The Devil's Chord: R + 6-6-6

A look inside diminished chords.

Ultimate Guitar

The Economy Of Scale: The laws of diminishing intervals

By now we are aware of how the building blocks of chords - varied harmonic interactions within sets of differing intervallic structures - fit together, but what happens when we take just one variable of the input stage, and then multiply that one interval which we like the sound of, building a whole chord out of only one particular interval? Or, make a mirrored image from the current intervallic relationships? Economics.

Economics is an environment of variables. Economies of scale are environments of variables within pre-determined systems of known variables. Chords are equations of intervals based within a pre-determined system of intervals, the scale. Their environment, the song you are playing.

The conclusions that we can draw, by analyzing the intervallic relationships between the chords in the flowchart above, are that strange chord names are simply inversions of the intervals which made up the chord in the first place - exactly the same way that chord inversions are a different order of notes, a different order of intervals creates a different kind of chord. Chord types are chords which are made of similar intervallic structures - seconds, minor thirds, major thirds, fourths, fifths, sixths, minor sixths, major sevenths, dominant sevenths. Minor chords will contain the exact opposite intervallic structure as their major counterparts - each being chords built of thirds. There are two types of thirds - major and minor. There are two types of sevenths - major and dominant. There are two types of sixths - minor and dominant. There are two types of fourths - perfect fifths and fourths. There are two types of fifths - perfect fourths and fifths. There are two types of seconds - ninths and seconds.

On the guitar, because it is possible to play only six notes or less, notes must then be eliminated from upper-extension chords. In a G13 chord, the first note to be eliminated is the perfect fourth, C; the second note is the fifth, D; the third note is the root note. Then the next note in the close race to be eliminated, is the third, B. If we eliminate the right notes, 13 chords can become negative sus chords. When I, IV & V are eliminated from the chord. The group of eliminated notes - I-IV-V – are cast way into negative space, making their own chords. Suspended chords. Csus2 = Gsus4 = G-C-D = I-IV-V. While considering intervals, we can make the following observations:

(C – E – G) = C Major   &   (E – C – G) = C/E   &   (A – C – E) = A Minor   &   (C – E – A) = Amin/C 

Major Triad = R + (Δ3 + m3)   &   Minor Triad = R + (m3 + Δ3)

XΔ7 = R + (Δ3 + m3 + Δ3)   &   Xmin7 = R + (m3 + Δ3 + m3)

R + (Δ3 + m3 + Δ3) = Δ7 chord   &   (Δ3 + Δ3 + m3) = Augmented Δ7 chord. 

If: (A + C + E + G) = A min7   &   X(min7) = R + (m3 + Δ3 + m3)   &   if: F#min7(b5) = (F# + A + C + E)   &   Xmin7(b5) = R + (m3 + m3 + Δ3)

Chords can be classified according to taxonomy:

  • The chord Domain: is where the chord roams – what is the song, progression, or scale structure?
  • The chord Kingdom: is where the chord rules – whom is the true, Great One?
  • The chord Phylum: is where the chord serves - where does this chord lay between I and VII, and where does it best serve I?
  • The chord Class: is relative to the intervals between each successive note - are they seconds, thirds, fourths, fifths, sixths, sevenths?
  • The chord Order: is relative to the order of those same intervals, between each successive note - is it a major third, then a minor third? If a chord contains both major and minor intervals, inverting the order of intervals changes the musical taxonomy.
  • The chord Family: is relative to the variable extensions introduced in the chord formula - is it a major seventh, or a dominant seventh?
  • The chord Genus: is dependent upon its relationship with major and minor - is it a major third, or a minor third? Neither, or both?
  • The chord Species: is the root note of the chord - what is the single note before any other interval or variable extensions are added?
We can conclude that introducing variable extensions, creates different chord families; inverting the order of notes, creates different intervals; different interval structures, creates different classes of chords; inverting the order of the class, creates different chord names. Same notes, different order. Same intervals, different order. Similar kinds of ideas, create results of differing outcomes. Similar ideas, through differing results, create complex answers. The root of anything is complex.

The Devil's Chord: R + (-6–6–6) & R =√±1

The diminished chord, or Co7, in common shorthand, is built of whole tones. Co - no seventh tone - is every other note in the whole tone scale. When adding the seventh tone, it gets diminished one step farther than a dominant seventh tone does. Here, the diminished seventh tone is equal to the sixth, while in a half-diminished chord, the seventh tone is diminished half as much to be a dominant seventh. 

