CoursesMusic Theory ICh. 8: Triads & Figured Bass
Chapter 8

Triads & Figured Bass

CHAPTER 8 • TRIADS & Figured Bass

Triad Structure

A triad is a three-note chord stacked in thirds. The lowest note of a triad, and the pitch that gives a name to the triad, is called the root. The middle note of the chord is called the third because it is a third higher than the root. The top note is called the fifth for the same reason as the third; it is a fifth higher than the root.

Triad & Chord Members
A triad is a three-note chord built by stacking two consecutive intervals of a third above a foundational root. The middle member is the third (a 3rd above the root) and the highest member is the fifth (a 5th above the root).
Ex. 8.1Triad Structure
CHAPTER 8 • TRIADS & Figured Bass

Triad Quality

There are four types or qualities of triads. The qualities are defined by the size of the intervals (measured below in half steps) between the root and third, then the third and fifth. Remember that four half steps is a major third and three half steps is a minor third:

  • Augmented: 4 + 4 half steps (e.g. C to E, E to G#)
  • Major: 4 + 3 half steps (e.g. C to E, E to G)
  • Minor: 3 + 4 half steps (e.g. C to Eb, Eb to G)
  • Diminished: 3 + 3 half steps (e.g. C to Eb, Eb to Gb)
Triad Qualities & Semitone Formulas
The four triad qualities are defined by their internal semitone interval structures: Major (4 + 3 half steps), Minor (3 + 4 half steps), Diminished (3 + 3 half steps), and Augmented (4 + 4 half steps).
Ex. 8.2Triad Qualities & Semitone Intervals

Plate I. Fig 1

CHAPTER 8 • TRIADS & Figured Bass

Triad Inversion

As described above, there are three notes in the triad and they are known as the root, third, and fifth. Regardless of how these notes are configured, they always retain their specific name. However, the lowest sounding note of a triad, or any chord as we’ll discover later, is always also referred to as the bass.

There are three inversions in which a triad can be placed: root position, first inversion, and second inversion. In root position, the root (which is also the name of the triad) is in the bass. Root-position triads always occupy consecutive lines or spaces on the staff (irrespective of clef). In first inversion, the third is in the bass, and in second inversion, the fifth is in the bass.

Remember that the root is the name of the chord (e.g., a G major triad has a G, B, and D—the G is the root). The bass is the lowest sounding note. If G is in the bass, it is both the root and the bass. If B, the third, is the lowest sounding note, it is both the third and the bass.

Chord Inversion & The Bass Note
Inversion describes which chord member occupies the lowest sounding voice (the bass). In root position, the root is in the bass; in first inversion, the third is in the bass; in second inversion, the fifth is in the bass. The root always gives the triad its name regardless of inversion.
Ex. 8.3Triad Inversions (G Major)
CHAPTER 8 • TRIADS & Figured Bass

Identifying Triads

When presented with an unknown triad, follow these steps to determine the name, quality, and inversion:

  • Determine the root by stacking the triad in thirds. If the notes are already on consecutive lines or spaces, it’s in root position and the bottom note is the root (i.e. the name of the triad). If the notes are not stacked in thirds, rearrange the notes until they are.
  • Determine the quality by measuring the intervals (half-step patterns) between the notes. Match the pattern with those listed above. The quality is easiest to determine when the triad is in root position, but inversion has no impact on quality.
  • Determine the inversion by identifying which note is in the bass. If it’s the root, it’s in root position. If the third is in the bass, it’s in first inversion. If the fifth is in the bass, it’s in second inversion.
Triad Identification Procedure
To identify an unknown triad: 1. Stack in thirds (rearranging pitches onto consecutive lines or spaces) to reveal the root. 2. Measure the intervals from the root to determine the quality (M, m, °, +). 3. Identify the bass note to determine the inversion (Root, 1st, or 2nd).
Ex. 8.4Rearranging Chords to Identify the Root

Because F is the root of the chord and the bottom interval is a M3 and the top interval is a m3, the chord is a F Major triad in first inversion.

CHAPTER 8 • TRIADS & Figured Bass

Figured Bass

Shorthand and systematic labelling systems have been used throughout music history to save time, ink, and space. Figured bass is one such system and we use it to indicate the inversion of triads and other types of chords.

It starts with a note presented on the bass staff. This note is the bass of the triad. Remember that the bass can be any of the triad components: root, third, or fifth. This bass note is the lowest sounding note of the chord.

The numbers/figures (or lack thereof) indicate the intervals to be formed above the bass to complete the triad. Musicians throughout history have used this shorthand notation to improvise harmonies above the bass. Today, we mainly use these figures in Roman numeral analysis to indicate chord types and inversions.

history_edu
Historical Note
Figured bass, or thoroughbass, was the backbone of Baroque ensemble performance. Keyboardists, lutenists, and harpists would “realize” the chords on the fly based on these numbers, providing an improvised harmonic accompaniment above the bass line.
CHAPTER 8 • TRIADS & Figured Bass

Figured Bass Nomenclature

The number(s) below the bass indicate the intervals to be played/written above the bass. A fifth is indicated 5, a third 3, a sixth 6, etc. The figured bass for a root-position triad would be 5 and 3. But since this is a shorthand designed for quick reading and ink saving, the convention is to not write the 5 or 3 for root position as they are understood to be there by default. So, a root-position triad in figured bass is indicated by a single note on the staff. This note is the bass and also understood to be the root.

To indicate first inversion, we need a sixth and third above the bass, notated as 6 and 3. But like the root position triad, the third is understood to be there (it’s an essential pitch to make all triads and will always be present) and so we don’t write it. The figured bass for first inversion triads is simply 6.

For a second-inversion triad we need both numbers: 6 and 4 (stacked vertically).

Figured bass numerals are always interpreted according to the key in which the music is written. For example, a root position triad in C major has C as the root, E as the third, and G as the fifth. To indicate this in figured bass, a C would be written on the staff with no numbers. If we wanted a C minor triad in the key of C major, we would need to lower the third by a half step to Eb. In figured bass notation, we indicate this with a b by itself. Accidentals appearing alone always refer to the third of the chord. We can also raise pitches a half step by placing a sharp in front of the figure. A slash through a number can also be used and means the same thing as a sharp.

Figured Bass Conventions
Root position: no figures (5 and 3 understood). First inversion:6 (short for 6/3). Second inversion:6/4. An accidental appearing alone always alters the third above the bass; a slash through a number raises that interval by a half step.
Ex. 8.5Figured Bass Realizations
Ex. 8.6Accidentals and Slashes in Figured Bass
Chapter 8 · Triads & Figured Bass

Triad Trainer

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Position:
Recall the triad quality and inversion
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Chapter 8 Quiz

Test your knowledge on this chapter’s material before moving on.