Diminished and augmented power chords

Question

The theory behind power chords is easy, you just take a major (or minor) chord and drop the 3rd. This leaves you with the 1st (root) and the 5th. The 8th (or root's octave) can also be included. A simple A power chord or A5 chord will have the notes A and E.

We can also apply this theory of power chords to diminished (a minor chord with a b5) or augmented (a major chord with a #5) chords which in theory should leave you with diminshed power chord (root plus b5) or an augmented power chord (root plus #5). As example, an Adim power chord will have the notes A and Eb and an Aaug power chord will have A and E#.

My question is, as there is really not much info about this available, is my theory behind dim and aug power chords correct, and where are such chords used and how common are they. I'm into rock music, which I know uses a lot of common power chords, but haven't seen anything like dim and aug power chords. Does other genres make use of this?

Answer 1

Here's the basic theory behind power chords according to Wikipedia:

When two or more notes are played through a distortion process that non-linearly transforms the audio signal, additional partials are generated at the sums and differences of the frequencies of the harmonics of those notes (intermodulation distortion). When a typical chord containing such intervals (for example, a major or minor chord) is played through distortion, the number of different frequencies generated, and the complex ratios between them, can make the resulting sound messy and indistinct.

However, in a power chord, the ratio between the frequencies of the root and fifth are very close to the just interval 3:2. When played through distortion, the intermodulation leads to the production of partials closely related in frequency to the harmonics of the original two notes, producing a more coherent sound. The intermodulation makes the spectrum of the sound expand in both directions, and with enough distortion, a new fundamental frequency component appears an octave lower than the root note of the chord played without distortion, giving a richer, more bassy and more subjectively 'powerful' sound than the undistorted signal.

So power chords are all about that simple 3:2 frequency ratio between the root and the perfect fifth.

So when you say...

We can also apply this theory of power chords to diminished (a minor chord with a b5) or augmented (a major chord with a #5) chords which in theory should leave you with diminshed power chord (root plus b5) or an augmented power chord (root plus #5).

I don't think that's really true. The fact that 6- and 8- semitone intervals are still called fifths ('diminished' and 'augmented', respectively) is an accident of terminology; they don't express the actual frequency relationship that makes a power chord special.

My question is, as there is really not much info about this available, is my theory behind dim and aug power chords correct, and where are such chords used and how common are they.

Diminished and augmented fifths played through distortion

1. Create a complex and dissonant sound which, as a continuing sound of long duration, could be subjectively unpleasant
2. Aren't really called 'power chords'

That's probably why you haven't found much mention of them!

Nevertheless, there is one situation where the diminished fifth played through distortion is common: In bluesy playing, when a player plays a root and also a fourth or diminished fifth which they then bend up to a perfect fifth. The momentary dissonance created as the higher note moves through the 'blue' fifth is one of the archetypal sounds of rock. This tends to be seen in lead playing in the higher register, where the dissonance created is less subjectively disagreeable.

Answer 2

The theory behind power chords is easy, you just take a major (or minor) chord and drop the 3rd.

Well, that's a bit like saying “making flatbread is easy: you just make a pizza and scrape off the tomatoes and cheese”. While it is possible to describe power chords this way (at least approximately), and can even explain quite well how they are used in some genres (in particular, rock that takes some elements from classical or just folk/pop harmony), I find it quite backwards to construct them this way.

See, thirds are not the basis of all harmony. In fact they are completely absent in some traditions, for instance Gregorian chant. When you start your theory from the Pythagorean scale, then everything is derived from fifths! A fifth is originally the interval between two notes whose frequency ratio is ³⁄₂ = 1.5, which makes for a very natural, coherent combination. A major second (full tone) in that system is simply two fifths minus an octave, and a “major third” (ditone) is two such seconds stacked.