The half-diminished chord, is made up of exactly the same notes as, the minor7(flat 5) chord - the names are synonymous.

While being related to the Whole Tone Scale, it is usually thought of in relation to other scales, such as the Major Scale. It's possibly the only chord whose root structure is the same as all of its four inversions, the diminished seventh chord can be thought of from both the major and the minor perspectives. When building this chord from the minor perspective, it is built of three consecutive minor third intervals. When building from the major perspective, it is built of three consecutive major sixth intervals. In this particular, harmonically symmetrical chord, major is equal to minor. Building it from the major perspective, however, makes it more fun to think about: R + 6-6-6!

Let's rock and roll, all night long, baby!

About the Author:
Dealey is a Vancouver, Canada based guitarist, songwriter, recording engineer and producer. He is the author of the forthcoming independent book, "The Relative Nature of Chords: A Street-Smart Field Guide for Guitar." Watch for exclusive excerpts on Ultimate-Guitar! You can support his ventures by supporting his music here - or talk to him about collaborating on your project by email to: info(a.t.)

48 comments sorted by best / new / date

    How is the diminished chord in the whole tone scale? You won't get a C diminished 7th chord by taking every other note of the C whole tone scale. You get a C augmented (C, E, G#) that way. The diminished 7th chord is not built of whole tones. It has no whole tones in it. It is built of root + 3 stacked minor thirds.Your lesson is very confusing and full of misinformation. For example: "There are two types of thirds - major and minor. There are two types of sevenths - major and dominant. There are two types of sixths - minor and dominant. There are two types of fourths - perfect fifths and fourths. There are two types of fifths - perfect fourths and fifths. There are two types of seconds - ninths and seconds." What? First you talk about major and minor thirds, then you talk about major and dominant sevenths (should be minor sevenths - dominant seventh is a chord, not an interval), then you talk about major and dominant sixths. There's no such thing as a dominant sixth. It's called minor sixth. And how are the two types of fifths "fourths and fifths"? A fourth is not the same as a fifth. You should be talking about perfect and diminished fifths (there's also an augmented one that is enharmonic to the minor sixth). And when talking about fourths, you should talk about augmented and perfect fourths. I also didn't understand your thought process when you were talking about the sus chords. What did they have to do with anything you were talking about in the lesson? Also, I have never heard of "domain", "kingdom", etc, when talking about chords.Cut the BS, get straight to the point. It's not that complex. And also know your sh!t before posting a lesson. BTW, I have never heard of "the devil's chord". Diminished chord is not the devil's chord. Tritone is usually referred to as "the devil's interval", though. People used to avoid it in old music because it sounded so dissonant. No need to involve random maths in this. They make you look more "scientific", but they actually have nothing to do with what you are talking about. For example, why "R + (-6–6–6) & R =√±1"? What does the square root have to do with anything? And also, if it actually was the square root of -1, we would be talking about imaginary numbers. That has nothing to do with music.
    The Harvest
    The diminished triad (C - Eb - Gb) is made up of every other note in the whole tone scale. The same way that the major triad is made up of every other note in the major scale. The minor triad is made up of every other note in the natural minor scale. That is how the diminished seventh chord is related to the whole tone scale. Seriously, dude, take a chill-pill. It's called music theory, not music fact. If you've never heard of something before, then don't cut straight to "BS" - before you even think about it. You've heard of "the devil's interval", so why pretend that "the devil's chord" is such a far stretch of your imagination? A chord is simply two or more intervals played simultaneously. The taxonomy is simply a metaphor for people who may be familiar with other structures in nature, and logic, to connect the world around us to the world of music. Some people do things in life other than music, and they may understand new concepts when they are put in context through concepts they are already familiar with. Music is math. Wave forms are definitely related to math. Notes are sine waves at a pretty fast frequency. Frequency is related to time. Rhythm is timing. Rhythmic waves are sawtooth forms at a relatively low frequency. Pile enough sawtooth waves together, and you will eventually get a smooth sine wave, or a note. A square root can be both positive and negative, a musical root can be as well - major and minor. If there is no minor sixth interval, then what is the sixth tone of the A natural minor scale? If the scale is A natural minor, the first tone of the scale (I) is: A. The sixth tone is: F. It's all about intervals, man. The sus chord paragraph was related to the construction of a 13 chord, and everything to do with the interval structure and construction of different chord types. The diminished 7th chord is the "devil's chord" because it is the root note, plus 3 consecutive sixth intervals - or minor thirds in reverse. 