I. Fundamentals

Roman Numerals and SATB Chord Construction

Samuel Brady and Kris Shaffer

Key Takeaways

  • is an analytical procedure in which musicians use Roman numerals to identify chords within the context of key signatures.
  • Roman numerals identify the of the chord’s root, its , and any extensions or the chord may include.
  • Uppercase Roman numerals denote major triads, and lowercase Roman numerals denote minor triads. A o symbol after a lowercase Roman numeral represents a diminished triad, while a + sign after an uppercase Roman numeral represents an augmented triad.
  • The Roman numeral quality of a seventh chord is dependent on the chord’s triad; the exceptions are half-diminished and fully diminished seventh chords, whose qualities are dependent on their chordal seventh.
  • When constructing a chord in , there are six rules to keep in mind: , , , , , and .

Writing Roman Numerals

Music theorists use to identify chords within the context of key signatures. Roman numerals identify the of the chord’s root, its , and any extensions or the chord may include. This is useful because Roman numerals convey the same information across major or minor key signatures; therefore utilizing Roman numerals can save time in the analysis of Western music.

example 1 shows three columns. The leftmost column shows Arabic numerals, the middle column shows the corresponding uppercase Roman numerals, and the rightmost column shows the corresponding lowercase Roman numerals:

Arabic Numeral Uppercase Roman Numeral Lowercase Roman Numeral
1 i
2 II ii
3 III iii
4 IV iv
5 V v
6 VI vi
7 VII vii

Example 1. Arabic and Roman numerals.

When typing uppercase Roman numerals, often the Latin alphabet letters “I” and “V” are used; likewise, when typing lowercase Roman numerals, often the Latin alphabet letters “i” and “v” are used, as can be seen in Example 1. It is important to note that Roman numerals IV/iv (4) and VI/vi (6) are often confused. It may be helpful to remember the difference by thinking of IV/iv (4) as one less than V/v (5), and VI/vi (6) as one more than V/v (5).

When handwriting uppercase Roman numerals, music theorists often add a small horizontal line across both the top and bottom of the numeral, in order to further distinguish between uppercase and lowercase. This difference is seen in example 2:

vs.

 

I   II   III   IV   V   VI   VII

Example 2. The difference between handwritten and typed Roman numerals.

There is no difference between handwritten and typed lowercase Roman numerals.

Roman Numerals and Triadic Quality

Music theorists use Roman numerals to identify the scale degree of a chord’s root, its quality, and inversion. For example: the first scale degree of a major key, [latex]\hat1[/latex] or do, is identified by Roman numeral “I,” the second scale degree of a major key, [latex]\hat2[/latex] or re, is identified by Roman numeral “ii,” etc.

Uppercase Roman numerals denote major triads, and lowercase Roman numerals denote minor triads. Lowercase Roman numerals followed by a superscript o symbol (such as viio) represent diminished triads. Uppercase Roman numerals followed by a + sign (for example, the rare V+) represent augmented triads. Roman numerals are generally placed below a score in the analysis of Western music.

Some music theorists prefer Roman numerals to reflect only the scale degree of a chord’s root, without distinguishing the chord’s quality by uppercase and lowercase Roman numerals. In such cases, all Roman numerals are uppercase. In this textbook, we privilege the distinction of triadic qualities as denoted by uppercase and lowercase Roman numerals.

Example 3 reproduces Example 7 from the Triads chapter, which shows the qualities of triads in major keys now including Roman numerals:

Example 3. Qualities of triads in major keys with Roman numerals. 

The Roman numerals and qualities of triads in major keys are as follows:

  • I: major
  • ii: minor
  • iii: minor
  • IV: major
  • V: major
  • vi: minor
  • vii°: diminished

Example 4 shows Example 8 from the Triads chapter, which depicts the qualities of triads in minor keys with the addition of Roman numerals:


Example 4. Qualities of triads in minor keys with Roman numerals. 

The Roman numerals and qualities of seventh chords in minor keys are as follows:

    • i: minor
    • ii°: diminished
    • III: major
    • iv: minor
    • v: minor
    • V: major (raised leading tone)
    • VI: major
    • VII: major
    • vii°: diminished (raised leading tone)

Note that the quality of v/V and VII/viio differs depending on whether or not the leading tone is raised.

