Discussion 6a - Roman Numerals in Harmonic Analysis

Class discussion

Note that the seventh dimnished chord and major V in minor needs the leading tone (ti) in diatonic harmony.

What does Cmin7/E-flat tell us?

• First inversion, E-flat is in the bass
• All 4 chord members (C Eb G Bb)
• We do not know what key we are in and how this chord functions within the key. It is completely removed from form

Roman numerals

• The roman numeral itself identifies the root. You can tell what note the root is because its number correlates directly to its scale degree. For example, in C major vi indicates an A minor chord because A is the sixth scale degree in that key. As we’ll see in a second, the root can be altered just like the other chord members
• Uppercase/lowercase identifies the third in relation to the root (major/minor)
• 5ths are assumed perfect unless there’s a +, a half-diminished, or a diminished sign in the superscript
  • The diminished sign is special because it indicates that both the fifth and seventh are lowered. You can tell the difference from the half-diminished sign because the latter has a slash through it (it’s cut in “half”)
• 7 by itself = dominant 7th. Can be altered with M, a half-diminished, or a diminished sign
  • Sometimes chords like IV7 are notated without the clarification that it’s a major seventh chord–you’re expected to know because a major seventh is diatonic. However, when we get past the Classical era this method breaks down because all kinds of crazy stuff starts happening with harmony from the Romantic era onward

Altering Roman numerals for non-diatonic chord qualities

• Can have any triad in any key as long as you know how it relates to the key
• Accidental in front alters the chord from its diatonic version. Ex: in C major, bVI = Ab major chord
  • Only sharps and flats are used this way–no naturals. Even in sharp keys, you would use a flat sign to indicate a lowered chord. Likewise, a sharp indicates a raised chord even in flat keys

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.