Harmony

For Week 1 of Analytical Techniques, we reviewed analysis of harmony. Concepts covered included: types of chords occurring in tonal music, functions of chords, non-harmonic tones, expressive corrections, the Neapolitan 6th chord, augmented 6th chords, common-tone diminished 7th chords, and chromatic third relationships. On Thursday night (March 21), we had our first optional Live Classroom in which the instructor walked us through our first Application. By Friday, we had to submit a Discussion Board post. On Saturday, we had our second weekly optional Live Classroom answering questions about our assignment which was due Monday, March 25.

Concepts

The main goal of this course is to develop a “multi-layered approach” to analyzing music using harmony, form/structure, melody, phrase structure & meter, ambiguity, and context. Each week adds a new “layer” to our approach. The layer of harmony was mostly review of Roman numeral analysis through the lens of theorist Hugo Riemann. Most of the concepts were things I taught in Music Fundamentals: types of triads and seventh chords, diatonic chords in major and minor modes, functions of chords, non-harmonic tones, and expressive corrections (secondary dominant and leading tone chords). I needed to review concepts like the Neapolitan 6th chord, Augmented 6th chords, and chromatic mediants. Unfortunately, the lecture material and course textbooks were not helpful for this purpose. There were a few modules that were helpful:

The key piece I remember about augmented sixth chords is their construction: An Italian 6th (It+6) is M3-A6. A French 6th (Fr+6) is M3+A4+A6. A German 6th (Ger+6) is M3+P5+A6 and sounds like a dominant 7th chord. What I learned (or relearned) this week is that theorists believe augmented sixth chords evolved out of the Phrygian half cadence in minor (iv6 - V) by raising the root of the iv chord to create an augmented 6th with the bass. This is demonstrated in the 2nd image above this paragraph. The first measure of the top line (a) shows IV6 - V in C major. The second measure shows iv6 - V in C minor. The third measure shows V6/V - V in either C major or minor. The final measure shows the outline of an Aug+6 - V in either C major or minor. Line (b) shows a fleshed out progression to an It+6, line (c) to a Ger+6, and line (d) to a Fr+6. Because of the P5 in the construction of a Ger+6 chord, parallel fifths can be avoided by inserting a 6/4 chord into the progression before the V chord.

The way most online resources have described the construction of these chords (N6, It+6, Fr+6, Ger+6) have been based on scale degrees. Squarespace does not let me use the ^ notation above numbers to denote scale degrees, so know for the list below, the Arabic numbers denote scale degrees.

  • N6: b2 + 4 + b6

  • It+6: b6 + 1 + #4

  • Fr+6: b6 + 1 + 2 + #4

  • Ger+6: b6 + 1 + 3 + #4

According to our lecture modules, the most commonly used chromatic notes are b2 (N6), #4 (Aug+6), and b6 (Aug+6 and chromatic mediants). They provided a very helpful Adobe Edge module pictured below. The first picture shows an empty module. By clicking on any key of the piano, the module filled in the most common chromatic alterations. You can see what it does for the key of C in the second picture.

Application and Live Classroom 1

After completing the lectures, there is an optional Application component—an analysis that uses skills similar to those in the required Assignment. The Application is always discussed during the first weekly Live Classroom. For this week, we were asked to provide a harmonic analysis for Chopin’s Prelude, Op. 28, No. 4 in E minor. Because I am borrowing the Burkhart Anthology from a friend, there was already some analysis penciled in. In an effort to test my own analysis chops and to continue learning the program, I entered the piece into Dorico, the notation software from Daniel Spreadbury and Steinberg. I then analyzed the resulting PDF on my iPad Pro with an Apple Pencil. I tried analyzing in GoodReader, but I am not happy with how the app “groups” annotations, making them difficult to go back and edit.

The piece was an excellent place to start because it is predominantly (pun not intended) diatonic with a few quirky tonicizations for finding Aug+6 and modal mixtures. In our Live Classroom, Mr. Berger took us through how he would analyze the piece with some key points about analysis in general:

  • Sonority (type of chord) equals function (Tonic, Subdominant, Dominant, Mediant)

    • Dominant 7th chords have a very specific sonority and are the most important chords for orienting harmony

    • Fully diminished 7th chords typically progress to a tonic chord unless they are a common-tone diminished 7th (CTº7, where 1 or more common tones are kept as the chord resolves)

    • Half-diminshed 7th chords are typically pre-dominant (iiø7) and only occasionally viiø7

  • When Classical composers modulate, they will typically use a pattern of “falling fifths” that usually include pre-dominant chords

  • Label tonicizations by putting a bracket beneath chords (as opposed to, for example, V7/V - V)

  • Never use a minor dominant chord. If you think you have found one, you have probably analyzed incorrectly.

