A Gap Between Theory and Practice

I arrived as a first-year student at the University of Southern California with a few months of piano lessons and an equal amount of music theory under my belt. I could figure out the key signature of a piece, or tell you what a triad was, and that was about it!

I managed to get good grades in my core classes of music theory, class piano and ear training, but I never mastered any of it. Analyzing music was like calculus: I knew how to “plug and chug,” but I didn’t understand how or why it worked, let alone why it mattered!

Music theory, in particular, always seemed purely academic, separate from my work in the practice room. With the exception of an occasional demonstration by a professor, theory was studied entirely on paper, rather than at an instrument, and as such it felt totally abstract. How could knowing different kinds of cadences and Neapolitan chords make me a better musician?

Occasionally I rehearsed with students who seemed to always know what chord we were playing, or would point out an interesting element in the music that I hadn’t noticed. While initially annoyed, I was mostly jealous of these students – they seemed to have a deeper insight into how the music worked!

My teachers, coaches and conductors also periodically exhorted me to “think like a composer.” I had a vague idea of what that meant. Drawing a comparison to the work of analyzing texts in my literature classes, I gathered it had something to do with considering how and why composers make decisions — why chose a certain chord, or a harmony, or a certain form?

But my own attempts at analyzing pieces were like stick figure drawings – short on detail and of little help in understanding the thought process of the composer let alone the inner workings of the music. I didn’t have enough mastery of the basics to make anything more than a cheap attempt at analysis.

I was frustrated by the yawning gap between the classroom and the practice room, but didn’t know how to bridge it. I knew I was missing something (or someone) to help me tie it all together.

Crossing the Gap

It wasn’t until the summer of 2018 that I began to bridge this “theoretical” gap. The catalyst was a week of training at the Dalcroze School of the Rockies, directed by Dr. Jeremy Dittus. This bridge was created in part by the intensely musical way that Dalcroze teaches the fundamentals of music – at an instrument or, more often, moving your body through space – but also in part due to how we were taught to practice.

As part of my Dalcroze training, I had to learn the I-IV-V⁷-I chord progression at the piano in all inversions in a number of keys at a set tempo. I was given this same assignment in piano class at USC, what was new was how I was taught to practice.

Dr. Dittus taught us a set of strategies to help internalize the progressions, and they were a game changer for me! Not only did I find myself more focused while practicing, but I internalized the progressions more deeply, and more quickly, than I had working on them in college. After a while I began to see pieces through a harmonic lens that I never had before – it was as if I had developed x-ray vision!

I was beginning to see what I had been missing all along. Understanding pieces even at this basic harmonic level gave me a view inside the guts of the piece and started me on the path to thinking like a composer.

Helping My Own Students

Most of the college students I work with are like I was — they come with very little training in the fundamentals of music. After my experience at the piano in my Dalcroze training, I thought about how to help my own students cross the divide between their classroom and studio work. And I knew I wanted them to be able to experience it on their own instrument, where they would feel an immediate impact. Since string players can’t easily play triads, arpeggios seemed like a natural entry point.

Background Knowledge

To be successful in this particular practice, the student needs a working knowledge of intervals, as well as the basic construction of triads and seventh chords. If any of that sounds like gobbledygook, here’s a good place to learn those concepts.

Arpeggios in many scale books follow this chord progression:

Memorizing the chord progression alone can be daunting, but it’s essential! Once the fingering and the sequence of chords have been memorized in one key, they have the freedom to transpose it up and down the fingerboard. (Whether or not they do that is another matter entirely: the story goes that Carl Flesch wrote out his arpeggio sequence in C major but found that his students weren’t playing it in any other key, which forced him to write his Scale System. Makes me wonder how many other method books arose from a frustrated teacher.)

Here’s what that the progression looks like in C Major/Minor written out in two octaves.

Chunking

Chunking is a technique to reduce the amount of information that needs to be memorized by grouping it into larger units. In the fantastic book “Moonwalking with Einstein: The Art & Science of Memory,” Joshua Foer uses the example of memorizing the number 0911200112071941. Breaking the number into chunks of four numbers 0911-2001-1207-1941 makes it easier to process. Going further and turning those numbers into two 8 digit chunks we can recognize them as dates – 09/11/2001 (September 11th attack) and 12/07/1941 (attack on Pearl Harbor). The strong emotions and imagery generated by those fateful dates makes those numbers MUCH more memorable! Now I just have to remember the order of the two events, and I can recall the entire sequence of numbers.

Helping students find meaningful ways to chunk the arpeggio sequence is essential to them memorizing it quickly and vividly. With some additional direction, it can also encourage them to search for memorable associations in their other music, putting them on the path to memorizing longer pieces.

To help a student memorize the chord progression, I start by showing them that there are three pairs of related chords. Here are those pairs along with their relationships:

i & I (vi⁶): Same chord, first major minor then major. I often teach the vi6 chord with this group too, since it’s the only chord without an obvious pair. Since it stands between the first two pairs of chords. I talk about it being “the outlier” or the “minor rebel” in the sequence.
IV^6/4 & iv^6/4 : Same chord, first major then minor.
diminished 7th & dominant 7th : These are the only 7th chords in the sequence. When learning these chords we also discuss the relationship between the V⁷ chord and the I chord.

Choosing chunks that have strong associations, and clearly elaborating those associations, helps the student remember the individual pairs. Going through the chord progression can also spark a discussion on good voice leading and why the sequence is written in the order it is. (Whether or not this is the chord progression we should actually practice is a topic for another post!)