Roman Numerals and Seventh Chord Quality

When labeling seventh chords with Roman numerals, a superscript “7” is added: for example, V7, ii7, and viio7. The Roman numeral quality of a seventh chord is dependent upon the quality of the chord’s triad. In other words, a seventh chord with a major triad, such as V7, will receive an uppercase Roman numeral. A seventh chord with a minor quality of triad, such as ii7 (in major keys), will receive a lowercase Roman numeral.

The Roman numeral quality of half-diminished and fully diminished seventh chords is dependent upon the quality of their chordal seventh, because both contain a diminished triad. Half-diminished seventh chords, which have a minor chordal seventh, receive the superscript “ø” symbol after their Roman numeral (for example viiø7); and fully diminished seventh chords, which have a diminished chordal seventh, receive the superscript “o” symbol (for example viio7).

Example 5 shows Example 8 from the Seventh Chords chapter, which depicts the qualities of seventh chords in major keys with the addition of Roman numerals:

Example 5. Qualities of seventh chords in major keys. 

The Roman numerals, qualities of seventh chords in major keys, and the music theory shorthand (in parentheses) are as follows:

    • I7: major seventh (MM7)
    • ii7: minor seventh (mm7)
    • iii7: minor seventh (mm7)
    • IV7: major seventh (MM7)
    • V7: dominant seventh (Mm7)
    • vi7: minor seventh (mm7)
    • viiø7: half-diminished seventh (ø7)

Example 6 reproduces Example 9 from the Seventh Chords chapter, which shows the qualities of seventh chords in minor keys, now including Roman numerals:

Example 6. Qualities of seventh chords in minor keys.

The Roman numerals, qualities of seventh chords in minor keys, and the music theory shorthand (in parentheses) are as follows:

    • i7: minor seventh (mm7)
    • iiø7: half-diminished seventh (ø7)
    • III7: major seventh (MM7)
    • iv7: minor seventh (mm7)
    • v7: minor seventh (mm7)
    • V7: dominant seventh (Mm7)
    • VI7: major seventh (MM7)
    • VII7: dominant seventh (Mm7)
    • vii°7: diminished seventh (o7)

Note that the quality of v7/V7 and VII7/viio7 differs depending on whether or not the leading tone is raised.

Additionally, major-seventh and dominant-seventh chords have the same Roman numeral nomenclature; in other words, a I7 chord and a V7 chord are written the same even though the former is a major seventh chord, and the latter is a dominant seventh chord. The difference would be discerned from the musical context.

Inversion

Roman numerals also denote inversions, shown through figured bass symbols (see the Inversion and Figured Bass chapter). For example, a superscript “6” represents a first inversion triad, and the figures “[latex]^4_3[/latex]” would indicate a second inversion seventh chord. Example 7 shows four different inverted chords with Roman numerals:

Example 7. Four inverted chords with Roman numerals and figures.

Notice that the figures always come after the Roman numerals.

Roman Numeral Analysis in a Musical Context

In order to complete a Roman numeral analysis, you must know the work’s key. Once identified, the key is written at the beginning of the work, directly under the key signature if one appears. The letter name of the key signature will be uppercase if it is major and lowercase if it is minor. It is also helpful to write a lowercase “m” following the letter name of the key if the key is minor; for example, if the key of a work is D minor, you would write “dm.” Be sure to apply any accidentals to the key signature if applicable (for example, if the key signature were E-flat major, you would write “E♭”).

Here are the steps for completing a Roman numeral analysis:

    1. Identify and write the key at the start of the work.
    2. If a chord is in inversion, stack it in root position (preferably mentally).
    3. Identify all the notes of a chord, taking its quality into account.
    4. Write the Roman numeral that corresponds with the scale degree of the chord’s root, keeping in mind the quality of the Roman numeral (uppercase, lowercase).
    5. Write any additional quality symbols ( o, ø+) as needed.
    6. Write any inversion or extension figures after the Roman numeral.

Example 8 shows a Roman numeral analysis for Johann Sebastian Bach’s chorale “Jesu meiner Seelen Wonne” (1642), which translates to “Jesus, delight of my soul.” When analyzing this chorale, ignore the notes in parentheses. It is recommended that you cover the Roman numerals in this example and try to generate them on your own before uncovering them:


Example 8. Roman numeral analysis of an excerpt of Johann Sebastian Bach’s  “Jesu, meiner Seelen Wonne,” (BWV 359).

