What’s The First Inversion of The Half-Diminished Seventh Chord?

Today, we’ll be doing a short study on the half-diminished seventh chord.

In this study, we’ll be considering its relationship with another chord quality – the minor sixth chord.

At the end of this lesson, you’ll be able to clearly see the differences and similarities between these related chords – the half-diminished seventh and the minor sixth chords.

“What Is The Half-Diminished Seventh Chord?”

Every traditional major scale has seven degrees. Chords built on the degrees of the scale are known as scale degree chords. The half-diminished seventh chord is built on the seventh degree of the major scale.

In the C major scale:

…the seventh scale degree is B.

Consequently, if we form a chord in thirds (aka – “tertian harmony“) starting from B using the C major scale as an underlying scale, we’ll have the B half-diminished seventh chord:

“Alright! Let me show you how it’s formed”

An interval of a third from B:

…is D:

Adding another third to B-D:

…produces B-D-F:

…plus another third (A):

…to form B-D-F-A:

…the half-diminished seventh chord.

Attention: To learn more about the half-diminished seventh chord, its definition, breakdown/analysis, and formation, click here.

Now that we’ve reviewed the half-diminished seventh chord, let’s look at its first inversion.

First Inversion Of The Half Diminished Seventh Chord

Inversion [in keyboard style] is the rearrangement of the notes of a chord [in alphabetic sequence]. Jermaine Griggs

There are basically two approaches to the inversion of chords – the chorale style and the keyboard style. In this post, we’ll be focusing on the latter.

In the keyboard style of inversion, we’re doing an octave transposition of the lowest chord tone. Check it out…

The B half-diminished seventh chord when played as B-D-F-A:

…has its root (B) as the lowest chord tone and is said to be in its root position.

If we transfer the root to a position that is an octave higher (aka – “octave transposition”), we’ll have the first inversion of the half-diminished seventh chord:

If we repeat the same thing, we can form the second and third inversions respectively…

The octave transposition of the lowest note in the first inversion of the B half-diminished seventh chord:

…which is D, produces the second inversion of the half-diminished seventh chord:

In the same vein, the octave transposition of the lowest note in the second inversion of the B half-diminished seventh chord:

…which is F, will produce the third inversion of the half-diminished seventh chord:

Now that we’ve seen the root position:

…first inversion:

…second inversion:

…and third inversion:

… of the B half-diminished seventh chord, let’s take a closer look at our focus in this post – the first inversion  of the half-diminished seventh chord.

The First Inversion Of The Half-Diminished Seventh Chord

This is the first inversion of the B half-diminished seventh chord:

If we break down this inversion of the B half-diminished seventh chord into intervals (aka – “intervallic components”), we’ll have…

D to F:

…a minor third interval.

D to A:

…a perfect fifth interval.

Be reminded that the minor third and perfect fifth intervals are the intervallic components of the D minor triad:

Right now, I guess I’m not the only one who’s seeing the D minor triad:

…in the first inversion of the B half-diminished seventh chord:

“Does the first inversion of the B half-diminished seventh chord look familiar?”

If you’re familiar with minor sixth chords, by now you should have seen that the first inversion of the B half-diminished seventh chord has exactly the same notes and spelling that the D minor sixth chord has.

What’s the difference between the first inversion of the B half-diminished seventh chord:

…and the D minor sixth chord:

You’ll find that out for yourself in the next segment.

What Do I Mean When I Say “She’s Fair”?

The meaning of the phrase “she’s fair” can vary from one context to another. It could mean that she’s fair in her judgment in one context and that she’s fair in complexion in another context.

The same thing can be said about the first inversion of the half-diminished seventh chord and the minor sixth chord. If you’re given the chord below:

…in a quiz and you’re asked to name it, would you name it as the first inversion of the B half-diminished seventh chord or as the D minor sixth chord?

Food for thought!

The Half-Diminished Seventh Chord vs The Minor Sixth Chord

Let’s end this study by looking at the similarities and differences between the half-diminished seventh chord and the minor sixth chord.

