Roman Numeral Analysis in Music

Roman Numeral Analysis is a valuable technique for analyzing the chords and progressions in a piece of music. You can use it to transpose the standard progressions, like the circle of 5ths progressions or blues, to any key.

In this article, you can learn about Roman numerals, their notations for triads, 7th chords, chord qualities, inversions, and the stepwise method of analysis of harmony of any given section of music with examples.

Read the complete article to know in depth about the Roman Numeral Analysis!

What are Roman Numerals

Most of you would have studied Roman Numerals in your primary school in the Maths class. It is a system developed by the Ancient Romans that use letters like I, V, X, L, C, D, and M and their combinations to represent the numbers. You don’t require all these letters, and just I and V are enough for all musical representations.

History of Use of Roman Numerals in Music

The earliest documented use of Roman numerals is found in the second part of the 18th century. But Gottfried Weber, in the 1820s, is considered to have made use of Roman numerals popular through his Theorie der Tonsetzkunst (or Theory of Musical Composition).

Specifically, he started using Capital numerals to designate the major chords and the lowercase ones for minor chords. He introduced the superscript symbols ‘o’ for the diminished chords and ‘7’ for the seventh chords.

What are Roman Numerals in Music Theory?

Roman numerals are used in music theory to designate the scale degrees and the chords based on them. Many texts use Arabic numerals with carets to denote the scale degrees themselves. In the Roman numeral system, the chords are designated as I, II, III, IV, V, VI, and VII in the roman numerals.

What do Roman numerals in chords mean?

The Roman numerals in the representation denote the scale degree names of the root note on which the particular chord is built. The Roman numerals represent the whole chords, not just the root. The I represents the tonic chord; the IV represents a subdominant chord, V is a dominant chord, and so on.

For example, the I chord in the key of the C major means that the chord is built on the first scale degree note of the C major scale and represents the tonic C major chord.

Similarly, the V chord in C represents the dominant G chord built on the fifth scale degree of the scale. In simple terms, the Roman numerals represent the scale degree names of a scale on which the chord’s root is based.

But what is important to understand is that the representation itself is independent of any particular scale. The IV chord in C major scale represents the F Major chord built on the fourth scale degree as the root, but the same notation will mean the G major chord in the key of D.

Roman Numerals and Chord Quality

Roman numerals do not just represent the scale degrees of the root of any chord.

They are designed to provide other information about the chords, like their sonorities or chord qualities, which allows you to distinguish between the major and minor chords, identify an augmented or a diminished chord, a 7th chord, an inversion in conjunction with the figured bass notation, and the secondary functions.

Uppercase Roman Numerals Vs. Lowercase Roman Numerals

The case of Roman numerals is used to distinguish between the major and minor triads. An uppercase roman numeral represents a major triad, while a lowercase roman numeral denotes a minor triad.

For example, in G major key, the I chord represented in the capital notation notates a G major Chord. The ii chord represents the A minor chord with notes [A C E], built on the second scale degree of the G major scale.

In the G minor key, the i chord represents the G minor, as a lowercase roman numeral shows it. The iv chord in G represents the D minor chord.

Augmented and Diminished Symbols

As you know, four types of basic triads can appear in your chord progression. You have seen the notation for the minor and major triads so far. Let us now look at the notation of the diminished and the augmented chords.

A diminished triad occurs on the seventh scale degree in a major scale and on the 2nd degree in a natural minor scale. They are denoted by scale degrees in the lowercase numerals followed by a small “o” as a superscript. Hence, the representation of diminished triads is vii^o in major keys and ii^o in minor keys.

An augmented triad does not occur naturally in the diatonic scales. It normally originates as the third triad in the harmonic minor scale or the melodic minor scale, where it is designated as an III+ chord.

But we can have them in a major or minor scale with a chromatic alteration, as a borrowed chord. A plus sign usually denotes augmented triads after the upper case Roman numerals. For example, if the 5th in C major chord is altered to G#, the resulting C augmented chord is notated as C⁺.

Roman Numerals and Seventh Chord Quality

The 7th chord is denoted by the number 7 in a superscript above the roman numerals. For example,

• The I⁷ denotes the tonic major seventh chords in major scales,
• The vi⁷ denotes the submediant 7th minor chords in major scales.
• The i⁷ represents the tonic 7th minor chords in minor scales.
• The V⁷ represents the dominant 7th chords in both major and minor scales.
• The I⁺⁷ represents the chromatically altered tonic augmented chord.

