MUSIC 370 - Music Theory 3

Karen Sunabacka

Estimated reading time: 15 minutes

Table of contents

The notes below are quite incomplete…

Week 1

Intro to course

Review of chapter 19: five steps

  • Analyzing the Soprano (REVIEW)
  • Choosing Harmonic path
  • Elaborating the soprano
  • Elaborating the lower voices
  • Decorating the cadential tonic


OP-01 Learning MuseScore Due Sep. 11 at 11:59pm

OP: online practice

Download musescore and create new document

  • title: OP-01 Swimming
  • Subtitle: In my friends pool
  • Composer: your name
  • Copyright: ©2020 your name

format -> page settings -> Paper size: Legal -> unclick two sided -> landscape

Note Entry

Press N to create new note. 6 is half note, 7 is whole note.

view -> play panel, inspector panel, which can change the playback speed.

then bass. Click on the bass stave, click voice 2, press N.

Shift + plus => ties

Figure bass

Click bass note, press ctrl + G to add. Space bar to next note.

Lower case o, diminished. Alt + space.

Prolongation brackets, roman numerals and other symbols

Prolongation brackets: Palettes -> lines -> pedal (both hooks angle). Click on a note, click on a pedal, then move the other end.

Add -> text -> roman numeral analysis

Palettes: Text -> open text


Save score to file

File name: Lastname / firstname + title of the score

export: pdf, mp3. Both to dropbox.


with Problem Set 0 (not required!)


T3B-01 DUE Mon. Sept 14

§22: Minuet

Review on chapter 22 and 6,4 chords.

§23: Primary mixture

Primary mixture on major keys/ minor keys.

Tonicization represent the broadest application of chromatics in major-minor tonality. But chromaticism need not always serve the interests of tonicization: we can intensify the harmonic events in a major-key or minor-key by introducing chords borrowed from the parallel mode. This process is called primary mixture.

PM in Major

lowering \(\hat 6 \) (and \(\hat 3 \))

Pre-dominant chords, mixture in tonic prolongation, plagal cadence

PM in minor

Picardy third: raise \(\hat 3 \) in the cadential I

When the Phrygian and minor modes are notated on the same tonic, their tonic patterns differ only in respect to the placement of their second degrees. Phrygian II chord can be introduced in a minor key by lowering \(\hat 2 \). The Phrygian II appears most often as a sixth chord in minor, where it is commonly called a Neapolitan 6th. We frequently meet the Neapolitan 6th as a pre-dominant chord.

Example: N6

The Phrygian II (the root-position chord) rarely appears as a pre-dominant harmony, owing to the discordant tritone leap in bass from \(\flat \hat 2\to\hat 5 \) (the dominant root). However, the Phrygian II can be introduced to enrich prolongations of minor chords in both modes.

homophony with PM

Elaborate chord, could do PM.

If soprano 7-8, 2-1, 4-3, we can do deceptive resolution. 2-3 doesn’t work cause it creates parallel fifth. With decoration, 2-4-3 in soprano avoids parallel fifth.

Minor prolongation including Neapolitan flat 6 on weak beat.

Subdominant prolongation (in primary tonic), PM.

PM in cadence. Before that, IV or II chord, can do PM.

After this, do a Plagal Cadence.


  • Step 1: Analyze a soprano, choose harmonic path and consider PM
  • Step 2: Compose a decorated bass.
    • soprano 1 2 3, bass 3 2 1
  • Step 3: Elaborate the soprano
  • Step 4: Add Inner Voices
    • not half diminished in minor key, only fully diminished
  • Step 5: decorated plagal cadence

If do a minor homophony, for chapter 23. Don’t apply plagal cadence in minor. It doesn’t help. End in major.

Soprano: Once you hit the final tonic with ties, just stay on that.

§24: Intensifying the Dominant

The Augmented 6th chords

Not tonicize, but intensify this motion to the dominant.

soprano: 8 7 8. bass: b6 5 1. Then introduce third voice, #4, which is A4 above the bass. Then fourth voice:

  • double the third: Italian \(^6_3 \)
  • enters on \(\hat 2 \), French \(^4_3 \)
  • perfect fifth above the bass (\(\hat 3 \) in minor, \(\flat \hat 3 \) in major), German \(^6_5 \). Note the unavoidable parallel fifth as 3\(\to \)2.

Italian 63

French 43

German 65

More on A6

It has always to resolve to dominant, but doesn’t always have to be on the strong beat.

These are embellishing chords, not pre-dominant, not elaborate.

Interpolated \(C _ 4 ^ 6 \):

  • Major: \(\flat 3\to \natural 3 \to 2 \to 1 \text{ or } 3 \)
  • Minor: no change on 3 since 3 has been flatted

Ex 24.18 The enharmonic German \(^6_5 \), only in major.

Ex 24.27 Noncadential A6

Common-Tone Diminished 7th

another embellishing chord.

only works in major key.

