Advanced Harmonic Analysis: Applied Chords, Modulation, and Form

Conceptual Overview of Applied Chords: Applied (or secondary) chords are used to tonicize a chord other than the tonic. These are typically organized as $V$ or $vii^{\circ}$ of a diatonic target chord.
Specific Tendency Tones and Their Targets:
- Sharp 1 ( $\sharp\hat{1}$ ): This chromatic tone acts as the leading tone to chord $ii$ . It is typically part of a $V^7/ii$ or $vii^{\circ 7}/ii$ .
- Sharp 2 ( $\sharp\hat{2}$ ): This chromatic tone leads to chord $iii$ . It functions as the leading tone for the chord associated with $iii$ , such as $V/iii$ or $vii^{\circ}/iii$ .
- Sharp 4 ( $\sharp\hat{4}$ ): This chromatic tone leads toward chord $V$ . It is often part of a $V^7/V$ or $vii^{\circ 7}/V$ .
- Sharp 5 ( $\sharp\hat{5}$ ): This tone leads toward chord $vi$ . In the key of $G$ major, this is a $D\sharp$ .
- The Case of Scale Degree 3 ( $\hat{3}$ ): Scale degree 3 remains unchanged when moving toward chord $IV$ because the interval between $iii$ and $IV$ is already a natural half-step. There is no chromatic "order tone" required for this transition.

Targeting Chord $ii$ (A minor):
- Leading Tone: $G\sharp$ .
- $V^7/ii$ Spelling: $E$ - $G\sharp$ - $B$ - $D$ .
- $vii^{\circ 7}/ii$ Spelling: $G\sharp$ - $B$ - $D$ - $F\natural$ .
- Common Tones: These two chords share the notes $G\sharp$ , $B$ , and $D$ , which explains their similar functional sound.
Targeting Chord $iii$ (B minor):
- Leading Tone: $A\sharp$ .
- $V^7/iii$ Spelling: $F\sharp$ - $A\sharp$ - $C\sharp$ - $E$ .
- $vii^{\circ 7}/iii$ Spelling: $A\sharp$ - $C\sharp$ - $E$ - $G\natural$ .
Targeting Chord $IV$ (C major):
- Note on Function: To create a dominant seventh chord (major-minor seventh), the native $F\sharp$ from the $G$ major scale must be lowered to $F\natural$ .
- $V^7/IV$ Spelling: $G$ - $B$ - $D$ - $F\natural$ .
- $vii^{\circ 7}/IV$ Spelling: $B$ - $D$ - $F\natural$ - $A\flat$ .
Targeting Chord $V$ (D major):
- Leading Tone: $C\sharp$ (Sharp 4, or $\sharp\hat{4}$ ).
- $V^7/V$ Spelling: $A$ - $C\sharp$ - $E$ - $G$ .
- $vii^{\circ 7}/V$ Spelling: $C\sharp$ - $E$ - $G$ - $B\flat$ .
Targeting Chord $vi$ (E minor):
- Leading Tone: $D\sharp$ (Sharp 5, or $\sharp\hat{5}$ ).
- $V^7/vi$ Spelling: $B$ - $D\sharp$ - $F\sharp$ - $A$ .
- $vii^{\circ 7}/vi$ Spelling: $D\sharp$ - $F\sharp$ - $A$ - $C\natural$ .

Tonicization: This is the temporary process of emphasizing a non-tonic chord. It provides a brief preparation for a chord, such as using an applied chord (e.g., $V/V$ ) to lead to $V$ .
Modulation: Modulation occurs when the music shifts to a new key area for an extended period. It involves a structural change rather than a brief emphasis.
Mozart Example (Piano Sonata in Bb Major):
- The exposition starts in $B\flat$ Major.
- Mozart introduces an $E$ natural ( $\sharp\hat{4}$ ), which acts as a chromatic tendency note.
- This note prepares the move to chord $V$ ( $F$ Major).
- Because the music then stays in $F$ Major for a significant duration and reaches a $PAC$ , this constitutes an actual modulation rather than mere tonicization.
Temporal Considerations:
- A chromatic sequence that lasts only a few seconds (e.g., 5 seconds) before returning to the home tonic is technically too temporary to be a true modulation in a structural sense.
- However, for academic/exam purposes, these brief shifts are often labeled as "modulations" to provide a terminology for analysis.

Parallel Period: A structure comprising an antecedent phrase and a consequent phrase.
- Antecedent Phrase: Often contains a sentential structure (basic idea, repetition, continuation) and typically ends with an inconclusive half cadence ( $HC$ ).
- Consequent Phrase: Often a repetition of the antecedent but ends with a conclusive perfect authentic cadence ( $PAC$ ).
Sentence Structure (Sentential Phrase): A design characterized by the ratio $2+2+4$ . It consists of:
- Basic Idea (2 measures).
- Repetition (2 measures).
- Continuation and Cadence (4 measures).

Phrasing: The opening involves a period structure. The first half is an antecedent ending in a half cadence ( $HC$ ), and the second half is a consequent ending in a perfect authentic cadence ( $PAC$ ).
Applied Chords for Variety:
- In measure 4, Schubert uses $E$ natural ( $\sharp\hat{4}$ ) as the leading tone in the base to form a $V^{6/5}/V$ .
- When the phrase repeats, he replaces the $V^{6/5}/V$ with a $vii^{\circ 7}/V$ ( $C\sharp$ - $E$ - $G$ - $B\flat$ ) to provide harmonic variety.
Sequential Passage:
- Following the initial phrasing, Schubert utilizes a descending circle of fifths sequence.
- Sequence Type: $D2$ (descending seconds) utilizing a $-5/+4$ root motion (e.g., $D$ to $G$ , $G$ to $C$ , $C$ to $F$ ).

Question (Audience member): Difficulties in visualizing the flat 7 related to chord $III$ .
Response: The flat 7 (or $\natural\hat{7}$ in a major key) is essentially the chordal seventh of the $V^7/IV$ . This note tonicizes the subdominant.
Mnemonic/Anecdote Regarding Bach: A mnemonic mentioned involves Johann Sebastian Bach adding a flat 7 to a tonic chord at the end of a piece to create a $V^7/IV$ modulation so he wouldn't have to look after his children (a humorous memory aid for remembering the flat 7 in tonicizations of chord $IV$ ).
Question: Does chord $III$ just remain unchanged?
Response: Yes, because the move from $iii$ to $IV$ is already a natural half-step ( $B$ to $C$ in the key of $G$ ), there is no need for an additional chromatic tone for that specific triadic connection.
Question: Will the test require designating a new key at every brief modulation point?
Response: No. The instructor will not ask for notations that have not been practiced in class. The test will prefer simple "Yes/No" answers regarding modulation and standard Roman numeral analysis as practiced in assignments. Use the questions as a guide and answer according to previous methods.
Question: What is the function of the chromatic tone $D\sharp$ in $G$ major?
Response: That is a sharp 5 ( $\sharp\hat{5}$ ), which signals a move toward chord $vi$ ( $E$ minor).