6 - 6 - 6. Get it? You guys should keep in mind that an augmented fourth is the exact same note as a flat fifth. Albeit, there would be a difference of Bb vs. A#, but it still remains the same frequency. Mick Goodrick's, Almanac of Guitar Voice-Leading is a pretty good explanation for the simplification of intervals. A fourth is a fifth in reverse. A second is a seventh in reverse. A ninth is the same distance from the root as a dominant seventh. A ninth is the opposite of a seventh.
    I know my comment was a bit harsh, but I felt like somebody had to do it. Your lesson was full of misinformation and it had a lot of off topic information as well. Was the lesson about diminished chords? If yes, then why are you talking about G13 and suspended chords? I, somebody who's studying music pedagogy, found the lesson really confusing. It jumped from one subject to another and lacked coherence. Not a good lesson. There may be a lot of good information in the lesson, but it doesn't matter if it jumps from one topic to another all the time. Try being more simple. Also, when talking about music theory, use the correct terms. That makes it way less confusing. Also, √-1=i (imaginary number). How can your root be an imaginary number? It makes no sense. It is random maths that has nothing to do with the subject. Yes, frequencies and intervals have to do with music. But the square root of -1 has nothing to do with this topic. So involving random maths like that just doesn't make any sense. It seemed like you were trying to prove something mathematically, but it just didn't work.
    The points in the article could be boiled down to a couple of sentences. First point: Chords are built of intervals, most of the time by stacking thirds on top of each other. Second point: Diminished 7th chord is built of root + three minor 3rds on top of each other - and you'll get the same result by stacking major 6ths on top of each other. Half-diminished 7th chord has a minor 7th, so the last third is not minor, it's major. The article made it look a lot more complex than it really was by jumping between different topics that were kind of unrelated, and adding a lot of useless jargon. And as I said, there's a lot of misinformation that confuses people even more.
    A chord is three notes or more. I appreciate anyone's attempt to share there knowledge, but it seemed like you didn't really know what you were talking about for a lot of it.
    The Harvest
    haha.. of course I put my foot in my mouth a bit at the very top of my comment..the augmented triad is every other note in the whole tone scale, C - E - G#, two pairs of major third intervals. The diminished version is a 1.5 scale conversion, i.e. minor. C - Eb - Gb, two pairs of minor third intervals.
    Wow. As if theory wasn't confusing enough, you've added math.
    The math was always there. To understand the chords on a deeper level you must know the intervals between the notes.
    i didnt read the whole article but im pretty sure its a joke
    The Harvest
    You couldn't be bothered to read it, yet you just couldn't stop yourself from sharing your very valuable opinion? You're a troll, thus, your opinions are completely worthless.
    historically, the devil's chord is the augmented fourth (also named the devil's fifth)
    The augmented 4th (also b5th) isn't a chord - it's an interval, also known as the tritone. This interval is comprised of 2 minor thirds and is present (actually it occurs twice) in the diminished 7 chord. For example: C diminished7: C Eb Gb Bbb(Bbb = A) C - Gb = b5th/tritone/aug4th Eb - Bbb (A) = b5th/tritone/aug4th
    and it's true, it's in the diminished 7 chord. you all write in english notation i'm not used to it
    well technically the tritone is an interval with a distance of three whole tones. Hence the name, tri(3) tone. Two minor thirds results in a diminished fifth and NEVER an augmented fourth. While a diminished fifth and an augmented fifth are enharmonic they are not the same thing. See the following... C to Eb is a minor third. Eb to Gb is a minor third. C to Gb is a diminished fifth (NOT an augmented fourth). C to Eb is a minor third. Eb to F# is an augmented second (NOT a minor third). C to F# is an augmented fourth and is NOT comprised of two minor thirds. A minor third is made up of three semitones or one and a half tones. An augmented second is also made up of a whole plus a half tone or three semitones. They are enharmonic, but an augmented second is NOT a minor third. Is this pedantic? Yes. Is it correct? Yes. Also, a seventh is major, minor, or diminished. An interval of a seventh is never dominant. Dominant is the name given to the