Music Theory, level 2A (Adduci)
MUSC 2A recommended reading list (Kostka and Payne, Tonal Harmony, 6th ed., on reserve at MLK Jr. Library):
- 1A Review: Ch. 1-15
- Ch. 16 - secondary dominant chords
- Ch. 17 - secondary leading tone chords
- Ch. 18 - pivot-chord modulation
- Ch. 20 - form
- Ch. 21 - modal mixture
- Ch. 22-23 - altered predominants
Welcome to the MUSC 2A page!
Please choose one of the following sections:
- A collection of music theory-related links from around the Web.
- The greensheet and other administrative documents
- Handouts given in class.
- Homework assignments and projects.
- Listening examples.
Web Links
This section contains links to internet sites designed to help you with music theory and ear training. The Internet is a fantastic resource for self-driven learning!
back to top of page
Greensheet
This section includes the greensheet and any other class policy documents.
Left-click to view, right-click to download.
back to top of page
Handouts
This section contains copies of the informational handouts given in class. Handouts that accompany music played in class can be found under Listening Examples, below.
- Part Writing handouts
- For a handout explaining the rules of Bach-style part-writing, and a list of abbreviations that I use when correcting part writing assignments, please refer to the MUSC 1A website.
- (2/3/14) In-Class Activity 1 - analysis of diatonic Bach fragments.
- (2/3/14) In-Class Activity 2 - part writing from figured bass.
- (2/24/14) In-Class Activity 3 - building secondary chords.
- (2/24/14) Flashcards you can use to build your own practice questions for secondary dominants and leading tones.
- (3/3/14) In-Class Review - a practice quiz on tonicizing chord groups, including the answer key.
- Form handouts
- (4/2/14) In-Class Activity 4 - part writing involving secondary chords.
- (4/16/14) In-Class Activity 5 - harmonic analysis involving secondary chords.
- Modulation handouts
- (4/2/14) Pivot Modulation examples, Set One (piano exercises)
- (4/15/13) Pivot Modulation examples, Set Two (chorale phrases)
- (4/15/13) Bach-style chorales illustrating pivot modulation.
- (4/23/14) In-Class Activity: Analysis of Bach's Prelude in C Major.
back to top of page
Assignments
This section contains copies of the homework assignments and projects given in class.
- Assignment 1 (1/27/14, due 1/29/14)
- Assignment 2 (1/29/14, due 2/5/14)
- Assignment 3 (2/5/14, due 2/12/14)
- Assignment 4 (2/12/14, due 2/26/14)
- Assignment 5 (2/26/14, due 3/5/14)
- Assignment 6 (3/5/14, due 3/12/14)
- Assignment 7 (4/2/14, due 4/9/14)
- Assignment 8 (4/9/14, due 4/16/14)
- Extra Credit Composition Project (due 5/7/14)
- Assignment 9 (4/23/14, due 4/30/14)
- Assignment 10 (4/30/14, due 5/12/14)
back to top of page
Listening Examples
This section contains links to musical examples referenced during class. The examples are provided for class purposes only.
You need the free Quicktime plugin to play these .mp3 files.
To play, left-click the excerpt title and then click "play" when the player opens.
- Secondary Dominants
- The coda (last 7 measures) of the slow movement from Marcello's oboe concerto in c minor contains one secondary dominant: V7/iv (CMm), resolving immediately to iv (Fm).
- This short excerpt from Beethoven's Symphony No. 1 in C Major demonstrates the power of tonicization, the technique of briefly making a chord other than the tonic of the key sound like "I". In the introduction to the first movement, there are three tonicizations in the first four bars, none of which are in the home key of C Major. The next eight bars are a prolongation of G, the dominant of C - by alternating between G7 (GMm) and C 6/4 (tonic six-four) the tension of the dominant is maintained without ever being resolved. The first true "tonic" C Major chord appears in bar 1 of the Allegro, measure 13 of the piece.
- The score for the introduction to movement 1.