Roman numeral analysis is not just limited to chorales; indeed, you can Roman numeral many different genres of music. Example 9 shows an excerpt from “Caro Mio Ben” (c. 1783), which translates to “Dearly beloved” and is attributed to Guiseppe Giodani, with a Roman numeral analysis:

Example 9. Roman numeral analysis of an excerpt of Giuseppe Giordani’s “Caro Mio Ben.”

Notice that Roman numerals can repeat, as in the first two chords of the first measure. This is a common occurrence and can be notated either with or without a repeating Roman numeral, as seen in the first measure of Example 9, or the second measure of example 8.

Writing Chords in SATB Style

Musicians simplify compositions into four parts (or voices) in order to make their harmonic content more readily accessible. This practice is called , abbreviated after the four common voice parts of a choir–– (S),  (A), (T), and (B). When constructing a chord in strict SATB style, there are six rules musicians generally follow:

These six parameters form the basis of counterpoint and part writing, explored further in the sections Counterpoint and Galant Schemas and Diatonic Harmony, Tonicization, and Modulation.

Stem Direction

On a grand staff in SATB style, the soprano and alto are written in the treble clef (upper staff), while the tenor and bass are written in the bass clef (lower staff). The soprano and tenor voices receive up-stems, while the alto and bass parts receive down-stems. If the stem direction is crossed, this is an error. There are two chords in Example 10, the first of which contains incorrect stemming, followed by the corrected version:

Example 10. Incorrect stemming, followed by a corrected version. 

Chord Construction

Be sure to check each chord for correct notes and accidentals, and make sure that your chords are not missing any notes. There are two chords in Example 11, the first of which contains an incorrect chord construction, followed by the corrected version:

Example 11. Incorrect chord construction followed by a corrected version.

It is important to note that the bass voice must always correspond with the inversion that the Roman numeral’s figures indicate. However, the order of the upper notes can be arranged in many ways. In other words, there is not necessarily just one correct way to voice a chord.

Range

There is a generally accepted range for each voice:

  • Soprano – C4 to G5
  • Alto – G3 to D5
  • Tenor – C3 to G4
  • Bass – F2 to D4

Example 12 depicts these ranges:

Example 12. Range of vocal parts. 

There are two chords in Example 13, the first of which contains notes which are out of range in the soprano and bass, followed by the corrected version:

Example 13. Notes in the soprano and bass are out of range, followed by a corrected version.

Spacing

There should be no more than an octave between upper voices (soprano and alto, alto and tenor). There should be no more than a twelfth between the tenor and bass.

Incorrect spacing is seen in Example 14. The soprano and alto are more than an octave apart, as are the alto and tenor. This is followed by the corrected version:

Example 14. Chord with incorrect spacing, followed by a corrected version.

Note that the most common spacing error occurs between the alto and tenor.

Voice Crossing

The ranges of voices should not cross. In other words, the soprano must always be higher than the alto, the alto must always be higher than the tenor, and the tenor must always be higher than the bass.

Voice crossing is seen in the first measure of Example 15, in which the soprano and alto voices are crossed:


Example 15. Voice crossing in the first measure, followed by a corrected version.

Doubling

In a triad, the note in the bass is usually doubled in an upper voice. However, there is an exception to this; the leading tone is never doubled. Other tendency tones, such as chordal sevenths, are also never doubled. Seventh chords don’t have any notes doubled because they contain four notes, one for each voice part.

Incorrect doubling is seen in the first measure of Example 16, where the leading tone is doubled, followed by a corrected voicing in the second measure:


Example 16. Incorrect doubling of the leading tone in soprano and tenor, followed by a corrected version.

Online Resources
Assignments from the Internet
  1. Roman Numeral Identification, pp. 15–16, 18 (.pdf), pp. 5–7 (.pdf), pp. 1, 3, 4 (.pdf), (.pdf.pdf.pdf.pdf)
  2. Roman Numeral Identification and Construction, p. 14 (triads) and 17 (seventh chords) (.pdf), p. 11 (.pdf), p. 8 (.pdf), p. 5 (.pdf), (website, website)
  3. Roman Numeral Construction, p. 22 (.pdf)
Assignments
  1. Roman Numerals Identification Assignment #1 (.pdf, .mscz, .mp3)
  2. Roman Numerals Identification Assignment #2 (.pdf, .mscz, .mp3)
  3. Roman Numerals Identification Assignment #3 (.pdf, .mscz, .mp3)

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OPEN MUSIC THEORY by Samuel Brady and Kris Shaffer is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License, except where otherwise noted.

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