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[P]
The Secrets of the Power Chord and More

By Blarney in Culture
Sun Nov 08, 2009 at 01:38:57 AM EST
Tags: guitar, music theory, intermodulation, distortion, harmony, diatonic (all tags)

Perhaps due to the popularity of certain rhythm games, the electric guitar seems to be making a bit of a comeback. I've been playing mine for most of my life, and like many others I love heavy, distorted guitar sounds and big, crunching power chords. Root-fifth power chords are easy to learn and easy to teach, but why are they so ubiquitous? And why root-fifth, anyway? How does distortion combine with musical intervals in order to generate big, bassy tones? A theory of distortion and musical intervals, with particular application to the electric guitar, is presented inside.


When you hear an electric guitar, it's almost always distorted. Even 'clean' electric guitar is usually somewhat distorted - a Fender Twin, the standard 'clean' guitar amp, has an order of magnitude more harmonic distortion than a typical home stereo. And 'crunch', 'metal', 'high-gain' tones carry even more distortion to them. Why do guitarists love distortion so much? It allows notes to be held and sustained, attack and decay to be manipulated, feedback to be induced, the touch sensitivity of the instrument controlled, and the production of the great variety of tones that the electric guitar has to offer. There are as many 'signature' tones as there are great guitarists, and distortion is a part of just about all of them.

Everyone who picks up a guitar learns the power chord almost immediately. Put a finger on the lowest string. Put another finger on the next string, 2 frets up. Play it loud! It's a big sound, especially with plenty of distortion. It's addictive. Compared to the sound of a single note, this root-fifth power chord is huge, monstrous! But why? Wikipedia will tell you that it generates a wide spectrum of harmonics, including a tone an octave below the fundamental. Big. Bassy. Loud. Most guitarists never think about the details of this. But the details are rewarding.

Any guitarist will tell you that distortion affects the tone of single notes, often drastically. But suppose you play 2 notes at a time? Distortion will generate sum and difference frequencies. This is a phenomenon known as intermodulation. The Wikipedia article linked to here, at this point in time, proudly proclaims that

Intermodulation should not be confused with general harmonic distortion (which does have widespread use in audio effects processing). Intermodulation specifically creates non-harmonic tones ("off-key" notes, in the audio case) due to unwanted mixing of closely spaced frequencies.'

WRONG WRONG WRONG WRONG WRONG!

This is a fairly common opinion. And it's wrong. All distortion will generate intermodulation. There's no escaping it! And the frequencies of intermodulated tones always have a linear relationship to the tones present in the original signal. Are they 'off key'? Not really. Even if not 'harmonic' they're definitely musically related. The confusion here is because distortion isn't just one thing. It's basically a function applied to the input signal, and this function can be characterized by a Taylor series. The harsh sounds mentioned in the Wikipedia entry refer to the intermodulation products produced by high-order terms of the Taylor series. Guitar effects and amplifiers are often designed to minimize these high-order terms. Although, as always, it's subjective. Some of us may like the mellow tones of Eric Clapton, while some of us like Atari Teenage Riot. It's art!

What makes a power chord really work? The simplest intermodulation products, the lowest terms in the Taylor series. The most prominent such terms in guitar distortion are the 2nd through 6th. The 'first' term is clean, undistorted signal, so we won't worry about it here. The fourth and fifth provide mostly high-frequency edge. So the low-end stuff that makes a power chord really MOVE is all about 2nd and 3rd order intermodulation products. A typical distortion tone for guitar has mostly odd-order distortion products - the 3rd will usually dominate. And now, it's time for math!

Suppose you are playing 2 tones at once, a 'diad' chord. Let them be pure sine waves for simplicity, let the lower-frequency tone have frequency X and the higher frequency tone have frequency Y. The lowest-frequency product from 2nd order intermodulation is going to be Y - X, while 3rd order intermodulation gives a tone of frequency 2X - Y.

