Discussion 6a - Roman Numerals in Harmonic Analysis

Class discussion

Why not just use leadsheet notation?

-they cannot imply a key

What information does a roman numeral communicate?

-The case of the roman numeral communicates if the third is major (Uppercase) or minor (lowercase)

-The number of the numeral shows you what scale degree the root is, and you can infer what tonic is

-If we know what the root is, we can figure out all of the other pitches based on the roman numeral

-Exception being viio7 in minor. 7th scale degree must be raised to leading tone.

-We can alter roots by writing full size accidentals to the left of the roman numeral. No Naturals! sharps and flats

-Fifths are default perfect

-Diminished fifths are marked as a degree symbol (o) superscript on the right side of the roman numeral

-Augmented fifths are marked as (+) superscript on the right side of the roman numeral

Seventh Chords

-If there is an inversion figure of 7, 6/5, 4/3, or 4/2, the seventh is accounted for

-Sevenths are default minor, because they are the most common, and because it makes alteration simpler. If we defaulted major 7, it would become the root of the chord if it was raised. Also, a diminished 7 would be doubly flatted, which gets confusing and hard to write.

Why not use the triangle for raised seventh?

-Lead sheet notation and roman numeral analysis do completely different things. They are equally useful, but we must keep them separate to preserve their usefulness.

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.