Half-diminished chord: the m7♭5 explained
A half-diminished chord is a four-note chord with a diminished triad plus a minor seventh: root, minor third, diminished fifth, minor seventh (3 + 3 + 4 half steps). It is written m7♭5 or with the symbol ø, and it is the ii chord of a minor key.
A half-diminished chord is a four-note chord that sounds dark, soft and slightly mysterious. It is a diminished triad with a minor seventh added on top. You will see it written as m7♭5 or with a circle crossed by a slash. It is one of the most important chords in jazz, and it also turns up in classical music and in many ballads.
The name sounds odd, so the first thing to clear up is why it is called half-diminished. We will do that below, after we build the chord and look at its sound.
How do you build a half-diminished chord?
Stack three intervals above the root. Count 3 half steps for the third, 3 more for the fifth, and 4 more for the seventh. The formula is 3 + 3 + 4. The intervals from the root are a minor third, a diminished fifth and a minor seventh.
| Note | Interval from the root | Half steps from the root |
|---|---|---|
| Root | unison | 0 |
| Third | minor third | 3 |
| Fifth | diminished fifth | 6 |
| Seventh | minor seventh | 10 |
Another easy way to build it: start with a minor seventh chord (such as Cm7 = C, E♭, G, B♭) and lower the fifth by one half step. That is exactly why the symbol is m7♭5.
Why is it called half-diminished?
A fully diminished chord with a seventh (the diminished seventh chord) has all minor thirds stacked: 3 + 3 + 3. Its seventh is a diminished seventh. The half-diminished chord goes only part of the way. It keeps the diminished triad at the bottom, but its seventh is a minor seventh, one half step higher than the diminished seventh.
| Chord | Formula | Seventh is | Symbol on C |
|---|---|---|---|
| Diminished seventh | 3 + 3 + 3 | diminished seventh (9 half steps) | Cdim7 or C°7 |
| Half-diminished seventh | 3 + 3 + 4 | minor seventh (10 half steps) | Cm7♭5 or Cø7 |
So one note changes. C diminished seventh has B𝄫 (which sounds like A), and C half-diminished seventh has B♭. That one half step changes the character from very tense to tense but a little warmer.
How do you write the symbol?
You may see this chord written several ways: Cm7♭5, Cmin7♭5, C-7♭5, Cø or Cø7. All mean the same chord. The ø symbol (a circle with a slash) is common in jazz books. Note that a plain circle, as in C°7, means the fully diminished seventh chord, which is a different sound.
Where does a half-diminished chord appear in a key?
In any major key, the seventh chord built on the seventh note is half-diminished. In C major it is B, D, F and A (Bm7♭5), all notes from the C major scale. In a natural minor key it appears on the second note. In A minor, the chord on B is again B, D, F, A.
In jazz, a very common minor key pattern is ii-V-i. In A minor that is Bm7♭5, E7 and Am. You can compare it with the major version in chord progressions.
How does it sound?
The half-diminished chord is dark and a bit unsettled, but softer than the diminished seventh. It tends to feel like it is leaning toward a dominant chord. In jazz ballads it adds a wistful quality. Players often describe it as sad, uneasy or gently tense. These descriptions are subjective, so listen and decide for yourself.
Where do you hear it?
Classical composers used half-diminished harmony long before jazz named it. Richard Wagner's opera Tristan und Isolde (1865) opens with a famous chord, often called the Tristan chord, that sounds like a half-diminished seventh chord. Analysts argue about how best to describe it, which is part of its fame. In jazz it is a staple of standards in minor keys, and in film music it signals mystery.
How can you practice it?
- Play a C minor seventh chord (C, E♭, G, B♭).
- Lower the G to G♭ and listen to the change.
- Play the ii-V-i in C minor: Dm7♭5, then G7, then Cm. Notice how each chord leads to the next.
- Play the ii-V-i in your favorite minor key slowly with a steady count.
Memory trick: half-diminished means one note short of fully diminished. Compare it to a minor seventh chord with a lowered fifth. Fully diminished also lowers the seventh.
Check yourself
1. What is the half step formula for a half-diminished seventh chord?
Answer: 3 + 3 + 4. A diminished triad (3 + 3) plus a minor seventh above the fifth (4 more).
2. How does half-diminished differ from fully diminished seventh?
Answer: Its seventh is minor. The fully diminished chord has a diminished seventh. The half-diminished has a minor seventh.
3. Which symbol means half-diminished?
Answer: Cø7. A circle with a slash is half-diminished. A plain circle is fully diminished.
4. Where is the half-diminished seventh chord in a major key?
Answer: On the seventh note. Seventh chords built on the seventh note of a major scale are half-diminished.
5. How do you build Cm7♭5 starting from Cm7?
Answer: Lower the fifth. The ♭5 in the symbol tells you to lower the fifth by one half step.