fifth scale degree. The seventh chord built on the fifth scale degree (built on the dominant) of a major scale is a major triad with a minor seventh (1 3 5 b7). This is the only diatonic seventh chord in a major scale that results in that type of seventh and so that specific seventh is called a dominant seventh chord. Similarly the chord built on the dominant (fifth scale degree) of the major scale serves a particular harmonic function which we call a dominant function. Often other chords also fulfil this function and can be labelled dominant. To summarize the word "dominant" describes: a scale degree, a type of seventh chord, and a harmonic function. It is NOT used to describe an interval quality. The only interval qualities are major, minor, perfect, augmented,and diminished(very rarely double augmented and double diminished). There are a few other little errors in there but it looks like someone else covered most of it in detail already.
    it can be a chord too, the root and the fourth+
    A chord has to have a minimum of three notes (or so has me been told)
    I guess that's object to discussion. There is the term dyad, which is a chord built from 2 notes, analogically to a triad consisting of 3 notes.
    Still not a chord. 2 notes = harmonic interval. 3+ notes = chord. 'dyad' is a term used by guitar players (mostly) who have decided that 'power-chord' makes them sound uneducated. Even in this context, something like a root and 4+ wouldn't be considered a 'dyad', as in most cases a 'dyad' is reserved for the root and fifth that work in place of a full major or minor triad.
    This is a very limiting classical theory dogma, and not reflective of the reality if music, even historically. Romantic era, modern era (as in early to mid 20th century), and especially jazz made much use of implied harmony, chord substitutions and often together. Dyads imply a chordal harmony, even if it may be ambiguous, deliberately or not. That's clearly based on the quite a few variables, including: key, resolutions, borrowed or secondary chords and modulations.
    But you can't call 2 notes a chord without a context. 2 notes can function as a chord, but you need a context for that. Without a context, 2 notes aren't a chord. But if we play B and F at the same time and then C and E at the same time, you will hear it as a V7-I in C major. Now we have a context and the two notes played together function as a chord. You can definitely imply harmony with two notes. You can even do it with a single note melody line.
    The Harvest
    Flat five = sharp four. If we were augmenting tones, the notes in C diminished seventh would become: C - D# - F# - A. Diminished means to make less, not to make more - hence the diminished chord would have a flat five instead of a sharp four.
    I would love some citations for some of these ideas, because it seems like a lot of taking simple ideas of music theory and making them a lot more complicated than necessary. Or is this "original work"?
    I know pretty much everything about theory and I didn't understand your lesson. GOOD JOB. Also, I lol'd "The chord Kingdom: is where the chord rules – whom is the true, Great One?"
    Thank you man. Great post. I'm working on learning music theory. I particularly appreciate the using metaphors to help us understand it. It seems to me music theory is a lot about perspective and maybe why so much disagreement and misunderstanding in it's structure?
    if you found this to be too complicated, you should go to guitar center and sell your guitar.
    What bollocks! If you don't have any prior knowledge of how all this works its complex! Devin Townsend can outguitar 999/1000 guitarists and he doesn't even know what a fricking diminished chord is! Now, Im personally trying to learn music theory, but until a year ago, I didn't even play anything, and frankly didn't care. But if you don't gradually build up your knowledge, itll be confusing. And for plenty people who haven't been doing this long, this is long, its bloody complicated, but filling your head with this stuff, doensnt make a shadow of a difference to how good a guitar player you can be. So quit being so obnoxious! Or are you Joe Satriani? If not sod off, I don't care what you understand, youre no better than the thousands of guitarists who don't get this.
    I study Jazz at university and this is just over complicating simple shit. No need to sell my guitar.
    I wish you had gone into the functions of this chord, rather than just what it is (although that too could use some revision). Just for shits and gigs, the function of a fully diminished chord in classical music is to transcend relative keys (for instance, modulation to the V, IV or vi in a major key) - from a diminished chord, you can go to eight different keys, some of which are completely unrelated to the original key. C07, for example, goes to C# major/C# minor, Bb major/ Bb minor (when spelled as an A07: C07 and A07 have the same notes, therefore, they are inversions of each other), G major/G minor (if inverted to an F#07 chord) or E major/E minor (if inverted to D#07).