Triads & Inversions

A photograph of Issa, Anita and Ruth Pointer singing into microphones on stage under a large chandelier. Issa, Anita and Ruth Pointer, performing together as The Pointer Sisters in New Jersey in 2006. As a vocal trio, The Pointer Sister are known for their rich harmonies.
(Detail from Rick Kramer | CC BY-2.0)

Many different kinds of chords are used in 12TET music, but the most basic, common form is the triad.

Tertial Harmony

In most 12TET music, chords are constructed using major and minor thirds, a system called tertial harmony. Diminished and augmented thirds, which sound like major seconds and perfect fourths, respectively, are not considered part of this system of harmony.

Triads

Tertial chords of many sizes — triads, tetrads, pentads, and so on — are common in 12TET music, but listeners often perceive the first three notes of a chord as foundational, and remaining notes as adding specific color. Dyads are often perceived as missing a third note, which is often aurally "filled in" by the listener.

Staff notation showing how a major third is often aurally perceived as a major triad, and how a perfect fifth is often aurally perceived as a major or minor triad.
Figure 1: A major third from F to A will often be perceived as a triad containing a C, and a perfect fifth from E to B will often be heard as implying a G or G#, depending on the tonal context.

Types of Triads

Using major and minor thirds, there are four possible types of triads: diminished, minor, major and augmented.

Staff notation showing a G diminished triad, with a minor third from G to B flat and a minor third from B flat to D flat; a G minor triad, with a minor third from G to B flat and a major third from B flat to D; a G major triad, with a major third from G to B and a minor third from B to D; and a G augmented triad, with a major third from G to B and a major third from B to D sharp.
Figure 2: The four possible triads, showing how each can be constructed using major and minor thirds.

Major and minor triads are often perceived as being consonant, and diminished and augmented triads are generally heard as dissonant.

Beginning with the a diminished triad, all three other triad types can be constructed by changing one note by a half step.

Staff notation showing an E flat diminished triad, then raising the B double flat to a B flat making an E flat minor triad, then raising the G flat to a G natural making an E flat major triad, then raising the B flat to a B natural making an E flat augmented triad.
Figure 3: Each type of triad can be changed into another type by changing one note by a half step.

Voicing

As long as they contain the three specific pitch classes, triads can be written in any order and with any kind of spacing. A single pitch class may be included in more than one octave, a process called doubling. The type of arrangement used is call the chord's voicing. When the notes are spread out widely, the chord is said to have an open voicing, and when the notes are placed close together it is called closed voicing.

Staff notation showing a D major chord with the notes D, F sharp, A, and D voiced very compactly, and another D major chord with the same notes spread across two octaves.
Figure 4: A D major triad in close position and in open position. In both cases, the note D is doubled.

Theorists often write triads and other chords in closed position stacked in thirds, a special voicing called basic form. The notes in a chord, or chord tones, are labeled based on their location when the chord is in basic form: the bottom note is called the root of the chord, the middle note is called the third, and the top note is called the fifth. These labels are used to describe members of the chord even when the chord is written in other voicings.

Staff notation showing an A minor chord with the notes A3, C4 and E4, and another with the notes C4, A4, E5 and A5. In both chords, all A notes are labeled as `root,` all C notes are labeled as `third,` and all E notes are labeled as `fifth.`
Figure 5: An A minor triad spelled in basic form and in an open position, with the component pitches labeled.

Inversions

Changing a chord's voicing can affect its sound. The aspect of voicing that has the most significant affect on the chord's sound is the chord's inversion, which is determined by what chord tone is the bass, or the lowest note in the chord.

Staff notation showing an F sharp major chord in four different voicings: one in basic form, and three in a more open voicing, with F sharp, A sharp and C sharp in the bass, respectively. The first two chords are labeled as `root position,` the third is labeled as `first inversion` and the fourth is labeled as `second inversion.`
Figure 6: An F# major triad spelled in different inversions. Note that the lowest sounding note determines the inversion, regardless of the arrangement of the rest of the chord.

Triads can be in three different inversions:

  • When the chord has the root in the bass, the chord is in root position. Root position is usually considered the most stable and consonant arrangement of the chord.
  • When the chord has the third in the bass, the chord is in first inversion. First inversion usually sounds consonant, but with less finality than root position.
  • When the chord has the fifth in the bass, the chord is in second inversion. Second inversion tends to sound unstable, as though it should resolve to a different chord.

Inversions are determined only by the chord note present in the bass; the structure, spacing and doubling of the rest of the chord has no affect on the chord's inversion.

Triads & Inversions: Summary

  • Tertial harmony is a system of chords constructed with major and minor thirds.
  • A triad is a chord consisting of three notes, comprising two major or minor thirds.
    • There are four possible triads in tertial harmony:
      • A major triad consists of a major third on bottom and a minor third on top.
      • A minor triad consists of a minor third on bottom and a major third on top.
      • A diminished triad consists of two minor thirds stacked together.
      • An augmented triad consists of two major thirds stacked together.
    • Major and minor triads are often perceived as being consonant, and diminished and augmented triads are usually heard as bring dissonant.
  • Triads can be written using doubling, and in various voicings.
    • Open voicing features chord tones spread out across a larger range.
    • Closed voicing features chord tones grouped more closely together.
    • Basic form arranges the chord as compactly as possible, without using any doubling.
  • A triad's inversion is determined by which chord tone is the bass.
    • If the chord's root is in the bass, the chord is in root position.
    • If the chord's third is in the bass, the chord is in first inversion.
    • If the chord's fifth is in the bass, the chord is in second inversion.

Exercises

Exercise 1: Description of Exercise

Exercise 2: Description of Exercise