How are diminished power chords formed?

Technically speaking there really is no such thing as the diminished power chord. A power chord by definition is, as you pointed out, simply the root and the fifth of a scale. The term “power chord” is strictly a contrivance of the electric guitarist. You can, however, play two notes, one being the first, or root, and the other being a diminished fifth. This is called playing an interval. It is also a very interesting interval, theory wise, because the diminished fifth is as far away as you can get from the root. Take a look:

A, Bb, B, C, C#, D, Eb, E, F, F#, G, G#, A

When A is your root note, Eb (or D#) is your diminished fifth (or augmented fourth). It is the sixth half step from either end of the scale. This is often referred to as a tritone, because it is the third full step from the root and it takes an additional three full steps to get back to the root. It is very common in jazz and classical music but very rare in most other guitar music. It is very key in what is known as the “whole tone” scale, that is, a scale that has no half steps in it whatsoever. Here it is in A:

A, B, C#, Eb, F, G, A

A diminished chord, as I’m sure you’re aware, consists of the root, the minor (or diminished) third AND the diminished fifth. If you will, it is a minor third on top of another minor third. Since the guitar, when standardly tuned, is tuned in fourths, it is almost impossible to play pure diminished chords in a movable style. What is usually used instead is a diminished seventh, which is a bizarre chord in and of itself but truly wonderful to work with.

This is four minor thirds on top of each other. It’s played on the first four strings and, in first position, it looks like this:

Ddim7:

E – 1st fret
B – open
G – 1st fret
D – open
A – don’t play
E – don’t play

Now the fun thing about this is that because of the intervals, you can play this same chord up and down the fret board. Think about it, the notes involved in this chord are D, F, Ab, and B (which is Cb, hence the “diminished” seventh). Look where else I can play these same notes:

Ddim7 (variation 1):

E – 4th fret
B – 3rd fret
G – 4 th fret
D – 3rd fret
A – don’t play
E – don’t play

Ddim7 (variation 2):

E – 7th fret
B – 6th fret
G – 7th fret
D – 6th fret
A – don’t play
E – don’t play

Ddim7 (variation 1):

E – 10th fret
B – 9th fret
G – 10th fret
D – 9th fret
A – don’t play
E – don’t play

And if this isn’t wild enough, think about this – depending on what note you choose as your root, you actually have FOUR different diminished seventh chords here at your disposal:

This is one crazy subject that tends to confuse the daylights out of people. I hope to write about it sometime this winter when I have enough free time to ensure that I write it well enough for people to understand the first time!