Half-Diminished Chord, Arpeggio & Locrian Scale on Guitar

The half-diminished chord, its arpeggio, and the Locrian scale are three ways of understanding and using the same harmonic sound.

1. The half-diminished chord: Eø7

An half-diminished seventh chord contains four notes (example in E):

E – G – Bb – D

Its formula is 1 – b3 – b5 – b7.

E is the root.

G is the minor third.

Bb is the diminished fifth.

D is the minor seventh.

It can be seen as a diminished triad with an added b7.

The diminished fifth gives the chord its characteristic unstable, tense sound.

Here below a basic drop 2 Em7b5 guitar voicing shape.

2. The half-diminished arpeggio

The arpeggio uses exactly the same notes as the chord, but plays them individually rather than simultaneously.

E – G – Bb – D 

The chord gives you the harmony; the arpeggio allows you to outline that harmony melodically, for example when improvising over an Eø7 chord.

3. The Locrian scale

The E Locrian scale contains seven notes:

E – F – G – A – Bb – C – D

Its formula is 1 – b2 – b3 – 4 – b5 – b6 – b7.

The Locrian scale is the seventh mode of the major scale.

Notice that all four notes of Eø7 appear in the scale:

E — root

G — minor third

Bb — diminished fifth

D — minor seventh

The other three notes : F (9), A (11), and C (13) expand the sound, giving you additional melodic possibilities.

4. How they connect

E Half-Diminished Chord

E – G – Bb – D

Play the notes together to create harmony.

E Half-Diminished Arpeggio

E – G – Bb – D

Play the same chord tones one at a time.

E Locrian Scale

E – F – G – A – Bb – C – D

Use the chord tones plus three additional notes to create melodies.

5. Applying it

Over an Eø7 chord, try this approach:

Start by playing E – G – Bb – D to establish the chord sound.

Add F (9), A (11), and C (13) from E Locrian to create melodic movement.

Resolve phrases to E, or emphasize the chord tones to reinforce the harmony.

Here are two basic exercises implying an Em7b5 arpeggio and an E Locrian line.

In a minor II–V–I progression, the half-diminished chord is the II chord, followed by the V chord (dominant seventh) and resolving to the minor I chord.

In E Locrian, our E half-diminished chord (Eø7) functions as the ii chord in D minor:

II: Em7b5 — E Locrian (E–F–G–A–Bb–C–D)

V: A7 — A altered or A Phrygian dominant, depending on the harmonic context

I: Dm7 or Dm(maj7), depending on the minor-key sound you want

The half-diminished arpeggio outlines the harmony of the ii chord, while E Locrian provides additional notes for improvisation. As the progression moves to A7 and resolves to D minor, listen for the chord tones guiding the movement.

The key idea: Use Eø7 to establish the minor II sound, E Locrian to develop melodic ideas, and then follow the harmony through V–I to D minor.

Here below an example in C minor taken from the PDF Method "40 Minor 2-5-1 Jazz Guitar Licks"