Definition
Every interval has two names: a number (second, third, fourth…), which counts the note names, and a quality, which counts the semitones. Besides perfect, major and minor there are the qualities augmented (a semitone more than major or perfect) and diminished (a semitone less than minor or perfect), and, more rarely, doubly augmented and doubly diminished.
The scheme of qualities
- Unison, fourth, fifth, octave: diminished – perfect – augmented.
- Second, third, sixth, seventh: diminished – minor – major – augmented.
| Interval | Example | Semitones | Enharmonically equivalent to |
|---|---|---|---|
| Augmented second | F–G# | 3 | minor third |
| Diminished third | G#–Bb | 2 | major second |
| Augmented fourth (tritone) | F–B | 6 | diminished fifth |
| Diminished fifth | B–F | 6 | augmented fourth |
| Augmented fifth | C–G# | 8 | minor sixth |
| Augmented sixth | Ab–F# | 10 | minor seventh |
| Diminished seventh | G#–F | 9 | major sixth |
| Diminished fourth | G#–C | 4 | major third |
| Augmented unison | C–C# | 1 | minor second |
Method of calculation
- Count the note names (F-G = second), ignoring accidentals.
- Compare with the “reference” interval of the major scale built on the lower note (in F major, F–G is a major second).
- Add or remove the semitones due to the accidentals: F–G# has one semitone more, so it is augmented.
Inversions
When an interval is inverted, the number is complemented to 9 and the quality is reversed: augmented becomes diminished and vice versa. The augmented fourth F–B becomes the diminished fifth B–F; the augmented sixth Ab–F# becomes the diminished third F#–Ab.
Where they are found
- In the major scale only one augmented or diminished interval appears between diatonic notes: the tritone between the fourth and seventh degrees (F–B in C).
- The harmonic minor has more: an augmented second between the sixth and seventh degrees (F–G# in A minor), a diminished seventh between the leading tone and the sixth degree (G#–F), a diminished fourth between the leading tone and the third degree (G#–C), an augmented fifth between the third and seventh degrees (C–G#).
- The augmented sixth comes from the homonymous chords (Italian, French, German).
Rule of resolution
In tonal music augmented intervals tend to expand and diminished ones to contract:
- augmented fourth F–B → sixth E–C;
- diminished fifth B–F → third C–E;
- augmented sixth Ab–F# → octave G–G;
- diminished seventh G#–F → fifth A–E.
This is why “correct” spelling matters: Ab–F# and Ab–Gb sound the same on the piano, but the first asks to open out onto G–G, the second is an ordinary minor seventh.
Typical errors
- Calling the augmented second F–G# a “minor third”: on the piano it sounds the same, but in A harmonic minor it is something else and behaves differently.
- Counting semitones without counting names: this leads to getting the interval number wrong.
- Writing the augmented second in a classical-style vocal melody without meaning to: it is considered hard to sing in tune and should be used deliberately (or avoided with the melodic minor).
Examples
- Bernstein, “Maria” (West Side Story): the melody opens with an augmented fourth that immediately resolves by rising a semitone.
- Black Sabbath, “Black Sabbath”: the riff is built on the tritone, the interval that gives it its unsettling character.
- The harmonic minor in “Orientalist” melodies and in neoclassical metal exploits precisely the augmented second.
- In Bach chorales the diminished seventh of the leading tone regularly closes onto a fifth.
How to use it in composition
- The tritone is the heart of the dominant (B–F inside G7): learning to resolve it is learning the cadence.
- The augmented second gives an exotic color to a melody: use it as a characterizing gesture, not by chance.
- Enharmonic equivalences between augmented and diminished intervals are the basis of enharmonic modulation.
Exercise
- Write all the augmented and diminished intervals starting from D, then invert them.
- Find in E harmonic minor all the intervals that are not major, minor or perfect.
- Resolve in two voices: augmented fourth Bb–E, diminished fifth E–Bb, augmented sixth C–A#.
Related topics
Intervals and their inversions; Simple and compound intervals; Enharmonic equivalence; The harmonic minor scale and its modes; Augmented sixth chords; Enharmonic modulation.