeggio iv

i – vii – i i–V –i

Tonic

)

V IIIx – V( ) III – V V–i –V Arpeggio V

i (i ) VI iv i – iv – i i – iv – i i–i –i (arpeggio )

MODULATION TO THE DOMINANT The pivot chord: 

chord common to both keys



must have identical spelling in both keys



V – I must establish the old key before the pivot



V – I must establish the new key after the pivot

CHORD

TONIC KEY C+

DOMINANT KEY G+

C E G

G B D

D F A

A C E

iii

E G B

B D F

F A C

C E G

G B D

D F A

A C E

E G B

vii

B D F

F A C

PIVOTS TONIC

DOMINANT

iii

*vi

* favoured Baroque pivot

MODULATION TO THE RELATIVE MAJOR CHORD i

TONIC KEY d-

RELATIVE MAJOR F+

D F A

F A C

E G B

G B D

III

iii

F A C

A C E

G B D

B D F

A C E

C E G

B D F

D F A

viio

C E G

E G B

VII

—

C E G

—

PIVOTS TONIC MINOR i

RELATIVE MAJOR =

viio

III

VII

xvi

MODULATION TO THE DOMINANT MINOR CHORD

TONIC KEY d-

DOMINANT MINOR a-

D F A

A C E

E G B

B D F

III

F A C

C E G

G B D

D F A

A C E

E G B

D F

F A C

viio

C E G

G B D

VII

C E G

G B D

PIVOTS TONIC MINOR

DOMINANT MINOR

III

VII

III

xvii

USE OF III AND

xviii

ROOT/QUALITY CHORD SYMBOLS Chord Type

Spelling

Root/Quality Symbol

Major

FAC

Minor

FA C

Augmented

FAC

Faug

Diminished

FA C

Fdim or F

Major/Minor 7th Chord

FACE

Minor/Minor 7th Chord

FA CE

Fm7

Half diminished 7th Chord

FA C

Cadential Chord

FAC–CEGB

F/C – C7

To indicate a chord in inversion, write the name of the chord as above followed by a slash, then the name of the bass note of the inversion. For example: F7 in first inversion would be F7/A F in second inversion would be F/C Fm7 in third inversion would be Fm7/E

xix

BAROQUE DANCES

DANCE

METER

CHARACTERISTICS

TEMPO MARKINGS

Allemande

4/4 or 2/4

Stately and dignified Usually a 16th note anacrusis Often a continuous flow of 16th notes

Allegretto Moderato Allegro moderato

Bourree

4/4 or 2/2

Quick duple time\Rhythmic and bright Steady quarter notes Usually a quarter note anacrusis

Vivace Allegro Allegro vivace

Courante

3/4, 3/2 or 3/8

Means â&#x20AC;&#x153;runningâ&#x20AC;? Quick triple time Even flow of running 8th notes

Allegro Vivo

Gavotte

4/4 or 2/2

French dance Usually two quarter note upbeats Mainly steady quarter notes

Allegro Vivace Allegro moderato

Gigue

6/8

May begin with an anacrusis Running 8th notes Very brisk tempo

Allegro Vivace Presto

Minuet

3/4 or 3/8

Elegant and graceful Unhurried tempo

Moderato grazioso Allegretto grazioso

Sarabande

3/4 or 3/2

Emphasis on the second beat Begins on the downbeat Very slow and solemn

Andante espressivo Lento Sostenuto

RELATED KEYS Related keys: * are one key on each side of the home key on the circle of 5ths * include both major and minor keys Major Key Example:

Related keys to A + using the circle of 5ths correspond to the root/quality names of the triads built on the scale degrees. E+ (V)

A+ (I)

D+ (IV)

c(iii)

f(vi)

b(ii)

Minor Key Example: (harmonic and natural minors)

Related keys to b- using the circle of 5ths correspond to the root/quality names of the triads built on the scale degrees of the natural minor scale. G+ D+ A+ (VI) (III) ( VII)

e(iv)

b(i)

f(v)

xxi

STRUCTURAL ANALYSIS FORMS FORM

Symmetrical Binary

Asymmetrical Binary

Rounded Binary

Ternary

STRUCTURE

2 Sections ‘A’ and ‘B’ Each section is repeated Sections are equal in length

2 sections ‘A’ and ‘B’ Each section is repeated ‘B’ is longer than ‘A’ Greater tonal development in ‘B’