The diminished 7th chords have a slight variation in their roman numeral representation from the diminished triads because they are two types – the half-diminished 7th and the full-diminished 7th.

The half-diminished 7th chord is represented by the symbol vii^ø7, while the full diminished has a similar notation to the triads with an additional ‘7’ superscript, vii^o7.

Chord Inversions in Roman Numerals

A combination of the roman numerals and the figured bass symbols notates the chord inversions. The roman numerals indicate the chord name, chord quality, and the scale degree numbers of the roots. The figured bass symbol on the sheet music tells you the inversion you need to play the chord in.

For example, the I, I⁶, and I^6/4 represent the tonic triads in their root position, first and second inversions. Similarly, for the subdominant chord in a major scale, the upper case numerals IV, IV⁶, and IV^6/4 represent the parent and the inverted chords.

Similarly, the 7th chord representation for inversions is.

• V⁷ represents the root position,
• V^6/5 is used for the 1st inversion,
• V^4/3 for the 2nd inversion, and
• V^4/2 is the 3rd inversion.

Representation of the Secondary Functions

The secondary chords are built to tonicize chords major/minor chords in any key other than the tonic chords. For example, if you want to tonicize the ii chord of a major scale, you can use

• Its secondary dominant chord, which is represented as V/ii (triads) or V⁷/ii (7th chords) in the roman numeral notation, or
• Its secondary leading tone chord is represented by viio/ii or vii^o7/ii.

Diatonic scales

You may know the process of harmonizing any scale. It involves the addition of two notes above each scale degree of the scale, resulting in the formation of the triads. Such triads represent root position diatonic chords of the key. The table below shows them.

Each type of scale produces a typical triad quality pattern which remains the same for that particular scale type. This is because each scale has a particular pattern of intervals (whole steps, half steps, or others) between the notes. It is advantageous if you know and remembers the qualities or the sonorities of the chords.

Major Scale Roman Numerals

The chord quality pattern for any major scale is given below in the table. As stated above, the pattern is consistent for major scales. Chords ii, iii, and vi in any major scale will be minor chords. This aspect of any scale makes the Roman numeral analysis more powerful, as we will discuss later.

Roman Numerals for Minor Scale

The pattern for the natural minor scale is given in the table below.

However, a natural minor scale has a subtonic 7th scale degree instead of a leading tone. This results in minor v and major VII chords rather than the dominant V chord with a strong resolution to the tonic. So, we normally use these chords from the harmonic minor scale, with the raised 7th resulting in the V and vii^o chords instead of v and VII. This is shown in the table below. The ii^o chord leads to a half-diminished 7th chord, while vii^o leads to a fully diminished 7th chord.

Triads of the Seven Modern Modes

The triads formed by the harmonization of the seven modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian) of the major scale are shown in the table below.

Don’t be confused by the nomenclature in the table above, as all designations are shown relative to the major scales (Ionian mode). Thus, relative to C Ionian mode, where ii is a D minor chord, a C Phrygian mode will have bII, which is a major chord with Db as its root note.

Use of different notations of the Roman Numerals

Some authors and composers use slightly different variations of the numerals. Let us just briefly apprise you of the same so that you can derive the meaning if you encounter them.

1. You may see only uppercase roman numerals with an additional symbol like a lowercase ‘m,’ ‘o,’ or ‘ø,’ or ‘7’. For example, IIm or VII^o for the minor and diminished chords in a major scale. An upper chord symbol with any symbol following it means it is not a major chord.
2. You may see symbols like V⁹, V¹¹, and V¹³ in the jazz context.
3. You may see symbols a, b, and c after the Roman numerals to indicate the inversion. This is particularly true for the United Kingdom. Ia, Ib, and Ic represent the tonic chord in root position, first inversion, and second inversion, respectively.

Why is Roman numeral analysis important?

In Western music, Roman numerals are used also to represent the chord progressions of any composition independent of the key. These are abstract chord progressions without being fixed to a particular key. This allows you to transpose the progression to any key.

For example, consider the popular jazz progression ii-V-I. In the key of C, the progression means Dm – G – C, which is equivalent to the predominant (supertonic) – dominant – tonic, as per the circle of fifths. In the key of A, this will mean a Bm – E – A progression.