  • Dominant 9th chords do occur in Classical music, and the 9 can be altered.

Discussion

Prompt: Begin by reading William Marvin's article, Introduction to Writing Analytical Essays, (pp. xi-xiv), in Engaging Music. In this article, Marvin outlines six steps in the development of an effective and insightful analytical essay. One of the most powerful arguments he makes, is the statement that "clear thought about music and clear writing about music are related-if you have difficulty articulating your thoughts on paper, chances are that the thoughts themselves are unclear." Select one of these six steps to apply to a work of your own choosing from the Burkhart Anthology. (The work need not be long or complex; a short movement from a larger piece will suffice.) Outline the application of this particular step to your selection in detail. Remember that clarity is one of the main goals of effective writing.

Marvin’s Steps

  1. Learn the Piece

  2. Begin to Analyze

  3. Research (when possible)

  4. Form a Thesis

  5. Write

  6. Revise, Revise, Revise!

Response: Beginning to Analyze Bach’s Prelude 1 in C Major (BWV 846) from The Well Tempered Clavier, Book 1

Marvin (2005) provided four considerations for analyzing any composition: form, melodic and harmonic language, temporal organization, and extraordinary features (p. xii). One might argue that by answering any of Marvin’s considerations, a theorist is also forming a thesis about the composition. For example, by choosing to use Roman numerals to analyze Bach’s Prelude 1 in C Major (BWV 845) from The Well-Tempered Clavier, Book 1 (Burkhart & Rothstein, 2012, pp. 109–110), I am forming the thesis that Bach wrote the piece using primarily tonal melodic and harmonic language. Going further into Marvin’s (2005) analysis step, if I am to articulate my “most profound insights about the music’s organization and meaning,” I am also conducting research (p. xii).

It was in my analysis and research of the work that I found an interesting fact that drew me to examine the piece more closely. Several scholars believed Christian Friedrich Gottlieb Schwencke, a cantor in Hamburg, inserted a measure between Bach’s measures 22 and 23 to attempt to correct the progression (Barber, 1970, p. 19). In Burkhart and Rothstein’s (2012) version, measure 22 contained an F# fully diminished seventh chord (p. 110). Measure 23 contained the pitches Ab, F, B, C, and D, which I analyzed as a common-tone diminished seventh chord with C functioning as a passing tone. Measure 24 contained a G dominant seventh chord. Schwencke’s inserted measure contained the pitches G, Eb, B, and C and was meant to smooth the bass progression from an Ab to an F# with G (Barber, 1970, p. 19).

The rest of the prelude is fairly straightforward. The piece begins in C major with an extended tonicization of the dominant from measures 5–11. There is a brief tonicization of D minor in measures 12 and 13 before progressing to the dominant in measure 14 and tonic in measure 15. Beginning in measure 26, Bach highlights the tension between the dominant-tonic resolutions with suspensions in and tonicizations of the dominant. The final three measures extend the tension further with a pedaled C and augmented rhythms in the bass.

Barber, E. (1970). Questions to the editor. Bach, 1(1), 19–22. Retrieved from https://www.jstor.org/stable/41639775

Burkhart, C., & Rothstein, W. (2012). Anthology for musical analysis (7th ed.). Boston, MA: Schirmer.

Marvin, W. (2005). Introduction to writing analytical essays. In D. Stein (Ed.), Engaging music: Essays in music analysis (pp. xi–xiv). New York, NY: Oxford University Press.

Assignment and Live Classroom 2

Prompt: The assignment for this week consists of a "problem set," containing three excerpts from a work for solo piano and two different string quartets. As we will explore in the coming weeks, there is much more to "analysis" than just assigning Roman numerals. That being said, an understanding of other aspects of a work's structure is always dependent on an understanding of the underlying harmonies, so it is vital that one clearly understands the harmonic structure first. You will complete a Roman numeral analysis of each of the three examples, accounting for all NCTs. Remember, the vertical/horizontal nexus in tonal harmony is vital to an understanding of how harmonies operate. One can not simply take a vertical slice of harmony—divorced from its horizontal context—to determine a Roman numeral.