Now let's consider a low power chord, low E and B above it. 80 Hz and 120 Hz. The 3rd order intermodulation product, usually the loudest, is 2*80Hz - 120Hz = 40 Hz, an octave below the chord's root! The 2nd order product is 120Hz - 80Hz = 40Hz as well. They reinforce each other, and this octave-down tone gives the power chord its grunt. Makes it work.

And now it's time for a more general theory. What about other musical intervals besides fifths? We can start by writing out the relative frequencies of a diatonic scale. Guitars do not play the diatonic scale, but an 'equal tempered' approximation in order to be tunable in all keys. Still, this is the best place for the math to start. Due to the phenomenon of beat tones, the diatonic intervals are what matters anyway. More explanation of this later.

CDEFGABC'
19/85/44/33/25/315/82

We can now use this scale to calculate 2nd & 3rd order low frequency intermodulation products for each interval found in the scale, as we did with the power chord (fifth).

Interval type2nd intermod (Y-X)3rd intermod (2X-Y)
Octave (C' - C)1=Cnone
Fifth (G - C)1/2='C1/2='C
Fourth (F - C)1/3=''F2/3='F

And we see that the fourth is a lot like the power chord. Just like in Smoke on the Water! It's a little muddier than the power chord, because the low-frequency products don't coincide as nicely, but it's got its own sound and charm to it. Let's continue through the intervals.

Interval type2nd intermod (Y-X)3rd intermod (2X-Y)
Major 3rd (E - C)1/4=''C3/4='G
Minor 6th (C' - E)3/4='G1/2='C
Minor 3rd (G - E)1/4=''C1=C
Major 6th (E' - G)1=C1/2='C

Now we look at the major and minor 3rds, and their inversions the 6ths. None of these have nicely coinciding low-frequency intermod products, so none of them are likely to hit like the power chord, but hey what does? Look at that 2-octave down tone for the major 3rd! Even deeper than the power chord, must sound good, right? Sadly, no. It's too low and just makes 3rds on the low strings sound muddy, unless you're Dave Mustaine and use the right EQ to keep the low end clean. Most people don't use low 3rds, but you can! What's really interesting here, to me, is the 2nd intermod product. Whenever you play 2 notes of a major chord, the second intermod product will provide a third note to fill it out, shifted down there in the bass! Like a harmonizer only pure, pure analog.

Except how do you get just the 2nd product? Just about all guitar distortion makes both 2nd and 3rd, with 3rd usually dominating. You can build an FX pedal if you want. But a really cool pedal to experiment with is the Foxx Tone Machine. Pretty, beautiful box, I think it's even US made, but if $200 is too much for you, you can get the Danelectro French Toast which is the same circuit in a cheap Chinese made plastic box that won't be as durable and may pick up random noise and radio interference too! I paid $25 for mine at the local music store. Not that I'm a miser, but hey it was there. Flip the 'octave' switch on it, turn 'fuzz' all the way down, it'll give you mostly 2nd order intermod. As you turn up 'fuzz' it brings in more 3rd. You can totally experiment with this thing, it's great. Not to mention the Octavia, it'll ring out the 2nd intermod product nice and loud if you can find one. There's many other pedals that do this sound too - look for octave-fuzz in general. NOT the frequency-dividing octave pedals, but a true octave fuzz. Try using the neck pickup. Roll down the tone. Crank up the bass on the amp. You'll get it!

Finishing up our interval table:

Interval type2nd intermod (Y-X)3rd intermod (2X-Y)
Major 2nd (D - C)1/8='''C7/8≈Bb(neutral 7)
Minor 7th (C' - D)7/8≈Bb(neutral 7)1/4=''C
Minor 2nd (F - E)1/12=''''F7/6≈Eb(neutral 3)
Major 7th (B - C)7/8≈Bb(neutral 7)1/8='''C
Tritone (B - F)13/24≈'Db19/24≈'Ab
These mostly sound so harsh that they're pretty much useless. The 'neutral 7' and 'neutral 3' are notes that don't fall on an actual fret very well, but are found in some harmonica tunings, and have some use in vocal music. Still the only one I really like to play with is the tritone. It really fills out into a full diminished chord. Sounds nicer than it really should. At least, when you've got the 2nd intermod product nice and clear, it sounds amazing!