That leads to music where thirds are mere melodic intervals, with no direct harmonical relation. In fact they are considered dissonances in such old music! If you've ever played an instrument in Pythagorean tuning, you may understand why: those thirds (frequency ratio ⁸¹⁄₆₄ ≈ 1.266) are jarringly wide.
Such music sure sounds quite different from what we're accustomed to today, but melodically it's actually quite similar, based on the same diatonic scales that still provide the majority of melodic material in western music.

In the Renaissance composers started to employ what would be considered our modern, consonant thirds: they discovered that if you make the thirds a bit narrower, you approach the frequency ratio ⁵⁄₄ = 1.25, which also sounds very coherent. Using that interval in the middle of a fifth gives you a major chord. That's how it's derived, none of that “major third plus minor third” nonsense.
The scale you get when taking Pythagorean and lowering the major thirds is called Ptolemaic scale, aka just intonation. It's still a diatonic scale.

Now, after Renaissance came Baroque, and Baroque composers loved to modulate between different keys. That's tricky if your theory is entirely based on diatonic scales (a diatonic scale looks completely different depending on which note you start from), so alternative tuning systems were developed. Basically these always made some compromises in the quality of the idea consonant intervals, in order to at least allow some consonance everywhere you could modulate to. The ideal is a system where the scale looks the same from every point – a regular grid. In fact it is possible to approximate every step on the Ptolemaic scale to almost inaudible deviation if you simply divide the octave into 31 equal steps. That was proposed in the late 17th century, but unfortunately (IMO) never really caught on – those many steps, most of which don't belong to the key you're in at any time, make it hard to build an easily-playable instrument. Eventually a simpler system caught on: 12-edo, aka “the” equal temperament. That's sufficient to approximate Pythagorean fifths very well, but actually deviates quite notably from the Ptolemaic thirds.

But especially on “soft, plain” instruments like piano, these thirds still sound quite nice in chords, and people just got used to hearing them as consonant. Hence this tuning system became pretty much universal on keyboards and guitars.

Fast forward to the 1960s: enter distortion. Distortion has a tendency to make consonant sounds fatter and dissonant sounds more dissonant. Fifths are undoubtably consonant (or, pure), and the 12-edo approximation doesn't significantly change that. So playing a fifth through distortion sounds just great – you have a powerchord.

Major thirds do, in principle, also sound nice; in fact any low-integer ratio morphs into a fat, resonant unity if you play it through distortion.

https://soundcloud.com/endolith/everything-is-a-power-chord-in-just-intonation

However, the distortion makes even quite small deviations from just intonation very obvious. In particular, the 12-edo approximation of thirds comes out really not that satisfying anymore, in fact it's quite a mess of unharmonic components.

Upshot: distortion has made 12-edo thirds dissonances again. Hence it really doesn't make sense anymore to construct harmony from thirds. Metal uses essentially Pythagorean-based harmony again, in which scales and modes matter a lot, not the major/minor story that some educators today like to derive from stacked thirds (which IMO makes mostly sense in Jazz, but not in many other genres).

Hence, diminished and augmented fifths can't be compared at all with powerchords, at least not when rendered in 12-edo. Though they are most definitely useful as dissonances, and in fact thus employed quite a bit in blues as well as in metal.

Answer 3

Like other chords, you form diminished and augmented chords from scales i.e. sequences of notes with a particular start note and interval sequence. For diminished chords, the interval sequence is 2,1,2,1,2,1,2,1, hence there are 8 notes rather than the usual 7. As an example, say we want to form the chord F diminished 7th (Fdim7). Using the above interval sequence, we form the scale: 1= F, 2=G, 3=Ab, 4=Bb, 5=B, 6=C#, 7=D, 8=E . Then to make the chord, we want the 1st, 3rd and 5th, (the triad), plus the 7th, which is F, Ab, B and D.

You can use this online tool to find chords http://www.chordresource.com/chordcharter/form/. Unlike other tools, it can display the notes and scale degrees (check the display options), plus it ranks alternative ways of playing a chord according to "playability". There's also a tutorial which explains how scales and chords are formed http://www.chordresource.com/tutorials/how_chords_are_formed .