Organising Pitch: Seventh Chords

Simon Perry

12 Organising Pitch: Seventh Chords

Introduction

A seventh chord is an extension of the triad. In its basic form, a seventh chord comprises a triad with an additional note placed a third higher than the fifth.

We designate the individual notes of a seventh chord in the same way as those of a triad. Building in thirds from the bottom up, therefore, we have: root, third, fifth and (now) seventh. These are shown on the left in Example 00, below.

Example 00: Basic anatomy of a seventh chord.

Compared to triads, seventh chords have more complex interval relationships. As shown on the right in Example 00 the four notes of a seventh chord in its basic form create six intervals in total (triads only have three intervals). In root position, these intervals comprise:

three thirds (between adjacent pairs of notes)
two fifths (between root and fifth and between third and seventh)
one seventh (between root and seventh)

Two triads a third apart marge to form a seventh chord

Another way to think of a seventh chord is to imagine a blend or superimposition of triads a third apart. This also explains why we have double the intervallic content even though we have only one additional note.

This chapter deals with the basics around seventh chords; more details on analysis and use of seventh chords is set out in other parts of this book.

The following are all fundamental in understanding the basics of seventh chords:

quality (major, minor, etc.)
naming conventions (chord symbols, Roman numerals, etc.)
inversions (figures, bass notes, etc.)

These are the same issues we find for the basic understanding of triads, but are now more varied and complex because we have increased the number of notes from three to four.

Although used in many different contexts in different ways, seventh chords are generally prevalent in all styles of Western music and in some (such as jazz), they are ubiquitous.

Seventh Chord Quality

The quality of seventh chords is determined by two factors:

the quality of the basic triad
the quality of the seventh formed over the root

Combining these factors leads to a wide range of possibilities. However, to manage the complexity, it’s useful to know that, while certain combinations of triad and seventh are theoretically possible, we find they are seldom encountered in common-practice. For example, we do not often find sevenths chords built on augmented triads, nor do we often find a diminished triad with a major seventh, for instance.

Therefore, in this chapter we cover only the seventh chords that are usually found in common practice.

In the table below, the main types are shown. To identify the quality of a seventh chord we use two terms, the first describes the triad and the second describes the seventh formed over the root. (The columns to the right showing chord symbols use A as the root, but this could be any pitch class.)

name	abbreviation	triad quality	seventh quality	symbol (root=A)	other symbols
major-major seventh chord (aka major seventh chord)	MM7	major	major	AM⁷	Amaj^7,\| A^Δ7\| A^Δ
major-minor seventh chord (aka dominant seventh chord)	Mm7	major	minor	A⁷
minor-minor seventh chord (aka minor seventh chord)	mm7	minor	minor	Am⁷	Amin⁷ \| A-⁷
half-diminished seventh chord	^ø7	diminished	minor	A^Ø7	Amin⁷^♭5 \| A-^7♭5
diminished seventh chord	°7	diminished	diminished	A°⁷	Adim⁷ \| Am^(♭7)♭5\| A−^(♭7)♭5

Using A as the root, these different sevenths are set out in Example 00, showing the complete interval content.

Example 00: Different qualities of seventh chord using A as root.

It is important to become familiar with the different sounds of these seventh chords. By far the most commonly used is the dominant seventh chord, but the others are also often found in various contexts and being able to distinguish aurally them is important.

Naming Conventions

The naming conventions around seventh chords are not that much different to those for triads, although there are now some minor irregularities and other details to get used to. As for triads, there a two main systems for labelling seventh chords: chord symbols and Roman numerals.

The (more-or-less) standard chord symbols have already been set out in the table above as well as in Example 00, using A as a reference point.

It is useful to note the following common terms:

Major-major seventh chords are seldom called that (unless absolute clarification is needed). In most contexts they are just called “major seventh chords.”
The same goes for minor-minor seventh chords, which are usually referred to simply as “minor seventh chords.”
Major-minor seventh chords are typically called “dominant sevenths.”

Dominant sevenths in classical vs popular styles

The dominant seventh chord is one of the most commonly used seventh chords in a variety of styles. In many popular styles and in jazz, it is not unusual to construct dominant sevenths on almost any scale degree, often in preference to a simple triads.

In common-practice Western classical music, dominant sevenths are mostly, often only, found constructed on the dominant scale degree ( $\hat{5}$ ). In the major mode and the harmonic minor, the dominant is the only degree that naturally produces a major-minor seventh (as shown below). This is how the chord derives its name.

Additionally, the way that dominant seventh chords are treated in classical and popular/jazz styles is quite different.

For these reasons, in Western common-practice classical music, we often speak of THE dominant seventh, in other styles we might just as easily speak of dominant sevenths in general, not associating the chord with a particular degree.

Inversions of Seventh Chords

Seventh chords have an additional inversion compared to triads, because there are now four notes which can form the bass note—root, third, fifth and (now) seventh.

