Lesson 17 · All 12 keys

Half-Diminished 7th Chord Trainer

Learn how a half-diminished 7th chord (also written m7♭5) is built one semitone-count at a time — a diminished triad plus a minor 7th on top — then put it to work with two MIDI exercises: playing all 12 half-diminished 7th chords around the circle of fourths, and a cadential I-V7-viiø7-I progression showing its diatonic leading-tone role, in every key.

How a half-diminished 7th chord is built

A half-diminished 7th chord (m7♭5) is a 4-note chord — a diminished triad with a minor 7th (not a diminished 7th) stacked on top. Every half-diminished 7th chord — in any of the 12 keys — is built the exact same way, by counting semitones to the right from a root note:

  1. Start on the root — the note that names the chord.
  2. Count 3 semitones to the right to land on the minor 3rd.
  3. From there, count 3 more semitones to the right (6 semitones from the root) to land on the diminished 5th.
  4. From there, count 4 more semitones to the right (10 semitones from the root) to land on the minor 7th.
Example — C♯ half-diminished 7th (C♯m7♭5): start on C♯, count 3 semitones right to reach E, 3 more to reach G, then 4 more to reach B. C♯‑E‑G‑B is the C♯m7♭5 chord. The pattern 3, 3, 4 (10 semitones total from root to top) is what makes a chord "half-diminished 7th" — every one of the 12 half-diminished 7th chords is this same shape, just moved to start on a different key.
Compare this to a fully-diminished 7th chord (Lesson 14), which counts 3, 3, 3 instead — a half-diminished chord raises that last interval by one semitone, turning the diminished 7th into an ordinary minor 7th. "Half" because only the triad underneath (root-3rd-5th) is diminished; the 7th itself isn't. This is the 7th chord a major scale builds naturally on its own leading-tone (7th) degree — unlike the fully-diminished 7th, it doesn't need to borrow any note from outside the scale, which is why it's also written viiø7 and shows up constantly as the ii chord of minor-key ii-V-i progressions.

Try it: pick a root and build the chord step by step

Step 1 of 4
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Chord toneNoteSemitones from rootMIDI #

All 12 half-diminished 7th chords at a glance

ChordRoot+3 semitones → 3rd+3 semitones → dim 5th+4 semitones → ♭7th

This MIDI exercise plays all 12 half-diminished 7th chords, one after another, moving around the circle of fourths — each chord's root sits a perfect 4th (5 semitones) above the last one: C → F → B♭ → E♭ → A♭ → D♭ → G♭/F♯ → B → E → A → D → G → back to C. Every chord is played as a full 4-note half-diminished 7th (root, minor 3rd, diminished 5th, and minor 7th together). Unlike the fully-diminished 7th chord, these 12 chords are all genuinely distinct — no shared enharmonic overlaps.

Chord 1 of 12
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The 12 chords, in circle-of-fourths order

#ChordRoot3rdDim 5th♭7th

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Key of C
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Progression in C

DegreeChordNotes