Chord Theory Notation with Roman Numerals:
Limitations and Solutions

Leo Brodie

Roman numeral analysis provides a systematic way to represent and study chord progressions and harmonic functions independent of any specific key. It allows us to analyze how chords relate to each other harmonically based on their scale degree functions (tonic, dominant, subdominant, etc.), and to easily transpose chord progressions to different keys.

The system of using Roman numeral analysis to represent chords and harmonic functions has its origins in the late 16th and early 17th centuries, but became codified in the the 18th century. As a result, while incredibly useful as an analytical tool, some of its features seem archaic today.

This paper is a work-in-progress. It aims to propose potential solutions to address the limitations inherent in Roman numeral analysis notation. This current draft is intended as a solicitation for feedback. My hope is that an interested community will develop and advance proposals such as these.

Key strengths of Roman numeral analysis

Roman Numeral analysis is a chord notation system based on scale degrees within a given key. Using the scale degrees rather than note names makes it possible to write chord progressions that can be read and played in any key, provided the musician has a basic understanding of music theory.

In this regard, Roman numeral analysis is similar to the Nashville Number system, which uses Arabic numerals. The Nashville system was developed by session musicians and excels at quickly conveying chord progressions for sight-reading. The purpose of Roman numeral analysis, on the other hand, is to abstract chord function. It lends itself to study and understanding, and is generally preferred for learning music theory.

An example of how Roman numeral analysis can be used to explore music theory is the way it can indicate the secondary dominant function. An E7 chord in the key of C can be annotated as III in Roman numeral analysis, but this representation fails to account for the presence of G#, a note not native to the key of C. In Roman numeral analysis, the notation V/vi can be employed to mean “the 5 of the minor 6.” This chord functions as the secondary dominant of Am, a chord naturally found within the key of C.

Issues with Roman numeral analysis

This proposal outlines several enhancements aimed at addressing the limitations of Roman numeral analysis:

Clarifying notation for minor keys within the context of modern popular music
Introducing a straightforward method for specifying a bass note other than the chord's root
Designating the top-line melody within a chord progression as an alternative to inversions
Indicating modulation without reference to specific keys

Minor Keys

The way in which Roman numeral analysis represents minor keys has a strong basis historically, but it with modern music it often introduces confusion and ambiguity. For traditional music in minor keys, we consider the root of the minor key as the 1, and spell the numeral with lowercase letters to make it minor. However, one source of confusion is the existence of multiple minor scales, notably natural, harmonic, or melodic minor. Depending on which of these is in use, the 6th and the 7th scale degrees can be different notes. For example, in A minor, the vii of the natural minor scale is G, while the vii of the harmonic minor scale is G#. Unless we know which scale is being used, the meaning of a vii chord is unclear.

Eastern European folk music is commonly based on the harmonic minor scale and features chords based on the one, four and five, such as:
Am Dm Am E7

In Roman numeral analysis, we write the notation like this:
i iv i V

In this case, we needn't be concerned about whether the scale is natural, harmonic, or melodic minor, since the D and E are the fourth and fifth scale degrees either way. The subdominant and dominant functions of these chords are clearly indicated by this analysis. We can feel the V chord at the end of the phrase pulling us back to the root minor chord, i.

Now consider the progression Am Dm G C. If a song consisted of these chords in a loop, should we notate it assuming it is in a major key or minor key? The progession begins with minor chords but ends on major chords. If we consider it to be a major key, even though it starts with a minor chord, we would write vi ii V I. This notation clearly shows the functional harmony at play, particularly the strong "ii V I" cadential movement at the end. On the other hand if we consider it to be in a minor key, we would write i iv ♭VII III. While not incorrect, it's potentially more confusing.

The major vs. minor quality of a song can get even more ambiguous with modern pop songs, which blend major, minor, and other modes. Common examples include these chord progressions:
Am F C G
Am F G Am

In this case, although we hear the key as A minor, the chords F and G present a problem in Roman numeral analysis. F and G may or may not be the 6 and 7 of the minor scales, depending on whether it is based on the natural, harmonic, or melodic minor scale.

David Bennett, in his excellent tutorials, addresses this ambiguity by introducing sharps or flats (see footnote). For example, for the chord progression
Am F G C
David writes it as
i ♭VI ♭III ♭VII

This paper argues that in cases where multiple modes in the same song, it's simpler and clearer to 'transpose' the song to the relative major. In the above example, we write our notation as if the key were C major instead of A minor. The analysis becomes:
vi IV I V
vi IV V vi

This approach highlights the subdominant and dominant functions of the IV and V chords respectively, just as the analysis of traditional minor key songs using the minor key as the root highlights the 4th and 5th as the subdominant and dominant respectively.