And now back to the question - why did I do all my math with diatonic intervals when a guitar uses equal tempered tuning that divides the octave into 12 equal parts? Well, all the intervals in equal tempered tuning are a bit off. This won't just move the intermodulation products, but will make them 'beat', just like when you're tuning and trying to make the beats go away. This is due to the higher harmonics interfering with each other. So you'll probably do a bit of bending to get the intervals as close to the pure diatonic ones as possible. It isn't easy to describe but it's not too hard to learn. Sometimes the damn frets are just not in the right places. Assuming you find an octave fuzz and set it up as described earlier, a good way to start experimenting is to play an A-C# diad on the G and B strings, up on the 14th fret. Hear the low A come thrumming out. Now hammer on the 15th fret on the B string, making an A-D diad, and the low A rises up to a low D! Harmony! Do the full 14-14-14 to 16-14-15 hammeron thing and you've got the "We will rock you" break. Yeah, this IS what Brian May is doing to sound so big!

You can hear similar sounds only far more wild when Jimi kicks in his Octavia in Who Knows, at about 6:40 in. Or heck, pretty much throughout Mudhoney's classic album Superfuzz BigMuff.

Something that I like to do with my French Toast pedal set for maximum 2nd intermod - suppose my band is holding an A7. I'll just blast out this simple chord:

E-9
B-8
G-9

E, G, and C#'. The G-C# tritone gives an intermod product that rings out at 'E, filling in with the E. The E and G give a low ''C while the E and C#' give a low A. The total effect is an A7 with an added C, yes, it's an inversion of the Hendrix chord!

Or just go wild. There's still a lot of noises out there to make. And the power chord is only the beginning.

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Related Links
o distortion
o power chord
o intermodul ation
o WRONG WRONG WRONG WRONG WRONG!
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o "We will rock you"
o Who Knows
o Hendrix chord
o Also by Blarney


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The Secrets of the Power Chord and More | 58 comments (28 topical, 30 editorial, 0 hidden)
YOU WROTE A LOT OF FAGGOT SHIT (1.20 / 24) (#1)
by razar on Fri Nov 06, 2009 at 01:41:28 AM EST

I READ THE FIRST PARAGRAPH AND CAN ANSWER YOUR QUESTION "WHY 'ROOT 5' [LOL LIKE ANYONE SAYS THAT YOU FUCKING FAGGOT] ANYWAY?'

HERE'S WHY POWER CHORDS ARE SO COMMON: SO NO TALENT WORTHLESS PIECES OF SHIT CAN PLAY THEM.

ON THE GUITAR, THEY ARE SIGNIFICANTLY EASIER TO FINGER THAN FULL ACTUAL CHORDS. A BARRED POWER CHORD IN A-FORM IS A LOT EASIER THAN A BARRED MAJOR CHORD IN A-FORM.

THAT'S ABOUT 10% OF IT. THE OTHER 90% IS BECAUSE LITTLE FAGGOT ASS PUSSIES LIKE YOU CAN'T FUCKING LEARN MUSIC THEORY.

YOU WRITE A SONG IN A? FINE. THEN FROM A, YOU GO TO B... BUT IS THAT Bm OR Bmaj? WHO CARES LET'S JUST POWER CHORD IT LOL.

BASICALLY PEOPLE WHO PLAY POWER CHORDS A LOT ARE IDIOTS.

+1FP

I JUST FUCKED A SHEEP


I DIDN'T BERATE YOU ENOUGH IN MY ORIGINAL MESSAGE (1.00 / 13) (#2)
by razar on Fri Nov 06, 2009 at 01:43:18 AM EST

YOU ARE ONE STUPID MOTHERFUCKER. EVEN THOUGH I'M GOING TO VOTE THIS +1 FP I HOPE THIS HSIT FUCKING DIES AND I HOPE YOUR WORTHLESS ASS GETS HIT BY A BUS AND DIES A VERY PAINFUL DEATH. I'M COMPLETELY SERIOUS.