Discussion: There were parts of this problem set that were very easy: identifying long tonal centers, Roman numeral analysis of diatonic sections, labeling cadences… I even began to do well identifying brief tonicizations and Augmented 6th chords. The first piece we analyzed was the second movement of Haydn’s String Quartet No. 65, Opus 76, No. 6. The second piece was Chopin’s Mazurka, Op. 7, No. 2 in A minor. This was the piece that gave me the most difficulty with a small section in the middle I struggled to identify chord functions. The last piece was the second movement of Beethoven’s String Quartet No. 1 in F major, Op. 18, No. 1.

For the assignment, I used the forScore app on my iPad Pro. This particular PDF reader is designed for sheet music, allowing for a large variety of annotations. I was able to write the required components of the assignment in one color while keeping my own notes in a different color, coming back through to erase my notes before submission. I will definitely continue using this as the course progresses.

Live Classroom 2: This session was completely student-driven, led by questions about the assignment. The instructor was careful not to give away answers, but reinforced several strong points form the first Live Classroom. Here are a few big points he discussed:

  • What is the consistent harmonic rhythm?

  • From Live Classroom 1: Sonority = Function

    • Dominant 7th chords will always be V7/X.

    • Fully Diminished 7th chords will almost always be viiº7/X, except when they are CTº7. Look at the chord in context to see how it resolves:

      • viiº7/X resolves up by half step.

      • CTº7 resolves to a chord with one or more common tones.

    • Half-Diminished 7th chords will usually be iiø7/X and only sometimes viiø7/X in major. Look at the chord in context to see how it resolves

      • iiø7/X functions as a pre-dominant chord.

      • viiø7/X resolves up by half step.

  • Any time you have an accidental outside of the key signature (with exception of raised leading tone in minor mode), you must rethink everything for that chord.

    • What is the sonority?

    • What is being tonicizied? Have you modulated?

      • 1 or 2 chords is a tonicization. Bracket to show toniciziation with a Roman numeral. Frequently a secondary dominant resolving to it’s tonic, potentially a pre-dominant chord too

      • Modulations require a confirming cadence (cadence in new key)

    • Is it modal mix?

      • The chord is functioning the same but being borrowed from the opposite mode. Usually borrowing minor key chords into a major key piece.

    • Chromatic Harmony

      • Neapolitan is a major bII chord. The Neapolitan can be tonicizied or modulated to.

      • Augmented 6th chord: Most common: Fr+6 and Ger+6

        • Fr+6: Two M3 separated by whole step (4 notes of whole tone scale). Usually resolves to V

        • Ger+6: Sounds like dominant 7th chord, except 7th is spelled enharmonically wrong (C-E-G-Bb is C7. C-E-G-A# is Ger+6 in E). Usually resolves to a 6/4 chord before V to avoid parallel 5ths.

  • Modulations

    • In minor key pieces, the most likely destination of modulation is the relative major. Occasionally, they modulate to the dominant. If a minor key modulates to the dominant, it will modulate to a dominant key area that is minor. If the dominant is being tonicizied, pre-dominant chords will typically be minor in quality.

    • A composer can modulate to any chord that exists in its original home key (Ex: In CM, a composer could modulate to Dm, Em, F, G, or Am. They won’t likely modulate to Bº)

    • Using modal mix, a composer could modulate between parallel major/minor. This adds potential modulations of the parallel mode.

    • Other things that can be modulated to: Neapolitan.

Comment

Burton Hable

Burton Hable is an instrumental music educator from Central Iowa. In 2013 he helped open Centennial High School in Ankeny, the first time in forty years that a school district in Iowa expanded to two high schools. He served there through 2018 as Assistant Director of Bands: conducting the 10th Grade Symphonic Band, directing the varsity Jazz Collective, co-directing the Centennial Marching and Pep Bands, teaching music theory, and providing individual and small group lessons to brass students in grades 6-12 at Prairie Ridge Middle School, Northview Middle School, and Centennial High School. During his tenure in Ankeny, enrollment in band grew from 450 to nearly 700, the jazz program expanded from four to seven ensembles, and ensembles under his direction were invited to perform at Iowa State University, Harper College, and the Veterans Day Parade in New York City.