Discussion 6a - Roman Numerals in Harmonic Analysis

Roman Ramble

“Why use Roman Numeral analysis?”

• It allows us to label chords in relation to the current key, which is essential for identifying harmonic patterns. The Roman numerals (I, ii, iii, IV, V, vi, viio) refer scale degree a chord is built on compared to the current tonic.

“What diatonic chord qualities are the same in major and minor?”

• The V chords are both major, in order to maintain dominant function.
• The chord built on the seventh scale degree are both diminished.

“How do we alter chords in roman numeral analysis?”

• Alter the root by putting a flat or sharp in front of the note. To have a chord built on the natural seventh in minor (Te), you must put a flat before the Roman numeral.
• To alter the third, change the case of the letter of the Roman numeral. A chord with a major third has capital letters (IV) and chords with a minor third have lowercase letters (iv).
• To alter the fifth, put a diminished or augmented sign after the Roman numeral. When no alteration is present, it is assumed that the fifth is a perfect fifth above the root.
• To indicate a major seventh, you must put a capital M before the 7. Otherwise, an unaltered 7 is assumed to be minor seventh interval. With fully-diminished or half-diminished chords, be sure to use the o or ø symbol before the 7.
• When you use inversion figures, a minor seventh interval is still assumed. The inversion figure (6/5, 4/3, 4/2) imply a minor seventh from the root, so be sure to notate if otherwise.

Chords we will NOT use for now:

• no Major 7 chords
• three chords have no purpose until later

Further Reading

From Open Music Theory

Labeling chords

There are two ways in which we will label chords according to function. The first is to label chords with Roman numerals, thoroughbass figures, and functional labels. When doing so, place the appropriate Roman numeral below the bass line, the thoroughbass figure above the bass line (since it represents the upper voices), and place a functional label T/S/D below the Roman numeral (no Tx; simply call a VI chord T). For now this label can simply apply T, S, or D to individual chords; in the future, we will alter this practice slightly in order to show functional prolongation. The first example shows individual chord functions, and the second example shows functional prolongation.

The second way to label a harmonic progression is what Quinn calls functional bass. Functional bass symbols combine a chord’s function (T, S, D, or Tx) with an Arabic numeral denoting the scale degree of its bass note. A tonic chord with do in the bass is T1, a dominant chord with ti in the bass is D7, etc. If the bass note is chromatically altered, use a + or – to denote raised or lowered (la and ti in minor do not count, since le, la, te, and ti all belong to minor, but you can use +/– for clarity if you like). And if there is a chromatically altered note anywhere in the chord, put the functional bass symbol inside square brackets: [S6], [S+4], [T–7], etc. (See Chromatically altered subdominant chords, Applied chords, and Modal mixture for more information on common chromatically altered chords.)

Quinn also advocates using what I call interpreted functional bass. This nomenclature uses the same symbols, but uses parentheses to denote contrapuntal prolongation and lower-case postscripts to explain the contrapuntal role of the embellishing chord (p for passing, n for neighbor, i for incomplete neighbor, d for divider, e for embellishing — all of these refer to the voice-leading pattern in the bass voice). Following is an example of interpreted functional bass.

In this text, we primarily use the first method of Roman numerals and (prolonged) harmonic functions, since it is the most common in North American music theory. However, functional bass can be helpful for identifying categories of chords that belong together. For example, in a dictation or transcription task, we might hear re in the bass but not know what specific chord it is. If context tells us it is likely a dominant chord, rather than subdominant, we can label it D2. This rules out II (a subdominant chord) but keeps open multiple dominant options like V^6/4 or VII⁶ until we are able to make a final determination. Similarly, when composing, there are patterns that might take an S4, with the specific chord (IV or II⁶) determined by voice-leading rather than harmonic syntax, but where a D4 chord (V^4/2) would be syntactically inappropriate, regardless of voice-leading.

Thus, when referring to specific chords, we will use Roman numerals to label the chords and functional labels to interpret their role in context. When referring to broader categories of chords, we will more often use functional bass.