Blog Posts Harmony Pedagogy Teaching Materials

Chord Inversions: They’re Not Just For Labeling Anymore

A Little Background

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”).

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How to Interpret Chord Symbols

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.

Blog Posts Online instruction Teaching Materials

Non-Chord Tones in Tchaikovsky’s “Romeo & Juliet”

Having trouble viewing this in the frame of this blog? Follow this link instead.


Blog Posts Composition & Orchestration Rhythm The Museum of Rhythmic Oddities!

Take a few pitches; shake, strain

A rare photograph of Irving Berlin and David Lang taken ca. 1935 and 2005.
A rare photograph of Irving Berlin and David Lang taken ca. 1935 and 2005.

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

[Listen to the music and see the first page of the score]

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. I became so exhilarated after listening it that I got on one of my favorite websites on the internet, and got a couple of the best turntables from their website to listen to this track on repeat. 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.

Blog Posts Pedagogy Rhythm

Rhythms are Boring; Rhythm Is Fascinating

spiralWhat 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.

Blog Posts Form & Melody Pedagogy

Motive: Beyond Simple Identification

My students frequently don’t “get” what I try to convey for analyzing motive in musical compositions. The challenge is that there are two things that are important for this topic:

  1. That motives can be located and that their transformations can be identified (look! it’s the motive from the beginning of the song! and it’s inverted!).
  2. That motives can be a structural element of music, that they can be used cleverly, and that their appearances can help to bring grace, drama, and “logic” to music.

The first item is fairly easy for me to teach and fairly easy for my students to learn. I introduce a series of terms (transposition, inversion, retrograde, elaboration, truncation/fragmentation, and so forth) and isolate musical motives in a passage of music. If the examples are clear enough, any student can identify a method of transformation.

But the second item on that list is harder; it demands thoughtful musical analysis, making the student look within phrases, across phrases, up and down the musical texture, compare melody to harmony, and more. It’s a real challenge. And I haven’t figured out a great way to make this “testable.” Mostly what I tend to do is give a song in lead-sheet format (Mancini & Mercer’s Moon River and Rodgers & Hart’s Bewitched are favorites) and ask students this question:

Blog Posts The Museum of Rhythmic Oddities!

The Museum Of Rhythmic Oddities! Exhibit #1: Mozart String Quintet in G Minor

5tetThis amazing passage of music makes for fun discussion, perceptive listening, and exploration of hemiola, syncopation, perception issues, and more. I typically teach it in first-semester music theory classes, but also adapt it for non-majors music as well.

The music in this “exhibit” is all taken from the second movement (Minuet & Trio) of Mozart’s String Quintet No. 4 in G Minor, K. 516.

It starts off easy

This exhibit begins with a simple task: what is the meter of this example, and what would an appropriate time signature and rhythmic notation be? Try conducting along with the recording.

Aural Skills Blog Posts Online instruction

Video Solfège: Creepy, But Effective!

Nobody practices solfèggio

Guido d'Arezzo
Guido d’Arezzo apologizes to a thousand years of students

Students don’t practice solfèggio for a panoply of reasons, most of which are good ones:

  • Practicing it is boring
  • They find it easy (they have good ears, good voices, and learn the syllables with little effort)
  • It is difficult for them and they are not motivated to do well (the “I’ll take the C” crowd)
  • They want to succeed but don’t have clear indicators to discern improvement. Some of these students practice a little, but not enough because they think they have “completed” practicing by running through exercises or because they give up in frustration.

Most students share the classic experience of sitting outside an office door, cramming melodies before performing for their professor, which is likely the only practice they put in before the exam. And, regardless of a student’s level of preparedness, many students will choke on a solfège exam because of bad nerves.

I’m going to take the following positions, which might not be shared by all music professors (but I imagine many of the points are common):

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Melodic Orientation vs. Dictation

Melodic Dictation

If ear training textbooks with CDs and various online musical trainers fairly represent standard practice, “traditional” melodic dictation is typically a four-bar exercise in which a starting pitch is given, a count-off is sounded, and a series of notes that resemble a melody is played on piano. I have some problems with this…

  1. If there is no accompaniment,  students miss out on a valuable asset for orienting metrically and tonality. How many melodic dictations have I seen that get “off” by a beat or are consistently a step (or two, or three) too high after a leap is missed?
  2. The best students are bored silly waiting for the rest of the class to finish.
  3. The most challenged students struggle with the first notes and never get to the end; they are discouraged seeing the top students wait and are likely hampered by the pressure of holding up the class.
  4. Dictation takes a long time and leaves little opportunity for giving/getting feedback. Even when I walk around looking over students’ shoulders, it’s hard to guide students without revealing details to others nearby.
  5. Little mistakes (a skipped beat, a missed leap, a chromatic step written as a diatonic step) can cause big trouble and a lot of wasted time.
  6. Dictation doesn’t build some basic skills (most important among them, I think, being how to orient tonally without being given a tonic or starting pitch).

Melodic Dictation Orientation

My favorite type of dictation activity turns many of these problems on their head. I call these elegant little exercises melodic orientations, and they look like this:

Notate the first eight tones of this melody, adding all necessary information for notation. The key signature has four sharps.staves
Blog Posts Composition & Orchestration

Orchestration project peeves

…a.k.a. “Has this student ever seen a page of printed music?” These things should (but do not) result in immediate failure and/or being made to sit in the corner.

Because a student isn’t thinking with their ears

  • When there is no tempo marked
  • When there are no dynamic markings at all. Or a tempo indication. Or articulations and slurs…
  • When an effect only lasts for one note

Blog Posts Online instruction Pedagogy

Syllabus boilerplate: Guidelines for email correspondence

mailNote: since I began including this in syllabi (and pointing it out at the beginning of each semester), emails from students have become… slightly… better. The good ones remember this when emailing me. The others can be ignored and referred back to the syllabus. Any other good solutions out there for elevating the tone of student/teacher e-correspondence?

Blog Posts Pedagogy

Theory Class Rocks!

Who doesn’t love the same music you do? Your students, probably.

None of your students cares what this man sang forty years ago.
None of your students cares what this man sang forty years ago.

First of all, let’s address the elephant in the room: popular music brought into the classroom by a professor will never be a student favorite. If a timely hit is brought to class to illustrate a point, it will soon enough be out of date. A classroom of students represents a spectrum of tastes, so while you are reaching the Zeppelin fans of the class, you are making the Beyoncé fans roll their eyes.

I think, though, that students appreciate learning from a variety of sources (rock and pop among them) since this illustrates an important concept:

Music theory embraces universal principles, not just irrelevant techniques of long-dead, elite composers.