Glossary
Tertiary
Glossary
Tertiary harmony refers to chords built from stacked major and minor thirds. In order to complete the octave, sometimes a perfect fourth must be employed (for example, major and minor triads).
Even basic tertiary harmony is only mostly thirds-based, with “near-thirds” (perfect fourths) needed, right from the start, so explaining chords as stacks of different-sized thirds (or near-thirds) already seems more confusing than it should be. The set-theoretic basis of explaining where common chords come from, and especially the concept of near-evenness—since it highlights the importance and usefulness of everything from the perfect fifth interval class, to triads, to dominant chords, to the pentatonic scale, to the diatonic scale—seems more useful, especially since the concepts apply more generally.
Augmented Triad
R 3 5
Major Third, Major Third
Major Triad
R 3 5
Major Third, Minor Third
Minor Triad
R ♭3 5
Minor Third, Major Third
Diminished Triad
R ♭3 ♭5
Minor Third, Minor Third
Major Seventh
R 3 5 7
Major Third, Minor Third, Major Third
Dominant Seventh
R 3 5 ♭7
Major Third, Minor Third, Minor Third
Minor Seventh
R ♭3 5 ♭7
Minor Third, Major Third, Minor Third
Minor Seventh ♭5 (Half-Diminished)
R ♭3 ♭5 ♭7
Minor Third, Minor Third, Major Third
Tertiary harmony refers to chords built from stacked major and minor thirds. In order to complete the octave, sometimes a perfect fourth must be employed (for example, major and minor triads).
Even basic tertiary harmony is only mostly thirds-based, with “near-thirds” (perfect fourths) needed, right from the start, so explaining chords as stacks of different-sized thirds (or near-thirds) already seems more confusing than it should be. The set-theoretic basis of explaining where common chords come from, and especially the concept of near-evenness—since it highlights the importance and usefulness of everything from the perfect fifth interval class, to triads, to dominant chords, to the pentatonic scale, to the diatonic scale—seems more useful, especially since the concepts apply more generally.
| Augmented Triad | R 3 5 | Major Third, Major Third |
| Major Triad | R 3 5 | Major Third, Minor Third |
| Minor Triad | R ♭3 5 | Minor Third, Major Third |
| Diminished Triad | R ♭3 ♭5 | Minor Third, Minor Third |
| Major Seventh | R 3 5 7 | Major Third, Minor Third, Major Third |
| Dominant Seventh | R 3 5 ♭7 | Major Third, Minor Third, Minor Third |
| Minor Seventh | R ♭3 5 ♭7 | Minor Third, Major Third, Minor Third |
| Minor Seventh ♭5 (Half-Diminished) | R ♭3 ♭5 ♭7 | Minor Third, Minor Third, Major Third |