Half-diminished seven chord (ø7)


Recall from Building a context lesson that we've defined a chord as being 3 or more distinct notes, usually played at the same time. (C and D are considered distinct, but C# and Db are not, nor are octaves of the same note).

Recall that chords come in two basic parts, a letter name (C, C#, etc.) also known as a root note (tonic, 1), and a descriptive part that abbreviates the name of the chord (is a short-hand for all the intervals of each distinct note from the root note).

Recall that an interval is the distance between two notes, and that we are using numbers (with accidentals) to describe these intervals.(ex. 5 = perfect fifth, etc.) For more info on intervals see interval lesson. to convert letters to numbers and numbers to letters, see the link below (bottom of page) on transposition.

Recall, we've previously defined the following chords:
major = 1,3,5
minor (m)= 1,b3,5
diminished (o)= 1,b3,b5
power chord (5) = 1,5,8(1)
dominant seventh chord = 1,3,5,b7
minor seventh chord = 1,b3,5,b7
major seventh chord = 1,3,5,7

Now we shall define the half-diminished seventh chord as:
m7b5 = 1,b3,b5,b7
Sometimes we write half-diminished seventh chords as m7b5 or ø7. (Ex. Cm7b5, Dø7, etc.)

Here are some open m7b5 chords to get you started:
Am7b5=X0101X, Bm7b5=X20201,
Dm7b5=XX0111, Em7b5=010030.

We should note from our definition (m7b5=1,b3,b5,b7) that a half-diminished seventh chord contains a diminished chord (diminished=1,b3,b5) within it.
We can think of a half-diminished seventh chord as a diminished chord with an added minor seventh note.

If we don't know how to play a m7b5 chord, we could substitute a diminished chord with the same root note in its place. We will no longer have the full flavor of the m7b5 chord, but the substitution should work.

We also note that a chord synonym for for i7b5 is biii6. In the key of C:
Bm7b5 = B,D,F,A = 1,b3,b5,b7
Dm6 = D,F,A,B = 1,b3,5,6

So you could use as a substitute for a m7b5 chord, a minor six chord a minor third higher than the m7b5 chord. (you could substitute Dm6 for Bm7b5)

Recalling how the chromatic scale maps out on a fretboard in standard tuning ( see interval lesson). We can map out the m7b5 chord on the fretboard (shown here in F).

|-1|--|--|b3|--|--|b5|--|--|--|b7|--|-1|
|--|--|--|b7|--|-1|--|--|b3|--|--|b5|--|
|b3|--|--|b5|--|--|--|b7|--|-1|--|--|--|
|b7|--|-1|--|--|b3|--|--|b5|--|--|--|--|
|--|b5|--|--|--|b7|--|-1|--|--|b3|--|--|
|-1|--|--|b3|--|--|b5|--|--|--|b7|--|-1|

We can cut this up into zones of one sort or another. In previous lessons, we've been looking at shapes based on octave patterns. (A-shape, E-shape, etc.). So below are the 5 shapes along with some voicings in TAB that go along with the shape. All of these are for Fm7b5. To change to to another m7b5 chord, we use the same process as for other moveable chords (barre chords, etc.).

Fm7b5 "E-shape"(root note on the 6th string)

|-1-|---|---|b3-|  
|---|---|---|b7-|
|b3-|---|---|b5-|
|b7-|---|-1-|---|
|---|b5-|---|---|
|-1-|---|---|b3-|
  1   2   3   4

|--1-1-1-------1-1-1-1--|
|--4-0-4---0---0-0-4-4--|
|--1-1-1-1-1-1-1-1-1-1--|
|--3-1-1-1-1-1-1-1-3-3--|
|--2-2-2-2-----2-----2--|
|--1-1-1-1-1-1----------|

