Half-diminished seventh chord

A half-diminished seventh chord is a four-note seventh chord built from a root, minor third, diminished fifth, and minor seventh (a diminished triad with a minor seventh on top). On the AP Music Theory exam it appears as viiø7 in major keys and iiø7 in minor keys.

What is Half-diminished seventh chord?

A half-diminished seventh chord is a seventh chord, meaning four distinct pitches stacked in thirds (PIT-1.O.1). Its recipe from the root up is a minor third, a diminished fifth, and a minor seventh. The easiest way to think about it is in two layers. The bottom three notes form a diminished triad. The top note sits a minor seventh above the root. That's the whole chord.

The "half" in the name tells you it's only partly diminished. The triad is diminished, but the seventh is minor, not diminished. In a fully diminished seventh chord, both the fifth AND the seventh are diminished. That one interval of difference is the entire distinction, and it's exactly what the AP exam likes to test. You'll see this chord written with the symbol ø7 (a slashed circle), and you'll hear it as dissonant but noticeably softer than a fully diminished seventh.

Why Half-diminished seventh chord matters in AP Music Theory

This term lives in Unit 3 (Music Fundamentals III: Triads and Seventh Chords) under Topic 3.1, and it directly supports learning objective AP Music Theory 3.1.A, which asks you to describe chord quality in both performed and notated music. That means two skills. By ear, you need to recognize the half-diminished sound as dissonant but less crunchy than fully diminished. On paper, you need to spell it (root, m3, d5, m7) and identify it from notation. It also matters because of where it naturally occurs. Build a seventh chord on scale degree 7 in a major key, or on scale degree 2 in a minor key, and you get half-diminished automatically. Knowing that shortcut saves you time on quality-identification questions.

How Half-diminished seventh chord connects across the course

Diminished seventh chord (Unit 3)

These two chords share the same diminished triad on the bottom. Only the seventh differs. Fully diminished has a diminished seventh (vii°7 on the leading tone in harmonic minor), while half-diminished has a minor seventh. If you can hear or spell that one interval, you can tell them apart every time.

Diminished triad (Unit 3)

Strip the seventh off a half-diminished seventh chord and you're left with a diminished triad. This is why learning triad qualities first makes seventh chords easy. Every seventh chord is just a triad plus one more third.

Dominant seventh chord (Unit 3)

Both chords contain a minor seventh above the root, but the dominant seventh sits on a major triad (M3, P5) while the half-diminished sits on a diminished triad (m3, d5). The exam loves giving you a recipe of intervals and asking which quality it builds, so know both formulas cold.

Chord inversion (Unit 3)

Like any seventh chord, the half-diminished can appear in root position or three inversions. Quality doesn't change when the chord flips, so you have to mentally restack the notes in thirds before judging whether you're looking at ø7 or something else.

Is Half-diminished seventh chord on the AP Music Theory exam?

This chord shows up most often in multiple-choice questions about seventh-chord quality, in two flavors. The first is interval-recipe questions, like "a four-note chord with a root, minor third, diminished fifth, and minor seventh has which quality?" The second is the comparison question, asking what interval distinguishes half-diminished from fully diminished (answer: the seventh). Aural questions can also play a seventh chord and ask you to name its quality, so practice hearing the difference between ø7 and °7. Watch for the scale-degree trap too. The seventh chord on the leading tone in harmonic minor is FULLY diminished (vii°7), not half-diminished, because the raised leading tone shrinks the seventh. Half-diminished is what you get on the leading tone in major (viiø7) or on scale degree 2 in minor (iiø7).

Half-diminished seventh chord vs Diminished seventh chord

Both chords start with the same diminished triad, so the bottom three notes are identical. The difference is the top interval. A half-diminished seventh has a minor seventh above the root (think B-D-F-A), while a fully diminished seventh has a diminished seventh above the root (B-D-F-Ab). One half step in one note changes the quality and the sound. Fully diminished is the more tense of the two because it's stacked entirely in minor thirds. On the exam, if the question says "vii°7 in harmonic minor," that's fully diminished; if it says the seventh is minor, you're in half-diminished territory.

Key things to remember about Half-diminished seventh chord

• A half-diminished seventh chord is spelled root, minor third, diminished fifth, minor seventh, which is a diminished triad with a minor seventh stacked on top.

• The only interval separating half-diminished from fully diminished is the seventh: minor seventh for half-diminished, diminished seventh for fully diminished.

• Half-diminished sevenths occur naturally as viiø7 in major keys and iiø7 in minor keys, while the leading-tone seventh in harmonic minor (vii°7) is fully diminished.

• The symbol for half-diminished is a slashed circle (ø7); a plain circle (°7) means fully diminished.

• By ear, a half-diminished seventh sounds dissonant but noticeably less tense than a fully diminished seventh, which is the quality distinction AP Music Theory 3.1.A asks you to describe.

Frequently asked questions about Half-diminished seventh chord

What is a half-diminished seventh chord?

It's a four-note seventh chord made of a root, minor third, diminished fifth, and minor seventh. In other words, a diminished triad with a minor seventh added above the root, written with the symbol ø7.

What's the difference between half-diminished and fully diminished seventh chords?

The seventh. Both chords contain a diminished triad, but half-diminished adds a minor seventh (B-D-F-A) while fully diminished adds a diminished seventh (B-D-F-Ab). That single half step is the interval AP questions ask about.

Is the leading-tone seventh chord half-diminished?

It depends on the key. In a major key, viiø7 is half-diminished. In harmonic minor, the raised leading tone makes vii°7 fully diminished, and that distinction is a common exam question.

Why is it called 'half' diminished?

Because only part of the chord is diminished. The triad (root, third, fifth) is diminished, but the seventh is minor rather than diminished. A fully diminished seventh diminishes both the fifth and the seventh.

How do I tell a half-diminished seventh from a minor seventh chord?

Check the fifth. A minor seventh chord has a perfect fifth (minor triad plus minor seventh), while a half-diminished seventh has a diminished fifth. The third and seventh are minor in both, so the fifth is the deciding interval.