I JUST FUCKED A SHEEP


[ Parent ]
Too lazy to get my guitar from the basement, but (2.25 / 4) (#3)
by Horseface Killah on Fri Nov 06, 2009 at 01:54:18 AM EST

What role do the sus4 chords play here? They usually blend in nicely with distorded, "bluesy" powerchords. They have a nice dissonant ring to them which gives some edge to what very easily becomes overdriven mud if you just keep hammering the powerchords.

Also: basslines consisting of the root note, the octave and the third above that. Also very nice when served with powerchords.

I'd guess (none / 1) (#4)
by Blarney on Fri Nov 06, 2009 at 02:20:15 AM EST

It's late and I'm tired and maybe we could get down and calculate partials but there's probably no need.

Take your A-E'-A' power chord. Distort it and now you have an 'A sitting at the bottom. It really looks like the harmonic series of a 'A, it's one big A note with lots of harmonic content. Now throw a D way up there and you'll have intermodulation throwing more D's down into the bass. The end product approaches a big A-D diad maybe repeated across a few octaves.

[ Parent ]

i came here to try and pick holes in it (2.40 / 5) (#5)
by Bert Sesame on Fri Nov 06, 2009 at 06:24:09 AM EST

but learnt something instead.

kudos!

whoa start off slow there buddy (3.00 / 10) (#7)
by lostincali on Fri Nov 06, 2009 at 07:47:55 AM EST

maybe add a section about playing nothing but scales for a few years.

"The least busy day [at McDonalds] is Monday, and then sales increase throughout the week, I guess as enthusiasm for life dwindles."

Finally (2.25 / 4) (#8)
by stuaart on Fri Nov 06, 2009 at 09:02:07 AM EST

Something worth reading. +1FP.

Linkwhore: [Hidden stories.] Baldrtainment: Corporate concubines and Baldrson: An Introspective


I have never touched a guitar (2.40 / 5) (#9)
by nostalgiphile on Fri Nov 06, 2009 at 09:55:15 AM EST

but now I can finally become Joey Santiago.

+1FP neverminding the atrocious formatting skills.

"Depending on your perspective you are an optimist or a pessimist[,] and a hopeless one too." --trhurler

It would be interesting (none / 0) (#16)
by TDS on Fri Nov 06, 2009 at 01:20:03 PM EST

to know if you could provoke the "French toast" effect out of either Amplitude or GuitarRig, really test how smart their signal path modelling is...

Good article btw, thanks.

And when we die, we will die with our hands unbound. This is why we fight.

power chords aren't addictive to me (none / 0) (#22)
by donnalee on Fri Nov 06, 2009 at 08:06:35 PM EST

I'd like to see a mathematical analysis of swing, but I hope it would be simpler, easier to understand ... you seem to be more interested in showing off your "brilliance" than sound :)

---
Guess I'll be adding this to tomorrow's comment dump!
Swing music is for old people and morons (2.00 / 3) (#38)
by Korean Loller Blader on Sat Nov 07, 2009 at 07:18:26 AM EST


D'oh! I can't seem to talk to the mod_
[ Parent ]
punk swings (none / 0) (#46)
by donnalee on Sat Nov 07, 2009 at 09:33:26 PM EST

the basslines of rock the casbah, come as you are...

---
Guess I'll be adding this to tomorrow's comment dump!
[ Parent ]
Dave Grohl really did swing (none / 1) (#49)
by Blarney on Sun Nov 08, 2009 at 10:24:10 AM EST

It was subtle but yes, there in just about every song. And the way Kurt accented the rhythm was very subtle but definitely there.

Most bands who covered specific Nirvana songs or their style in general failed to swing. It was a vital part of their sound.