Fm7b5 "D-shape" (root note on the 4th string)

|---|b3-|---|---|
|---|b7-|---|-1-|
|---|b5-|---|---|
|-1-|---|---|b3-|
|---|---|---|b7-|
|---|b3-|---|---|
  3   4   5   6 

|--4-4-4---4-4--|
|--4-4-6---6-4--|
|--4-4-4-4-4-4--|
|--3-3-3-3---3--|
|----6-6-6-6-6--|
|--------4---4--|

Fm7b5 "C-shape" (root note on the 5th string)

|---|---|b5-|---| |---|-1-|---|---| |---|---|---|b7-| |---|b3-|---|---| |---|b7-|---|-1-| |---|---|b5-|---| 5 6 7 8 |------7-7-7--| |--6-6-6-6-6--| |--8-8-8-8-8--| |--6-6-6---6--| |--8-8-8-6----| |----7---7----|

Fm7b5 "A-shape" (root note on the 5th string)

|---|---|---|b7-|
|---|b3-|---|---|
|b7-|---|-1-|---|
|---|b5-|---|---|
|-1-|---|---|---|
|---|---|---|b7-|
  8   9  10  11

|--11-11-11--7--7-----------|
|---9--9--9--9--9--9--9--9--|
|--10-10-10--8--8--8-10--8--|
|---9--9--9--9--9--9--9-----|
|---8--8-----8--8--8-----8--|
|------7--------7----11-----|

Fm7b5 "G-shape" (root note on the 6th string)

|---|b7-|---|-1-|
|---|---|b5-|---|
|-1-|---|---|b3-|
|---|---|---|b7-|
|---|b3-|---|---|
|---|b7-|---|-1-|
 10  11   12  13

|-11-----------|
|-12----12-----|
|-10-10-10-----|
|-13-13-13-13--|
|-11-11-11-11--|
|-13-13----13--|

Ok. So we can make many different voicings out of a given chord (many more than shown here). Choosing for ourselves just what voicing we're going to use to interpret a chord is one part of developing our own style.

CHORDS in CONTEXT

We often see m7b5 chords written in songs, but there is a way to understand why they pop up where they do? Usually.

Recall, that we harmonized the major scale to get the chords (triads):
I-ii-iii-IV-V-vi-viio (in the key of C: C-Dm-Em-F-G-Am-Bo)
and the seventh chords:
Imaj7-ii7-iii7-IVmaj7-V7-vi7-viiø7 (in C:
Cmaj7-Dm7-Em7-Fmaj7-G7-Am7-Bø7)

We can see here that the only chord in the major scale with a half-diminished 7th chord is the 7.

Where else does the m7b5 chord turn up?
Without getting into the modes of these scale systems as well, we find m7b5 chords in the natural minor, harmonic minor, and melodic minor scales (also in their modes).

In the natural minor (minor scale, or aeolian mode), the m7b5 is the ii7b5 (in the key of Am: ii7b5= (Bm7b5= B,D,F,A), Am= (A,C,E)). All note movements are within a whole-step.

In the harmonic minor scale, the m7b5 chord is the ii7b5.

In the melodic minor scale, the m7b5 chord occurs twice, as vi7b5 and vii7b5.(in the key of Am: vi7b5 = (F#m7b5 = F#,A,C,E), vii7b5 = (G#m7b5 = G#,B,D,F#)).

So let's consider some progressions.

The most common progression in jazz is ii7-V7 or ii7-V7-I. A minor key variation of this is iiø7-V7-i (found in the melodic minor scale)(Key of Am: Bø7-E7-Am).
Another common progression similar in structure is I-#iø7-ii7-V7 (in C: C-C#ø7-Dm7-G7).

In Bossa Nova, #iø7 is sometimes used as a substitute for Imaj7
(C#ø7 in place of Cmaj7).

The reverse is seen often in rock and blues where the m7b5 in the major scale is often replaced with a major chord a half-step below the original chord. (In C: replace Bø7 with Bb or Bbmaj7). This is often seen as a borrowed chord, but that need not be the case.