Like triads, the root of a seventh chord does not change with inversions, nor does the quality. Only the bass note changes. Example 00, below, shows the process for inverting seventh chords in their basic form and can be compared to Example 00 in the chapter on triads.

Example 00: The basic process of inverting seventh chords.

Labelling Inversions of Seventh Chords

As for triads, there are two basic ways of labelling the inversions of seventh chords. We can use chord symbols with a slash and bass note or we can use figures. In this book we will concentrate on using figures, both as part of figured bass and with Roman numerals. However, it is useful to recall the system of using chord symbols.

Labelling Inversions Using Chord Symbols

As show above in Example 00, the a letter is used to identify the root of the seventh chord, followed by a suffix indicating what kind of seventh chord is built on the root. Root position is assumed unless the symbol is followed by a slash and another letter which indicates the bass note (being another note of the seventh chord). Some examples are given below (which can be compared to Example 00 in the chapter on triads).

Example 00: Seventh chord inversions identified using chord symbols (bass notes shown in red).

Diatonic seventh chords

Diatonic seventh chords are formed on roots of the major or minor scale using notes from the diatonic collection. With all the possibilities in the variant minor forms it becomes harder to keep track of all the possible qualities of seventh chords derived from the difference forms of the scale. Rather than cover all theoretical possibilities, for the moment we just outline the standard seventh chords in minor in Example 00 below (which can be compared to Example 00 in the chapter of triads), showing the chords as derived from scale segments expressed as sol-fa syllables. Colour coding shows the different qualities and the full intervallic content is also given.

Example 00: Seventh-chord qualities for major and minor scales using sol-fa syllables.

The qualities for seventh chords on each degree of the scale for major and minor in practical use is, therefore as follows:

root degree	major scale	minor scale	comments on minor scale
tonic	major seventh (MM7)	minor seventh (mm7)	subtonic (so) forms seventh
supertonic	minor seventh (mm7)	half-diminished 7th (^ø7)
mediant	minor seventh (mm7)	major seventh (MM7)	subtonic (so) forms fifth
subdominant	major seventh (MM7)	minor seventh (mm7)
dominant	dominant seventh (Mm7)	dominant seventh (Mm7)	leading note (si) forms third
submediant	minor seventh (mm7)	major seventh (MM7)
subtonic	n/a	dominant seventh (Mm7)	subtonic (so) forms root
leading note	half-diminished 7th (^ø7)	diminished 7th (°7)	leading note (si) forms root

Generally the differences in the minor scale depend on whether the subtonic (so) or leading note (si) is used as a member of the seventh chord in question. This is self-defining where the subtonic or leading note form the root. For the tonic and mediant seventh chords in minor, the natural minor’s subtonic is used, whereas the harmonic minor’s leading note is used for the dominant (with only occasional and very specific exceptions, which are explained elsewhere).

Roman numerals

As for triads, Roman numerals are used to identify diatonic seventh chords according to the scale degree that forms the root of the seventh chord. These are shown in Example 00 below using C as tonic for both major and minor scales.

Example 00: Roman numerals for diatonic seventh on all degrees of the major and minor scales (using C as tonic)

Seventh chords on all degrees of the C major and C minor scale shown with Roman numerals reflecting degree number and quality

As for chord symbols, a superscript Arabic numeral 7 indicates inclusion of the seventh above the basic triad. The quality of the seventh-chord is indicated by altering the case of the Roman numeral and other symbols. However, this process is not systematic and does rely on context to some extent.

A Roman numeral in upper case with $\begin{smallmatrix}7\\&\end{smallmatrix}$ indicates that the basic triad is major, but there is no distinction between a major or minor seventh, that is the $\begin{smallmatrix}7\\&\end{smallmatrix}$ attached to an upper case Roman numeral does not tell use whether we have a major-major seventh or a major-minor seventh chord. We need to know the context:

In major keys, I $\begin{smallmatrix}7\\&\end{smallmatrix}$ and IV $\begin{smallmatrix}7\\&\end{smallmatrix}$ are understood to be major sevenths, while V $\begin{smallmatrix}7\\&\end{smallmatrix}$ is a major-minor seventh chord (the dominant seventh)
In minor keys, III $\begin{smallmatrix}7\\&\end{smallmatrix}$ and VI $\begin{smallmatrix}7\\&\end{smallmatrix}$ are understood to be major sevenths, which both V $\begin{smallmatrix}7\\&\end{smallmatrix}$ and VII $\begin{smallmatrix}7\\&\end{smallmatrix}$ (the subtonic seventh chord) have dominant seventh qualities (major-minor).