- The recording of the intro.
- Form
- Phrase structure
- Part of the challenge in harmonic analysis is in deciding where each phrase begins and ends. This is vital so that we can then decide what types of cadences are being used, and if there are any modulations.
- Example: the introduction to Don McLean's "American Pie." Where do the phrases end? What cadences are used? What key is the song in? What chords are being used?
- ABA form
- variants of ABA form:
- AB (binary) form
- ABA' (rounded binary) form
- Minuet and Trio form
- Sonata Allegro form
- Rondo form
- Sonata Rondo form
- Pivot Chord Modulation
- This is the smoothest possible way to change keys. One chord that has a function in both the starting key and the new key is used as a doorway - that chord has a dual function, operating in both keys at the same time. In early Common Practice usage (Baroque/Classical periods) these modulations tended to be between closely-related keys only (keys only one accidental apart on the circle of fifths), and the pivot chord had to be diatonic in both keys.
- Example 1: modulation from F Major to d minor.
- Example 2: modulation from F Major to B-flat Major.
- There may be more than one possible pivot chord. The pivot chord is typically a pre-dominant chord, but when in doubt I like to pivot as early as possible.
- In many cases, because closely-related keys are being used there are not many accidentals and it could be possible to analyze the entire selection in one key. However, if you observe carefully you will notice small (or large) errors in reasoning when doing this. Perhaps you might see a non-functional chord progression, like a viio chord that does not move to I as it should, or you may see a high frequency of chords that should be rare, such as iii. Maybe an incorrect cadence occurs. Use your instincts and if something doesn't feel right to you, it probably isn't. This does assume that you are paying attention, however! In analysis, as in all other activities in life, attention to detail is extremely important.
- In example 1 above, it is technically possible to analyze the entire excerpt in F Major with no modulation. However, this gives a final cadence of V/vi - vi, which is not a deceptive cadence (V - vi) or any other type. Therefore, the chorale must not be in F Major at this point. Additionally in F Major beats 1-3 of measure 3 would show V/vi - IV, which is an incorrect resolution of the secondary dominant, so the chorale can't be in F Major at that point, either.
- In example 2 above, analyzing the entire chorale in F Major creates two significant problems. First, in the third measure there is a Cmm chord. In F Major this would be minor v7, borrowed from the parallel minor. Technically possible, but in practice this would never happen on V in a Major key, and if it did happen it would occur somewhere very important, such as in a half cadence, and not in the middle of the phrase on a weak beat. Second, in F Major the final cadence would be V7/IV - IV, which is not a cadence.
- Now, a mini rant on the importance of being observant: the music student faced with analyzing the above chorale may not even notice the trouble they are in. This is because they probably would have analyzed measure 4 beat 2 as a I7 chord since they forgot that I7 is a Major-Major 7th chord while the harmony shown is Major-minor (hence, V7/IV). They would then go on to construct their final cadence as I - IV and label it as a plagal cadence, completely unaware that not only is that not a plagal cadence, but the real issue is that the chorale isn't even in the original key anymore. They also missed the final warning sign: measure 4 taken as a whole is a standard tonic-6/4 - dominant 7 - tonic formula, a cliche in this style, and the formula only works in B-flat Major, not in F Major.
- On a seemingly-unrelated side note, the famous Simpsons "monorail" episode ends with an "escalator to nowhere." Citizens of Springfield blithely ride the escalator several hundred feet into the air, only to be surprised when it drops them onto nothing and they fall to the ground. Why were they even riding it in the first place? It doesn't go anywhere! How could they spend several minutes riding the escalator and never look around and think, "something's not right here, maybe I should get off." How does this apply to the music student? Pay attention to detail, and do your homework when you are not being distracted by something else (TV, Facebook, IM...).
- Further examples of pivot chord modulation:
- Example 3: Bach, Minuet in G Major, Anh. 114.
- Example 4: Haydn, Symphony No. 6 again, this time the second movement.