The similarities

Although you’ve already seen the similarities between the half-diminished seventh chord and the minor sixth chord, let’s highlight them once more.

Similarity in spelling

The half-diminished seventh chord and the minor sixth chord share exactly the same spelling. Did you know that…

The third inversion of the D minor sixth chord:

…has exactly the same spelling as the root position of the B half-diminished seventh chord:

Alternatively, the first inversion of the B half-diminished seventh chord:

…also has the same spelling as the root position of the D minor sixth chord:

Similarity in discordance

The half-diminished seventh and the minor sixth chords are tritonic.

Tritonic chords are chords that contain the tritone which is arguably the harshest interval that makes chords sound unstable, unpleasant and have a tendency to resolve to another chord.

The B half-diminished seventh chord:

…has a diminished fifth interval (aka – “tritone”) formed between its first and fifth tones – B and F:

The same thing goes for the D minor sixth chord:

…where the augmented fourth interval (aka – “tritone”) is formed between its third and sixth tones – F and B:

This accounts for the harshness associated with both chord qualities and most importantly, it explains why they are not commonly used like major and minor seventh chords.

The differences

The half-diminished seventh and minor sixth chords differ from each other in quality and tonal function.

Difference in quality

The half-diminished seventh chord is basically a diminished triad (with an additional note that is a minor seventh above the root of the diminished triad.

The B half-diminished seventh chord:

…is basically a B diminished triad with an additional note that is a minor seventh above the root of the B diminished triad, which is A in this case. The D minor sixth chord:

…on the other hand, is basically a D minor triad with an additional note that is a major sixth above the root of the D minor triad, which is B.

Is that clear? Alright let’s look at the difference in tonal function.

Difference in tonal function

The tonal function (or simply function) of a chord refers to what it can be used as, within the environment of tonality or key.

The difference in quality between the half-diminished seventh chord and the minor sixth chords implies that they differ in tonal function.

The tonal function of the minor triad is as chord 2, chord 3, or chord 6 while that of the diminished triad is as chord 7. So, what I’m saying in essence is that chords of minor and diminished qualities have different tonal functions assigned to them in a key environment.

While the half-diminished seventh chord functions as chord 7, the minor sixth chord may function as chord 2 within the key environment.

Due to their difference in tonal function, you can distinguish one from the other.

Final Words

The half-diminished seventh chord and the minor sixth chords are related by inversion.

If you take a minor sixth chord and keep inverting it, you’ll bump into a chord that has exactly the same spelling as the half-diminished seventh chord.

Here’s the inversion of the D minor sixth chord…

Root position:

…to the first inversion:

…to the second inversion:

…to the third inversion:

…and back to the root position.

What are the similarities and differences between the third inversion of the D minor sixth:

…and the B diminished seventh chords?

The same thing is obtainable with the half-diminished seventh chord. Its first inversion has exactly the spelling of a minor sixth chord and we already covered that in an earlier segment.

The D minor sixth chord:

…has the same spelling with the first inversion of the B half-diminished seventh chord:

…while the B half-diminished seventh chord:

…has the same spelling with the third inversion of the D minor sixth chord:

If you’re familiar with the art of inversion, you can figure these out.

This is where we’ll draw the curtains for today’s lesson. I hope you what we’ve covered so far would help you disambiguate the half-diminished seventh chord from the minor sixth chord.

See you next time.

P.S.

To learn more about 16 different chords – triads, sixths, sevenths, and ninths, join our free 16-week chord revival program.

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Chuku Onyemachi

Head of Education at HearandPlay Music Group

Onyemachi "Onye" Chuku is a Nigerian musicologist, pianist, and author. Inspired by his role model (Jermaine Griggs) who has become his mentor, what he started off as teaching musicians in his Aba-Nigeria neighborhood in April 2005 eventually morphed into an international career that has helped hundreds of thousands of musicians all around the world. Onye lives in Dubai and is currently the Head of Education at HearandPlay Music Group and the music consultant of the Gospel Music Training Center, all in California, USA.

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