A third case is found in the so-called Andalusian Cadence:
Am G F E7

Musicially, this is best be described as a natural minor scale, because F and G are in the natural scale of Am. But as David Bennett notes, it would be ambiguous to write it as:
i VII VI V

On the other hand, it's important to emphasize that the final chord is a dominant seventh chord. So In this case, David Bennett's approach seems best, where we keep the progression in the minor key but 'force' the ambiguous 6 and 7 chords:
i ♭VII ♭VI V

In summary, this proposal aims to reconcile multiple goals, including retaining clarity on dominant and subdominant chord functions by rooting the scale such that these chords are numered 5 and 4 respectively, and eliminating ambiguity of mutliple possible minor scales.

Inversions and Figured Bass

Before delving into other parts of this proposal, let’s review related features of traditional Roman numeral analysis related to inversions. These are areas where Roman numeral analysis seems especially confusing.

In music theory, inversions are arrangements of the notes in a chord from top to bottom. In Roman numeral analysis, inversions are indicated using figured bass notation, in which small Arabic numerals specify the interval between the lowest note in the chord and each of the other two notes. For example, in a root-position triad C–E–G, the intervals above bass note C are a third and a fifth.

(from Pianote without permission for this draft)

For the root position, the intervals of 3 and 5 are considered the default, and do not need to be spelled out. For the first inversion (E–G–C), the intervals are 3 and 6 (even though the lower interval is actually a minor 3). By convention, the 3 is not shown, so the chord is written I⁶. For the second inversion, the intervals are 4 and 6. In figured bass, these are shown one above the other: .

This paper proposes eliminating figured bass notation from Roman numeral analysis entirely, and instead using other ways to express the bass note and the top note.

Indicating the Bass Note Similarly to Slash Chords

In popular music, the “slash chord” indicates a bass note that is not the root of the chord. For example, C/E indicates a C chord with E in the bass. Slash chords are easy to read, but they are not compatible with Roman Numeral analysis because the slash symbol (/) is reserved to indicate the secondary chord relationship, as seen earlier.

Conventional Roman numeral analysis implies the bass note via inversion notation. The reader must infer what inversion is used by reading the figured bass numbers, and then infer from the inversion what the bass note is supposed to be. This complexity increases when four notes are played. Furthermore, this notation is limited to bass notes that are already part of the chord. No other bass note can be indicated, as with C/D, C/F, or any other combination.

In today’s music, the bass note is not necessarily related to the concept of inversions. For example, keyboard players treat the bass note as the lowest note on their left hand, while inversions are the domain of the right hand. In bands, the bassline and chords are generally played on different instruments. This aspect of Roman numeral analysis may be the area most in need of improvement.

This paper proposes the use of subscript Arabic numerals to denote bass notes. For instance, in the key of C,

F/A = IV₃
F/C = IV₅
C/Ab = I♭₆

The Arabic numerals reference the scale degree of the chord, not of the key. In the first example, ‘3’ indicates A, the third degree of the F major scale.

Consider this progression:

I V/IV3 IV

In this progression, the V/IV utilizes Roman analysis slash notation to indicate the dominant chord of the IV chord. The “five of the four” results in a dominant chord built on the tonic but with a dominant sound. For example, in the key of C, V/IV implies the C7 chord, which is subdominant to the IV chord (F) that follows.

The subscript ‘3’ specifies that the bass note is the 3rd position of the resulting chord. Therefore, in the key of C:

V/IV₃ = C7/E

The complete progression is then understood as:

C C7/E F

As another example,

II♭₇ = D/C

The ♭7 subscript indicates that the bass note is the flat seventh of the chord. (Depending on the context, this could also be written as V/V♭7.)

The “Soul Dominant” Chord (V9sus4)

In contemporary popular music, the “soul dominant” chord can be thought of as a IV chord on top and a five in the bass (“4 over 5”). For example, in the key of C, it is denoted with the slash chord F/G.

But in Roman numeral analysis, the slash chord approach is not the way to denote this chord. Functionally, the chord represents a dominant V rather than a IV in the key of C. As David Bennett has pointed out, a more accurate notation for this chord is G9sus4. (G11 is sometimes used, but the B-natural at the 3rd position can clash with the C in the 11th position. Specifying the sus4 resolves this potential clash.)

In Roman numeral analysis, V9sus4 is the preferred notation. A subscript notation is not needed here.

Inversions and the Topline

Inversions become particularly significant when analyzing progressions. Consider the progression:

I V I

This progression may be played simply as:

But suppose we aim to emphasize a strong resolution and the top note ending on the tonic:

In this paper, we use the term topline to refer to the melody produced by consecutive top notes of successive chords. Our proposed solution involves using superscript numerals to specify the top note when needed. The previous example would be notated:

I³ V⁵ I¹

Here, the top note for the first chord is the 3 of the chord (E); the top note for the second chord is the 5 of the chord (D); the top note for the third chord is the 1 (C).