- Example 5: Telemann, Fantasia in D Minor, movement 1
- Example 6: Bach, Polonaise from Orchestral Suite No. 2 in B Minor (c. 1738)
- Example 7: Clementi, Sonatina in G Major, Op. 36, No. 2
- In more advanced usage, chromatic pivot chords are allowed: the pivot chord does not have to be diatonic, as long as is functional in both keys (for example, V/V could be a pivot chord). This will be addressed in MUSC 3A - for Theory 2, assume that all pivot modulations are between closely related keys only, using only pivot chords that are diatonic in both keys.
- Modal Mixture (also known as borrowed chords / modal borrowing)
- The concept of "modal mixture" means that composers are writing their music to emphasize a particular note as "tonic" rather than trying to establish a sense of Major or minor tonality.
- In practice this means that a particular composer (in particular, Dvorák, Brahms and Schubert are noted for their use of modal mixture) will use all possible harmonies that relate to a certain tonic pitch. If the "key" is G, then composers are free to use any chords from either G Major or g minor tonalities. All of these chords are considered "diatonic." In simple terms, there is now less of a distinction between Major and minor - there is just Tonic.
- Please note that modal mixture only applies to a Major key and its parallel minor, or to a minor key and its parallel Major; not to any other "modes" of a particular tonic. Don't get confused by different uses of the word "modal."
- In its simplest form modal mixture is a single borrowed chord. In most cases, the music is in a major key, and a chord is borrowed from the parallel minor to embellish the Major tonality. Remember that in a Major key there are only 7 diatonic chords, while in a minor key there are 13. Composers began "importing" (borrowing) the more-rich sonorities from minor to spice up their Major-tonality music. The minor mode is already more rich harmonically, so it is much less common to see chords borrowed from the parallel Major key.
- The most common borrowed chords are diminished, such as iio and vio from the parallel minor. The minor iv and v chords are also popular borrowed chords.
- Another common borrowed chord is the "Picardy Third," a borrowed I chord at the very end of a piece written in minor. This can happen at any point in the music, but it is only called a "Picardy Third" when it is the final chord of the piece.
- In more advanced usage modal mixture may involve either an extended section of music in the parallel key or many rapid alterations between Major and parallel minor (often changing the quality of the tonic chord many times: I - i - I - i).
- When changing from Major to parallel minor (and back), the tonal center is not changing, so it is not a modulation. When only the mode is changing, we call the process mutation. Since the music is not modulating, a cadence is not necessary to "confirm" the new mode. This means that modal mixture is a very flexible process and can happen very rapidly.
- ANALYSIS: When only a few chords are borrowed, analyze them with the correct Roman numeral for their quality and function. Then add (BC) to show that the chord has been borrowed from the parallel key. If an extended section is involved (as in the Dvorák example below), write the name of the new key and analyze in that key rather than writing (BC) on every chord.
- Example Three: Beethoven, Symphony No. 9 in D Minor, Op. 125, movement four (1824). At this point in the movement Beethoven has just concluded a long transitional section/fugato in the key of b minor. At the end of the transition there is a dominant pedal (F#) accompanying a B Major chord that Beethoven then restates as a b minor chord, before continuing on to D Major for the next section. Analysis: all in b minor, with the B Major chord labelled I (BC).
- Example Four: Brahms, Symphony No. 2 in D Major, Op. 73, movement three (1887). This movement begins in G Major but features many shifts between G Major and g minor before the end of the first large section. At the end of the first section the harmony changes from I to i several times in a row. Analysis: all in G major, labeling the g minor chords as i (BC).
- Example Five: Dvorák, Symphony No. 8 in G Major, Op. 88, movement two (1889). This movement begins in E-flat major, but moves frequently between E-flat Major, c minor and C Major. The excerpt ends in C Major (the end of the first large section of the movement). As you listen to the excerpt, try to hear the cadences that confirm modulations, and also listen for the moments when Dvorák mutates between C Major and c minor without a cadence.