A lower case Roman numeral with $\begin{smallmatrix}7\\&\end{smallmatrix}$ always indicates a minor seventh chord—a minor basic triad and a minor seventh

A lower case Roman numeral with ^ø $\begin{smallmatrix}7\\&\end{smallmatrix}$ indicates a half-diminished seventh chord (diminished triad with minor seventh)

A lower case Roman numeral with ° $\begin{smallmatrix}7\\&\end{smallmatrix}$ indicates a (fully) diminished seventh chord (diminished triad with diminished seventh)

Inversions and figures

Compared to triads, the figuring for inversions of seventh chords is a little more complex, although it does not take too much to get the hang of it. The main thing to remember is that the figures tell you what intervals you find above the bass note. This is summarised in the following table:

inversion	bass note	intervals above the bass note
root position	root	third, fifth, seventh
first inversion	third	third, fifth, sixth
second inversion	fifth	third, fourth, sixth
third inversion	seventh	second, fourth, sixth

From this, the full figuring for the inversions of seventh chords are as follows:

Root position: $\begin{smallmatrix}7\\5\\3\end{smallmatrix}$
First inversion: $\begin{smallmatrix}6\\5\\3\end{smallmatrix}$
Second inversion: $\begin{smallmatrix}6\\4\\3\end{smallmatrix}$
Third inversion: $\begin{smallmatrix}6\\4\\2\end{smallmatrix}$

As illustrated in Example 00, below, these figures are placed directly beneath the triad in question, as shown in the example below. The figures are always stacked vertically and the higher number is always at the top.

Example 00: Figuring for triads in root position, first inversion and second inversion (bass notes shown in red).

Abbreviated figuring

The figuring above is the full figuring. In standard usage, abbreviation figures are used, which provide enough information in most cases, unless context demands full figuring. The standard abbreviated figures for seventh chords are as follows:

Root position—only $\begin{smallmatrix}7\\&\end{smallmatrix}$ is shown, $\begin{smallmatrix}5\\3\end{smallmatrix}$ is assumed beneath.
First inversion—only $\begin{smallmatrix}6\\5\end{smallmatrix}$ is shown, $\begin{smallmatrix}&\\&\\3\end{smallmatrix}$ is assumed beneath.
Second inversion—only $\begin{smallmatrix}4\\3\end{smallmatrix}$ is shown, $\begin{smallmatrix}6\\&\end{smallmatrix}$ is assumed above.
Third inversion— $\begin{smallmatrix}4\\2\end{smallmatrix}$ is shown, $\begin{smallmatrix}6\\&\end{smallmatrix}$ is assumed above.

The abbreviated figures for seventh chords are shown in Example 00, with the full figuring underneath.

Example 00: Abbreviated and full figuring for triads in root position, first inversion and second inversion (bass notes shown in red).

Realising Figures with Triads and Seventh Chords

Once you understand the fundamental principles of figures, working out the notes implied by figured bass is not difficult.

Figures tell us what notes (pitch classes, non-octave specific) appear above a bass note according to the intervals indicated by the actual and implied figures.

In its simplest form, realising figured bass is a fairly mechanical process. There are essentially two steps involved:

For each bass note determine what pitch classes are indicated by the figures (including implied figures).
Decide what order and what range to place these depending on the context and style.

The following examples demonstrate step 1 above, showing a figured bass note followed by its realisation in its simplest form.

Example 00: Realisation of figured bass notes to form seventh chords.

Single notes with figures are shown followed by simple realisations to seventh chords in different inversions.

In the examples above we have shown how the numbers in the full figuring lead to pitch classes according to interval size above the given bass note. The dotted arrows then show the placement of the these pitch classes in close position. In the realisation we have provided a chord symbol (above the staff) and Roman numeral interpretation below the staff.

Note that in the Roman numerals, the attached figuring numerically the same as the figuring for the bass note. In the case of Example 00 (c), the $\sharp$ prefixed to 4 in the figuring is not required in the figuring with the Roman numeral. This is because for the figured bass note we need information about the precise pitch class required. Without the $\sharp$ sign the rendering would give F $\natural$ . In contrast, the Roman numeral g: vii° $\begin{smallmatrix}4\\3\end{smallmatrix}$ tells us that the pitch classes are F $\sharp$ , A, C and E $\flat$ (the leading-note seventh chord in G minor), so no inflections by accidentals are required in the figure.

As shown in the chapter on triads, the ways in which a figured bass can be realised vary and are dependent of style and context. In the example below (which can be compared to Example 00 in the chapter on triads), we show that the order, double and placement of the pitch classes indicated by a bass note with figures can vary. However, the pitch classes themselves remain constant.

Example 00: Various realisations of a figured bass note to produce a seventh chord in different contexts

Bass note D with figure natural 6/5 is shown in centre with five different realisations around the outside, including basic close position, open position on a single staff, "keyboard style," "SATB," and string quartet score.

In the example above, the single note with figures (figured bass) indicates B°⁷/D or, in C minor, vii° $\begin{smallmatrix}6\\5\end{smallmatrix}$ . The pitch classes required above D are, F, A, and B $\natural$ . The examples on the outside show various ways this chord could be realised.