Ex 24.29: CT is creating chromatism to chordal 3rd (\(\hat 7 \)), chordal 5th (\(\hat 2 \)): \(\sharp \hat 6\to \hat 7, \sharp \hat 1 \to \hat 2 \).

In summary for CT\(^\circ \)7 voice leading is:

  • \(\sharp 6 \to 7 \)
  • \(\sharp 1 \to 2 \)
  • \(5\to 5 \) (the common tone!)
  • \(3\to 2 \) for V and V6 or \(3\to 4 \) for V7 and all inversions


Step 1: correct homophony from chapter 19.

Step 2: Where can new chords go? PM, A6, CTo7 (remember this has to be in Major)

Step 3: Remove some decoration, and allow for a slight reworking places where PM, Aug 6 and CTo7 can work

Step 4: Get the framework set-up again, with new harmonization altering what is needed to allow for PM as well. Insert CTo

Step 5: Fill in the inner voices, and make sure the voice leading works and is pleasing!

§25: Intensifying the Tonic

The Augmented Dominant

Only available in major. Better to use on a weak beat, cause might create A2 in the voice leading. \(\hat 2 \to \sharp \hat 2 \to \hat 3 \). Can have a triad, or have augmented dominant 7th.

The Diminished Dominant 4-3

Can be used in both major or minor. Start with V7 chord in second inversion, and find \(\hat 2 \) in bass, then \(\hat 2 \to \flat \hat 2 \to \hat 1 \). Best done in weak beat.

Example 25.26, could on strong beat. In minor, \(\flat \hat 3\to \flat \hat 2 \to \hat 1 \).

CTdim7 to I, I6 and C6/4

  • \(\hat 5 \to \sharp \hat 4 \to \hat 5 \)
  • \(\hat 5 \to \hat 6 \to \hat 5 \) or \(\hat 3 \to \hat 6 \to \hat 5 \) or \(\hat 1\to \hat 6\to \hat 5 \)
  • \(\hat 3\to \hat \sharp \hat 2\to \hat 3 \)
  • \(\hat 1 \to \hat 1\) (common tone)

Ex 25.30: could use CT before \(C_4^6 \)

Ex 25.31: pre-cadential dominant \(\to \) CT \(\to \) C6/4

The extended Authentic Cadence

Authentic Cadence ends on \(\hat 3 \) in romantic century. \(\hat 4\to \hat 3 \) or \(\hat 2\to \hat 3 \) in soprano.

The plagal 6-5

Plagal cadence: Soprano \(\hat 1 \to \hat 4\to \hat 3 \)

IV I cadence. Ex 25.12: 4-1 close in the bass, 1-2-3 passing motion on soprano. 1 is elided, 2 moves back to occupy the strong beat, and 3 is raised to create the Picardy third characteristic of this cadence. Resulting chord is called plagal \(^6_5 \).

The plagal 4-3

Wanna introduce 878. diminished in minor (example below), half diminished in major.

Also an example, plagal 65 to plagal 43.

§26: Formal Modulation

This is the week after reading week. It serves as a break thus it’s a lighter week.

A local tonic can be confirmed briefly within the phrase within the phrase as a momentary inflection or prolonged as a more emphatic event - the process of tonicization. A local tonic can also be established at the phrase cadence or prolonged into the cadence, where it offers a more serious challenge to the primary tonic - the process of phrase modulation. Or, a local tonic can be extended in duration to govern an entire section of the music, creating a secondary tonal region that presents a significant opposition to the primary key: this process is called formal modulation.


First one: start in f# minor, ends in relative major. Second one: F major, ends in V.

§27: The Chromatic Sequence

Like its diatonic model, a chromatic model can serve as a transitional passage between two chords within the same tonal area.

Other possibilities are not presented here because I am not going to use them…

4 chromatic options for Deceptive Resolution Chromatic Sequence

  • Interpolated Applied Dominants
  • Harmonic Elision
  • PM minor: Phrygian II Major
  • Aug 6th

Some refreshers: Deceptive Resolutions of Secondary Dominants

Composing a Chromatic Sequence

  1. Choosing a sequence and setting-up the framework
  2. Completing the first measure that resolves well into measure 2
  3. completing the sequence to the cadence (completing measures 2 and 3)
  4. Completing the sequence (the cadence, figured bass and analysis)

§28: Secondary Mixture

In chapter 23, we met the process of primary mixture: combine a key’s major and minor modes in shared harmonic relationships. Here we meet a second means of key enhancement. Melodic chromaticism again informs the process; but where a chromatic pitch in primary mixture serves to introduce a chord belonging to the music’s parallel mode, here a chromatic pitch acts to convert the quality of a chord belonging to the music’s prevailing mode. Can be elaborative chord, be tonicized, or formal modulation. This process is called secondary mixture.

