Last year, I tried out a technique for enhancing student engagement in online courses: crowd-sourcing representative examples of course topics.
Responding to a complaint from students that online quizzes were too difficult and extra credit options were needed, I offered students an opportunity to demonstrate comprehension by locating their own musical examples. This can be a tedious part of my work — finding “exemplary” musical passages that demonstrate each facet of a lesson. This way, I open up the possibility of getting something out of it, too; the best submissions can be incorporated into my course materials.
The process is simple: I create a Dropbox folder for each lesson in which students may submit three examples that fit specified constraints. One task, for example, was to submit (on annotated sheet music) three examples of musical modulations that exhibited different approaches: pivot modulation by common chord, direct modulation, and pivot modulation by change of chord quality. To earn full extra credit, they needed to find one of each and they needed to be correct and correctly labeled. Their examples also had to be unique among the class; no choosing a passage that had already been used by another student. If examples did not earn extra credit, the student may submit more batches of examples until they get it right, but only before the weekly unit quiz.
Once I received their files, I would add markup comments on their PDFs to show if each example was correct or incorrect, and make a note about why it was a good or weak example. Since the Dropbox folder is public, students could then examine their peers’ examples and learn from the successes and shortfalls.
A starting point for engaging students is picking a great example. With the right music, a student’s curiosity can be piqued and a great piece of music engaged. For almost any topic, I tend to follow these principles:
Find a single piece or whole section that illustrates all (or most) of the concepts of the lesson. Little excerpts don’t give students a chance to appreciate how the topic can affect a musical whole. It’s fun to analyze a whole piece or section of music since it feels like you are really unpacking the music; it’s hard to engage a single phrase of music and then another… and then another… and feel like you are doing much more than identification.
Famous tunes give the impression that theory class applies to “real” music (sorry: songs from Winterreise aren’t famous in most student circles). Children’s songs are often terrific. There is a chance that students might recognize Classical war-horses from having heard them in another class, a commercial, as a ring-tone (Turkish Rondo, anyone?). Continue reading →
Chord inversions are the second thing music students learn about chords, right after how to spell chords over a given root (what the pitches of D Major or F♯ Diminished is). For those who are new to the topic, follow this link.
Chord inversions are mostly taught by looking at chords in the easiest possible manner: as close-position triads or as block chords in simple four-voice chorales. When they are studied like this, students can quickly learn how to identify a chord’s position (either root position or inversion) and assign it a numeric label: 5/3 or 7 for root position, 6 or 6/5 for first inversion, and so forth.
It is much more difficult to apply the concept of inversions to music that doesn’t move in block chords, and in most music, the bass is elaborated in some way, complicating the matter. Sometimes they are ornamented with passing tones and such between “structural” tones, and when a bass line is genuinely florid (as in much classical or jazz music) it becomes very tricky indeed.
So, Why Do They Matter?
Why do we study chord inversions? To many students, it’s tedious busywork to parse the pitches that make up a chord, figure out which is lowest, and assign a numeric label. Some of the point may be to dwell a while on spelling chords. It is also an introduction to the idea of following one note of a chord to the next, which introduces the subject of voice-leading, which is often a primary concern of harmony courses (though that is increasing being considered “old-fashioned”).
The ability to read a chord symbol and name the pitches of its chord is an essential skill for all musicians. I use it constantly in all of my music theory, analysis and orchestration courses to quickly describe musical harmony while dispensing of the need to suss out harmony from a written-out texture. It is, of course, also the foundation of jazz and pop improvisation.
Students of classical music often do not learn how to interpret these symbols beyond plain triads, so I am providing this lesson as an introduction for those students.
It’s may seem like a huge stretch to find parallels between the music of Tin Pan Alley songsmith Irving Berlin and avant-garde postminimalist David Lang, but here’s a great meeting point in two pieces of music separated by more than 60 years: the use of systematic rhythmic permutation.
Cheating, Lying, Stealing (1993) was David Lang’s breakthrough piece, putting him on the map as a hugely influential composer. I remember hearing it for the first time back then and being dumbstruck by its visceral energy and rhythmic unpredictability. There’s something about its clangorous instrumentation — especially in its “rhythm section” of kick drum and brake drums — that I feel establishes a perfect balance of metric “orientation” and “disorientation.” I’m especially thinking about its first third (up to 3’50″ on the Bang on a Can All-Stars recording) and its last minute (starting at 9’36″). For years, I never attempted to figure out if a pattern guided his process — I just marveled at the clanky rhythms.
There is a pattern under it all, of course, and it’s fun to figure out. SPOILER ALERT: I’m going to tell you what it is, so if you want to give it a shot first, here’s a tip. Skip the first two bars (the intro) and take the music in dictation, all in 4/4 meter, separating the treble and bass lines to consider separately. See if you can find what’s going on.
What do students learn about rhythm? Mostly these things, which are all essentials:
Rhythm (in most music…) is based on a series of steady “beats,” which are somehow organized into metric patterns (duple or triple, simple or compound, and so forth) based on surface patterns in the music.
Musical notes indicate relative duration: a whole note = two half notes = four quarter notes = eight eighth notes, and so on.
These notes may be organized to “play nicely” with the meter, or to “rub against” it, which would indicate a “pick-up,” a syncopation, or something called hemiola. Students should be able to define hemiola once and are not asked about it after their second week of school until the third semester, in which they will point it out in music by Brahms.
But that’s pretty much where rhythm ends in textbooks. Steven Laitz goes a little further by writing a few paragraphs on what makes rhythm… well… what makes rhythm. There is harmonic rhythm (patterns made from when harmony moves from chord to chord), there is change of musical patterning, and a few others based on changes in texture, dynamics, and register. It’s accompanied by a confusing diagram of eight bars from a Mozart sonata.