- Example Six: Schubert, "Die liebe Farbe" - No. 16 from Die schöne Müllerin, Op. 25, D. 795 (1823). This strophic song uses two modal inflections to color its minor key: the Major I (BC), and the minor v (making the piece sound Aeolian).
- REMINDER: Chords that already exist in a minor key because of the harmonic/melodic minor scale forms are not considered to be chords of modal mixture. Therefore, they do not need to be analyzed with the (BC) indication. For example, while the Major V chord in a minor key does exist in the parallel major, the chord is primarily created by raising the leading tone (harmonic minor), not through modal borrowing.
- Altered Pre-Dominants (Neapolitan and Augmented-Sixth Chords)
- The Neapolitan Chord
- An altered version of the diatonic supertonic chord, the Neapolitan is a Major triad with the lowered supertonic as its root ("flat two"). For example, in the key of C Major, the Neapolitan is a D-flat Major triad. The Neapolitan usually appears in first inversion. This chord is most common in minor keys, but it works in Major as well.
- It is analyzed as "N", not as "II" or "bII", and if it is in first inversion, the complete analysis is N6 ("Neapolitan Six").
- As it is a pre-dominant chord, the Neapolitan usually resolves to V and then to I: the bass resolves up by step from Fa to Sol, and the lowered supertonic (Ra) moves to the leading tone (Ti) in the V chord, and then to tonic (Do) in the I chord. Examples:
- Beethoven, Piano Sonata No. 14 in C-Sharp Minor, Op. 27 No. 2, "Moonlight," first movement (excerpt). The chord
progression here is i - i4/2 - VI - N6 - [V7 - i6/4 - V7] - i (IAC)
- Elfman, "Batman Theme" (excerpt) from Batman (1989).
- Berwald, Overture to "Estrella de Soria" (1862)
- The Augmented-Sixth Chord
- This is an altered version of the diatonic subdominant chord. The chord contains the interval of an Augmented Sixth (Aug6), where it gets its name. As a pre-dominant chord, the Aug6 chord typically resolves to V.
- The Aug6 chord appears in three different varieties, which have been given nationalistic names: the Italian chord, the French chord, and the German chord. These names do not imply country of origin or sole ownership of these chords.
- When analyzing an Aug6 chord, label it by type: It (Italian), Fr (French), or Ger (German). Avoid using a generic "Aug6" label.
- All forms of the Aug6 chord contain three specific scale degrees: tonic (scale degree 1, or "Do"), lowered submediant (b6, or "Le"), and raised subdominant (#4, or "Fi"). The lowered submediant pitch is usually in the bass, giving the Aug6 interval between b6 and #4. Note that in a minor key, the submediant is already "flat" compared to the parallel major, and does not need to be altered further. In the keys of C Major and c minor, the Aug6 chord is spelled F#-Ab-C, with Ab in the bass.
- In addition to the three standard notes, each form of the Aug6 chord also contains one additional "color" note:
- The Italian chord doubles the tonic pitch (Do). In C Major: F#, Ab, C, C
- The French chord adds the supertonic pitch (2, "Re"). In C Major: F#, Ab, C, D
- The German chord adds the lowered submediant pitch (b3, "Me" not "Mi"). In C Major: F#, Ab, C, Eb
- Listening examples:
- Italian Aug6 Chord: Beethoven, Symphony No. 5 in C Minor, Op. 67 (first movement excerpt). Chord progression: i // V // i - V - i - V - i - V - i - It - V (HC)
- French Aug6 Chord: Beethoven, Piano Sonata No. 4 in E-flat Major, Op. 7 (second movement excerpt). This movement is in C Major. The recording is of measures 72-78; the French chord appears twice during this section.
- German Aug6 Chord: Michael Haydn, Requiem in C Minor (end of Kyrie movement). This is a standard presentation of the German chord: it resolves to i6/4 and then moves to V for an authentic cadence on I (BC).
Click to go back to the top of the page.
Click to return to the main menu.