  Primary Mixture Secondary Mixture
Major \(\flat \hat 6 \): II, IV
\(\flat \hat 3 \): I
\(\flat \hat 6, \flat \hat 3 \): VI
(borrowed from minor)
\(\sharp \hat 5 \): iii becomes III
\(\sharp \hat 1 \): vi becomes VI
minor \(\flat \hat 2 \): II Phrygian or N6
\(\sharp \hat 3 \): I
\(\sharp \hat 6 \): IV, II
\(\sharp \hat 6, \sharp \hat 3 \): VI
\(\flat \hat 4 \): bII becomes bii
\(\flat \hat 1 \): VI becomes vi

Secondary Mixture in Major

Raising \(\hat 5 \) in a major key will alter the chordal third of III, converting the chord’s quality from minor to major.

Example 28.4: When VI follows major III.

Ex 28.7: When major VI is prolonged, then it must be tonicized to the prolongation. Secondary mixture is a bit jarring than PM because it doesn’t borrow from another mode.

Ex 28.9: When II follows major VI. We need to make sure voice leading works: \(\sharp \hat 1\to \hat 2 \)

Secondary Mixture in Minor

Ex 28.10 (a): Not a prolongation. It’s minor VI which embellishes I.

Ex 28.10 (b): Subdominant prolongation, minor mode IV6

Ex 28.11: Enharmonic resolution, going from elaborative SM to dominant: \(\flat \hat 1 \to (\sharp)\hat 7 \)

Ex 28.12: The minor Neapolitan 6.

The Stable Six-four chord

Chapter 12: Passing 64, Cadential 64. Chapter 22: Neighbor, Pedal, Arp 64. Some refreshers

The applied dominant that introduces this chord confirms the chordal fourth as a local tonic, permitting the stable \(^6_4 \) to function harmonically as a consonant chord. In a major key, the stable \(^6_4 \) will occasionally sound as a modally borrowed subdominant.

Ex 28.20 (score from IMSLP): mm. 2 is Nbr \(^6_4 \), mm. 6 is Stable \(^6_4 \)

Ex 28.21: Reinterpreting the passing \(^6_4 \)


The Cadential Pedal Extension

A pedal extension allows the music’s momentum to carry past the authentic cadence into elaborations of the cadential tonic.

§29: The Romance

The Romance resembles the Notturno. We invent a two-part theme, with each part repeated. This is immediately succeeded by a new theme as a middle subject, of the same description as the former, but in another key, each part of which may also be repeated. A return is then made to the first theme, without repetition, or else embellished, at pleasure. A more or less developed conclusion completes the whole.

By Carl Czerny

Cantilena: “song melody”, used in instrumental music.

History of the instrumental romance:

  • ca.1200 - ca.1400: Medieval Period in Spain (romance) in Italy (romanza)
  • ca.1400 - ca.1600’s: Renaissance in Spain and Italy
  • ca.1600 - ca.1800: Baroque & Classical + in France, Germany & Italy

Formal Design

A B A’
Period 1, P1, P2, P2 ||: Period 1 :||: Period 2 :|| Period 1’, Period 2’
Major Key Parallel Minor Key or related key (reprise) Major key
andante or adagio agitato andante or adagio
theme called: cantilena Melodic line. Rests. RESTLESS theme cantilena theme is elaborated.

Intro before A, retransition between B and A’. After A’, coda.

A section

Period 1

  • Introduction in accompanying voices, then ONE voice presents first period of the cantilena
  • first period then repeats.
  • cadence of the first period will be an internal cadence. NOT PAC in primary tonic.

Period 2

  • One voice presents the second period of cantilena.
  • The second period then repeats.
  • The cadence of the second period will be PAC in the primary tonic.

B section

  • An agitato character to contrast the lyricism of the cantilena
  • The melodic line can spin out in a dense figuration articulated in compressed rhythmic patterns
  • The melodic line can also fragment into short, leaping motives punctuated by rests.
  • Rests can also interrupt melodic figures or displace their strong-beat entries, to accentuate the characteristic restlessness of the agitato theme.
  • Tone repetition can be introduced in single statement or reiterated motivically, to emphasise the line’s essential urgency.
  • Short appoggiaturas and rhythmically displaced passing and neighbouring tones can be introduced to good effect here (keep the broader suspension and retardation figures in the cantilena melody in the A section)
  • parallel minor or related key
  • 2 periods, repeated sign
  • change of meter/tempo
  • accompanying voices reinforce the agitato nature of this section

The retransition

  • The retransition acts as a connective link leading from the B section to a varied reprise of the A section
  • The retransition is four to six measures long and begins anywhere and ends on \( \hat 2,\hat 4 \) or \( \hat 7 \) to accommodate the dominant.


  • The romance closes in a coda, the counterpart to the introduction (but the coda is much longer!)
  • The coda is four to six measures long and is a cadential pedal extension.
  • The tonic chord will occupy the first and final measures and the bass will sound \( \hat 1 \) through the coda

The reprise

  • The reprise typically features an elaboration of the primary theme (the cantilena)
  • The accompanying voices can recall figuration from the B section as a means of unifying the structure
  • The reprise proceeds without repeats

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