[ Parent ]

since louis, it's a vital part of any sound (none / 1) (#51)
by donnalee on Sun Nov 08, 2009 at 01:31:46 PM EST

From Flea Master Session 2:

"The first record that I ever got, which was Louis Armstrong and the Hot Five ... " (1:30)

"... and Louis Armstrong, who was probably the greatest musician that ever lived ..." (1:52)

"... when I first started playing trumpet, before I started playing the bass, and of course I wanted to be as cool as Louis Armstrong and still [looks at camera], my whole life is based on one day perhaps you know approaching the level of cool of Louis Armstrong, and you know, aging with grace and dignity like he did" (2:00)

"This old guy said to me, this real old guy, and I was playing trumpet, and I thought I was pretty hot, and he said, he goes 'Let me tell you one thing', he goes 'lots of, lots of cats, they play high, they play fast, they play with all kinds of technique, you see these guys, they can play every trick in the book and every lick in the book, but no one, NO ONE, ever played music like Louis Armstrong.' And he was completely right. " (2:16)


---
Guess I'll be adding this to tomorrow's comment dump!
[ Parent ]

I think it's imporatnt to point out that Nirvana (none / 1) (#54)
by Korean Loller Blader on Sun Nov 08, 2009 at 06:54:09 PM EST

was about as punk as Poison. See how Dave grohl went and did that updated Creedence thing after Nivarna? Yeah.
D'oh! I can't seem to talk to the mod_
[ Parent ]
Good point. (none / 1) (#53)
by Korean Loller Blader on Sun Nov 08, 2009 at 06:53:07 PM EST

Punk is also shallow waters for absolute fucking morons.
D'oh! I can't seem to talk to the mod_
[ Parent ]
marilyn manson did a swing song too (none / 0) (#55)
by anaesthetica on Sun Nov 08, 2009 at 06:54:30 PM EST

http://www.youtube.com/watch?v=BITnk3-D_Fw

—I'm the little engine that didn't.
k5: our trolls go to eleven
[A]S FAR AS A PERSON'S ACTIONS ARE CONCERNED, IT IS NOT TRUE THAT NOTHING BUT GOOD COMES FROM GOOD AND NOTHING BUT EVIL COMES FROM EVIL, BUT RATHER QUITE FREQUENTLY THE OPPOSITE IS THE CASE. ANYONE WHO DOES NOT REALIZE THIS IS IN FACT A MERE CHILD IN POLITICAL MATTERS. max weber, politics as a vocation


[ Parent ]
OOPS, MEANT TO VOTE -1 BUT VOTED +1FP BY MISTAKE (1.14 / 7) (#28)
by razar on Fri Nov 06, 2009 at 09:44:41 PM EST

PLEASE VOTE -1 TO CANCEL OUT MY VOTE... THANKS

I JUST FUCKED A SHEEP


i rored the first time that one worked for me (none / 0) (#31)
by Jobst of Moravia on Fri Nov 06, 2009 at 11:10:51 PM EST


---
              __
   .,-;-;-,. /'_\ ---Did this Negro say "Street Moor"?
 _/_/_/_|_\_\) /
'-<_><_><_><_>=\
 `/_/====/_/-'\_\
  ""     ""    ""

[ Parent ]

+1FP, not about MC (none / 0) (#29)
by Enlarged to Show Texture on Fri Nov 06, 2009 at 10:29:07 PM EST




"Those people who think they know everything are a great annoyance to those of us who do." -- Isaac Asimov
WIPO (none / 0) (#30)
by Enlarged to Show Texture on Fri Nov 06, 2009 at 10:29:39 PM EST

Carlos Santana


"Those people who think they know everything are a great annoyance to those of us who do." -- Isaac Asimov
I'll give the benefit of the doubt (none / 0) (#40)
by Del Griffith on Sat Nov 07, 2009 at 11:25:32 AM EST

and hope this ends the MDC rampage.

-------
I...I like me. My wife likes me. My customers like me. Because I'm the real article. What you see is what you get. - Me


Awesome article, but for one thing (none / 0) (#42)
by anaesthetica on Sat Nov 07, 2009 at 03:35:32 PM EST

It's hard to believe you could write a whole article about power chords and not mention Link Wray and "Rumble".