2 sections ‘A’ and ‘B’ Each section is repeated Portion of ‘A’ returns as part of ‘B’, but is altered to stay in the tonic key

3 section structure ‘A’ returns after ‘B’ and is identical to the first ‘A’ Return of ‘A’ may be a da capo Return of ‘A’ may be fully written out First ‘A’ and ‘B’ are repeated, but return of ‘A’ is not

DIAGRAM

KEY STRUCTURE

: A :: B : A=B

‘A’ moves from: *major to dominant or *minor to relative major or *minor to dominant minor

: A :: B :

same as symmetrical binary

: A :: B A’ :

same as symmetrical binary

A≠B

: A :: B : Fine

Da capo

: A :: B : A 

‘A’ must end in the home key because it is the end of the piece ‘B’ can be in the key of: *the dominant if ‘A’ is major *the relative minor or dominant minor if ‘A’ is minor

MELODIC DEVELOPMENT IDEAS 1.

Repetition

Repeat up a 5th or down a 4th

Repeat up a 2nd

Repeat with rhythmic and/or melodic variation using non-chord notes

Inversion

Continue in a similar style

Four More Ideas for Building Melody 1.

Chord outlines

Motives in sequence

Same rhythm, new melody

Same melody, new rhythm

xxiii

MELODY WRITING PROCEDURE 1.

Name the key.

Lay out the bars for the piece. Especially watch for repeat signs and pickups.

Square bracket the phrases. Don’t forget that the pickup (if there is one) will apply to every phrase.

Try to identify the type of dance indicated by the opening. Consider the tempo of the dance while deciding an appropriate harmonic rhythm.

Put in the cadence chords: Cadence 1 – imperfect in the home key Cadence 2 – perfect in the home key Cadence 3 – imperfect in the home key Cadence 4 – perfect in the home key

Analyze all the motives of the given opening.

Write implied harmony for the four phrases, keeping approximately the same harmonic rhythm.

Rewrite the opening of the first phrase at the start of phrase 4.

Complete the melody using the motives and your implied progression.

10.

Add chord symbols, bass part and cadence name at each cadence.

11.

Use the “Melody Writing Checklist”, page xxv.

xxiv

MELODY WRITING CHECKLIST Try to answer YES to each of the following questions: 1.

Are the melodic endings of sections A and B closed (2-1 or 7-8)?

Do all the LNâ&#x20AC;&#x2122;s rise melodically?

Have melodic augmented intervals been avoided? (augmented 2nds and 4ths are the ones to look for, and especially in the minor key)

Is the harmonic rhythm mostly consistent?

Does the implied harmonic progression make sense?

Can all non-chord notes be accounted for?

Does the phrase follow a shape through the natural rise and fall of pitch?

Is the melodic span a perfect octave or less? Does the melody never move more than one octave in the same direction?

Is there unity through repetition of rhythmic and melodic motives?

10.

Is there interest and variety in the motives?

11.

Are new motives used more than once?

12.

Have the necessary rests been included in the bass clef?

13.

Are the stems of notes going in the right direction?

xxv

INSTRUCTIONS FOR BUILDING THE KEY SLIDE RULE The key slide rule is a handy tool which makes it easy to quickly spell chords in any key. Make the slide rule in order to help complete goal 2 and then use it throughout the lessons as needed. 1. Use the template below to cut out a piece of light cardboard (an old cereal box works well). Also copy the markings on the piece.

iii

vii

ii ii

IIIx III

iv IV

V v

vii VII

i I3

2. Use a sharp edge to cut through the cardboard along the two vertical lines near the left and right edges of the rectangle. 3. Cut out another piece of cardboard using the template on the next page. Again, copy the markings. 4. Slide the second piece of cardboard through the slits on the first piece. The rest of goal 2 will describe how to use this slide rule.

(G)

(A)

(B)

(C)

(D)

(E)

(F)

(G)

(A)

(B)

(C)

(D)

(E)