Introduction to Roman Numeral Analysis (Harmonic Analysis)

As we dig into music theory, we often analyze music. As we label the chords and scales, we may ask the question, “How does all this fit together?”

We can use Roman numerals to label the relationships between the chords in a piece of music.

What Is Harmonic Analysis?

Music is a language. And we can use the analogy of written languages to understand harmonic analysis.

Letters make words. Words make sentences. Sentences make paragraphs. Paragraphs make books.

And each sentence has nouns, verbs, adjectives and pronouns. Subjects and predicates and all the rest.

Music is the same….

Notes make chords. Chords make sections. Sections make pieces.

Harmonic analysis is the exploration of how the chords fit together. We name each chord and note how it relates to the other chords and the rest of the piece.

Notes of a C major scale.

First, What Chord Is It?

The first step of harmonic analysis is asking the question, “What chord is this?

We look at the given notes, and decide what chords make up the piece.

Chords in a key have different qualities (major, minor, etc.)

We label chords major or minor (or less frequently, diminished or augmented). Some chords have a 7th, others don’t .

So for each musical bit, we can label the chord (harmony) upon which that bit is built.

And when we have our list of chords, we start to wonder, “How do these chords work together?”

Chords in the key of C

How Chords Work Together Within A Key

The root (the namesake) of a scale has a sort of gravity – a pull. We want to return to it.

Each piece of music has a main “key”, which is the scale the piece primarily uses. The chords of the piece come from this scale.

And because of this “gravity”, the chords in a key lead the ear back to the root chord.

Composers may use this tendency to craft elegant surprises. They may temporarily change the gravity to lead to a different chord.

And as it all becomes more complex, we need a way to keep track of what is what, in relation to the root chord. The answer to this is Roman Numerals.

Roman Numeral Analysis for Chords

Using Roman numerals, we can label each chord by its place in the key.

In the key of C, C is “one”, or in Roman numerals, I.
D is II (2). E is III (3). And so on.

We use upper-case Roman numerals for major chords. And we use lower-case Roman numerals for minor chords.

Chords in the key of C, labeled using Roman numerals

Outliers: When a Chord is Not in the Key

But what happens when we find a chord that doesn’t seem to fit into our tidy system? What if the chord is not in the key of the piece?

In this case, we have to call it something. Usually, there is a correct answer. Sometimes the naming of a chord is open to interpretation.

But most often, if a chord is outside the original key, there’s a good reason.

It could be simple change of chord quality. For instance, many Motown hits change the quality of the IV chord from major to minor. This ‘minor four” gives a distinctive sound.

Likewise, in much of blues music, almost every chord is a 7 chord. This is characteristic of the style. It creates the sound we know as “blues”.

Other times, the outside chord is what we call a “secondary chord”. These use the gravity spoken of above to lead to a different chord in the key (other than the root chord).

For instance, the V7 chord (the chord built on the fifth scale degree of the key) is the called the “dominant”. This chord strongly leads to the root chord. We can use this powerful ear-leading to point to the chords that lead to the root.

As as example, in the key of C, the fifth note is G. The chord built on this is G7, which is the “dominant”. To make the pull to the root even stronger, we can first lead to the G7, using the dominant (V chord) of G. Here, D7 is the V7 of G.

A common chord progression is: ii, V7, I. (2,5,1)
In the key of C, this is: Dm, G7, C.

Using D7 instead of D-minor strengthens the forward pull.

This is called a “secondary dominant”. It’s also called the V7 of V (“five seven of five”), written V7/V.

We can also have V7/ii, or any other secondary chord. But V7/V is by far the most common.

Ongoing Study and Practice

Harmonic analysis can get complicated very quickly. And because of this, it may be best to hold it lightly.

As time goes by, and we learn more and more about how harmony works, it gets easier. We see the common patterns and recognize the common outliers.

But until then, it may be best to label what you can, and release the rest. It’s okay to simply call a chord by its name (rather than number).

And if you don’t know the chord, you can name it anything that will help you remember it (such as “the weird chord”.).

Labeling and seeking relationships between chords helps us memorize and recall music. We can memorize the chords. This is called “theoretical memory”. And this can join our aural, visual and muscle memory.

As we mature as musicians, we can enjoy using Roman numeral analysis to learn our music. We can delight in the clever twists composers bring us. It’s another layer of music we can embrace and enjoy.

Allen Mathews

Hi, I’m Allen Mathews. 

I started as a folk guitarist, then fell in love with classical guitar in my 20’s. Despite a lot of practice and schooling, I still couldn’t get my music to flow well. I struggled with excess tension. My music sounded forced. And my hands and body were often sore. I got frustrated, and couldn’t see the way forward. Then, over the next decade, I studied with two other stellar teachers – one focused on the technical movements, and one on the musical (he was a concert pianist). In time, I came to discover a new set of formulas and movements. These brought new life and vitality to my practice. Now I help guitarists find more comfort and flow in their music, so they play more beautifully.
Click here for a sample formula.

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