Also, it's hard to see any serious mention of Dave Mustaine after his lulzy part in Some Kind of Monster, where he cries about his failed career to Lars.  http://www.youtube.com/watch?v=53VRr-w7mac

In any case, I'm going to dig out my Big Muff π distortion box and have a go at repairing it.  Thanks!

—I'm the little engine that didn't.
k5: our trolls go to eleven
[A]S FAR AS A PERSON'S ACTIONS ARE CONCERNED, IT IS NOT TRUE THAT NOTHING BUT GOOD COMES FROM GOOD AND NOTHING BUT EVIL COMES FROM EVIL, BUT RATHER QUITE FREQUENTLY THE OPPOSITE IS THE CASE. ANYONE WHO DOES NOT REALIZE THIS IS IN FACT A MERE CHILD IN POLITICAL MATTERS. max weber, politics as a vocation


His career's fine (none / 0) (#52)
by Have A Nice Day on Sun Nov 08, 2009 at 05:22:39 PM EST

It's his life that was a fucking mess. Always preferred 'deth to metallica.

--------------
Have A Nice Day may have reentered the building.
[ Parent ]
WHAT THE FUCK (1.20 / 5) (#56)
by bride of spidy on Mon Nov 09, 2009 at 09:05:46 AM EST

didn't i tell you guys only MC comics on the front? fucking people.


a simpler way to put it... (none / 0) (#57)
by mikelist on Sat Jan 02, 2010 at 07:13:08 AM EST

...a power chord diad leaves the third out of the way, so depending on context, it can be either major or minor. if the bass or rhythm parts include the third or other notes from the scale, they can change the tension from major to minor, and other harmonies as well.

this allows the metal guitarist to be a preening ass, who rides on the coattails of his band, yet gets all the babes.

JESUS (none / 0) (#58)
by The Hanged Man on Thu Jan 28, 2010 at 05:24:53 PM EST


-------------

Dificile est saturam non scribere - Juvenal
Not so technical, just going with my ears (none / 0) (#59)
by SacredSalt on Fri Jul 30, 2010 at 06:18:27 AM EST

and 20+ years of playing experience. On many amps I would agree with you, a lot of chords don't take to certain kinds of distortion as blissfully as a power chord. I avoided certain chords for heavily distorted work because of it.

Then I brought a Koch Powertone II.  Perhaps it has some type of filtering that reduces certain orders of harmonics, or maybe its just the nearly 35lb output transformers they put in them, and maybe the choke is helping in some way, but even with massive well beyond anything any Mesa with a stomp box in front of it could produce distortion - all of the notes still ring true, and many of those same chords that sound dismal on say a Bugera v22, or a Peavey Classic 50 suddenly sound fantastic on the Koch amp. Its distortion isn't Aiken Invader, or Reinhardt Titan lush, but its still pretty rich.

I agree with you that the secondary harmonics are adding to the sense of fullness. Even if you are just playing with mild plexi tones (clean with just a hint of grit for those who don't know the lingo) this is still a factor, and probably part of the reason many people prefer the sound single ended tube amps over more common class AB push/pull designs.  There is a fair bit a difference in the harmonic overtones that are generated between the two.

Sometimes chords, and even single notes sound better played at different points along the fretboard. Its probably some of the same thing. No guitar is perfectly in tune from one open to fret 22 or 24. There is always some compromise. Sometimes the thicker string, or thinner string provides a different amount of energy to the pickups, or some pickups are adjusted differently across the strings, have different response to certain frequencies, and amps favor certain frequencies over others. The end result though, is even those minor differences, whether the tuning is slightly off, and this generates different harmonics, or its in the pickup - some things just sound better than others.

Some guitars just have sweeter spots than others too, and the harmonic theory would account for that as well.  

The Secrets of the Power Chord and More | 58 comments (28 topical, 30 editorial, 0 hidden)
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