Topic 10 Otherchords

To end this lesson, we’ll mention how musical chords can actually be of different types, i.e. with four, five and six notes and more. In particular the quadriads (four-note chords) are very common in music, and one of these is called a diminished seventh chord, abbreviated as such: C dim7. It is derived from the diminished triad we have just seen, but adds a further interval. Let’s take the example of the G# dim7 chord. Here are the notes it’s made from: G#; B; D; F. Try building it in the chromatic wheel. It will look like this:

A square. Indeed, in this case, the interval distances between the various notes that form the chord are always the same, namely 3 sT. Like the augmented triad, the diminished quadriad is also perfectly symmetrical. Just as a square remains square whatever side it assumes as a base, so the diminished quadriad retains its symmetry and can be named starting from any note of which it is made.


G# dim7 = B dim7 = D dim7 = F dim7

Generalizing we could then say that:

square = quadriad diminished seventh

Given its symmetry, how many different squares can be constructed on the regular dodecagon inscribed in a circle? And consequently, how many dim7 chords can you build? Once you have found them, name them.

Try assigning a sound to all chords seen. Look for the notes on a piano and concentrate on the sensations these chords arouse in you. You will thus be able to fix in your memory that a certain geometric figure corresponds to a specific chord and therefore to a specific emotion, i.e. the one you have assigned to it

As we said, there are many possible chords: Try to build the following in the chromatic circle:

C7 (it reads ‘C seventh’ and is formed by the notes C-E-G-Bb).

C7/b5 (it reads ‘C seventh, flat fifth’ and is formed by the notes C-E-Gb-Bb)

What geometric shapes are represented? Describe them and look for any special features.


We end this lesson with a philosophical reflection. As you can hear from listening to how these chords sound, what looks a bit “disordered” from a geometric point of view, our ear perceives it as very pleasant and natural. Conversely what appears “beautiful” and perfect from a geometric point of view, is rather hard and dissonant to the ear.

I’ll leave you to draw your own conclusions!