Main Body
14 Roman numerals
Learning goals for Chapter 14
In this chapter, we will learn:
- How to identify chords in a major or minor key with Roman numeral labels
- How to construct chords in a major or minor key, given Roman numeral labels
- How to combine Roman numerals with figured bass symbols to represent chords in various contexts
Roman numerals
We have already studied chord symbols, which are used as a practical system for musicians playing from lead sheets. People studying music also use these symbols for analytical purposes. The primary drawback to using lead sheet symbols is that they do not convey any sense of harmonic function; instead, we are given only the root, quality, and inversion of the chord. This means that the G major triad, for example, has the same lead sheet symbol whether it appears in G major (as the tonic triad) or in C major (as the dominant triad).
In order to convey tonal function, which lead sheet symbols do not do, music analysts often prefer to use a system of labeling, where each chord is given a numeral label based on the scale degree number of its root within a key.
Furthermore, this system also indicates quality. An uppercase Roman numeral signifies a major triad, and a lowercase Roman numeral indicates a minor triad. Augmented triads use an uppercase Roman numeral followed by the “+” symbol, and diminished triads use a lowercase numeral followed by the “o” symbol. Using this system, the triad built on tonic is I or i, supertonic is ii or iio, dominant is V, and so forth. Example 14‑1 shows the Roman numerals and their corresponding qualities in major keys, using the key of A major.
Example 14‑1. Roman numerals in A major
The qualities for each triad in minor keys are different from those in major keys. Moreover, since there are three forms of the minor scale, sometimes there is more than one quality a triad can assume in a minor key. Usually, the form of the scale is used for deriving chords (hence its name, harmonic minor), but sometimes the or scale may be used. Example 14‑2 shows the Roman numerals and the most common corresponding qualities in minor keys. Notice that some of the chords require the addition of the leading tone (raised scale-degree 
, “ti”) in minor. This results in two different chords built on scale degree : the (built on lowered , “te”) and the (built on raised , “ti”).
Example 14‑2. Roman numerals in A minor
Analysis with Roman numerals can be combined with figured bass symbols to show inversion as well. This results in a very powerful analytical system that conveys a great deal of information with just a few symbols. Example 14‑3 shows all the inversions of the tonic triad using Roman numerals and figured bass symbols.
Example 14‑3. All positions of the tonic triad in A major
Example 14‑4 shows the Roman numerals for seventh chords and their qualities in major keys. The qualities of seventh chords may also be indicated with various modifications to the Roman numerals. For major seventh chords and major-minor sevenths, simply add a “7” after an uppercase Roman numeral. Note the difference in quality between I7 and IV7 (major seventh chords) and V7 (a major-minor seventh chord), even though they use the same symbol (7). For minor sevenths, add a “7” after a lowercase numeral. Half-diminished seventh chords use a lowercase numeral followed by “ø7,” and fully diminished sevenths use a lowercase numeral followed by “o7.”
Example 14‑4. Seventh chords in A major
Example 14‑5 shows the Roman numerals for seventh chords and their qualities in minor keys. Again, any uppercase Roman numeral with a 7 may indicate either a major or major-minor seventh chord quality. In minor keys, major seventh chords include III7 and VI7, whereas V7 (derived from ) and VII7 (derived from ) are major-minor. In addition, when is used, viio7 (built on the leading tone) is fully diminished.
Example 14‑5. Seventh chords in A minor
Video: T32 Roman numerals in major and minor keys (6:58)
This video shows how to determine Roman numerals for triads in major and minor keys.
EXERCISE 14-1 Roman numeral identification
Beneath the staff, label each chord with a Roman numeral, adding figured bass symbols when appropriate. Above the staff, label each chord with a lead-sheet chord symbol. The first is done for you.
EXERCISE 14-2 Roman numeral chord construction
On the staff below or on a separate sheet of staff paper, spell each chord given the key signature, Roman numeral, and figured bass symbol. Remember that sometimes it will be necessary to raise the leading tone in minor keys.
Supplemental resources for Chapter 14
in music theory, a symbol that shows both the scale degree number and the quality of a chord in a key; e.g., in C major, the Roman numeral I represents any C major triad
scale that features the following interval pattern: whole - half - whole - whole - half - A2 - half
scale that features the following interval pattern: whole - half - whole - whole - half - whole - whole; also the scale that corresponds with the minor key signature
scale that has the following interval pattern: ascending whole - half - whole - whole - whole - whole - half; descending whole - whole - half - whole - whole - half - whole; resembles the parallel major when ascending, except for scale degree 3, and resembles natural minor in its descending form
triad built on the scale degree a whole step below tonic ("te" in moveable-do solfege), derived from the natural minor scale
triad built on the scale degree a half step below tonic ("ti" in moveable-do solfege), derived from the major and harmonic minor scales
