Diminished Chords

In a post a while ago, I spoke about symmetric scales which have specific properties that cause them to behave quite differently to "regular" diatonic scales but more importantly give them a very distinct sound and lack of "rootedness" in any specific tonality.

The most commonly used symmetric scale is probably the whole-half/half-whole/octatonic/diminished scale. While it is possible to construct a lot of different chords out of their pitch material, we very often use them as source for diminished chords.

When we talk about diminished chords, we usually refer to 4 note chords that are constructed  effectively out of minor thirds:

In a more theoretical approach, it is a chord constructed out of the root, minor third, diminished fifth and diminished seventh (hence the double flat).

There's also a shorter version of that chord which is the diminished triad which however doesn't have a profoundly different quality.

Looking at diminished chords from a purely theoretical side can allows some quite fascinating observations based on their symmetry which reflect back to their musical functions.

In general, we can say that there are only three different diminished chords that start repeating after the three possibilities.

In the right hand the chords are repeating exactly each bar with the left hand "declaring" a different chord tone as fundamental each time.

https://soundcloud.com/robin-hoffmann/diminished-possibilities/s-vygEx5x7mwm

In consequence, this also means that every diminished chord could have each of its chord tone as root note:

https://soundcloud.com/robin-hoffmann/cdim-inversion/s-THwxm9Td4qf

Passing Diminished Chords

A quite frequent use of diminshed chords is as so called passing diminished. For instance ,in a originally diatonic world of C major you could insert a C#dim in between the chord Progression C-Dm resulting in C-C#dim-Dm

https://soundcloud.com/robin-hoffmann/passing-diminished/s-FYCx40WO9og

This would work equally well if the third chord above was a D major. 

In fact, you could insert such a passing diminished before any chord if you place it a semitone below its target chord. The simplest way to understand this would be to imagine the diatonic chords of a C major scale (C, Dm, Em, F, G, Am, Bdim). If you now use all the "black keys" in between to construct diminished chords on, each of these function as a passing diminished towards the chord a semitone higher:

https://soundcloud.com/robin-hoffmann/passing-diminished-2/s-De0SYxfIq6w

The one from A#dim to Bdim is sonically a little less successful as the target chord is a diminished triad as well but still it creates a halfway pleasant impression.

By now you might have noticed that these passing diminished chords feel pretty much like a dominant and upon closer inspection, they posess one of the key features of a dominant which would be the tension of an inherent tritone wanting to resolve.

For instance this classic tritone resolution can be found in F#dim going to G where in the first chord F# and C form a tritone that resolves to G and B. By the rules of tritone substitution this one could even resolve to Db (by resolving the F# and C not inwards to G and B but outwards to F and Db) but let's not complicate matters even more.

But you might have also noticed that a diminished chord consist exclusively out of tritones. No matter how you invert it, the interval between each chord tone and the second next tone is a tritone.

So obviously we have some sort of "super dominant" chord here.

In fact, we can transform each diminished chord into a "proper" dominant that we can understand more easily if we just understand them as a dominant7(b9) chord without root.

https://soundcloud.com/robin-hoffmann/diminished-dominant/s-lOkzITWDLaa

This now makes a little more sense as we can also clearly see V-I cadences that make these dominant impressions more plausible theoretically.

But that doesn't let us off the hook with these many tritones as again, we could see every diminished chord as four different rootless dominant7(b9) chords.

The first bar shows these alternatives while the other four bars show how these options resolve.

https://soundcloud.com/robin-hoffmann/dominant-alternatives/s-P7FDyqfz8Fa

In this rapid succession it is quite fascinating to observe how your musical perception get's slightly overwhelmed by which structural element of the chord it needs to focus on to understand the plausibility of the resolution. 

Notice how these four possible root notes combined form another diminished chord (e.g. Adim).

If you now combine the four notes of the chord in bar one in the right hand plus these four possible root notes you end up with the scale of the diminished (whole-half) scale:

This explains why this scale is prefered to use over diminished chords as opposed to the half-whole alternative. 

The bottom line here is that in most cases, diminished chords serve a dominant function without effectively being a "true dominant" (unless you extend it by another root note as shown above). They can function as colouristic effects as well without serving a candential purpose but generally our ear tends to understand them as dominants. With their many ways to resolve, a lot of chords following them can feel plausible.

Stylistically speaking, they have become rather unpopular in modern scoring as they imply a quite old fashioned sound (with composers from the 18th/19th century using them excessively bleeding into the golden age of film scoring). Also, in Jazz, diminished chords serving as passing diminished feel rather old fashioned but are definitely more tolerable when you're scoring a period piece (Giacchino's Score for UP comes to mind). More modern use of the diminished scale prefer to stay away from diminished chords (and construct other chords out of the scale material) as well as preventing classical cadential motion based on diminished chords. Nevertheless, as always, even if concepts are not part of your everyday work routine it sharpens your musical understanding to know how they work.