Dissertation Diary 2015-03-03

I took a week off last week to run errands and get some other things done. However, since last updating the blog, I have written a couple more bits for chapter 3.5 and this morning I did a bunch of edits on chapter 3. I have 2 advising meetings this week, and I hope to catch up on readings before the end of the term (hopefully a week from Friday) so I can take both finals and spring break weeks off.


Here’s the most recent (really not-so-good) bit of chapter 3.5 [the missing examples are Bach’s Chaconne, also found at https://functionalanalysis.wordpress.com/2014/01/23/extras-from-week-3/ ]:

Class findings from last winter

During the winter quarter of 2014, I had an opportunity to test-drive Functional Analysis with undergrad students.[1] Thanks to the help of my advising professors, I was able to teach a class of my own devising. After spending a quarter planning materials, assignments, and lesson plans, I recruited former students and other interested parties to participate. We met for an hour twice a week for the 10 week quarter. Much of the class was presenting core theory concepts to students who were already familiar with Roman numerals, but one student was a freshman and one was not a music major at all. I felt each student performed admirably to their level.

While the following conclusions are speculative and not measurement based, initial results are positive. The class covered most diatonic and chromatic harmonic topics in ten weeks. While initially intended to be a translation course, mostly teaching new labels but not new constructs, the class found the new perspectives on harmony led to new connections between musical ideas. Not only did they learn new labels for chords, but my students also learned new things about various repertoire, started to get a better grasp at analysis in general, and explored how music works on multiple levels. I kept a record of lesson synopses and assignments on a blog.[2]

Because of the translation nature of the class, we were able to cover nearly a year’s worth of harmonic topics in 10 weeks. I believe that Functional Analysis also contributed to the speed of topics, as even our less experienced students more or less kept up. I received positive feedback about Functional Analysis from all of my students.

The reactions of students in my class were uniformly positive. Some are still using this system and prefer it to Roman numerals, because Functional Analysis is faster for them than with Roman numerals. Another said that it was making clear the chord and harmonic concepts he was learning in his core theory classes, especially Aural Skills, by emphasizing the functional pillars, clearly differentiating between stable and decorating chords, and having fewer categories to sort chords into.[3]

Student feedback was overwhelmingly positive, with comments [edited for grammar] such as:

  • “I appreciated the opportunity to shed more light on how music ticks. I loved that I could apply this even without a great deal of music theory analysis experience.”
  • “It helped give perspective to functional/structural aspects of music. Rather than trying to look at I and vi or ii6 and IV as separate things, it helps me to understand these as variations of a function.

Helped me to put chord progressions in perspective, and helped me in my ear-training by listening first for functionality, rather than specific chord-types.”

  • “It shows a much faster analysis of a piece of music.”

Some new ways of looking at things were challenging at first (different conceptualizations of sixth chords and relations in minor, for example), but by the end of the quarter, all students wrote papers on a piece of their choosing, using FA to help them uncover something new (to them) about the piece.

Throughout the course we worked with concrete examples from the music literature, finding functional pillars before describing their elaborations. Advanced students were also asked to write some progressions to consider how function affects voice leading. One of the favorite homework assignments was one comparing various iterations of the chordal pattern of the Bach Chaconne from the D minor Partita for Unaccompanied Violin. A similar exercise was attempted with different versions of famous Bach Chorales (Herzlich tut mich verlangen) and with Functional Analysis it was quite easy to analyze and track the changes to the functional pillars of the phrase.

The following examples from the class, Examples 28 and 29, show how Functional Analysis helps lead to better phrase and motivic understanding. These examples are two versions of a harmonic analysis of the Bach Chaconne from the Partita in d minor. Example 28 show the Chaconne analyzed with Roman numerals and Example 29 shows it analyzed with Functional Analysis. This comparison allows us to see the functions change from the stable basis of the chaconne pattern.

Example 28

With Roman numerals, it is possible to see the changes as the chaconne pattern mutates. Different predominants are used, the V comes in different flavors and at slightly different times. However, with Functional Analysis, most changes can be seen as less drastic, for example, merely an added tone in measure 8. Additionally, since the functional areas of the phrase are clearer, it is easier to see when the predominant area changes length (mm. 10-11, 14-15) or the dominant starts early (mm.12, 16).

Example 29

Pros and cons (sticky wickets)

Some of the things that were challenging were reversed relations in minor, chords with multiple labels, relearning how P6 works, voice leading (which I thought more about later, after the class), and for one of my most advanced students, using Functional Analysis on the edge of tonality – trying to analyze Reger.

After the quarter was over, I also got some question on how one would teach voice leading with Functional Analysis. After all, that’s why we make students learn figured bass, right? I spent a couple hours with a friend trying to work out how to approach this problem,[4] and we determined that Functional Analysis could take advantage of the split bass/upper voice numerals, and decide to over-show detail for the purposes of teaching voice leading. Additionally, the fact that the pitches that have certain resolutions are always the same number (the leading tone is always 3 of Dominant, the 7th of a chord is always 7) makes it easier to track these resolutions.

[1] I documented my course with a blog: https://functionalanalysis.wordpress.com/2013/12/12/syllabus-and-schedule/

[2] functionalanalysis.wordpress.com.

[3] Ryan Ponto, personal communication.

[4] Milo Fultz, May 10th.

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