Diminished 7th Fundamentals

December 02, 2017

This article is about diminished 7th arpeggios and how I go about laying down the fundamentals for students to understand and play them. I always try and aim for deep understanding over surface level understanding - the latter may be sufficient to pass an exam, but does very little to prepare students for their musical future. So with that in mind, here are the first questions we need to pose:

1. What is a chord?
2. What is an arpeggio?
3. What is a 7th chord/arpeggio?
4. What is a diminished chord/arpeggio?

I think it’s important to clarify these 3 points with students, no matter what their experience level. I would also revisit these questions every lesson before attempting to play the arpeggio, until I am sure the student understands what we are playing and why. I like to get as fundamental as possible when providing answers to these questions, and demonstrate practically on an instrument wherever possible. So here is my attempt at an explanation:

What is a chord?

A chord is simply multiple notes played simultaneously. I would add to this that the most common type of chord is called a triad, which is a 3-note chord consisting of stacked 3rds.¹ This is a great demo opportunity, and the piano is perfect for visualising chords if there is one nearby! Here are some examples:

1. What is an arpeggio?

   An arpeggio is simply a chord, played one note at a time! Easy enough? I would demo this one, too. They look like this:

2. What is a 7th chord/arpeggio?

   We’ve already explained what a triad is. To build on this, a 7th chord is a 4-note chord, that is created by stacking an additional 3rd on top of the triad. This 4th note represents an interval of a 7th above the root.

3. What is a diminished chord/arpeggio?

   Diminished triads are unique in that they consist of two minor 3rd intervals. They are diminished because the perfect 5th interval that you would usually find in a major/minor triad has been squashed by a half-step to become a diminished 5th.

Diminished 7th chords actually come in 2 flavours, but for now we are only going to consider the full diminished 7th. Building on the diminished triad, the diminished 7th chord simply adds another minor third to complete the 4 note chord. The diminished 7th chord is therefore most easily remembered as a 4-note chord built entirely of minor 3rds².

The most awesome realisation of this whole journey is that the interval from the top note of the chord, to the root note in the next octave is ALSO A MINOR 3rd 😱. That reduces multi-octave diminished 7th arpeggios to long strings of minor 3rds one after the other! It also means (and here’s the real clincher), there are really only three truly unique diminished 7th arpeggios in existence - all the others are in fact the same as one of these three, just starting from different points in the never-ending string of minor 3rds.

I hope you can help your students come all the way through to this final conclusion, because the idea of only really having to learn three different diminished arpeggios, and then you know them all?! Well, that’s pretty cool.

If you happen to be a violin teacher, you can go on and read about how I like to approach teaching diminished 7th arpeggios on the violin.

Footnotes.

1. I have skipped it here, but it is often appropriate to delve into intervals a bit here, too.
2. This is specific to full diminished chords, of course, however this distinction can usually be explained at a later time.