This topline notation does not replace standard extensions as seen in chords like C7, CΔ7, and C9, which are fundamental qualities of the chord.

In the following example, we might use this notation to emphasize the chromatic descent of the top note of the progression:

I⁵ II³ IV¹ I³

We might notate George Harrison’s “Something” as follows:

I¹ IΔ7⁷ V/IV⁷ IV³

Note that in IΔ7⁷, the Δ7 indicates the quality of the chord, while the superscript 7 refers to the topline, representing the seventh position of the major chord. Both notations refer to the same note, but the superscript emphasizes that it is part of a descending voice.

Observe that the superscript in V/IV⁷ represents the flat-7. It is the 7th degree of the secondary dominant. By itself, V/IV implies the dominant 7, but the superscript 7 calls it out as part of the topline.

Here’s another example where the topline is an important element of the sound:

vi7⁵ II⁹ V9sus4⁶ I³

There are two popular songs that use this or a similar topline. Does the topline make them more recognizable?

Bass and Topline Together

We propose replacing the notation for inversions with distinct notations for the bass notes and the topline. Both notations can be used at the same time. Going back to the I V I example, in addition to indicating the descending topline, suppose we want to use the 5 as a “pedal” bass note in the first two chords. In the key of C, the intended notes are:

We can combine the bass note subscript with the top note superscript, like this:

I₅³ V⁵ I¹

When both appear, the notations are staggered, with the bass note coming first. This makes it easier to create this notation in word processing applications such as Microsoft Word. The staggered notation also differentiates this notation from figured bass notation.

Modulation

In some songs, modulation to a different key is integral to the composition. The challenge with Roman numeral analysis is to notate the modulation without referencing named keys. Neither Roman numeral analysis nor Nashville numbering system offer a standard way to do this.

Our proposal is to indicate the modulation with either a plus or minus sign followed by the number of half steps (semitones) to modulate. For example, ‘+2’ specifies modulating up one whole step.

If the modulation occurs between sections, it can be placed on a separate line. If it occurs during a measure, it can be placed before the next chord in the new key.

The following example modulates up one half step:

ii iii IVma7 V9sus4 I I ii +1 V
It's up to you - New York, New York
I I I7
New York, New York

Specifying modulation in this way is recommended only if the new key center can be considered permanent. For temporary modulations (a few chords within a section, for example), notate those chords relative to the original key.

Tentative proposal: Notating Bass “Melodies” and Pedal point

In the previous section, we represented bass notes according to scale degree relative to the chord. This choice represents the sound or function of the chord better than representing the scale position within the key of the song.

However, some cases involving the notation of bass notes over many chords suggest that there could be a benefit to expressing the bass notes relative to the key. One instance is when the same note is used as a pedal point over a series of chords. It makes sense to use the same bass notation for every chord.

Alternately, certain songs employ a bass line with strong voice leading, such that the bass could be considered to have its own melody. The song “Chim Chim Cher-ee” from Mary Poppins features a bass line that descends chromatically:

If the community agrees there is a strong need for this, my tentative proposal is to again use subscript notation, but with Roman numerals instead of Arabic, in the same way that Roman numeral analysis expresses the scale position of the chord relative to the key.

A progression using pedal point such as G F/G Am/G G in the key of G, would be written as

I_I ♭VI_I ii_I I_I

“Chim Chim Cher-ee” would be expressed as

i_i V+_VII i_♭VII IV_VI iv_♭VI i_V II_♭V V_V

(Remember that in this proposal, minor keys are named according to the major scale.

The Name “Roman Numeral Analysis”

One goal of this proposal is to make the notation simpler and more modern, while retaining the original benefits. Personally I find the phrase “Roman Numeral Analysis” to be awkward. I propose we call it “Chord Theory Notation/” This phrase emphasizes its value in understanding music theory, in contrast to Nashville notation, which is aimed at session musicians wishing to simplify transposing.

Additional Questions

This paper is not yet published, and still in flux. I am open to suggestions for improvement.

I mentioned that the top line should not be used to indicate the quality of a chord, such as I9 or I6. But in the case of a sus-4 chord, in some cases that feels more like an embellishment. I’m inclined to indicate a cadence with a temporary sus 4, without naming the chord Vsus4:

V4 V

Or do you feel that the sound of the suspension is important enough to include in the chord name?

When denoting a major 7 chord, is it preferable to include ‘maj’ or the symbol Δ, or simply use ‘7’? For example, does IV7 suffice rather than IVΔ7, since the 7th degree of the IV’s scale is always major? This is a question of eliminating ambiguity versus knowledge of music theory.
Or in this case would be enough to indicate the topline note with I7. Again, are we changing the quality of the chord or just adding a major seven to the top?