Similar to I-#iø7-ii7-V7, is IVmaj7-#ivø7-V7-I. We often see Half-diminished seventh chords (and diminished seventh chords; o7 = 1,b3,b5,bb7) as passing chords, where maybe due to a moving voice, they eare temporarily created in the movement. the 2 above progressions can be seen as the root note ascending in half-steps creating the movement from some type of major chord to some type of diminished chord a half-step higher.

Having now looked at all 4 seventh chords created by stacking thirds in the major scale we can reconsider the circle of 5ths in the major scale using 7th chords.
Starting from 1, we could have: (in C)
Cmaj7-Fmaj7-Bø7-Em7-Am7-Dm7-G7-C.
Or the minor variant (borrowing from Harm. min. as well):in Am:
Am7-Dm7-G7-Cmaj7-Fmaj7-Bø7-E7-Am

(the last one can be heard on the Beatles album "Abbey road", on the songs "golden slumbers", "carry that weight", "you never give me your money")

INVERSIONS and CHORD SYNONYMS

We can invert 4 note chords, just like 3 note chords. For our purposes, we wish to know when a particular bass note is or is not in our chord, and when we can substitute m7b5 chords for other chords without having added or subtracted any distinct notes from our previous chord (what chords can be seen as different spellings of the m7b5 chord?) We will use Bm7b5 as our example to be inverted and renamed.

Bm7b5= B,D,F,A (root position, 1 is in the bass)

1rst inversion, 3rd is in the bass
Bm7b5/D = D,F,A,B what D chord is this?
D,F,A,B = 1,b3,5,6
we could call this Dm6.

2nd inversion, 5th is in the bass
Bm7b5/F= F,A,B,D what F chord is this?
F,A,B,D = 1,3,#4/b5,6
We could call this F6(#4), or F6b5

3rd inversion, 7th in the bass.
Bm7b5/A = A,B,D,F which A chord is this?
A,B,D,F = 1,2,4,b6
you have options, such as
A+5add9sus4, Asus2(4)b6

So for a i6, we could substitute vi7b5

for I6(#4), I6b5, we could substitute #iv7b5 or bv7b5.

and for I+5add9sus4 or Isus2(4)b6 we could substitute ii7b5.

Some extensions often found on the m7b5 chord are listed below for the intermediate/advanced student to work through and explore:

m7b5 = 1,b3,b5,b7
m7b9b5 = 1,b3,b5,b7,b9
m9b5 = 1,b3,b5,b7,9
m11b9b5 = 1,b3,b5,b7,b9,11
m11b5 = 1,b3,b5,b7,9,11
m11b13b9b5 = 1,b3,b5,b7,b9,11,b13
m13b9b5 = 1,b3,b5,b7,b9,11,13
m11b13b5 = 1,b3,b5,b7,9,11,b13
m7b13b11b9b5 = 1,b3,b5,b7,b9,b11,b13

If you don't know how to play one of these chords, there's a good chance you could get away with substituting a m7b5 for it (of course, you'll lose part of the flavor, but in a jam...). it might be helpful to learn some m7b5 shapes without 5's in them (allowing a chord shape that can be used with either m7 extensions or half-dim extensions).

Here are some in F (Fm7b5(no5))
Fm7b5 = 1X11XX (E-shape, root on 6th string)
Fm7b5 = XX3X44 (D-shape, root on 4th string)
Fm7b5 = X8686X (C-shape, root on 5th string)
Fm7b5 = X8X89X (A-shape, root on 5th string)
Fm7b5 = XXX10 9 11 (G-shape, root on 3rd string)
Fm7b5 = 13 11 13XXX (G-shape, root on 6th string)

Peace,
Chris Roberts


How do I change all those numbers to letters (for notes, chords, etc.)? Here's a transposition chart simianmoon.com/snglstringtheory/guitar/8theory3.html

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Last updated January 1, 2003.
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