Identify and write melodic and harmonic intervals by number and quality, and construct major, minor, augmented and diminished triads and their inversions

What this dot point is asking

SEAB wants you to name any interval by its number and its quality, and to build and invert the four triad types. The central insight is that an interval needs two pieces of information: the number, counted from the letter names, and the quality, fixed by the exact size in semitones. The same two-step logic then builds triads by stacking thirds, and inversions are just the same three notes reordered.

The answer

Naming an interval: number then quality

An interval is the distance between two notes. Name it in two steps:

1. Number. Count the letter names from the lower note to the upper note, inclusive. C to G is C, D, E, F, G, five letters, so a fifth. C to E is a third.
2. Quality. Fix the exact size in semitones. Seconds, thirds, sixths and sevenths are major or minor; unisons, fourths, fifths and octaves are perfect. Widening a perfect or major interval by a semitone makes it augmented; narrowing it makes it diminished.

Common interval sizes

Counting in semitones from the lower note:

• Minor third = 3 semitones; major third = 4 semitones.
• Perfect fourth = 5 semitones; augmented fourth (tritone) = 6 semitones.
• Perfect fifth = 7 semitones.
• Octave = 12 semitones.

An interval can be melodic (the notes sound one after another) or harmonic (they sound together).

The four triad types

A triad is three notes a third apart: a root, a third above it, and a fifth above the root. The quality depends on the two stacked thirds:

• Major triad: major third then minor third (for example C, E, G).
• Minor triad: minor third then major third (for example C, E flat, G).
• Diminished triad: two minor thirds (for example C, E flat, G flat).
• Augmented triad: two major thirds (for example C, E, G sharp).

Inversions and figured bass

A triad is in root position when the root is the lowest note. Reordering moves the chord into an inversion:

• First inversion: the third is in the bass, labelled $\frac{6}{3}$ (usually shortened to 6).
• Second inversion: the fifth is in the bass, labelled $\frac{6}{4}$.

The notes are the same; only the bass note and the spacing change, which alters the colour and stability of the chord.

Examples in context

Example 1. Hearing major versus minor. A song that opens on a bright, settled chord is likely built on a major triad, while a darker, more plaintive opening often uses a minor triad. Training the ear to hear the size of the third, four semitones for major, three for minor, is the foundation of chord identification in the listening paper.

Example 2. A second-inversion chord at a cadence. Composers often place a tonic chord in second inversion just before the dominant at a cadence, a so-called cadential six-four, to heighten the arrival. Recognising the unstable $\frac{6}{4}$ sound and its resolution is a small but rewarding detail in analysis.

Try this

Q1. Explain the two steps for naming any interval. [2 marks]

• Cue. First count the letter names inclusively from the lower note to fix the number; then count the semitones to fix the quality (major, minor, perfect, augmented or diminished).

Q2. Build the four triad types on the note G and state the thirds in each. [4 marks]

• Cue. Major G, B, D (major then minor third); minor G, B flat, D (minor then major); diminished G, B flat, D flat (two minor thirds); augmented G, B, D sharp (two major thirds).

Q3. Describe the difference between root position and first inversion of a triad. [2 marks]

• Cue. In root position the root is the lowest note; in first inversion the third is the lowest note (figured 6), with the same three pitches reordered.