Chunking is itself a helpful strategy for memorization, but what’s perhaps more interesting is that when an arpeggio is mastered, the arpeggio itself becomes a chunk! It has turned into something that the player can glance at and instantly execute with minimal effort (hat tip to Nathan Cole for helping me see that connection).

That effortlessness can only result from a deep internalization of the arpeggio as a unit AND the ability to recognize it in a piece of music. More on that later!

Memorizing Individual Arpeggios

To memorize an individual arpeggio, I start by having the student construct it from scratch, WITHOUT music. Since they’ve memorized the sequence, they know the chord to be played and now must work to recall the three notes that make up the given chord. It requires most students a lot of “brain sweat” to work out the individual notes of each chord AND figure out where each note is on the fingerboard! If they struggle, I’ll ask them leading questions, shepherding them through the construction of the chord. It’s a bit of a socratic method of teaching arpeggios!

Sure, it would be much faster to just put the music in front of them and have them play! But this work is a variety of active recall, and is scientifically proven to be one of the most effective ways to learn. By the time they’re on the other side of the process, they OWN these arpeggios in a much different way than if they had simply memorized them by rote. Mastery is worth that extra time!

I usually teach one group of arpeggios in each lesson, so 3 lessons for the whole sequence. This gives each group time to simmer, and the student time to experiment with the practice strategies outlined below. Most of these methods are directly adapted from my Dalcroze work.

Say the Roman Numeral
To reinforce the memory of the chord progression, I’ll have the student say the roman numeral before they start playing any given arpeggio.

Say/Sing the Note Names
The student says or sings the note names BEFORE they play the note. This forces them to know what note they’re playing BEFORE they play AND to hear it in their head.

It’s surprising how often we don’t know what note we’re playing! By linking the sound with its name and a precise location on the fingerboard, we create a more detailed map of its geography.

Furthermore, if a student knows that they are playing a note corresponding to an open string, they know they can listen for sympathetic vibrations from the instrument to help with intonation and maximize resonance.

Say/Sing the Fingering
Saying or singing the fingering BEFORE playing ensures that the ear and the mind are leading the finger, instead of the other way around! This is especially helpful at the beginning of the process.

If the arpeggios have already been mastered with one set of fingerings this is also a helpful way to work on a new set.

Say/Sing the Intervals
Saying or singing the intervals in the arpeggio helps understand the physical distances between the notes, as well as the construction of the chord. It also helps with intonation: if the student is aware that there is a Perfect 4th between the 2nd and 3rd notes of a vi6 chord, then they know that playing those notes together would be a good way to check if they’re in tune!

Saying how far apart the notes are in whole or half steps is another great way to imagine the physical distance in the hand, especially when the interval goes across strings.

Say/Sing the Root
Knowing the root of the chord also helps with intonation. If you were to tune to a drone, this is likely the note you would set it to. In the context of a string quartet, this is the note the cellist would likely play. In our C major/C minor arpeggios the root of the first two chords is C, then A for the 3rd chord and F for the next two chords.

Say/Sing the Scale Degree
Knowing the scale degree of the note being played helps with understand the function of the chord, the inversion, and the intervals.

I have a student practice with 2 or 3 of these methods per lesson. Each one creates a different layer in the student’s memory – a bit like a Google map that allows you to view only the terrain, or the transit routes or the traffic. Every additional layer adds a more nuanced understanding of what’s being played.

Different students will connect with certain methods more than others. Giving them the whole toolkit allows them the opportunity to discover for themselves which layers are most vivid for them. In addition, these practice methods are HARD! A student HAS to think and/or audiate while practicing, they can’t just go on autopilot, which is what many of us do when we practice scales or technical exercises!

At their core, these practice methods are simply examples of good deliberate practice.

Linking to the Repertoire

Memorizing arpeggios is a great first step to getting a student to think harmonically. But to bring it home, it’s important to show examples of chords and arpeggios “in the wild” of their own repertoire.

One of my current students recently struggled with this passage in the Brahms E-flat Sonata:

I asked the student what sort of figure made up each of these gestures. He noticed they were arpeggios, and we discussed how they were in a slightly different configuration, or a slightly different species, of arpeggio than the ones we typically practice. Next I had him go measure by measure and figure out the tonality of each arpeggio, writing the roots of each chord in his music. With this knowledge in hand (and brain!), the student made short work of the passage! We surveyed the rest of the movement, taking note of similar arpeggiated figures and discussing how they could be dispatched (at least technically!) with little effort.

Students are often shocked at how often figures like arpeggios occur in their music – most have never really registered them before! I sometimes feel like the guide my wife and I had on our recent trip to Costa Rica. During our tour through the jungle, we would be walking along, looking at seemingly empty trees, when our guide would stop suddenly and point out a group of sleeping bats not 3 feet away from us!

Sleeping bats in a tree hollow - Carara National Park, Costa Rica

We were oblivious to what was right in front of us because we didn’t know what to look for, or how to see.

Likewise, students often don’t know what to look for in their music. Often, with just a few examples, their eyes open to a harmonic world that lay hiding in plain sight.

As studio teachers it’s important we don’t take this way of looking for granted! Taking time to show students the benefits a working knowledge of harmony brings to their playing can inspire them to bring more of their theoretical knowledge into the practice room and help them develop into musicians that make more informed musical choices.