You often have instruments in a band that can play specific keys only, like the B-flat clarinet and an E-flat saxophone. They can play the progression based on the roman numerals provided in their key from the same sheet music.

The Roman numerals allow you to identify the chords in the context of any given key signature and analyze the harmony of the composition. The analysis includes identifying the quality, inversions, extensions, etc. Once the chords and their inversions are identified, you can deduce back the chord progressions to help you play them easily.

Analyzing with Roman Numerals

With all this background, let us now delve into the main topic of how to analyze the Roman numerals you encounter on sheet music. The steps are detailed below:

1. You need to establish the key of the section of the music first. If the key signatures are given, identifying the key becomes relatively easy. But you still need to differentiate between the relative pairs that carry the same key signatures. This is usually done by examining the first and the last measures on the sheet music. In most cases, the piece of music will begin and end with the tonic chords.
2. If the key signature is not explicitly given, you must establish it by looking at the notes and their accidentals.
3. Once you have established the key, the next step is to find out the root of each chord. You may have first to distinguish whether you have a triad or a 7th chord by looking at any doubled notes. Then use your knowledge of diatonic numbers in the figured bass to establish the root.
4. Establish the sonority of the chord – Major, Minor, Dominant, Diminished, Augmented from the notes of the chord.
5. Fins the place of the chord in the scale by the scale degree of the root and its quality and assign it a Roman Numeral accordingly.
6. Take care to include the symbols for diminished, augmented, and 7th chords appropriately.
7. Include the figured bass numbers in the representation to indicate the inversion correctly.

Examples of Roman Numeral Analysis

Let us carry out the Roman numeral analysis of the diagram given below to understand the concepts and steps more clearly.

The detailed analysis follows the steps indicated in the previous section.

1. The key signature for the piece of music is given, and it has three sharps. The key could be A Major or F# minor. The notes with sharps in these keys are F#, C#, and G#.
2. We note that there are seven chords in the piece of music. Let us proceed and identify the chords at the beginning and the end to zero down at the exact key.
3. The first chord has notes [F#, C#, F#, and A]. It has three distinct notes, F#, C#, and A, so it is a triad [F#, A, C#]. It has intervals of m3 and M3. Hence it is an F# minor chord.
4. The last chord has notes [F#, A, C#, and F#]. It is also a triad with the same notes as in the last step. We know that it is an F# minor triad. Since both the first and last chords are F# minor, we can safely conclude that it is the i chord, and F# minor is the key of the piece of music. Let us now analyze the balance chords in the same way.
5. The second chord has notes [E#, C#, G#, and C#]. Here E# is in the bass. The diatonic numbers from the E to G# and C# are 3 and 6 (since G# is at the interval of a third from E# and C# is at a sixth interval). Hence this chord is in the first inversion, and E# is a third of the chord. So the chord is a triad with the notes [C#, E#, and G#], which is a V chord (C# major) since C# is at the 5th scale degree of the F# minor scale.
6. Observe that the scale given is F# minor, with E as a natural seventh-degree note. It has been raised to E# to form a dominant V chord by placing the # symbol over and above the key signature.
7. The third chord has notes [F#, A, F#, and C#]. We know from above that it is an F#m chord. So, we have i – V⁶ – i, progression so far.
8. The fourth chord has notes [D, B, F#, and B]. From bass D, the diatonic numbers are 3 to F# and 6 to B, so it is a 1st inversion triad with doubled B. So the given chord is a minor chord [B, D, F#] in the first inversion, iv⁶.
9. The fifth chord carries notes [C#, C#, F#, and A]. The diatonic numbers from the bass C# are 4 (to F#) and 6 (to A). So the chord is the tonic chord in the second inversion, i^6/4.
10. The 6th chord has notes [C#, C#, E, G#]. We know from step 5 in our analysis that it is a V chord, but this time in the root position.
11. So the overall progression for the piece of music is i – V⁶ – i – iv⁶ – i^6/4 – V – i. It is shown below in the updated diagram.

Conclusion

We hope, our article on the Roman numeral analysis has given you valuable insights into how to represent chords using roman notations and analyzing the harmony of any given piece of music. Still, if you require any clarifications or want to share your valuable experiences, please provide comments in the section below.